2024

Hox gene activity directs physical forces to differentially shape chick small and large intestinal epithelia. Hasreet K. Gill, Sifan Yin, Nandan L. Nerurkar, Tyler R. Huycke, L. Mahadevan and Clifford J. Tabin, Developmental Cell . 7 August 2024.
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Hox transcription factors play crucial roles in organizing developmental patterning across metazoa, but how these factors trigger regional morphogenesis has largely remained a mystery. In the developing gut, Hox genes help demarcate identities of intestinal subregions early in embryogenesis, which ultimately leads to their specialization in both form and function. Although the midgut forms villi, the hindgut develops sulci that resolve into heterogeneous outgrowths. Combining mechanical measurements of the embryonic chick intestine and mathematical modeling, we demonstrate that the posterior Hox gene HOXD13 regulates biophysical phenomena that shape the hindgut lumen. We further show that HOXD13 acts through the transforming growth factor β (TGF-β) pathway to thicken, stiffen, and promote isotropic growth of the subepithelial mesenchyme—together, these features lead to hindgut-specific surface buckling. TGF-β, in turn, promotes collagen deposition to affect mesenchymal geometry and growth. We thus identify a cascade of events downstream of positional identity that direct posterior intestinal morphogenesis.

The developmental mechanics of divergent buckling patterns in the chick gut. Hasreet K. Gill, Sifan Yin, John C. Lawlor, Tyler R. Huycke, Nandan L. Nerurkar, Clifford J. Tabin and L. Mahadevan, PNAS. Volume 121, Issue 28, 6 May 2024.
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Tissue buckling is an increasingly appreciated mode of morphogenesis in the embryo, but it is often unclear how geometric and material parameters are molecularly determined in native developmental contexts to generate diverse functional patterns. Here, we study the link between differential mechanical properties and the morphogenesis of distinct anteroposterior compartments in the intestinal tract—the esophagus, small intestine, and large intestine. These regions originate from a simple, common tube but adopt unique forms. Using measured data from the developing chick gut coupled with a minimal theory and simulations of differential growth, we investigate divergent lumen morphologies along the entire early gut and demonstrate that spatiotemporal geometries, moduli, and growth rates control the segment-specific patterns of mucosal buckling. Primary buckling into wrinkles, folds, and creases along the gut, as well as secondary buckling phenomena, including period-doubling in the foregut and multiscale creasing-wrinkling in the hindgut, are captured and well explained by mechanical models. This study advances our existing knowledge of how identity leads to form in these regions, laying the foundation for future work uncovering the relationship between molecules and mechanics in gut morphological regionalization.

Active hydraulics and odd elasticity of muscle fibres. Suraj Shankar and L. Mahadevan, Nature Physics. 08 July 2024.
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Muscle is a complex, hierarchically organized, soft contractile engine. To understand the limits on the rate of contraction and muscle energetics, we construct a coarse-grained multiscale model that describes muscle as an active sponge. Our analysis of existing experiments across species and muscle types highlights the importance of spatially heterogeneous strains and local volumetric deformations. Our minimal theoretical model shows how contractions induce intracellular fluid flow and power active hydraulic oscillations, yielding the limits of ultrafast muscular contractions. We further demonstrate that the viscoelastic response of muscle is naturally non-reciprocal—or odd—owing to its active and anisotropic nature. This enables an alternate mode of muscular power generation from periodic cycles in spatial strain alone, contrasting with previous descriptions based on temporal cycles. Our work suggests a revised view of muscle dynamics that emphasizes the multiscale spatiotemporal origins of soft hydraulic power, with potential implications for physiology, biomechanics and locomotion.

The sex of organ geometry. Laura Blackie, Pedro Gaspar, Salem Mosleh, Oleh Lushchak, Lingjin Kong, Yuhong Jin, Agata P. Zielinska, Boxuan Cao, Alessandro Mineo, Bryon Silva, Tomotsune Ameku, Shu En Lim, Yanlan Mao, Lucía Prieto-Godino, Todd Schoborg, Marta Varela , L. Mahadevan and Irene Miguel-Aliaga, Nature.  Volume 630, pages 392-400, 29 May 2024.
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Organs have a distinctive yet often overlooked spatial arrangement in the body1,2,3,4,5. We propose that there is a logic to the shape of an organ and its proximity to its neighbours. Here, by using volumetric scans of many Drosophila melanogaster flies, we develop methods to quantify three-dimensional features of organ shape, position and interindividual variability. We find that both the shapes of organs and their relative arrangement are consistent yet differ between the sexes, and identify unexpected interorgan adjacencies and left–right organ asymmetries. Focusing on the intestine, which traverses the entire body, we investigate how sex differences in three-dimensional organ geometry arise. The configuration of the adult intestine is only partially determined by physical constraints imposed by adjacent organs; its sex-specific shape is actively maintained by mechanochemical crosstalk between gut muscles and vascular-like trachea. Indeed, sex-biased expression of a muscle-derived fibroblast growth factor-like ligand renders trachea sexually dimorphic. In turn, tracheal branches hold gut loops together into a male or female shape, with physiological consequences. Interorgan geometry represents a previously unrecognized level of biological complexity which might enable or confine communication across organs and could help explain sex or species differences in organ function.

3D Hydrogel Encapsulation Regulates Nephrogenesis in Kidney Organoids. Bryan A. Nerger, Sumit Sinha, Nathan N. Lee, Maria Cheriyan, Pascal Bertsch, Christopher P. Johnson, L. Mahadevan, Joseph V. Bonventre and David J. Mooney,  Advanced Materials. Volume 36, Issue 14, 05 January 2024.  
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Stem cell-derived kidney organoids contain nephron segments that recapitulate morphological and functional aspects of the human kidney. However, directed differentiation protocols for kidney organoids are largely conducted using biochemical signals to control differentiation. Here, the hypothesis that mechanical signals regulate nephrogenesis is investigated in 3D culture by encapsulating kidney organoids within viscoelastic alginate hydrogels with varying rates of stress relaxation. Tubular nephron segments are significantly more convoluted in kidney organoids differentiated in encapsulating hydrogels when compared with those in suspension culture. Hydrogel viscoelasticity regulates the spatial distribution of nephron segments within the differentiating kidney organoids. Consistent with these observations, a particle-based computational model predicts that the extent of deformation of the hydrogel–organoid interface regulates the morphology of nephron segments. Elevated extracellular calcium levels in the culture medium, which can be impacted by the hydrogels, decrease the glomerulus-to-tubule ratio of nephron segments. These findings reveal that hydrogel encapsulation regulates nephron patterning and morphology and suggest that the mechanical microenvironment is an important design variable for kidney regenerative medicine.

2023

A mechanochemical model recapitulates distinct vertebrate gastrulation modes. Mattia Serra, Guillermo Serrano Nájera, Manli Chuai, Alex M. Plum, Sreejith Santhosh, Vamsi Spandan, Cornelis J. Weijer and L. Mahadevan, Science Advances. Volume 9, Issue 49, 6 Dec 2023.  
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During vertebrate gastrulation, an embryo transforms from a layer of epithelial cells into a multilayered gastrula. This process requires the coordinated movements of hundreds to tens of thousands of cells, depending on the organism. In the chick embryo, patterns of actomyosin cables spanning several cells drive coordinated tissue flows. Here, we derive a minimal theoretical framework that couples actomyosin activity to global tissue flows. Our model predicts the onset and development of gastrulation flows in normal and experimentally perturbed chick embryos, mimicking different gastrulation modes as an active stress instability. Varying initial conditions and a parameter associated with active cell ingression, our model recapitulates distinct vertebrate gastrulation morphologies, consistent with recently published experiments in the chick embryo. Altogether, our results show how changes in the patterning of critical cell behaviors associated with different force-generating mechanisms contribute to distinct vertebrate gastrulation modes via a self-organizing mechanochemical process.

Learning to write with the fluid rope trick. Gaurav Chaudhary, Stephanie Christ, A. John Hart and L. Mahadevan, Soft Matter. 23 October 2023
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The rapid evolution of three-dimensional (3D) printing technology has enabled new manufacturing capabilities1,2 and allowed for the creation of complex patterns via the additive deposition of complex materials through a computer-controlled nozzle. However, the ultimate limits on print quality are imposed by the rheodynamics of the printed material that is a function of material rheology and the ability to design robust print paths for the nozzle. Defects in printing typically arise in non-uniformly extruded/deposited material and instabilities such as folding and coiling of fluid jets.3 A simple protocol to prevent these defects follows by forcing the nozzle trajectory to exactly mimic the target print pattern from a very small height offset.

Statics and diffusive dynamics of surfaces driven by p-atic topological defects. Farzan Vafa and L. Mahadevan, Soft Matter. 09 August 2023
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In biology, epithelial morphogenesis of thin sheet-like structures in plants and animals is responsible for the vast majority of functional structures that make up organs and organisms. These may be modeled effectively as two-dimensional surfaces whose geometry is driven by active processes that are intimately connected to the presence of orientational order in the tangent plane that modifies the embedding and in turn is modified by it. The nature of in-plane order is akin to that of polar molecules, liquid crystals, etc., or more generally to p-fold rotational order, denoted as ‘‘p-atics’’.1 There is a growing body of evidence suggesting that topological defects, singular disruptions of the rotational order, play a crucial role in guiding or controlling morphogenesis, as seen in experimental observations of cell extrusion and apoptosis,2 mound formation,3,4 layer formation,5 and body shaping using bulges, pits and tentacles.6 These observations suggest a natural question: how might one construct a theoretical framework that accounts for the dynamics of topological defects on non-uniform surfaces which themselves deform in response to the forces induced by the defects?

Beak morphometry and morphogenesis across avian radiations. Salem Mosleh,  Gary P. T. Choi, Grace M. Musser, Helen F. James, Arhat Abzhanov and L. Mahadevan, Royal Society. 18 August 2023
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Adaptive avian radiations associated with the diversification of bird beaks into a multitude of forms enabling different functions are exemplified by Darwin’s finches and Hawaiian honeycreepers. To elucidate the nature of these radiations, we quantified beak shape and skull shape using a variety of geo- metric measures that allowed us to collapse the variability of beak shape into a minimal set of geometric parameters. Furthermore, we find that just two measures of beak shape—the ratio of the width to length and the normal- ized sharpening rate (increase in the transverse beak curvature near the tip relative to that at the base of the beak)—are strongly correlated with diet. Finally, by considering how transverse sections to the beak centreline evolve with distance from the tip, we show that a simple geometry-driven growth law termed ‘modified mean curvature flow’ captures the beak shapes of Darwin’s finches and Hawaiian honeycreepers. A surprising consequence of the simple growth law is that beak shapes that are not allowed based on the developmental programme of the beak are also not observed in nature, suggesting a link between evolutionary morphology and development in terms of growth-driven developmental constraints.

Contractility-Induced Phase Separation in Active Solids. Sifan Yin and L. Mahadevan, Volume 131, Iss. 14, 2 October 2023.
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Experiments over many decades are suggestive that the combination of cellular contractility and active phase separation in cell-matrix composites can enable spatiotemporal patterning in multicellular tissues across scales. To characterize these phenomena, we provide a general theory that incorporates active cellular contractility into the classical Cahn-Hilliard-Larché model for phase separation in passive viscoelastic solids. Within this framework, we show how a homogeneous cell-matrix mixture can be destabilized by activity via either a pitchfork or Hopf bifurcation, resulting in stable phase separation and/or traveling waves. Numerical simulations of the full equations allow us to track the evolution of the resulting self-organized patterns in periodic and mechanically constrained domains, and in different geometries. Altogether, our study underscores the importance of integrating both cellular activity and mechanical phase separation in understanding patterning in soft, active biosolids in both in vivo and in vitro settings.

Evaporation-Driven Cellular Patterns in Confined Hyperelastic Hydrogels. Baudouin Saintyves, Romain Pic, L. Mahadevan and Irmgard Bischofberger, Volume. 131, Iss. 11, 15 September 2023.
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When a hyperelastic hydrogel confined between two parallel glass plates begins to dry from a lateral boundary, the volume lost by evaporation is accommodated by an inward displacement of the air-hydrogel interface that induces an elastic deformation of the hydrogel. Once a critical front displacement is reached, we observe intermittent fracture events initiated by a geometric instability resulting in localized bursts at the interface. These bursts relax the stresses and irreversibly form air cavities that lead to cellular networks. We show that the spatial extent of the strain field prior to a burst, influenced by the air-hydrogel interfacial tension and the confinement of the gel, determines the characteristic size of the cavities.

Optimal intercellular competition in senescence and cancer. Thomas C. T. Michaels and L. Mahadevan, Royal Society. Volume 479, Issu 2276, 30 August 2023.
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Effective multicellularity requires both cooperation and competition between constituent cells. Cooperation involves sacrificing individual fitness in favour of that of the community, but excessive cooperation makes the community susceptible to senescence and ageing. Competition eliminates unfit senescent cells via natural selection and thus slows down ageing, but excessive competition makes the community susceptible to cheaters, as exemplified by cancer and cancer-like phenomena. These observations suggest that an optimal level of intercellular competition in a multicellular organism maximizes organismal vitality by delaying the inevitability of ageing. We quantify this idea using a statistical mechanical framework that leads to a generalized replicator dynamical system for the population of cells that changes their vitality and cooperation due to somatic mutations that make them susceptible to ageing and/or cancer. By accounting for the cost of cooperation and strength of competition in a minimal setting, we show that our model predicts an optimal value of competition that maximizes vitality and delays the inevitability of senescence or cancer. The results have implications for the design of strategies aimed at delaying ageing in biological, technical and social systems that exhibit similar processes.

How to grow a flat leaf. Salem al-Mosleh and L. Mahadevan, Physical review letters. Volume 131, Issu 9, 31 August 2023.
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Growing a flat lamina such as a leaf is almost impossible without some feedback to stabilize long wavelength modes that are easy to trigger since they are energetically cheap. Here we combine the physics of thin elastic plates with feedback control theory to explore how a leaf can remain flat while growing. We investigate both in-plane (metric) and out-of-plane (curvature) growth variation and account for both local and nonlocal feedback laws. We show that a linearized feedback theory that accounts for both spatially nonlocal and temporally delayed effects suffices to suppress long wavelength fluctuations effectively and explains recently observed statistical features of growth in tobacco leaves. Our work provides a framework for understanding the regulation of the shape of leaves and other leaflike laminar objects.

Ethics inside the black box: integrating science and technology studies into engineering and public policy curricula. Christopher Lawrence, Sheila Jasanoff, Sam Weiss Evans, Keith Raffel and L. Mahadevan, Science and Engineering Ethics. Volume 29, Article number: 23 , 22 June 2023.
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There is growing need for hybrid curricula that integrate constructivist methods from Science and Technology Studies (STS) into both engineering and policy courses at the undergraduate and graduate levels. However, institutional and disciplinary barriers have made implementing such curricula difficult at many institutions. While several programs have recently been launched that mix technical training with consideration of “societal” or “ethical issues,” these programs often lack a constructivist element, leaving newly-minted practitioners entering practical fields ill-equipped to unpack the politics of knowledge and technology or engage with skeptical publics. This paper presents a novel format for designing interdisciplinary coursework that combines conceptual content from STS with training in engineering and policy. Courses following this format would ideally be team taught by instructors with advanced training in diverse fields, and hence co-learning between instructors and disciplines is a key element of the format. Several instruments for facilitating both student and instructor collaborative learning are introduced. The format is also designed for versatility: in addition to being adaptable to both technical and policy training environments, topics are modularized around a conceptual core so that issues ranging from biotech to nuclear security can be incorporated to fit programmatic needs and resources.

Geometric mechanics of ordered and disordered kirigami. G. Chaudhary, L. Niu, Q. Han, M. Lewicka and L. Mahadevan, Proceedings of the Royal Society (A). Volume 479, Issue 2274, 07 June 2023.
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The presence of incomplete cuts in a thin planar sheet can dramatically alter its mechanical and geometrical response to loading, as the cuts allow the sheet to deform strongly in the third dimension, most beautifully demonstrated in kirigami art-forms. We use numerical experiments to characterize the geometric mechanics of kirigamized sheets as a function of the number, size and orientation of cuts. We show that the geometry of mechanically loaded sheets can be approximated as a composition of simple developable units: flats, cylinders, cones and compressed Elasticae. This geometric construction yields scaling laws for the mechanical response of the sheet in both the weak and strongly deformed limit. In the ultimately stretched limit, this further leads to a theorem on the nature and form of geodesics in an arbitrary kirigami pattern, consistent with observations and simulations. Finally, we show that by varying the shape and size of the geodesic in a kirigamized sheet, we can control the deployment trajectory of the sheet, and thence its functional properties as an exemplar of a tunable structure that can serve as a robotic gripper, a soft light window or the basis for a physically unclonable device. Overall our study of disordered kirigami sets the stage for controlling the shape and shielding the stresses in thin sheets using cuts.

Image cognition using contour curvature statistics. Andrew Marantan, Irina Tolkova and L. Mahadevan, Proceedings of the Royal Society (A). Volume 479, Issue 2274, 1471-2946, 07 June 2023.
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Drawing on elementary invariance principles, we propose that a statistical geometric object, the probability distribution of the normalized contour curvatures (NCC) in the intensity field of a planar image has the potential to categorize objects. We show that NCC is sufficient for discriminating between cognitive categories such as animacy, size and type, and demonstrate the robustness of this metric to variation in illumination and viewpoint, consistent with psychological experiments. A generative model for producing artificial images with the observed NCC distributions highlights the key features that our metric captures, and those that it does not. More broadly, our study points to the need for statistical geometric approaches to cognition that build in both the statistics and the natural invariances of the visual world.

An additive framework for kirigami design. Levi H. Dudte, Gary P. T. Choi, Kaitlyn P. Becker and L. Mahadevan, Nature Computational Science. Volume 3, pages 443–454, 25 May 2023.
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We present an additive approach for the inverse design of kirigami-based mechanical metamaterials by focusing on the empty (negative) spaces instead of the solid tiles. By considering each negative space as a four-bar linkage, we identify a simple recursive relationship between adjacent linkages, yielding an efficient method for creating kirigami patterns. This allows us to solve the kirigami design problem using elementary linear algebra, with compatibility, reconfigurability and rigid-deployability encoded into an iterative procedure involving simple matrix multiplications. The resulting linear design strategy circumvents the solution of a non-convex global optimization problem and allows us to control the degrees of freedom in the deployment angle field, linkage offsets and boundary conditions. We demonstrate this by creating a large variety of rigid-deployable, compact, reconfigurable kirigami patterns. We then realize our kirigami designs physically using two simple but effective fabrication strategies with very different materials. Altogether, our additive approaches present routes for efficient mechanical metamaterial design and fabrication based on ori/kirigami art forms.

Defect-mediated dynamics of coherent structures in active nematics. Mattia Serra, Linnea Lemma, Luca Giomi, Zvonimir Dogic and L. Mahadevan, Nature Physics. 19, 1355–1361, 25 May 2023.
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Active fluids, such as cytoskeletal filaments, bacterial colonies and epithelial cell layers, exhibit distinctive orientational coherence, often characterized by nematic order and its breakdown, defined by the presence of topological defects. In contrast, little is known about positional coherence, that is, whether there is an organization in the underlying fluid motion—despite this being both a prominent and an experimentally accessible feature. Here we characterize the organization of fluid motion in active nematics using the notion of Lagrangian coherent structures by analyzing experimental data of two-dimensional mixtures of microtubules and kinesin, as well as numerical data obtained from the simulation of the active nematodynamic equations. Coherent structures consist of moving attractors and repellers, which orchestrate complex motion. To understand the interaction of positional and orientational coherence, we analyse experiments and simulations and find that +1/2 defects move and deform the attractors, functioning as control centres for collective motion. Additionally, we find that regions around isolated +1/2 defects undergo high bending and low stretching/shearing deformations, consistent with the local stress distribution. The stress is the minimum at the defect, whereas high differential stress along the defect orientation induces folding. Our work offers a new perspective to describe and control self-organization in active fluids, with potential applications to multicellular systems.

Localization in musical steelpans. Petur Bryde and L. Mahadevan, Proceedings of the Royal Society (A). Volume 479, Issue 2273, 17 May 2023.
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The steelpan is a pitched percussion instrument that takes the form of a concave bowl with several localized dimpled regions of varying curvature. Each of these localized zones, called notes, can vibrate independently when struck, and produce a sustained tone of a well-defined pitch. While the association of the localized zones with individual notes has long been known and exploited, the relationship between the shell geometry and the strength of the mode confinement remains unclear. Here, we explore the spectral properties of the steelpan modelled as a vibrating elastic shell. To characterize the resulting eigenvalue problem, we generalize a recently developed theory of localization landscapes for scalar elliptic operators to the vector-valued case, and predict the location of confined eigenmodes by solving a Poisson problem. A finite-element discretization of the shell shows that the localization strength is determined by the difference in curvature between the note and the surrounding bowl. In addition to providing an explanation for how a steelpan operates as a two-dimensional xylophone, our study provides a geometric principle for designing localized modes in elastic shells.

Direct force measurement and loading on developing tissues in intact avian embryos. Chon U. Chan, Fengzhu Xiong, Arthur Michaut, Joana M. N. Vidigueira, Olivier Pourquie and L. Mahadevan, Development (2023). Volume 150, Issue 9 6 April 2023.
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Developmental morphogenesis is driven by tissue stresses acting on tissue rheology. Direct measurements of forces in small tissues (100 µm-1 mm) in situ, such as in early embryos, require high spatial precision and minimal invasiveness. Here, we introduce a control-based approach, tissue force microscopy (TiFM), that integrates a mechanical cantilever probe and live imaging with closed-loop feedback control of mechanical loading in early chicken embryos. By testing previously qualitatively characterized force-producing tissues in the elongating body axis, we show that TiFM quantitatively captures stress dynamics with high sensitivity. TiFM also provides the means to apply stable, minimally invasive and physiologically relevant loads to drive tissue deformation and to follow the resulting morphogenetic progression associated with large-scale cell movements. Together, TiFM allows us to control tissue force measurement and manipulation in small developing embryos, and promises to contribute to the quantitative understanding of complex multi-tissue mechanics during development.

Explosive rigidity percolation in kirigami. Gary P.T. Choi, Lucy Liu and L. Mahadevan, Proceedings of the Royal Society (A). Volume 479, Issue 2271 20 February 2023.
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Controlling the connectivity and rigidity of kirigami, i.e. the process of cutting paper to deploy it into an articulated system, is critical in the manifestations of kirigami in art, science and technology, as it provides the resulting metamaterial with a range of mechanical and geometric properties. Here, we combine deterministic and stochastic approaches for the control of rigidity in kirigami using the power of k choices, an approach borrowed from the statistical mechanics of explosive percolation transitions. We show that several methods for rigidifying a kirigami system by incrementally changing either the connectivity or the rigidity of individual components allow us to control the nature of the explosive transition by a choice of selection rules. Our results suggest simple lessons for the design of mechanical metamaterials.

Dynamics of cooperative excavation in ant and robot collectives. S Ganga Prasath, Souvik Mandal, Fabio Giardina, Jordan Kennedy, Venkatesh N Murthy, L. Mahadevan, eLife.  2022;11:e79638. Februrary 2, 2023 .
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The solution of complex problems by the collective action of simple agents in both biologically evolved and synthetically engineered systems involves cooperative action. Understanding the resulting emergent solutions requires integrating across the organismal behavior of many individuals. Here, we investigate an ecologically relevant collective task in black carpenter ants Camponotus pennsylvanicus: excavation of a soft, erodible confining corral. These ants show a transition from individual exploratory excavation at random locations to spatially localized collective exploitative excavation and escape from the corral. Agent-based simulations and a minimal continuum theory that coarse-grains over individual actions and considers their integrated influence on the environment leads to the emergence of an effective phase space of behaviors, characterized in terms of excavation strength and cooperation intensity. To test the theory over the range of both observed and predicted behaviors, we use custom-built robots (RAnts) that respond to stimuli to characterize the phase space of emergence (and failure) of cooperative excavation. Tuning the amount of cooperation between RAnts, allows us to vary the efficiency of excavation and synthetically generate the entire range of macroscopic phases predicted by our theory. Overall, our approach shows how the cooperative completion of tasks can arise from simple rules that involve the interaction of agents with a dynamically changing environment that serves as both an enabler and a modulator of behavior.

Combined measures of mimetic fidelity explain imperfect mimicry in a brood parasite–host system. Tanmay Dixit, Gary P. T. Choi, Salem al-Mosleh, Jess Lund, Jolyon Troscianko, Collins Moya, L. Mahadevan and Claire N. Spottiswood.  Biology Letters, 19, 20220538, February 15, 2023.
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The persistence of imperfect mimicry in nature presents a challenge to mimicry theory. Some hypotheses for the existence of imperfect mimicry make differing predictions depending on how mimetic fidelity is measured. Here, we measure mimetic fidelity in a brood parasite–host system using both trait-based and response-based measures of mimetic fidelity. Cuckoo finches Anomalospiza imberbis lay imperfectly mimetic eggs that lack the fine scribbling characteristic of eggs of the tawny-flanked prinia Prinia subflava, a common host species. A trait-based discriminant analysis based on Minkowski functionals—that use geometric and topological morphometric methods related to egg pattern shape and coverage—reflects this consistent difference between host and parasite eggs. These methods could be applied to quantify other phenotypes including stripes and waved patterns. Furthermore, by painting scribbles onto cuckoo finch eggs and testing their rate of rejection compared to control eggs (i.e. a response-based approach to quantify mimetic fidelity), we show that prinias do not discriminate between eggs based on the absence of scribbles. Overall, our results support relaxed selection on cuckoo finches to mimic scribbles, since prinias do not respond differently to eggs with and without scribbles, despite the existence of this consistent trait difference.

Rheomergy: collective behaviour mediated by active flow-based recruitment. Ganga Prasath and L. Mahadevan . Proceedings of the Royal Society (A), Volume 479,  Issue 2269, January 11, 2023.
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The physics of signal propagation in a collection of organisms that communicate with each other both enables and limits how active excitations at the individual level reach, recruit and lead to collective patterning. Inspired by the spatio-temporal patterns in a planar swarm of bees that use pheromones and fanning flows to recruit additional bees, we develop a theoretical framework for patterning via active flow-based recruitment. Our model generalizes the well-known Patlak–Keller–Segel model of diffusion dominated aggregation and leads to an enhanced phase space of patterns spanned by two dimensionless parameters that measure the scaled stimulus/activity and the scaled chemotactic response. Together these determine the efficacy of signal communication via fluid flow (which we dub rheomergy) that leads to a variety of migration and aggregation patterns, consistent with observations.

Reconstruction of distinct vertebrate gastrulation modes via modulation of key cell behaviors in the chick embryo.Manli Chuai, Guillermo Serrano Nájera, Mattia Serra, L  Mahadevan and Cornelis J. Weijer. Science Advances, 9(1), January 04, 2023.
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The morphology of gastrulation driving the internalization of the mesoderm and endoderm differs markedly among vertebrate species. It ranges from involution of epithelial sheets of cells through a circular blastopore in amphibians to ingression of mesenchymal cells through a primitive streak in amniotes. By targeting signaling pathways controlling critical cell behaviors in the chick embryo, we generated crescent- and ring-shaped mesendoderm territories in which cells can or cannot ingress. These alterations subvert the formation of the chick primitive streak into the gastrulation modes seen in amphibians, reptiles, and teleost fish. Our experimental manipulations are supported by a theoretical framework linking cellular behaviors to self-organized multicellular flows outlined in detail in the accompanying paper. Together, this suggests that the evolution of gastrulation movements is largely determined by changes in a few critical cell behaviors in the mesendoderm territory across different species and controlled by a relatively small number of signaling pathways.

2022

An allometric prior enhances acoustic niche partitioning signal. Edvin Memet, Brian FarrellL. Mahadevan and Christoph A. Weber. The Royal Society Interface. Volume 19, Issue 197, December 14, 2022 .
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The acoustic niche hypothesis suggests that vocal signals of sympatric animal species are structured so as to minimize acoustic interference and facilitate communication. Accordingly, each species attempts to establish its own acoustic bandwidth so that intra-species signals are not masked. Detecting a non-random partitioning of the frequency spectrum among sympatric species could constitute evidence for the existence of acoustic avoidance behaviour. However, results from previous studies have been mixed or inconclusive, possibly as a consequence of overlooking the importance of physiological and ecological constraints. Here we introduce an improved test that incorporates prior information on body mass to account for the allometric correlation between mass (size) and vocalization frequency. By correcting for the bias induced by this correlation, the new test uncovers evidence of acoustic niche partitioning as a function of frequency in several tropical bird communities that would not be detected under a more standard test. Separately, we introduce a spatial version of the acoustic partitioning test which, in theory, could prove effective when data are collected from multiple sites located in close spatial proximity.

Enhanced potency of aggregation inhibitors mediated by liquid condensates. Thomas C. T. Michaels, L. Mahadevan and Christoph A. Weber. Physical Review Research. Volume 4, ISSUE 4, December 08, 2022 .
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Liquid condensates are membraneless organelles that form via phase separation in living cells. These condensates provide unique heterogeneous environments that have much potential in regulating a range of biochemical processes from gene expression to filamentous protein aggregation—a process linked to Alzheimer's and Parkinson's diseases. Here we theoretically study the physical interplay between protein aggregation, its inhibition, and liquid-liquid phase separation. Our key finding is that the action of protein aggregation inhibitors can be strongly enhanced by liquid condensates. The physical mechanism of this enhancement relies on the partitioning and colocalization of inhibitors with their targets inside the liquid condensate. Our theory uncovers how the physicochemical properties of condensates can be used to modulate inhibitor potency, and we provide experimentally testable conditions under which drug potency is maximal. Our findings suggest design principles for protein aggregation inhibitors with respect to their phase-separation properties.

Matrix viscoelasticity controls spatiotemporal tissue organization. Alberto Elosegui-Artola, Anupam Gupta, Alexander J. Najibi, Bo Ri Seo, Ryan Garry, Christina M. Tringides, Irene de Lázaro, Max Darnell, Wei Gu, Qiao Zhou, David A. Weitz, L. Mahadevan & David J. Mooney. Nature Materials. Volume 22, 117–127, December 01, 2022 .
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Biomolecular and physical cues of the extracellular matrix environment regulate collective cell dynamics and tissue patterning. Nonetheless, how the viscoelastic properties of the matrix regulate collective cell spatial and temporal organization is not fully understood. Here we show that the passive viscoelastic properties of the matrix encapsulating a spheroidal tissue of breast epithelial cells guide tissue proliferation in space and in time. Matrix viscoelasticity prompts symmetry breaking of the spheroid, leading to the formation of invading finger-like protrusions, YAP nuclear translocation and epithelial-to-mesenchymal transition both in vitro and in vivo in a Arp2/3-complex-dependent manner. Computational modelling of these observations allows us to establish a phase diagram relating morphological stability with matrix viscoelasticity, tissue viscosity, cell motility and cell division rate, which is experimentally validated by biochemical assays and in vitro experiments with an intestinal organoid. Altogether, this work highlights the role of stress relaxation mechanisms in tissue growth dynamics, a fundamental process in morphogenesis and oncogenesis.

Muscular hydraulics drive larva-polyp morphogenesis. Anniek Stokkermans, Aditi Chakrabarti,Kaushikaram Subramanian, Ling Wang, Sifan Yin, Prachiti Moghe, Petrus Steenbergen, Gregor Mönke, Takashi Hiiragi, Robert Prevedel, L. Mahadevan Aissam lkmi. Current Biology. Volume 32, Issue 21, September 16, 2022 .
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Development is a highly dynamic process in which organisms often experience changes in both form and behavior, which are typically coupled to each other. However, little is known about how organismal-scale behaviors such as body contractility and motility impact morphogenesis. Here, we use the cnidarian Nematostella vectensis as a developmental model to uncover a mechanistic link between organismal size, shape, and behavior. Using quantitative live imaging in a large population of developing animals, combined with molecular and biophysical experiments, we demonstrate that the muscular-hydraulic machinery that controls body movement also drives larva-polyp morphogenesis. We show that organismal size largely depends on cavity inflation through fluid uptake, whereas body shape is constrained by the organization of the muscular system. The generation of ethograms identifies different trajectories of size and shape development in sessile and motile animals, which display distinct patterns of body contractions. With a simple theoretical model, we conceptualize how pressures generated by muscular hydraulics can act as a global mechanical regulator that coordinates tissue remodeling. Altogether, our findings illustrate how organismal contractility and motility behaviors can influence morphogenesis.

Modular representation and control of floppy networks. Siheng Chen, Fabio Giardina, Gary P. T. Choi and L. Mahadevan. Proceedings of the Royal Society. Volume 478, Issue 2264, October 10, 2022.
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Geometric graph models of systems as diverse as proteins, DNA assemblies, architected materials and robot swarms are useful abstract representations of these objects that also unify ways to study their properties and control them in space and time. While much work has been done in the context of characterizing the behaviour of these networks close to critical points associated with bond and rigidity percolation, isostaticity, etc., much less is known about floppy, underconstrained networks that are far more common in nature and technology. Here, we combine geometric rigidity and algebraic sparsity to provide a framework for identifying the zero energy floppy modes via a representation that illuminates the underlying hierarchy and modularity of the network and thence the control of its nestedness and locality. Our framework allows us to demonstrate a range of applications of this approach that include robotic reaching tasks with motion primitives, and predicting the linear and nonlinear response of elastic networks based solely on infinitesimal rigidity and sparsity, which we test using physical experiments. Our approach is thus likely to be of use broadly in dissecting the geometrical properties of floppy networks using algebraic sparsity to optimize their function and performance.

A continuous statistical-geometric framework for normative and impaired gaits. Krithika Swaminathan, Irina Tolkova, Lauren Baker, Dheepak Arumukhom Revi, Louis N. Awad, Conor J. Walsh and L. Mahadevan. The Royal Society Interface. Volume 19, Issue 196, November 02, 2022 .
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A quantitative analysis of human gait patterns in space–time provides an opportunity to observe variability within and across individuals of varying motor capabilities. Impaired gait significantly affects independence and quality of life, and thus a large part of clinical research is dedicated to improving gait through rehabilitative therapies. Evaluation of these paradigms relies on understanding the characteristic differences in the kinematics and underlying biomechanics of impaired and unimpaired locomotion, which has motivated quantitative measurement and analysis of the gait cycle. Previous analysis has largely been limited to a statistical comparison of manually selected pointwise metrics identified through expert knowledge. Here, we use a recent statistical-geometric framework, elastic functional data analysis (FDA), to decompose kinematic data into continuous ‘amplitude’ (spatial) and ‘phase’ (temporal) components, which can then be integrated with established dimensionality reduction techniques. We demonstrate the utility of elastic FDA through two unsupervised applications to post-stroke gait datasets. First, we distinguish between unimpaired, paretic and non-paretic gait presentations. Then, we use FDA to reveal robust, interpretable groups of differential response to exosuit assistance. The proposed methods aim to benefit clinical practice for post-stroke gait rehabilitation, and more broadly, to automate the quantitative analysis of motion.

Active entanglement enables stochastic, topological grasping. Kaitlyn Becker, Clark Teeple, Nicholas Charles, Yeonsu Jung, Daniel Baum, James C. Weaver,L. Mahadevan and Robert Wood. Proceedings of the National Academy of Sciences. Volume 119, October 10, 2022 .
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Grasping, in both biological and engineered mechanisms, can be highly sensitive to the gripper and object morphology, as well as perception and motion planning. Here, we circumvent the need for feedback or precise planning by using an array of fluidically actuated slender hollow elastomeric filaments to actively entangle with objects that vary in geometric and topological complexity. The resulting stochastic interactions enable a unique soft and conformable grasping strategy across a range of target objects that vary in size, weight, and shape. We experimentally evaluate the grasping performance of our strategy and use a computational framework for the collective mechanics of flexible filaments in contact with complex objects to explain our findings. Overall, our study highlights how active collective entanglement of a filament array via an uncontrolled, spatially distributed scheme provides options for soft, adaptable grasping.

Detecting Lagrangian coherent structures from sparse and noisy trajectory data. Saviz Mowlavi, Mattia Serra, Enrico MaiorinoL. Mahadevan Journal of Fluid Mechanics. Volume 948, September 06, 2022 .
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Many complex flows such as those arising from the collective motion of ocean plastics in geophysics or motile cells in biology are characterized by sparse and noisy trajectory datasets. We introduce techniques for identifying Lagrangian coherent structures (LCSs) of hyperbolic and elliptic nature in such datasets. Hyperbolic LCSs, which represent surfaces with maximal attraction or repulsion over a finite amount of time, are computed through a regularized least-squares approximation of the flow map gradient. Elliptic LCSs, which identify regions of coherent motion such as vortices and jets, are extracted using DBSCAN – a popular data clustering algorithm – combined with a systematic parameter selection strategy. We deploy these methods on various benchmark analytical flows and real-life experimental datasets ranging from oceanography to biology and show that they yield accurate results, despite sparse and noisy data. We also provide a lightweight computational implementation of these techniques as a user-friendly and straightforward Python code.

Active Nematic Defects and Epithelial Morphogenesis. Farzan Vafa, L. MAHADEVAN  Physical Review Letters. Volume 129, Issue 9, 26 August 2022.
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Inspired by recent experiments that highlight the role of nematic defects in the morphogenesis of epithelial tissues, we develop a minimal framework to study the dynamics of an active curved surface driven by its nematic texture. Allowing the surface to evolve via relaxational dynamics leads to a theory linking nematic defect dynamics, cellular division rates, and Gaussian curvature. Regions of large positive (negative) curvature and positive (negative) growth are colocalized with the presence of positive (negative) defects. In an ex-vivo setting of cultured murine neural progenitor cells, we show that our framework is consistent with the observed cell accumulation at positive defects and depletion at negative defects. In an in-vivo setting, we show that the defect configuration consisting of a bound +1 defect state, which is stabilized by activity, surrounded by two −1/2 defects can create a stationary ring configuration of tentacles, consistent with observations of a basal marine invertebrate Hydra.

Optimal policies for mitigating pandemic costs: a tutorial model. M Serra, S al-Mosleh, S Ganga Prasath, V Raju, S Mantena, J Chandra, S Iams L. MAHADEVAN  Physical Biology. Volume 19, 9 August 2022 .
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There have been a number of pharmaceutical and non-pharmaceutical interventions associated with COVID-19 over the past two years. Various non-pharmaceutical interventions were proposed and implemented to control the spread of the COVID-19 pandemic. Most common of these were partial and complete lockdowns that were used in an attempt to minimize the costs associated with mortality, economic losses and social factors, while being subject to constraints such as finite hospital capacity. Here, we use a minimal model posed in terms of optimal control theory to understand the costs and benefits of such strategies. This allows us to determine top-down policies for how to restrict social contact rates given an age-structured model for the dynamics of the disease. Depending on the relative weights allocated to mortality and socioeconomic losses, we see that the optimal strategies range from long-term social-distancing only for the most vulnerable, partial lockdown to ensure not over-running hospitals, and alternating-shifts, all of which lead to significant reduction in mortality and/or socioeconomic losses. Crucially, commonly used strategies that involve long periods of broad lockdown are almost never optimal, as they are highly unstable to reopening and entail high socioeconomic costs. Using parameter estimates from data available for Germany and the USA early in the pandemic, we quantify these policies and use sensitivity analysis in the relevant model parameters and initial conditions to determine the range of robustness of our policies. Finally we also discuss how bottom-up behavioral changes affect the dynamics of the pandemic and show how they can work in tandem with top-down control policies to mitigate pandemic costs even more effectively.

Geometry, Analysis, and Morphogenesis: problems and prospects. Marta Lewicka, L. Mahadevan  The American Mathematical Society. Volume 59, 331-369 May 23, 2022 .
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The remarkable range of biological forms in and around us, such as the undulating shape of a leaf or flower in the garden, the coils in our gut, or the folds in our brain, raise a number of questions at the interface of biology, physics, and mathematics. How might these shapes be predicted, and how can they eventually be designed? We review our current understanding of this problem, which brings together analysis, geometry, and mechanics in the description of the morphogenesis of low-dimensional objects. Starting from the view that shape is the consequence of metric frustration in an ambient space, we examine the links between the classical Nash embedding problem and biological morphogenesis. Then, motivated by a range of experimental observations and numerical computations, we revisit known rigorous results on curvature-driven patterning of thin elastic films, especially the asymptotic behaviors of the solutions as the (scaled) thickness becomes vanishingly small and the local curvature can become large. Along the way, we discuss open problems that include those in mathematical modeling and analysis along with questions driven by the allure of being able to tame soft surfaces for applications in science and engineering.

Optimal transport and control of active drops. Suraj Shankar, Vidya Raju and L. Mahadevan,  Proceedings of the National Academy of Sciences. ,119 (35), e2121985119, August 24, 2022
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Understanding the complex patterns in space–time exhibited by active systems has been the subject of much interest in recent times. Complementing this forward problem is the inverse problem of controlling active matter. Here, we use optimal control theory to pose the problem of transporting a slender drop of an active fluid and determine the dynamical profile of the active stresses to move it with minimal viscous dissipation. By parametrizing the position and size of the drop using a low-order description based on lubrication theory, we uncover a natural “gather–move–spread” strategy that leads to an optimal bound on the maximum achievable displacement of the drop relative to its size. In the continuum setting, the competition between passive surface tension and active controls generates richer behavior with futile oscillations and complex drop morphologies that trade internal dissipation against the transport cost to select optimal strategies. Our work combines active hydrodynamics and optimal control in a tractable and interpretable framework and begins to pave the way for the spatiotemporal manipulation of active matter.

Elastohydrodynamics of contact in adherent sheets. Stéphane Poulain, Andreas Carlson, Shreyas Mandre and L. Mahadevan,  Journal of Fluid Mechanics. (2022), vol. 947, A16.
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Adhesive contact between a thin elastic sheet and a substrate arises in a range of biological, physical and technological applications. By considering the dynamics of this process that naturally couples fluid flow, long-wavelength elastic deformations and microscopic adhesion, we analyse a sixth-order thin-film equation for the short-time dynamics of the onset of adhesion and the long-time dynamics of a steadily propagating adhesion front. Numerical solutions corroborate scaling laws and asymptotic analyses for the characteristic waiting time for adhesive contact and for the speed of the adhesion front. A similarity analysis of the governing partial differential equation further allows us to determine the shape of a fluid-filled blister ahead of the adhesion front. Finally, our analysis reveals a near-singular behaviour at the moving elastohydrodynamic contact line with an effective boundary condition that might be useful in other related problems.

Statistics and topology of fluctuating ribbons. Ee Hou Yong, Farisan Dary, Luca Giomi and L. Mahadevan,  Proceedings of the National Academy of Sciences. 119(32), e2122907119, August 2, 2022
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Ribbons are a class of slender structures whose length, width, and thickness are widely separated from each other. This scale separation gives a ribbon unusual mechanical properties in athermal macroscopic settings, for example, it can bend without twisting, but cannot twist without bending. Given the ubiquity of ribbon-like biopolymers in biology and chemistry, here we study the statistical mechanics of microscopic inextensible, fluctuating ribbons loaded by forces and torques. We show that these ribbons exhibit a range of topologically and geometrically complex morphologies exemplified by three phases—a twist-dominated helical phase (HT), a writhe-dominated helical phase (HW), and an entangled phase—that arise as the applied torque and force are varied. Furthermore, the transition from HW to HT phases is characterized by the spontaneous breaking of parity symmetry and the disappearance of perversions (that correspond to chirality-reversing localized defects). This leads to a universal response curve of a topological quantity, the link, as a function of the applied torque that is similar to magnetization curves in second-order phase transitions.

Quasicrystal kirigami. Lucy Liu, Gary P. T. Choi and L. Mahadevan,  Phys. Rev. Research, 4(3), 033114 – Published 10 August 2022
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Kirigami, the art of introducing cuts in thin sheets to enable articulation and deployment, has become an inspiration for a novel class of mechanical metamaterials with unusual properties. Here we complement the use of periodic tiling patterns for kirigami designs by showing that quasicrystals can also serve as the basis for designing deployable kirigami structures, and analyze the geometrical, topological, and mechanical properties of these aperiodic kirigami structures.

The ecology and evolution of human-wildlife cooperation. Dominic L. Cram, Jessica E. M. van der Wal, Natalie Uomini, Mauricio Cantor, Anap I. Afan, Mairenn C. Attwood, Jenny Amphaeris, Fatima Balasani, Cameron J. Blair, Judith L. Bronstein, Iahaia O. Buanachique, Rion R. T. Cuthill, Jewel Das, Fábio G. Daura-Jorge, Apurba Deb, Tanmay Dixit, Gcina S. Dlamini, Edmond Dounias, Isa I. Gedi, Martin Gruber, Lilian S. Hoffmann, Tobias Holzlehner, Hussein A. Isack, Eliupendo A. Laltaika, David J. Lloyd-Jones, Jess Lund, Alexandre M. S. Machado, L. Mahadevan, Ignacio B. Moreno, Chima J. Nwaogu ,Raymond Pierotti, Seliano A. Rucunua, Wilson F. dos Santos, Nathalia Serpa, Brian D. Smith, Hari Sridhar, Irina Tolkova, Tint Tun, João V. S. Valle-Pereira, Brian M. Wood, Richard W. Wrangham and Claire N. Spottiswoode. People Nature, August 2022, 841-855, 4,(4)
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1. Human-wildlife cooperation is a type of mutualism in which a human and a wild, free-living animal actively coordinate their behaviour to achieve a common beneficial outcome.
2. While other cooperative human-animal interactions involving captive coercion or artificial selection (including domestication) have received extensive attention, we lack integrated insights into the ecology and evolution of human-wildlife cooperative interactions.
3. Here, we review and synthesise the function, mechanism, development, and evolution of human-wildlife cooperation.
4. Active cases involve people cooperating with greater honeyguide birds and with two dolphin species, while historical cases involve wolves and orcas.
5. In all cases, a food source located by the animal is made available to both species by a tool-using human, coordinated with cues or signals.
6. The mechanisms mediating the animal behaviours involved are unclear, but they may resemble those underlying intraspecific cooperation and reduced neophobia.
7. The skills required appear to develop at least partially by social learning in both humans and the animal partners. As a result, distinct behavioural variants have emerged in each type of human-wildlife cooperative interaction in both species, and human-wildlife cooperation is embedded within local human cultures.
8. We propose multiple potential origins for these unique cooperative interactions, and highlight how shifts to other interaction types threaten their persistence.
9. Finally, we identify key questions for future research. We advocate an approach that integrates ecological, evolutionary and anthropological perspectives to advance our understanding of human-wildlife cooperation. In doing so, we will gain new insights into the diversity of our ancestral, current and future interactions with the natural world.

Safeguarding human–wildlife cooperation. Jessica E. M. van der Wal, Claire N. Spottiswoode, Natalie T. Uomini, Mauricio Cantor, Fábio G. Daura-Jorge, Anap I. Afan, Mairenn C. Attwood, Jenny Amphaeris, Fatima Balasani, Colleen M. Begg, Cameron J. Blair, Judith L. Bronstein, Iahaia O. Buanachique, Rion R. T. Cuthill, Jewel Das, Apurba Deb, Tanmay Dixit, Gcina S. Dlamini, Edmond Dounias, Isa I. Gedi, Martin Gruber, Lilian S. Hoffmann, Tobias Holzlehner, Hussein A. Isack, Eliupendo A. Laltaika, David J. Lloyd-Jones, Jess Lund, Alexandre M.S.Machado, L. Mahadevan, Ignacio B. Moreno, Chima J. Nwaogu, Valdomiro L. Pereira, Raymond Pierotti, Seliano A. Rucunua, Wilson F. dos Santos, Nathalia Serpa, Brian D. Smith, Irina Tolkova, Tint Tun, João V. S. Valle-Pereira, Brian M. Wood, Richard W. Wranghama and Dominic L. Cram. Conservation Letters, July/August 2022,15(4), e12886
[ONLINE ARTICLE] [DOI] [View PDF] [Download PDF] Abstract
Human–wildlife cooperation occurs when humans and free-living wild animals actively coordinate their behavior to achieve a mutually beneficial outcome. These interactions provide important benefits to both the human and wildlife communities involved, have wider impacts on the local ecosystem, and represent a unique intersection of human and animal cultures. The remaining active forms are human–honeyguide and human–dolphin cooperation, but these are at risk of joining several inactive forms (including human–wolf and human–orca cooperation). Human–wildlife cooperation faces a unique set of conservation challenges, as it requires multiple components—a motivated human and wildlife partner, a suitable environment, and compatible interspecies knowledge—which face threats from ecological and cultural changes. To safeguard human–wildlife cooperation, we recommend: (i) establishing ethically sound conservation strategies together with the participating human communities; (ii) conserving opportunities for human and wildlife participation; (iii) protecting suitable environments; (iv) facilitating cultural transmission of traditional knowledge; (v) accessibly archiving Indigenous and scientific knowledge; and (vi) conducting long-term empirical studies to better understand these interactions and identify threats. Tailored safeguarding plans are therefore necessary to protect these diverse and irreplaceable interactions. Broadly, our review highlights that efforts to conserve biological and cultural diversity should carefully consider interactions between human and animal cultures.

Geometric control of topological dynamics in a singing saw. Suraj Shankar, Petur Bryde and L. Mahadevan.  Proceedings of  the National Academy of  Sciences, Vol. 119 | No. 17
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A common handsaw can be converted into a bowed musical instrument capable of producing exquisitely sustained notes when its blade is appropriately bent. Acoustic modes localized at an inflection point are known to underlie the saw’s sonorous quality, yet the origin of localization has remained mysterious. Here we uncover a topological basis for the existence of localized modes that relies on and is protected by spatial curvature. By combining experimental demonstrations, theory, and computation, we show how spatial variations in blade curvature control the localization of these trapped states, allowing the saw to function as a geometrically tunable high-quality oscillator. Our work establishes an unexpected connection between the dynamics of thin shells and topological insulators and offers a robust principle to design high-quality resonators across scales,from macroscopic instruments to nanoscale devices, simply through geometry.

Rectified random cell motility as a mechanism for embryo elongation. Ido Regev, Karine Guevorkian, Anupam Gupta, Olivier Pourquie and L. Mahadevan. Development (2022) 149, dev199423.
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The body of vertebrate embryos forms by posterior elongation from a terminal growth zone called the tail bud. The tail bud is a source of highly motile cells that eventually constitute the presomitic mesoderm (PSM), a tissue that plays an important role in elongation movements. PSM cells establish an anterior-posterior cell motility gradient that parallels a gradient associated with the degradation of a specific cellular signal (FGF) known to be implicated in cell motility. Here, we combine the electroporation of fluorescent reporters in the PSM with time-lapse imaging in the chicken embryo to quantify cell diffusive movements along the motility gradient. We show that a simple microscopic model for random cell motility induced by FGF activity along with geometric confinement leads to rectified tissue elongation consistent with our observations. A continuum analog of the microscopic model leads to a macroscopic mechano-chemical model for tissue extension that couples FGF activity-induced cell motility and tissue rheology, and is consistent with the experimentally observed speed and extent of elongation. Together, our experimental observations and theoretical models explain how the continuous addition of cells at the tail bud combined with lateral confinement can be converted into oriented movement and drive body elongation

Combing a double helix. Thomas B. Plumb-Reyes, Nicholas Charles and L. Mahadevan. Soft Matter. 2022 18, 2767.
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Combing hair involves brushing away the topological tangles in a collective curl, defined as a bundle of interacting elastic filaments. Using a combination of experiment and computation, we study this problem that naturally links topology, geometry and mechanics. Observations show that the dominant interactions in hair are those of a two-body nature, corresponding to a braided homochiral double helix. This minimal model allows us to study the detangling of an elastic double helix driven by a single stiff tine that moves along it and leaves two untangled filaments in its wake. Our results quantify how the mechanics of detangling correlates with the dynamics of a topological quantity, the link density, that propagates ahead of the tine and flows out the free end as a link current. This in turn provides a measure of the maximum characteristic length of a single combing stroke in the many-body problem on a head of hair, producing an optimal combing strategy that balances trade-offs between comfort, efficiency and speed of combing in hair curls of varying geometrical and topological complexity.

Thermoregulatory morphodynamics of honeybee swarm clusters. Jacob M. Peters, Orit Peleg and L. Mahadevan. Journal of Experimental Biology (2022) 225, jeb242234
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During reproductive swarming, honeybee clusters of more than 10,000 individuals that hang from structures in the environment (e.g. tree branches) are exposed to diurnal variations in ambient temperature for up to a week. Swarm clusters collectively modulate their morphology in response to these variations (i.e. expanding/ contracting in response to heating/cooling) to maintain their internal temperature within a tolerable range and to avoid exhausting their honey stores prematurely. To understand the spatiotemporal aspects of thermoregulatory morphing, we measured the change in size, shape and internal temperature profiles of swarm clusters in response to dynamic temperature ramp perturbations. Swarm clusters showed a two-fold variation in their volume/density when heated from 15°C to 30°C. However, they did not reach an equilibrium size or shape when held at 30°C for 5 h, long after the core temperature of the cluster had stabilized. Furthermore, the changes in cluster shape and size were hysteretic, contracting in response to cooling faster than expanding in response to heating. Although the base contact diameter of the cluster increased continuously when the swarm was heated, the change in length of the swarm (base to tip) over time was non- monotonic. Consequently, the aspect ratio of the swarm fluctuated continuously even when held at a constant temperature. Taken together, our results quantify the hysteretic and anisotropic morphological responses of swarm clusters to ambient temperature variations while suggesting that both mechanical constraints and heat transfer govern their thermoregulatory morphodynamics.

A buckling-sheet ring oscillator for electronics-free, multimodal locomotion. Won-Kyu Lee, Daniel J. Preston, Markus P. Nemitz1, Amit Nagarkar, Arthur K. MacKeith, Benjamin Gorissen, Nikolaos Vasios, Vanessa Sanchez2, Katia Bertoldi , L. Mahadevan , George M. Whitesides. Sci. Robot. 7, eabg5812 (2022).
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Locomotion of soft robots typically relies on control of multiple inflatable actuators by electronic computers and hard valves. Soft pneumatic oscillators can reduce the demand on controllers by generating complex movements required for locomotion from a single, constant input pressure, but either have been constrained to low rates of flow of air or have required complex fabrication processes. Here, we describe a pneumatic oscillator fabricated from flexible, but inextensible, sheets that provides high rates of airflow for practical locomotion by combining three instabilities: out-of-plane buckling of the sheets, kinking of tubing attached to the sheets, and a system-level instability resulting from connection of an odd number of pneumatic inverters made from these sheets in a loop. This device, which we call a “buckling-sheet ring oscillator” (BRO), directly generates movement from its own interaction with its surroundings and consists only of readily available materials assembled in a simple process— specifically, stacking acetate sheets, nylon film, and double-sided tape, and attaching an elastomeric tube. A device incorporating a BRO is capable of both translational and rotational motion over varied terrain (even without a tether) and can climb upward against gravity and downward against the buoyant force encountered under water.

Euclid’s Random Walk: Developmental Changes in the Use of Simulation for Geometric Reasoning. Yuval Hart, L. Mahadevan, Moira R. Dillon. Cognitive Science 46 (2022) e13070
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Euclidean geometry has formed the foundation of architecture, science, and technology for millennia, yet the development of human’s intuitive reasoning about Euclidean geometry is not well understood. The present study explores the cognitive processes and representations that support the development of humans’ intuitive reasoning about Euclidean geometry. One-hundred-twenty-five 7- to 12-year-old children and 30 adults completed a localization task in which they visually extrapolated missing parts of fragmented planar triangles and a reasoning task in which they answered verbal questions about the general properties of planar triangles. While basic Euclidean principles guided even young children’s visual extrapolations, only older children and adults reasoned about triangles in ways that were consistent with Euclidean geometry. Moreover, a relation beteen visual extrapolation and reasoning appeared only in older children and adults. Reasoning consistent with Euclidean geometry may thus emerge when children abandon incorrect, axiomatic-based reasoning strategies and come to reason using mental simulations of visual extrapolations.

Geometrical dynamics of edge-driven accretive surface growth C. Nadir Kaplan and L. Mahadevan. Proceedings of the Royal Society A. January 2022. Volume 478 Issue 2257.
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Accretion of mineralized thin wall-like structures via localized growth along their edges is observed in physical and biological systems ranging from molluscan and brachiopod shells to carbonate–silica composite precipitates. To understand the shape of these mineralized structures, we develop a mathematical framework that treats the thin-walled shells as a smooth surface left in the wake of the growth front that can be described as an evolving space curve. Our theory then takes an explicit geometric form for the prescription of the velocity of the growth front curve, along with compatibility relations and a closure equation related to the nature of surface curling. Solutions of these equations capture a range of geometric precipitate patterns seen in abiotic and biotic forms across scales. In addition to providing a framework for the growth and form of these thin-walled morphologies, our theory suggests a new class of dynamical systems involving moving space curves that are compatible with non-Euclidean embeddings of surfaces.

2021

Balancing efficiency and homogeneity of biomaterial transport in networks. S. Liese, L. Mahadevan and A. Carlson. Europhysics Letters, Vol. 135 | No. 5
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Transport of biomaterial in tubular networks is ubiquitous in nature, where examples include the endoplasmic reticulum, leaf venation or vessel networks in vertebrates. Flow feedback by adjustment of the local tube radius in response to a fluid flow is a pivotal mechanism to optimize the transport properties of a network. To describe liquid transport in tubular networks we develop a minimal mathematical model, which includes the interplay of the viscous flow feedback and the tubes elastic bending energy while conserving the network material. Flow feedback in pitted, branched and loopy networks is shown to lower their resistance, as compared to a feedback-free system, by local adaptations without the need for additional network material. Flow feedback in particular reduces the resistance in pitted and branched networks, directly linked with a reduction in the effective number of neighboring tubes. In loopy networks we find a direction-dependent flow resistance, with a prevailing transport direction set by the network geometry.

Geometry and dynamics link form, function and evolution of finch beaks. S. al-Mosleh, G.P.T. Choi, A. Abzhanov and L. Mahadevan. Proc. Natl. Acad. Sci. (118) 46, e2105957118, 2021.

[ONLINE ARTICLE] [View PDF] [Download PDF] Abstract
Darwin’s finches are a classic example of adaptive radiation, exemplified by their adaptive and functional beak morphologies. To quantify their form, we carry out a morphometric analysis of the three-dimensional beak shapes of all of Darwin’s finches and find that they can be fit by a transverse parabolic shape with a curvature that increases linearly from the base toward the tip of the beak. The morphological variation of beak orientation, aspect ratios, and curvatures allows us to quantify beak function in terms of the elementary theory of machines, consistent with the dietary variations across finches. Finally, to explain the origin of the evolutionary morphometry and the developmental morphogenesis of the finch beak, we propose an experimentally motivated growth law at the cellular level that simplifies to a variant of curvature-driven flow at the tissue level and captures the range of observed beak shapes in terms of a simple morphospace. Altogether, our study illuminates how a minimal combination of geometry and dynamics allows for functional form to develop and evolve.

Instabilities and patterns in a submerged jelling jet. A. Chakrabarti, S. Al-Mosleh, and L. Mahadevan. Soft Matter, 2021,17, 9745.
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When a thin stream of aqueous sodium alginate is extruded into a reacting calcium chloride bath, it polymerizes into a soft elastic tube that spontaneously forms helical coils due to the ambient fluid drag. We quantify the onset of this drag-induced instability and its nonlinear evolution using experiments, and explain the results using a combination of scaling, theory and simulations. By co-extruding a second (internal) liquid within the aqueous sodium alginate jet and varying the rates of co-extrusion of the two liquids, as well as the diameter of the jet, we show that we can tune the local composition of the composite filament and the nature of the ensuing instabilities to create soft filaments of variable relative buoyancy, shape and mechanical properties. All together, by harnessing the fundamental varicose (jetting) and sinuous (buckling) instabilities associated with the extrusion of a jelling filament, we show that it is possible to print complex three-dimensional filamentous structures in the ambient fluid.

Totimorphic assemblies from neutrally stable units. G. Chaudhary, S. Ganga Prasath, E. Soucy, and L. Mahadevan. Proc. Natl. Acad. Sci. (118) 42, e2107003118, 2021.

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Inspired by the quest for shape-shifting structures in a range of applications, we show how to create morphable structural materials using a neutrally stable unit cell as a building block. This unit cell is a self-stressed hinged structure with a one-parameter family of morphing motions that are all energetically equivalent. However, unlike kinematic mechanisms, the unit cell is not infinitely floppy and instead exhibits a tunable mechanical response akin to that of an ideal rigid-plastic material. Theory and simulations allow us to explore the properties of planar and spatial assemblies of neutrally stable elements, and solve the inverse problem of designing assemblies that can morph from one given shape into another. Simple experimental prototypes of these assemblies corroborate our theoretical results and show that the addition of switchable hinges allows us to create load-bearing structures. Altogether, totimorphs pave the way for structural materials whose geometry and deformation response can be controlled independently and at multiple scales.

Compact reconfigurable kirigami.
G.P. T. Choi , L.H. Dudte, and L. Mahadevan. Phys. Rev. Res., 3, 043030, 2021.

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Kirigami involves cutting a flat, thin sheet that allows it to morph from a closed, compact configuration into an open deployed structure via coordinated rotations of the internal tiles. By recognizing and generalizing the geometric constraints that enable this art form, we propose a design framework for compact reconfigurable kirigami patterns, which can morph from a closed and compact configuration into a deployed state conforming to any prescribed target shape, and subsequently be contracted into a different closed and compact configuration. We further establish a condition for producing kirigami patterns and mechanisms which are reconfigurable and rigid deployable allowing us to connect the compact states via a zero-energy family of deployed states. All together, our inverse design framework lays out a path for the creation of shape-morphing material structures.

The cusp of the apple.
A. Chakrabarti, T.C.T. Michaels, E. Sun, S. Yin and  L. Mahadevan, Nature Physics, 17, 1125-29, 2021.

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Singularities are common in diverse physical systems1 and lead to universal structures. This universality suggests that they should also naturally arise in biological systems, where active growth, autonomous motion, kinesis and taxis focus deformations in spacetime, as exemplified in the morpho- genetic processes determining biological size and shape4. A familiar example of a morphogenetic singularity is seen in the humble apple, which forms in the neighbourhood of the stalk as the apple grows. Here we study the geometry and morpho- genesis of the cusp of an apple by combining observations of fruit growth with a simple theory, finite element simulations and controlled swelling experiments using a physical gel sim- ulacrum. Our observations show that the axisymmetric cusp develops into a self-similar form, which can be understood in terms of a mechanical theory for the inhomogeneous growth of a soft sphere. Physical experiments using local inhibition in swelling gels corroborate our theoretical predictions. These experiments further show that axisymmetric cusps can lose stability and become lobed. We use simulations to show that the number of cuspidal lobes depends on the ratio of the size of the stalk to the size of the sphere, as well as the amplitude and periodicity of perturbations that mimic the role of fruit anatomy, consistent with observations of multi-cusped fruits.

Genetic architecture of floral traits in bee- and hummingbird-pollinated sister species of Aquilegia (columbine). M.B. Edwards, G. P. T. Choi, N. J. Derieg, Y. Min, A. C. Diana, S. A. Hodges, L. Mahadevan, E. M. Kramer, and E. S. Ballerini,  Evolution, 75 (9): 2197–2216, 2021.
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Interactions with animal pollinators have helped shape the stunning diversity of flower morphologies across the angiosperms. A common evolutionary consequence of these interactions is that some flowers have converged on suites of traits, or pollination syndromes, that attract and reward specific pollinator groups. Determining the genetic basis of these floral pollination syndromes can help us understand the processes that contributed to the diversification of the angiosperms. Here, we characterize the genetic architecture of a bee-to-hummingbird pollination shift in Aquilegia (columbine) using QTL mapping of 17 floral traits encompassing color, nectar composition, and organ morphology. In this system, we find that the genetic architectures underlying differences in floral color are quite complex, and we identify several likely candidate genes involved in anthocyanin and carotenoid floral pigmentation. Most morphological and nectar traits also have complex genetic underpinnings; however, one of the key floral morphological phenotypes, nectar spur curvature, is shaped by a single locus of large effect.

Wallpaper group kirigami. L. Liu, G. P. T. Choi, and L. Mahadevan, Proc. R. Soc. A, 477, 20210161, 2021.
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Kirigami, the art of paper cutting, has become a paradigm for mechanical metamaterials in recent years. The basic building blocks of any kirigami structures are repetitive deployable patterns that derive inspiration from geometric art forms and simple planar tilings. Here, we complement these approaches by directly linking kirigami patterns to the symmetry associated with the set of 17 repeating patterns that fully characterize the space of periodic tilings of the plane. We start by showing how to construct deployable kirigami patterns using any of the wallpaper groups, and then design symmetry-preserving cut patterns to achieve arbitrary size changes via deployment. We further prove that different symmetry changes can be achieved by controlling the shape and connectivity of the tiles and connect these results to the underlying kirigami-based lattice structures. All together, our work provides a systematic approach for creating a broad range of kirigami-based deployable structures with any prescribed size and symmetry properties.

Feedback control of protein aggregation. A. J. Dear, T.C. T. Michaels, T. P. J. Knowles, and L. Mahadevan, J. Chem. Phys. 155, 064102 (2021)
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The self-assembly of peptides and proteins into amyloid fibrils plays a causative role in a wide range of increasingly common and currently incurable diseases. The molecular mechanisms underlying this process have recently been discovered, prompting the development of drugs that inhibit specific reaction steps as possible treatments for some of these disorders. A crucial part of treatment design is to determine how much drug to give and when to give it, informed by its efficacy and intrinsic toxicity. Since amyloid formation does not proceed at the same pace in different individuals, it is also important that treatment design is informed by local measurements of the extent of protein aggregation. Here, we use stochastic optimal control theory to determine treatment regimens for inhibitory drugs targeting several key reaction steps in protein aggregation, explicitly taking into account variability in the reaction kinetics. We demonstrate how these regimens may be updated “on the fly” as new measurements of the protein aggregate concentration become available, in principle, enabling treatments to be tailored to the individual. We find that treatment timing, duration, and drug dosage all depend strongly on the particular reaction step being targeted. Moreover, for some kinds of inhibitory drugs, the optimal regimen exhibits high sensitivity to stochastic fluctuations. Feedback controls tailored to the individual may therefore substantially increase the effectiveness of future treatments.

Book Review Think Before You Compute: A Prelude to Computational Fluid Dynamics, E. J. Hinch, in  Physics Today, July 2021.
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An additive algorithm for origami design. L.H. Dudte, G. P. T. Choi, and L. Mahadevan, Proc. Natl. Acad. Sci. (118)  21, e2019241118, 2021.
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Inspired by the allure of additive fabrication, we pose the problem of origami design from a different perspective: How can we grow a folded surface in three dimensions from a seed so that it is guaranteed to be isometric to the plane? We solve this problem in two steps: by first identifying the geometric conditions for the compatible completion of two separate folds into a single developable fourfold vertex, and then showing how this foundation allows us to grow a geometrically compatible front at the boundary of a given folded seed. This yields a complete marching, or additive, algorithm for the inverse design of the complete space of developable quad origami patterns that can be folded from flat sheets. We illustrate the flexibility of our approach by growing ordered, disordered, straight, and curved-folded origami and fitting surfaces of given curvature with folded approximants. Overall, our simple shift in perspective from a global search to a local rule has the potential to transform origami-based metastructure design.

A measure of morphodynamics. M. Serra and L. Mahadevan,  SIAM News, Volume 54/ Issue 3 April 2021.
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Puckering and wrinkling in a growing composite ring. T. C. T. Michaels, R. Kusters L. Mahadevan, Proc. R. Soc. A, 477, 20200999, 2021
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Pattern formation driven by differential strain in constrained elastic systems is a common motif in many technological and biological systems. Here we introduce a biologically motivated case of elastic patterning that allows us to explore the conditions for the existence of local puckering and global wrinkling patterns: a soft growing composite ring adhered elastically to a constraining rigid ring. We explore how differential growth of the soft ring and the elastic resistance to shear and stretching deformations induced by soft adherence lead to a range of phenomena that include uniform aperture-like modes, localized puckers that are Nambu–Goldstone-like modes and global wrinkles in the system. Our analysis combines computer simulations of a discrete rod model with a nonlinear stability analysis of the differential equations in the continuum limit. We provide phase diagrams and scaling relations that reveal the nature and extent of the deformation patterns. Overall, our study reveals how geometry and mechanics conspire to yield a rich phenomenology that could serve as a guide to the design of programmable localized elastic deformations while being relevant for the mechanical basis of biological morphogenesis.

Elastic-instability enabled locomotion. A. Nagarkar, W-K. Lee, D. Preston, M. Nemitz, N. Deng, G. Whitesides and L. Mahadevan, Proc. Natl. Acad. Sci., 118 (8), e2013801118, 2021.
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Locomotion of an organism interacting with an environment is the consequence of a symmetry-breaking action in space-time. Here we show a minimal instantiation of this principle using a thin cir- cular sheet, actuated symmetrically by a pneumatic source, using pressure to change shape nonlinearly via a spontaneous buckling instability. This leads to a polarized, bilaterally symmetric cone that can walk on land and swim in water. In either mode of loco- motion, the emergence of shape asymmetry in the sheet leads to an asymmetric interaction with the environment that generates movement––via anisotropic friction on land, and via directed iner- tial forces in water. Scaling laws for the speed of the sheet of the actuator as a function of its size, shape, and the frequency of ac- tuation are consistent with our observations. The presence of eas- ily controllable reversible modes of buckling deformation further allows for a change in the direction of locomotion in open arenas and the ability to squeeze through confined environments––both of which we demonstrate using simple experiments. Our simple approach of harnessing elastic instabilities in soft structures to drive locomotion enables the design of novel shape-changing ro- bots and other bioinspired machines at multiple scales.

 Static adhesion hysteresis in elastic structures. E. Memet, F. Hilitski, Z. Dogic and L. Mahadevan, Soft Matter, DOI: 10.1039/d0sm02192j, 2021.
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Adhesive interactions between elastic structures such as graphene sheets, carbon nanotubes, and microtubules have been shown to exhibit hysteresis due to irrecoverable energy loss associated with bond breakage, even in static (rate-independent) experiments. To understand this phenomenon, we start with a minimal theory for the peeling of a thin sheet from a substrate, coupling the local event of bond breaking to the nonlocal elastic relaxation of the sheet and show that this can drive static adhesion hysteresis over a bonding/debonding cycle. Using this model we quantify hysteresis in terms of the adhesion and elasticity parameters of the system. This allows us to derive a scaling relation that preserves hysteresis at different levels of granularity while resolving a seeming paradox of lattice trapping in the continuum limit of a discrete fracture process. Finally, to verify our theory, we use new experiments to demonstrate and measure adhesion hysteresis in bundled microtubules.

Self-organized biotectonics of termite nests. A. Heyde, L. Guo, C. Jost, G. Theraulaz and L. Mahadevan, Proc. Natl. Acad. Sci., 118 (5) e2006985118, 2021.
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The termite nest is one of the architectural wonders of the liv- ing world, built by the collective action of workers in a colony. Each nest has several characteristic structural motifs that allow for efficient ventilation, cooling, and traversal. We use tomography to quantify the nest architecture of the African termite Apicotermes lamani, consisting of regularly spaced floors connected by scattered linear and helicoidal ramps. To understand how these elaborate structures are built and arranged, we formulate a minimal model for the spatiotemporal evolution of three hydrodynamic fields—mud, termites, and pheromones— linking environmental physics to collective building behavior using simple local rules based on experimental observations. We find that floors and ramps emerge as solutions of the governing equations, with statistics consistent with observations of A. lamani nests. Our study demonstrates how a local self-reinforcing biotectonic scheme is capable of generating an architecture that is simultaneously adaptable and functional, and likely to be relevant for a range of other animal-built structures.

Models for benthic bipedalism. F. Giardina and L. Mahadevan, Royal Society - Interface 18: 20200701, 2021.
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Walking is a common bipedal and quadrupedal gait and associated with terrestrial and aquatic organisms. Inspired by recent evidence of the neural underpinnings of primitive aquatic walking in the little skate Leucoraja erinacea, we introduce a theoretical model of aquatic walking that reveals robust and efficient gaits with modest requirements for body morphology and control. The model predicts undulatory behaviour of the system body with a regular foot placement pattern, which is also observed in the animal, and additionally predicts the existence of gait bistability between two states, one with a large energetic cost for locomotion and another associated with almost no energetic cost. We show that these can be discovered using a simple reinforcement learning (RL) scheme. To test these theoretical frameworks, we built a bipedal robot and show that its behaviours are similar to those of our minimal model: its gait is also periodic and exhibits bistability, with a low efficiency gait separated from a high efficiency gait by a ‘jump’ transition. Overall, our study highlights the physical constraints on the evolution of walking and provides a guide for the design of efficient biomimetic robots.

2020

Control of connectivity and rigidity in prismatic assemblies. P. T. Choi, S. Chen and L. Mahadevan, Proc. R. Soc. A 476: 20200485, 2020.
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How can we manipulate the topological connectivity of a three-dimensional prismatic assembly to control the number of internal degrees of freedom and the number of connected components in it? To answer this question in a deterministic setting, we use ideas from elementary number theory to provide a hierarchical deterministic protocol for the control of rigidity and connectivity. We then show that it is possible to also use a stochastic protocol to achieve the same results via a percolation transition. Together, these approaches provide scale-independent algorithms for the cutting or gluing of three-dimensional prismatic assemblies to control their overall connectivity and rigidity.

Mechanical coupling coordinates the co-elongation of axial and paraxial tissues in avian embryos. F. Xiong, W. Ma, B. Benazeraf,  L. Mahadevan, and O. Pourquie.  Dev. Cell. 55,  354–366, 2020.
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Tissues undergoing morphogenesis impose mechanical effects on one another. How developmental programs adapt to or take advantage of these effects remains poorly explored. Here, using a combination of live imaging, modeling, and microsurgical perturbations, we show that the axial and paraxial tissues in the forming avian embryonic body coordinate their rates of elongation through mechanical interactions. First, a cell motility gradient drives paraxial presomitic mesoderm (PSM) expansion, resulting in compression of the axial neural tube and notochord; second, elongation of axial tissues driven by PSM compression and polarized cell intercalation pushes the caudal progenitor domain posteriorly; finally, the axial push drives the lateral movement of midline PSM cells to maintain PSM growth and cell motility. These interactions form an engine-like positive feedback loop, which sustains a shared elongation rate for coupled tissues. Our results demonstrate a key role of inter-tissue forces in coordinating distinct body axis tissues during their co-elongation.

Flow-driven branching in a frangible porous medium. N. Derr, D. Fronk, C. Weber, A. Mahadevan, C. Rycroft and L. Mahadevan, Phys. Rev. Lett., 125, 158002, 2020.
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Channel formation and branching is widely seen in physical systems where movement of fluid through a porous structure causes the spatiotemporal evolution of the medium. We provide a simple theoretical framework that embodies this feedback mechanism in a multiphase model for flow through a frangible porous medium with a dynamic permeability. Numerical simulations of the model show the emergence of branched networks whose topology is determined by the geometry of external flow forcing. This allows us to delineate the conditions under which splitting and/or coalescing branched network formation is favored, with potential implications for both understanding and controlling branching in soft frangible media.

Coordinated crawling via reinforcement learning. S. Mishra, W. van Rees, L. Mahadevan, Royal Society-Interface, 17: 20200198,  2020.
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Rectilinear crawling locomotion is a primitive and common mode of loco- motion in slender soft-bodied animals. It requires coordinated contractions that propagate along a body that interacts frictionally with its environment. We propose a simple approach to understand how this coordination arises in a neuromechanical model of a segmented, soft-bodied crawler via an itera- tive process that might have both biological antecedents and technological relevance. Using a simple reinforcement learning algorithm, we show that an initial all-to-all neural coupling converges to a simple nearest-neighbour neural wiring that allows the crawler to move forward using a localized wave of contraction that is qualitatively similar to what is observed in Drosophila melanogaster larvae and used in many biomimetic solutions. The resulting solution is a function of how we weight gait regularization in the reward, with a trade-off between speed and robustness to proprioceptive noise. Overall, our results, which embed the brain–body–environment triad in a learning scheme, have relevance for soft robotics while shedding light on the evolution and development of locomotion.

Mechanical basis for fibrillar bundle morphology. T. Michaels, E. Memet, and L. Mahadevan, Soft Matter , 16, 9306-18, 2020.
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Understanding the morphology of self-assembled fibrillar bundles and aggregates is relevant to a range of problems in molecular biology, supramolecular chemistry and materials science. Here, we propose a coarse-grained approach that averages over specific molecular details and yields an effective mechanical theory for the spatial complexity of self-assembling fibrillar structures that arises due to the competing effects of (the bending and twisting) elasticity of individual filaments and the adhesive interactions between them. We show that our theoretical framework accounting for this allows us to capture a number of diverse fibril morphologies observed in natural and synthetic systems, ranging from Filopodia to multi-walled carbon nanotubes, and leads to a phase diagram of possible fibril shapes. We also show how the extreme sensitivity of these morphologies can lead to spatially chaotic structures. Together, these results suggest a common mechanical basis for mesoscale fibril morphology as a function of the nanoscale mechanical properties of its filamentous constituents.

Optimal control of aging in complex networks E. Sun, T. Michaels, and L. Mahadevan, Proc. Natl. Acad. Sci., 117, 20404-410, 2020.
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Many complex systems experience damage accumulation, which leads to aging, manifest as an increasing probability of system collapse with time. This naturally raises the question of how to maximize health and longevity in an aging system at minimal cost of maintenance and intervention. Here, we pose this question in the context of a simple interdependent network model of aging in complex systems and show that it exhibits cascading failures. We then use both optimal control theory and reinforcement learning alongside a combination of analysis and simulation to determine optimal maintenance protocols. These protocols may motivate the rational design of strategies for promoting longevity in aging complex systems with potential applications in therapeutic schedules and engineered system maintenance.

Elastohydrodynamic scaling law for heart rates. E. Virot, V. Spandan, L. Niu, W. M. van Rees, and L. Mahadevan, Phys. Rev. Lett.,  125, 058102, 2020.
[DOI] [View PDF] [Download PDF] Abstract
Animal hearts are soft shells that actively pump blood to oxygenate tissues. Here, we propose an allometric scaling law for the heart rate based on the idea of elastohydrodynamic resonance of a fluid-loaded soft active elastic shell that buckles and contracts axially when twisted periodically. We show that this picture is consistent with numerical simulations of soft cylindrical shells that twist-buckle while pumping a viscous fluid, yielding optimum ejection fractions of 35%–40% when driven resonantly. Our scaling law is consistent with experimental measurements of heart rates over 2 orders of magnitude, and provides a mechanistic basis for how metabolism scales with organism size. In addition to providing a physical rationale for the heart rate and metabolism of an organism, our results suggest a simple design principle for soft fluidic pumps.

Suspension jams in a leaky microfluidic channel. J. S. Yodh, V. Spandan, and L. Mahadevan, Phys. Rev. Lett.  125, 044501, 2020.
[DOI] [View PDF] [Download PDF] Abstract
Inspired by the jamming in leaky systems that arises in many physiological and industrial settings, we study the propagation of clogs in a leaky microfluidic channel. By driving a colloidal suspension through such a channel with a fluid-permeable wall adjoining a gutter, we follow the formation and propagation of jams and show that they move at a steady speed, in contrast with jams in channels that have impermeable walls. Furthermore, by varying the ratio of the resistance from the leaky wall and that of the gutter, we show that it is possible to control the shape of the propagating jam, which is typically wedge shaped. We complement our experiments with numerical simulations, where we implement an Euler-Lagrangian framework for the simultaneous evolution of both immersed colloidal particles and the carrier fluid. Finally, we show that the particle ordering in the clog can be tuned by adjusting the geometry of the leaky wall. Altogether, the leaky channel serves both as a filter and a shunt with the potential for a range of uses.

Self-excited motions of volatile drops on swellable sheets A. Chakrabarti, G.P-T. Choi, and L. Mahadevan, Phys Rev Lett., 124, 258002, 2020.
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When a volatile droplet is deposited on a floating swellable sheet, it becomes asymmetric, lobed and mobile. We describe and quantify this phenomena that involves nonequilibrium swelling, evaporation and motion, working together to realize a self-excitable spatially extended oscillator. Solvent penetration causes the film to swell locally and eventually buckle, changing its shape and the drop responds by moving. Simultaneously, solvent evaporation from the swollen film causes it to regain its shape once the droplet has moved away. The process repeats and leads to complex pulsatile spinning and/or sliding movements. We use a one-dimensional experiment to highlight the slow swelling of and evaporation from the film and the fast motion of the drop, a characteristic of excitable systems. Finally, we provide a phase diagram for droplet excitability as a function of drop size and film thickness and scaling laws for the motion of the droplet.

Early warning signals in motion inference. Y. Hart, M. Vaziri-Pashkam, and L. Mahadevan, PLOS Computational Biology, 16 (5), 2020.
[DOI] [View PDF] [Download PDF] Abstract
The ability to infer intention lies at the basis of many social interactions played out via motor actions. We consider a simple paradigm of this ability in humans using data from experiments simulating an antagonistic game between an Attacker and a Blocker. Evidence shows early inference of an Attacker move by as much as 100ms but the nature of the informational cues signaling the impending move remains unknown. We show that the transition to action has the hallmark of a critical transition that is accompanied by early warning signals. These early warning signals occur as much as 130 ms before motion ensues—showing a sharp rise in motion autocorrelation at lag-1 and a sharp rise in the autocorrelation decay time. The early warning signals further correlate strongly with Blocker response times. We analyze the variance of the motion near the point of transition and find that it diverges in a manner consistent with the dynamics of a fold-transition. To test if humans can recognize and act upon these early warning signals, we simulate the dynamics of fold-transition events and ask people to recognize the onset of directional motion: participants react faster to fold-transition dynamics than to its uncorrelated counterpart. Together, our findings suggest that people can recognize the intent and onset of motion by inferring its early warning signals.

Dynamic morphoskeletons in development. M. Serra, S. Streichan, M. Chuai, C. J. Weijer, and L. Mahadevan, Proc. Natl. Acad. Sci.,  117, 11444–11449, 2020.
[DOI] [View PDF] [Download PDF] Abstract
Morphogenetic flows in developmental biology are characterized by the coordinated motion of thousands of cells that organize into tissues, naturally raising the question of how this collective organization arises. Using only the kinematics of tissue deformation, which naturally integrates local and global mechanisms along cell paths, we identify the dynamic morphoskeletons behind morphogenesis, i.e., the evolving centerpieces of multicellular trajectory patterns. These features are model- and parameter-free, frame-invariant, and robust to measurement errors and can be computed from unfiltered cell-velocity data. We reveal the spatial attractors and repellers of the embryo by quantifying its Lagrangian deformation, information that is inaccessible to simple trajectory inspection or Eulerian methods that are local and typically frame-dependent. Computing these dynamic morphoskeletons in wild-type and mutant chick and fly embryos, we find that they capture the early footprint of known morphogenetic features, reveal new ones, and quantitatively distinguish between different phenotypes.

Mechanics and kinetics of dynamic instability. T.C.T. Michaels, S. Feng, H. Liang, and L Mahadevan, eLife, 9:e54077, 2020.
[DOI] [View PDF] [Download PDF] Abstract
During dynamic instability, self-assembling microtubules (MTs) stochastically alternate between phases of growth and shrinkage. This process is driven by the presence of two distinct states of MT subunits, GTP- and GDP-bound tubulin dimers, that have different structural properties. Here, we use a combination of analysis and computer simulations to study the mechanical and kinetic regulation of dynamic instability in three-dimensional (3D) self-assembling MTs. Our model quantifies how the 3D structure and kinetics of the distinct states of tubulin dimers determine the mechanical stability of MTs. We further show that dynamic instability is influenced by the presence of quenched disorder in the state of the tubulin subunit as reflected in the fraction of non-hydrolysed tubulin. Our results connect the 3D geometry, kinetics and statistical mechanics of these tubular assemblies within a single framework, and may be applicable to other self-assembled systems where these same processes are at play.

Rotation of a submerged finite cylinder moving down a soft incline. B. Saintyves, B. Rallabandi, T. Jules, J. Ault, T. Salez, C. Schonecker, H. A. Stone and L. Mahadevan, Soft Matter,  16, 4000-06, 2020.  
[DOI] [View PDF] [Download PDF] Abstract
A submerged finite cylinder moving under its own weight along a soft incline lifts off and slides at a steady velocity while also spinning. Here, we experimentally quantify the steady spinning of the cylinder and show theoretically that it is due to a combination of an elastohydrodynamic torque generated by flow in the variable gap, and the viscous friction on the edges of the finite-length cylinder. The relative influence of the latter depends on the aspect ratio of the cylinder, the angle of the incline, and the deformability of the substrate, which we express in terms of a single scaled compliance parameter. By independently varying these quantities, we show that our experimental results are consistent with a transition from an edge-effect dominated regime for short cylinders to a gap-dominated elastohydrodynamic regime when the cylinder is very long.

Deterministic and stochastic control of kirigami topology S. Chen, P. T. Choi, L. Mahadevan, Proc. Natl. Acad. Sci., 117 (9) 4511-4517, 2020.
[DOI] [View PDF] [Download PDF] Abstract
Kirigami, the creative art of paper cutting, is a promising paradigm for mechanical metamaterials. However, to make kirigami-inspired structures a reality requires controlling the topology of kirigami to achieve connectivity and rigidity. We address this question by deriving the maximum number of cuts (minimum number of links) that still allow us to preserve global rigidity and connectivity of the kirigami. A deterministic hierarchical construction method yields an efficient topological way to control both the number of connected pieces and the total degrees of freedom. A statistical approach to the control of rigidity and connectivity in kirigami with random cuts complements the deterministic pathway, and shows that both the number of connected pieces and the degrees of freedom show percolation transitions as a function of the density of cuts (links). Together, this provides a general framework for the control of rigidity and connectivity in planar kirigami.

Poisson’s ratio and residual strain of freestanding ultra-thin films. G. K.Cuddalorepatta, W. M.van Rees, L. Han, D. Pantuso, and L. Mahadevan, Joost J. Vlassak, J. Mech. Phys. Solids,  137, 103821, 2020.
[DOI] [View PDF] [Download PDF] Abstract
The Poisson’s ratio and residual strain of ultra-thin films (<100 nm) are characterized using the phenomenon of transverse wrinkling in stretched bridges. The test methodology utilizes residual stress driven structures and easy to replicate clean-room fabrication and metrology techniques that can be seamlessly incorporated into a thin-film production assembly line. Freestanding rectangular ultra-thin film bridges are fabricated using dimensions that generate repeatable transverse wrinkling patterns. Numerical modeling based on the non-linear Koiter plate and shell energy formulation is conducted to correlate the Poisson’s ratio and residual strain to the measured wrinkling deformation. Poisson’s ratio affects the peak amplitudes without significantly changing the wavelength of the wrinkles. By contrast, the strain affects both the wavelength and amplitude. The proof of concept is demonstrated using 65 nm thick copper films. A Poisson’s ratio of 0.34 ± 0.05 and a tensile residual strain of

Biophysical principles of choanoflagellate self-organization. B. T. Larson, T. Ruiz-Herrero , S. Lee , S. Kumar, and L. Mahadevan, and N. King, Proc. Natl. Acad. Sci., 117 (3) 1303-1311, 2020.
[DOI] [View PDF] [Download PDF] Abstract
Inspired by the patterns of multicellularity in choanoflagellates, the closest living relatives of animals, we quantify the biophysical processes underlying the morphogenesis of rosette colonies in the choanoflagellate Salpingoeca rosetta. We find that rosettes reproducibly transition from an early stage of 2-dimensional (2D) growth to a later stage of 3D growth, despite the underlying variability of the cell lineages. Our perturbative experiments demonstrate the fundamental importance of a basally secreted extracellular matrix (ECM) for rosette morphogenesis and show that the interaction of the ECM with cells in the colony physically constrains the packing of proliferating cells and, thus, controls colony shape. Simulations of a biophysically inspired model that accounts for the size and shape of the individual cells, the fraction of ECM, and its stiffness relative to that of the cells suffices to explain our observations and yields a morphospace consistent with observations across a range of multicellular choanoflagellate colonies. Overall, our biophysical perspective on rosette development complements previous genetic perspectives and, thus, helps illuminate the interplay between cell biology and physics in regulating morphogenesis.

2019

Topology, geometry and mechanics of strongly stretched and twisted filaments: solenoids, plectonemes, and artificial muscle fibers. N. Charles, M. Gazzola, L. Mahadevan,  Phys. Rev. Lett. , 123, 208003, 2020.
[DOI] [View PDF] [Download PDF] Abstract
Soft elastic filaments that can be stretched, bent, and twisted exhibit a range of topologically and geometrically complex morphologies. Recently, a number of experiments have shown how to use these building blocks to create filament-based artificial muscles that use the conversion of writhe to extension or contraction, exposing the connection between topology, geometry, and mechanics. Here, we combine numerical simulations of soft elastic filaments that account for geometric nonlinearities and self-contact to map out the basic structures underlying artificial muscle fibers in a phase diagram that is a function of the extension and twist density. We then use ideas from computational topology to track the interconversion of link, twist, and writhe in these geometrically complex physical structures to explain the physical principles underlying artificial muscle fibers and provide guidelines for their design.

Computational analysis of size, shape and structure of insect wings. M.K. Salcedo, J. Hoffmann, S. Donoughe and L. Mahadevan, Biology Open  8, bio040774, 2019.
[DOI] [View PDF] [Download PDF] Abstract
The size, shape and structure of insect wings are intimately linked to their ability to fly. However, there are few systematic studies of the variability of the natural patterns in wing morphology across insects. We have assembled a dataset of 789 insect wings with representatives from 25 families and performed a comprehensive computational analysis of their morphology using topological and geometric notions in terms of (i) wing size and contour shape, (ii) vein topology, and (iii) shape and distribution of wing membrane domains. These morphospaces are complementary to existing methods for quantitatively characterizing wing morphology and are likely to be useful for investigating wing function and evolution. This Methods and Techniques paper is accompanied by a set of computational tools for open use.

Shape-shifting structured lattices via multimaterial 4D printing. J.W. Boley, W.M. van Rees, C. Lissandrello, M.N. Horenstein, R.L. Truby, A. Kotikian, J.A. Lewis, and L. Mahadevan, Proc. Natl. Acad.  Sci.,  116 (42) 20856-20862, 2019.
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Thin shape-shifting structures are often limited in their ability to morph into complex and doubly curved shapes. Such transformations require both large in-plane expansion or contraction gradients and control over extrinsic curvature, which are hard to achieve with single materials arranged in simple architectures. We solve this problem by 4-dimensional printing of multiple materials in heterogeneous lattice designs. Our material system provides a platform that achieves in-plane growth and out-of-plane curvature control for 4-material bilayer ribs. The lattice design converts this into large growth gradients, which lead to complex, predictable 3-dimensional (3D) shape changes. We demonstrate this approach with a hemispherical antenna that shifts resonant frequency as it changes shape and a flat lattice that transforms into a 3D human face.

Size control of the inner ear via hydraulic feedback. K.R. Mosaliganti, I. A. Swinburne, C.U. Chan, N.D. Obholzer, A. A. Green, S. Tanksale, L Mahadevan, and S.G. Megason, eLife 2019;8:e39596. 2019.
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Animals make organs of precise size, shape, and symmetry but how developing embryos do this is largely unknown. Here, we combine quantitative imaging, physical theory, and physiological measurement of hydrostatic pressure and fluid transport in zebrafish to study size control of the developing inner ear. We find that fluid accumulation creates hydrostatic pressure in the lumen leading to stress in the epithelium and expansion of the otic vesicle. Pressure, in turn, inhibits fluid transport into the lumen. This negative feedback loop between pressure and transport allows the otic vesicle to change growth rate to control natural or experimentally-induced size variation. Spatiotemporal patterning of contractility modulates pressure-driven strain for regional tissue thinning. Our work connects molecular-driven mechanisms, such as osmotic pressure driven strain and actomyosin tension, to the regulation of tissue morphogenesis via hydraulic feedback to ensure robust control of organ size.

Controlled gliding and perching through deep-reinforcement-learning. G.Novati, L. Mahadevan, and P. Koumoutsakos, Physical Review Fluids 4, 093902, 2019.
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Controlled gliding is one of the most energetically efficient modes of transportation for natural and human powered fliers. Here we demonstrate that gliding and landing strategies with different optimality criteria can be identified through deep-reinforcement-learning without explicit knowledge of the underlying physics. We combine a two-dimensional model of a controlled elliptical body with deep-reinforcement-learning (D-RL) to achieve gliding with either minimum energy expenditure, or fastest time of arrival, at a predetermined location. In both cases the gliding trajectories are smooth, although energy/time optimal strategies are distinguished by small/high frequency actuations. We examine the effects of the ellipse's shape and weight on the optimal policies for controlled gliding. We find that the model-free reinforcement learning leads to more robust gliding than model-based optimal control strategies with a modest additional computational cost. We also demonstrate that the gliders with D-RL can generalize their strategies to reach the target location from previously unseen starting positions. The model-free character and robustness of D-RL suggests a promising framework for developing robotic devices capable of exploiting complex flow environments.

Genetic and Mechanical Regulation of Intestinal Smooth Muscle Development T. R. Huycke, B.M. Miller, H. K. Gill, N. L. Nerurkar, D. Sprinzak, L. Mahadevan, C. J. Tabin, Cell 179, 90–105. 2019.
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The gastrointestinal tract is enveloped by concentric and orthogonally aligned layers of smooth muscle; however, an understanding of the mechanisms by which these muscles become patterned and aligned in the embryo has been lacking. We find that Hedgehog acts through Bmp to delineate the position of the circumferentially oriented inner muscle layer, whereas localized Bmp inhibition is critical for allowing formation of the later-forming, longitudinally oriented outer layer. Because the layers form at different developmental stages, the muscle cells are exposed to unique mechanical stimuli that direct their alignments. Differential growth within the early gut tube generates residual strains that orient the first layer circumferentially, and when formed, the spontaneous contractions of this layer align the second layer longitudinally. Our data link morphogen-based patterning to mechanically controlled smooth muscle cell alignment and provide a mechanistic context for potentially understanding smooth muscle organization in a wide variety of tubular organs.

Random sequential adsorption of spheres on a cylinder E. Memet, N.Tanjeem, C. Greboval, V. N. Manoharan and L. Mahadevan EPL, 127 (2019) 38004. 2019.
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Inspired by observations of beads packed on a thin string in such systems as sea-grapes and dental plaque, we study the random sequential adsorption of spheres on a cylinder. We determine the asymptotic fractional coverage of the cylinder as a function of the sole parameter in the problem, the ratio of the sphere radius to the cylinder radius (for a very long cylinder) using a combination of analysis and numerical simulations. Examining the asymptotic structures, we find weak chiral ordering on sufficiently small spatial scales. Experiments involving colloidal microspheres that can attach irreversibly to a silica wire via electrostatic forces or DNA hybridization allow us to verify our predictions for the asymptotic coverage.

Geometric localization in supported elastic struts TCT Michaels, R. Kusters, AJ Dear, C. Storm, JC Weaver, L. Mahadevan, Proceedings of the Royal Society A 475, 20190370. 2019.
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Localized deformation patterns are a common motif in morphogenesis and are increasingly finding applications in materials science and engineering, in such instances as mechanical memories. Here, we describe the emergence of spatially localized deformations in a minimal mechanical system by exploring the impact of growth and shear on the conformation of a semi-flexible filament connected to a pliable shearable substrate. We combine numerical simulations of a discrete rod model with theoretical analysis of the differential equations recovered in the continuum limit to quantify (in the form of scaling laws) how geometry, mechanics and growth act together to give rise to such localized structures in this system. We find that spatially localized deformations along the filament emerge for intermediate shear modulus and increasing growth. Finally, we use experiments on a 3D-printed multi-material model system to demonstrate that external control of the amount of shear and growth may be used to regulate the spatial extent of the localized strain texture.

Programming shape using kirigami tessellations G. P. T. Choi, L. H. Dudte and L. Mahadevan, Nature Materials 18, 999–1004. 2019.
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Kirigami tessellations, regular planar patterns formed by partially cutting flat, thin sheets, allow compact shapes to morph into open structures with rich geometries and unusual material properties. However, geometric and topological constraints make the design of such structures challenging. Here we pose and solve the inverse problem of determining the number, size and orientation of cuts that enables the deployment of a closed, compact regular kirigami tessellation to conform approximately to any prescribed target shape in two or three dimensions. We first identify the constraints on the lengths and angles of generalized kirigami tessellations that guarantee that their reconfigured face geometries can be contracted from a non-trivial deployed shape to a compact, non-overlapping planar cut pattern. We then encode these conditions into a flexible constrained optimization framework to obtain generalized kirigami patterns derived from various periodic tesselations of the plane that can be deployed into a wide variety of prescribed shapes. A simple mechanical analysis of the resulting structure allows us to determine and control the stability of the deployed state and control the deployment path. Finally, we fabricate physical models that deploy in two and three dimensions to validate this inverse design approach. Altogether, our approach, combining geometry, topology and optimization, highlights the potential for generalized kirigami tessellations as building blocks for shape-morphing mechanical metamaterials.

The effect of step size on straight-line orientation L. Khaldy, O. Peleg, C. Tocco, L. Mahadevan, M. Byrne and M. Dacke Journal of the Royal Society Interface 16 20190181. 2019.
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Moving along a straight path is a surprisingly difficult task. This is because, with each ensuing step, noise is generated in the motor and sensory systems, causing the animal to deviate from its intended route. When relying solely on internal sensory information to correct for this noise, the directional error generated with each stride accumulates, ultimately leading to a curved path. In contrast, external compass cues effectively allow the animal to correct for errors in its bearing. Here, we studied straight-line orientation in two different sized dung beetles. This allowed us to characterize and model the size of the directional error generated with each step, in the absence of external visual compass cues (motor error) as well as in the presence of these cues (compass and motor errors). In addition, we model how dung beetles balance the influence of internal and external orientation cues as they orient along straight paths under the open sky. We conclude that the directional error that unavoidably accumulates as the beetle travels is inversely proportional to the step size of the insect, and that both beetle species weigh the two sources of directional information in a similar fashion.
Evolution of avian egg shape: underlying mechanisms and the importance of taxonomic scale C. Sheard, D. Akkaynak, EH Yong, L. Mahadevan & J. A. Tobias, IBIS 161 (4) 15 July 2019.
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Dynamics of growth and form in prebiotic vesicles
T. Herrero-Ruiz, T. Fai, L. Mahadevan, Physical Review Letters 123, 038102, 2019.
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The growth, form, and division of prebiotic vesicles, membraneous bags of fluid of varying components and shapes is hypothesized to have served as the substrate for the origin of life. The dynamics of these out-of-equilibrium structures is controlled by physicochemical processes that include the intercalation of amphiphiles into the membrane, fluid flow across the membrane, and elastic deformations of the membrane. To understand prebiotic vesicular forms and their dynamics, we construct a minimal model that couples membrane growth, deformation, and fluid permeation, ultimately couched in terms of two dimensionless parameters that characterize the relative rate of membrane growth and the membrane permeability. Numerical simulations show that our model captures the morphological diversity seen in extant precursor mimics of cellular life, and might provide simple guidelines for the synthesis of these complex shapes from simple ingredients.

Optimal strategies for inhibition of protein aggregation T.C. Michaels, C. Weber and L. Mahadevan, PNAS 116 (29) 14593-14598, 2019.
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Protein aggregation has been implicated in many medical disorders, including Alzheimer’s and Parkinson’s diseases. Potential therapeutic strategies for these diseases propose the use of drugs to inhibit specific molecular events during the aggregation process. However, viable treatment protocols require balancing the efficacy of the drug with its toxicity, while accounting for the underlying events of aggregation and inhibition at the molecular level. To address this key problem, we combine here protein aggregation kinetics and control theory to determine optimal protocols that prevent protein aggregation via specific reaction pathways. We find that the optimal inhibition of primary and fibril-dependent secondary nucleation require fundamentally different drug administration protocols. We test the efficacy of our approach on experimental data for the aggregation of the amyloid-(1-42) peptide of Alzheimer’s disease in the model organism Caenorhabditis elegans. Our results pose and answer the question of the link between the molecular basis of protein aggregation and optimal strategies for inhibiting it, opening up avenues for the design of rational therapies to control pathological protein aggregation.

Hydraulic control of mammalian embryo size and cell fate
C.J. Chan, M. Costanzo, T. Ruiz-Herrero, G. Monke, R. Petrie, L. Mahadevan, T. Hiiragi, Nature 571, 112–116, 2019.
[DOI] [View PDF] [Download PDF] Abstract
Size control is fundamental in tissue development and homeostasis1,2. Although the role of cell proliferation in these processes has been widely studied, the mechanisms that control embryo size—and how these mechanisms affect cell fate—remain unknown. Here we use the mouse blastocyst as a model to unravel a key role of fluid-filled lumen in the control of embryo size and specification of cell fate. We find that there is a twofold increase in lumenal pressure during blastocyst development, which translates into a concomitant increase in cell cortical tension and tissue stiffness of the trophectoderm that lines the lumen. Increased cortical tension leads to vinculin mechanosensing and maturation of functional tight junctions, which establishes a positive feedback loop to accommodate lumen growth. When the cortical tension reaches a critical threshold, cell–cell adhesion cannot be sustained during mitotic entry, which leads to trophectoderm rupture and blastocyst collapse. A simple theory of hydraulically gated oscillations recapitulates the observed dynamics of size oscillations, and predicts the scaling of embryo size with tissue volume. This theory further predicts that disrupted tight junctions or increased tissue stiffness lead to a smaller embryo size, which we verified by biophysical, embryological, pharmacological and genetic perturbations. Changes in lumenal pressure and size can influence the cell division pattern of the trophectoderm, and thereby affect cell allocation and fate. Our study reveals how lumenal pressure and tissue mechanics control embryo size at the tissue scale, which is coupled to cell position and fate at the cellular scale.

Spatio-temporal integration in plant tropisms
Y. Meroz, R. Bastien and L. Mahadevan Interface 16, 20190038, 2019.
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Tropisms, growth-driven responses to environmental stimuli, cause plant organs to respond in space and time and reorient themselves. Classical experiments from nearly a century ago reveal that plant shoots respond to the integrated history of light and gravity stimuli rather than just responding instantaneously. We introduce a temporally non-local response function for the dynamics of shoot growth formulated as an integro-differential equation whose solution allows us to qualitatively reproduce experimental observations associated with intermittent and unsteady stimuli. Furthermore, an analytic solution for the case of a pulse stimulus expresses the response function as a function of experimentally tractable variables, which we calculate for the case of the phototropic response of Arabidopsis hypocotyls. All together, our model enables us to predict tropic responses to time-varying stimuli, manifested in temporal integration phenomena, and sets the stage for the incorporation of additional effects such as multiple stimuli, gravitational sagging, etc.

Spatial control of irreversible protein aggregation
C. Weber, T.C. Michaels and L. Mahadevan, eLife 8:e42315, 2019.
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Liquid cellular compartments form in the cyto- or nucleoplasm and can regulate aberrant protein aggregation. Yet, the mechanisms by which these compartments affect protein aggregation remain unknown. Here, we combine kinetic theory of protein aggregation and liquid-liquid phase separation to study the spatial control of irreversible protein aggregation in the presence of liquid compartments. We find that even for weak interactions aggregates strongly partition into the liquid compartment. Aggregate partitioning is caused by a positive feedback mechanism of aggregate nucleation and growth driven by a flux maintaining the phase equilibrium between the compartment and its surrounding. Our model establishes a link between specific aggregating systems and the physical conditions maximizing aggregate partitioning into the compartment. The underlying mechanism of aggregate partitioning could be used to confine cytotoxic protein aggregates inside droplet-like compartments but may also represent a common mechanism to spatially control irreversible chemical reactions in general.

A multiphase theory for spreading microbial swarms and films
S. Srinivasan, N.C. Kaplan, L. Mahadevan, eLife 8:e42697, 2019.
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Bacterial swarming and biofilm formation are collective multicellular phenomena through which diverse microbial species colonize and spread over water-permeable tissue. During both modes of surface translocation, fluid uptake and transport play a key role in shaping the overall morphology and spreading dynamics. Here we develop a generalized two-phase thin-film model that couples bacterial growth, extracellular matrix swelling, fluid flow, and nutrient transport to describe the expansion of both highly motile bacterial swarms, and sessile bacterial biofilms. We show that swarm expansion corresponds to steady-state solutions in a nutrient-rich, capillarity dominated regime. In contrast, biofilm colony growth is described by transient solutions associated with a nutrient-limited, extracellular polymer stress driven limit. We apply our unified framework to explain a range of recent experimental observations of steady and unsteady expansion of microbial swarms and biofilms. Our results demonstrate how the physics of flow and transport in slender geometries serve to constrain biological organization in microbial communities.

Rigidity percolation and geometric information in floppy origami S. Chen, L. Mahadevan, PNAS 116 (17) 8119-8124, 2019.
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Origami structures with a large number of excess folds are capable of storing distinguishable geometric states that are energetically equivalent. As the number of excess folds is reduced, the system has fewer equivalent states and can eventually become rigid. We quantify this transition from a floppy to a rigid state as a function of the presence of folding constraints in a classic origami tessellation, Miura-ori. We show that in a fully triangulated Miura-ori that is maximally floppy, adding constraints via the elimination of diagonal folds in the quads decreases the number of degrees of freedom in the system, first linearly and then nonlinearly. In the nonlinear regime, mechanical cooperativity sets in via a redundancy in the assignment of constraints, and the degrees of freedom depend on constraint density in a scale-invariant manner. A percolation transition in the redundancy in the constraints as a function of constraint density suggests how excess folds in an origami structure can be used to store geometric information in a scale-invariant way.

Morphogenesis of termite mounds S. A. Ocko , A. Heyde, and L. Mahadevan, PNAS 116(9) 3379-3384; published ahead of print February 11, 2019.
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Several species of millimetric-sized termites across Africa, Asia, Australia, and South America collectively construct large, metersized, porous mound structures that serve to regulate mound temperature, humidity, and gas concentrations. These mounds display varied yet distinctive morphologies that range widely in size and shape. To explain this morphological diversity, we introduce a mathematical model that couples environmental physics to insect behavior: The advection and diffusion of heat and pheromones through a porous medium are modified by the mound geometry and, in turn, modify that geometry through a minimal characterization of termite behavior. Our model captures the range of naturally observed mound shapes in terms of a minimal set of dimensionless parameters and makes testable hypotheses for the response of mound morphology to external temperature oscillations and internal odors. Our approach also suggests mechanisms by which evolutionary changes in odor production rate and construction behavior coupled to simple physical laws can alter the characteristic mound morphology of termites.

Collective ventilation in honeybee nests J.M. Peters, O. Peleg, L. Mahadevan, J. R. Soc, Interface 16: 20180561. 2019.
[DOI] [View PDF] [Download PDF] Abstract
European honey bees (Apis mellifera L.) live in large congested nest cavities with a single opening that limits passive ventilation. When the local air temperature exceeds a threshold, the nests are actively ventilated by bees fanning their wings at the nest entrance. Here, we show that colonies with relatively large nest entrances use an emergent ventilation strategy where fanning bees self-organize to form groups, separating regions of continuous inflow and outflow. The observed spatio-temporal patterns correlate the air velocity and air temperature along the entrances to the distribution of fanning bees. A mathematical model that couples these variables to known fanning behaviour of individuals recapitulates their collective dynamics. Additionally, the model makes predictions about the temporal stability of the fanning group as a function of the temperature difference between the environment and the nest. Consistent with these predictions, we observe that the fanning groups drift, cling to the entrance boundaries, break-up and reform as the ambient temperature varies over a period of days. Overall, our study shows how honeybees use flow-mediated communication to self-organize into a steady state in fluctuating environments.

Molecular control of macroscopic forces drives formation of the vertebrate hindgut N.L. Nerurkar, CH Lee, L. Mahadevan & C.J. Tabin, Nature 565, 2019.
[DOI] [View PDF] [Download PDF] Abstract
The embryonic gut tube is a cylindrical structure from which the respiratory and gastrointestinal tracts develop1. Although the early emergence of the endoderm as an epithelial sheet2,3 and later morphogenesis of the definitive digestive and respiratory organs4,5,6 have been investigated, the intervening process of gut tube formation remains relatively understudied7,8. Here we investigate the molecular control of macroscopic forces underlying early morphogenesis of the gut tube in the chick embryo. The gut tube has been described as forming from two endodermal invaginations—the anterior intestinal portal (AIP) towards the rostral end of the embryo and the caudal intestinal portal (CIP) at the caudal end—that migrate towards one another, internalizing the endoderm until they meet at the yolk stalk (umbilicus in mammals)1,6. Migration of the AIP to form foregut has been descriptively characterized8,9, but the hindgut is likely to form by a distinct mechanism that has not been fully explained10. We find that the hindgut is formed by collective cell movements through a stationary CIP, rather than by movement of the CIP itself. Further, combining in vivo imaging, biophysics and mathematical modelling with molecular and embryological approaches, we identify a contractile force gradient that drives cell movements in the hindgut-forming endoderm, enabling tissue-scale posterior extension of the forming hindgut tube. The force gradient, in turn, is established in response to a morphogenic gradient of fibroblast growth factor signalling. As a result, we propose that an important positive feedback arises, whereby contracting cells draw passive cells from low to high fibroblast growth factor levels, recruiting them to contract and pull more cells into the elongating hindgut. In addition to providing insight into the early gut development, these findings illustrate how large-scale tissue level forces can be traced to developmental signals during vertebrate morphogenesis.

2018

Self-Assembly-Mediated Release of Peptide Nanoparticles through Jets Across Microdroplet Interfaces A. Levin, T. C. T. Michaels, T. O. Mason, T. Müller, L. Adler-Abramovich, L. Mahadevan, M. E. Cates, E. Gazit, and T. P. J. Knowles  ACS Appl. Mater. Interfaces , 10, 27578−27583. 2018.
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The release of nanoscale structures from microcapsules, triggered by changes in the capsule in response to external stimuli, has significant potential for active component delivery. Here, we describe an orthogonal strategy for controlling molecular species’ release across oil/water interfaces by modulating their intrinsic self-assembly state. We show that although the soluble peptide Boc-FF can be stably encapsulated for days, its self-assembly into nanostructures triggers jet-like release within seconds. Moreover, we exploit this self-assembly-mediated release to deliver other molecular species that are transported as cargo. These results demonstrate the role of self-assembly in modulating the transport of peptides across interfaces.

Localized patterns in crushed conical shells O. Gottesman, E. Vouga, S. M. Rubinstein and L. Mahadevan  EPL , 124:14005, 2018.
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We use experiments and numerical simulations to study the rapid buckling of thinwalled cones as they impact a solid surface at high velocities. The buildup of air pressure inside the cone localizes the deformations to the impacting interface with the solid surface, leading to the hierarchical formation of an ordered pattern of small rhomboidal cells. In contrast, when the inner air pressure is not allowed to develop, the ordered pattern is destabilized and the cone collapses in a highly disordered state on long length scales. Numerical simulations confirm that the transition between ordered and disordered crumpling is governed by the competition between the elastic deformation energy of the shells and the work required to pressurize the air. Our results show how dynamic stabilization via tensioning suppresses long wavelength subcritical instabilities in shells and leads to the localization and propagation of short wavelength patterns.

Mechanics of biomimetic 4D printed structures Wim M. van Rees, Elisabetta A. Matsumoto, A. Sydney Gladman, Jennifer A. Lewis and L. Mahadevan,  Soft Matter, 2018.
[DOI] [View PDF] [Download PDF] Abstract
Recent progress in additive manufacturing and materials engineering has led to a surge of interest in shape-changing plate and shell-like structures. Such structures are typically printed in a planar configuration and, when exposed to an ambient stimulus such as heat or humidity, swell into a desired three-dimensional geometry. Viewed through the lens of differential geometry and elasticity, the application of the physical stimulus can be understood as a local change in the metric of a two dimensional surface embedded in three dimensions. To relieve the resulting elastic frustration, the structure will generally bend and buckle out-of-plane. Here, we propose a numerical approach to convert the discrete geometry of filament bilayers, associated with print paths of inks with given material properties, into continuous plates with inhomogeneous growth patterns and thicknesses. When subject to prescribed growth anisotropies, we can then follow the evolution of the shapes into their final form. We show that our results provide a good correspondence between experiments and simulations, and lead to a framework for the prediction and design of shape-changing structures.

Meniscus instabilities in thin elastic layers John S. Biggins and L. Mahadevan,  Soft Matter , 14, 7680-7689, 2018.
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We consider meniscus instabilities in thin elastic layers perfectly adhered to, and confined between, much stiffer bodies. When the free boundary associated with the meniscus of the elastic layer recedes into the layer, for example by pulling the stiffer bodies apart or injecting air between them, then the meniscus will eventually undergo a purely elastic instability in which fingers of air invade the layer. Here we show that the form of this instability is identical in a range of different loading conditions, provided only that the thickness of the meniscus, a, is small compared to the in-plane dimensions and to two emergent in-plane length scales that arise if the substrate is soft or if the layer is compressible. In all such situations, we predict that the instability will occur when the meniscus has receded by approximately 1.27a, and that the instability will have wavelength l E 2.75a. We illustrate this by also calculating the threshold for fingering in a thin wedge of elastic material bonded to two rigid plates that are pried apart, and the threshold for fingering when a flexible plate is peeled from an elastic layer that glues the plate to a rigid substrate

Planar morphometrics using Teichmüller maps Gary P. T. Choi and L. Mahadevan,  Proceedings of the Royal Society  A 474:20170905, 2018.
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Inspired by the question of quantifying wing shape, we propose a computational approach for analysing planar shapes. We first establish a correspondence between the boundaries of two planar shapes with boundary landmarks using geometric functional data analysis and then compute a landmark-matching curvature-guided Teichmüller mapping with uniform quasi-conformal distortion in the bulk. This allows us to analyse the pair-wise difference between the planar shapes and construct a similarity matrix on which we deploy methods from network analysis to cluster shapes. We deploy our method to study a variety of Drosophila wings across species to highlight the phenotypic variation between them, and Lepidoptera wings over time to study the developmental progression of wings. Our approach of combining complex analysis, computation and statistics to quantify, compare and classify planar shapes may be usefully deployed in other biological and physical systems.

Collective mechanical adaptation of honeybee swarms O. Peleg, J. M. Peters, M. K. Salcedo and L. Mahadevan,  Nature Physics Letters , 2018.
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Honeybee Apis mellifera swarms form large congested treehanging clusters made solely of bees attached to each other 1 .How these structures are maintained under the influence of dynamic mechanical forcing is unknown. To address this, we created pendant clusters and subject them to dynamic loads of varying orientation, amplitude, frequency and duration. We find that horizontally shaken clusters adapt by spreading out to form wider, flatter cones that recover their original shape when unloaded. Measuring the response of a cluster to an impulsive pendular excitation shows that flattened cones deform less and relax faster than the elongated ones (that is, they are more stable). Particle-based simulations of a passive assemblage suggest a behavioural hypothesis: individual bees respond to local variations in strain by moving up the strain gradient, which is qualitatively consistent with our observations of individual bee movement during dynamic loading. The simulations also suggest that vertical shaking will not lead to significant differential strains and thus no shape adaptation, which we confirmed experimentally. Together, our findings highlight how a super-organismal structure responds to dynamic loading by actively changing its morphology to improve the collective stability of the cluster at the expense of increasing the average mechanical burden of an individual.

Generalized Erdös numbers for network analysis Greg Morrison, Levi H. Dudte and L. Mahadevan,  Royal Society Open Science , 172281, 2018.
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The identification of relationships in complex networks is critical in a variety of scientific contexts. This includes the identification of globally central nodes and analysing the importance of pairwise relationships between nodes. In this paper, we consider the concept of topological proximity (or ‘closeness’) between nodes in a weighted network using the generalized Erdo´´s numbers (GENs). This measure satisfies a number of desirable properties for networks with nodes that share a finite resource. These include: (i) real-valuedness, (ii) non-locality and (iii) asymmetry. We show that they can be used to define a personalized measure of the importance of nodes in a network with a natural interpretation that leads to new methods to measure centrality. We show that the square of the leading eigenvector of an importance matrix defined using the GENs is strongly correlated with well-known measures such as PageRank, and define a personalized measure of centrality that is also well correlated with other existing measures. The utility of this measure of topological proximity is demonstrated by showing the asymmetries in both the dynamics of random walks and the mean infection time in epidemic spreading are better predicted by the topological definition of closeness provided by the GENs than they are by other measures.

The statistical shape of geometric reasoning Yuval Hart, Moira R. Dillon, Andrew Marantan, Anna L. Cardenas, Elizabeth Spelke & L. Mahadevan, Nature-Scientific Reports , 8:12906, 2018.
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Geometric reasoning has an inherent dissonance: its abstract axioms and propositions refer to perfect, idealized entities, whereas its use in the physical world relies on dynamic perception of objects. How do abstract Euclidean concepts, dynamics, and statistics come together to support our intuitive geometric reasoning? Here, we address this question using a simple geometric task – planar triangle completion. An analysis of the distribution of participants’ errors in localizing a fragmented triangle’s missing corner reveals scale-dependent deviations from a deterministic Euclidean representation of planar triangles. By considering the statistical physics of the process characterized via a correlated random walk with a natural length scale, we explain these results and further predict participants’ estimates of the missing angle, measured in a second task. Our model also predicts the results of a categorical reasoning task about changes in the triangle size and shape even when such completion strategies need not be invoked. Taken together, our fndings suggest a critical role for noisy physical processes in our reasoning about elementary Euclidean geometry.

A tissue-engineered scale model of the heart ventricle L.A. MacQueen S. P. Sheehy, C. O. Chantre, J. F. Zimmerman, F. S. Pasqualini, X. Liu, J. A. Goss, P. H. Campbell, G. M. Gonzalez S-J Park, A. K. Capulli, J. P. Ferrier, T. F. Kosar, L. Mahadevan, W. T. Pu, and K.K. Parker,  Nature Biomedical Engineering , 2018.
[DOI] [View PDF] [Download PDF] Abstract
Laboratory studies of the heart use cell and tissue cultures to dissect heart function yet rely on animal models to measure pressure and volume dynamics. Here, we report tissue-engineered scale models of the human left ventricle, made of nanofibrous scaffolds that promote native-like anisotropic myocardial tissue genesis and chamber-level contractile function. Incorporating neonatal rat ventricular myocytes or cardiomyocytes derived from human induced pluripotent stem cells, the tissue-engineered ventricles have a diastolic chamber volume of ~500 µl (comparable to that of the native rat ventricle and approximately 1/250 the size of the human ventricle), and ejection fractions and contractile work 50–250 times smaller and 104–108 times smaller than the corresponding values for rodent and human ventricles, respectively. We also measured tissue coverage and alignment, calcium-transient propagation and pressure–volume loops in the presence or absence of test compounds. Moreover, we describe an instrumented bioreactor with ventricular-assist capabilities, and provide a proof-of-concept disease model of structural arrhythmia. The model ventricles can be evaluated with the same assays used in animal models and in clinical settings.

Multifunctional ferrofluid-infused surfaces with reconfigurable multiscale topography W. Wang, J. V. I. Timonen, A. Carlson, D-M. Drotlef, C. T. Zhang, S. Kolle, A. Grinthal, T-S. Wong, B. Hatton, S. H. Kang, S. Kennedy, J. Chi, R. T. Blough, M. Sitti, L. Mahadevan & J. Aizenberg,  Nature  559, 2018.
[View PDF] [Download PDF] Abstract
Developing adaptive materials with geometries that change in response to external stimuli provides fundamental insights into the links between the physical forces involved and the resultant morphologies and creates a foundation for technologically relevant dynamic systems1,2 . In particular, reconfigurable surface topography as a means to control interfacial properties3 has recently been explored using responsive gels4 , shape-memory polymers5 , liquid crystals6–8 and hybrid composites9–14, including magnetically active slippery surfaces12–14. However, these designs exhibit a limited range of topographical changes and thus a restricted scope of function. Here we introduce a hierarchical magnetoresponsive composite surface, made by infiltrating a ferrofluid into a microstructured matrix (termed ferrofluid-containing liquid-infused porous surfaces, or FLIPS). We demonstrate various topographical reconfigurations at multiple length scales and a broad range of associated emergent behaviours. An applied magneticfield gradient induces the movement of magnetic nanoparticles suspended in the ferrofluid, which leads to microscale flow of the ferrofluid first above and then within the microstructured surface. This redistribution changes the initially smooth surface of the ferrofluid (which is immobilized by the porous matrix through capillary forces) into various multiscale hierarchical topographies shaped by the size, arrangement and orientation of the confining microstructures in the magnetic field. We analyse the spatial and temporal dynamics of these reconfigurations theoretically and experimentally as a function of the balance between capillary and magnetic pressures15–19 and of the geometric anisotropy of the FLIPS system. Several interesting functions at three different length scales are demonstrated: self-assembly of colloidal particles at the micrometre scale; regulated flow of liquid droplets at the millimetre scale; and switchable adhesion and friction, liquid pumping and removal of biofilms at the centimetre scale. We envision that FLIPS could be used as part of integrated control systems for the manipulation and transport of matter, thermal management, microfluidics and fouling-release materials.

Reprogrammable Braille on an elastic shell J.Y. Chung, A. Vaziri, and L. Mahadevan. Proceedings of the National Academy of Sciences (USA)  115, 29, 7509-7514. 2018.
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We describe a minimal realization of reversibly programmable matter in the form of a featureless smooth elastic plate that has the capacity to store information in a Braille-like format as a sequence of stable discrete dimples. Simple experiments with cylindrical and spherical shells show that we can control the number, location, and the temporal order of these dimples, which can be written and erased at will. Theoretical analysis of the governing equations in a specialized setting and numerical simulations of the complete equations allow us to characterize the phase diagram for the formation of these localized elastic states, elastic bits (e-bits), consistent with our observations. Given that the inherent bistability and hysteresis in these low-dimensional systems arise exclusively due to the geometrical-scale separation, independent of material properties or absolute scale, our results might serve as alternate approaches to small-scale mechanical memories.

Microtubules soften due to cross- sectional flattening E. Memet, F. Hilitski, M.A Morris, W. J. Schwenger, Z. Dogic, L Mahadevan, eLife 7:e34695. 10.7554/eLife.34695
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We use optical trapping to continuously bend an isolated microtubule while simultaneously measuring the applied force and the resulting filament strain, thus allowing us to determine its elastic properties over a wide range of applied strains. We find that, while in the lowstrain regime, microtubules may be quantitatively described in terms of the classical Euler-Bernoulli elastic filament, above a critical strain they deviate from this simple elastic model, showing a softening response with increasingdeformations. A three-dimensional thin-shell model, in which the increased mechanical compliance is caused by flattening and eventual buckling of the filament cross-section, captures this softening effect in the high strain regime and yields quantitative values of the effective mechanical properties of microtubules. Our results demonstrate that properties of microtubules are highly dependent on the magnitude of the applied strain and offer a new interpretation for the large variety in microtubule mechanical data measured by different methods.

Differential activity-driven instabilities in biphasic active matter C. A. Weber, C. H. Rycroft, and L. Mahadevan,  Physical Review Letters  120, 248003, 2018.
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Active stresses can cause instabilities in contractile gels and living tissues. Here we provide a generic hydrodynamic theory that treats these systems as a mixture of two phases of varying activity and different mechanical properties. We find that differential activity between the phases causes a uniform mixture to undergo a demixing instability. We follow the nonlinear evolution of the instability and characterize a phase diagram of the resulting patterns. Our study complements other instability mechanisms in mixtures driven by differential adhesion, differential diffusion, differential growth, and differential motion.

Photosynthetic artificial organelles sustain and control ATP-dependent reactions in a protocellular system K. Y.Lee, S-J Park, K. A. Lee, S-H Kim, H. Kim, Y. Meroz, L Mahadevan, K-H Jung, T. K. Ahn, K. K. Parker & K. Shin,  Nature Biotechnology  36, 6, 2018.
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Inside cells, complex metabolic reactions are distributed across the modular compartments of organelles1,2. Reactions in organelles have been recapitulated in vitro by reconstituting functional protein machineries into membrane systems3–5. However, maintaining and controlling these reactions is challenging. Here we designed, built, and tested a switchable, light-harvesting organelle that provides both a sustainable energy source and a means of directing intravesicular reactions. An ATP (ATP) synthase and two photoconverters (plant-derived photosystem II and bacteriaderived proteorhodopsin) enable ATP synthesis. Independent optical activation of the two photoconverters allows dynamic control of ATP synthesis: red light facilitates and green light impedes ATP synthesis. We encapsulated the photosynthetic organelles in a giant vesicle to form a protocellular system and demonstrated optical control of two ATP-dependent reactions, carbon fixation and actin polymerization, with the latter altering outer vesicle morphology. Switchable photosynthetic organelles may enable the development of biomimetic vesicle systems with regulatory networks that exhibit homeostasis and complex cellular behaviors.

Forward and inverse problems in the mechanics of soft filaments M. Gazzola, L. H. Dudte, A. G. McCormick and L. Mahadevan,  Royal Society Open Science  5: 171628, 2018.
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Soft slender structures are ubiquitous in natural and artificial systems, in active and passive settings and across scales, from polymers and flagella, to snakes and space tethers. In this paper, we demonstrate the use of a simple and practical numerical implementation based on the Cosserat rod model to simulate the dynamics of filaments that can bend, twist, stretch and shear while interacting with complex environments via muscular activity, surface contact, friction and hydrodynamics. We validate our simulations by solving a number of forward problems involving the mechanics of passive filaments and comparing them with known analytical results, and extend them to study instabilities in stretched and twisted filaments that form solenoidal and plectonemic structures. We then study active filaments such as snakes and other slender organisms by solving inverse problems to identify optimal gaits for limbless locomotion on solid surfaces and in bulk liquids.

Competing failure modes in finite adhesive pads T. Cohen, C.U. Chan, L. Mahadevan, Soft Matter 2018.
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Thin adhesive pads used to attach objects to each other often fail catastrophically. Here we consider the nature of failure of such a pad under loading parallel to the adhesive substrate. To determine the modes of failure of the pad and to understand what limits its load bearing capacity, we conduct experiments with finite pads composed of a soft adhesive layer with a stiff backing and load them parallel to the surface of adhesion. We find that two different peeling mechanisms emerge as a function of the slenderness of the adhesive pad: an interfacial peeling mechanism that starts close to the pulling end for very long pads, and an unstable curling mechanism that starts at the opposite end for relatively short pads. A minimal theoretical framework allows us to explain our observations and reveals the adhesive bond stiffness as a dominant parameter in defining the peeling mode. A phase diagram that delineates the different regimes of peeling modes brings our experiments and theory together. Our results suggest that unstable peeling by curling may be more common than previously thought, and could perhaps occur naturally in such examples as the gecko foot.

Topology, geometry, and mechanics of z-plasty E.A. Matsumoto, H. Liang and L. Mahadevan,  Physical Review Letters  120, 068101, 2018.
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Reconstructive surgeries often use topological manipulation of tissue to minimize postoperative scarring. The most common version of this, Z-plasty, involves modifying a straight line cut into a Z shape, followed by a rotational transposition of the resulting triangular pedicle flaps, and a final restitching of the wound. This locally reorients the anisotropic stress field and reduces the potential for scarring. We analyze the planar geometry and mechanics of the Z-plasty to quantify the rotation of the overall stress field and the local forces on the restitched cut using theory, simulations, and simple physical Z-plasty experiments with foam sheets that corroborate each other. Our study rationalizes the most typical surgical choice of this angle, and opens the way for a range of surgical decisions by characterizing the stresses along the cut.

Mechanics and statistics of the worm-like chain A. Marantan and L Mahadevan,  American Journal of Physics 86 (2), 86-94, 2018.
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The worm-like chain model is a simple continuum model for the statistical mechanics of a flexible polymer subject to an external force. We offer a tutorial introduction to it using three approaches. First, we use a mesoscopic view, treating a long polymer (in two dimensions) as though it were made of many groups of correlated links or “clinks,” allowing us to calculate its average extension as a function of the external force via scaling arguments. We then provide a standard statistical mechanics approach, obtaining the average extension by two different means: the equipartition theorem and the partition function. Finally, we work in a probabilistic framework, taking advantage of the Gaussian properties of the chain in the large-force limit to improve upon the previous calculations of the average extension

2017

Joseph B. Keller (1923–2016) A Whittemore, G Papanicolau, D Cohen, L Mahadevan, B Matkowsky,  Notices of the American Mathematical Society  64, 606-615.
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Joseph Bishop Keller was an applied mathematician of world renown, whose research interests spanned a wide range of topics, including wave propagation, semi-classical mechanics, geophysical fluid dynamics, operations research, finance, biomechanics, epidemiology, biostatistics, and the mathematics of sports. His work combined a love of physics, mathematics, and natural phenomena with an irrepressible curiosity to pursue explanations of practical and often playful enigmas.

Organ size control via hydraulically gated oscillations Teresa Ruiz-Herrero, Kévin Alessandri, Basile V. Gurchenkov, Pierre Nassoy and L. Mahadevan,  Development  144, 4422-4427, 2017.
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Hollow vesicular tissues of various sizes and shapes arise in biological organs such as ears, guts, hearts, brains and even entire organisms. Regulating their size and shape is crucial for their function. Although chemical signaling has been thought to play a role in the regulation of cellular processes that feed into larger scales, it is increasingly recognized that mechanical forces are involved in the modulation of size and shape at larger length scales. Motivated by a variety of examples of tissue cyst formation and size control that show simultaneous growth and size oscillations, we create a minimal theoretical framework for the growth and dynamics of a soft, fluidpermeable, spherical shell. We show that these shells can relieve internal pressure by bursting intermittently, shrinking and re-growing, providing a simple mechanism by which hydraulically gated oscillations can regulate size. To test our theory, we develop an in vitro experimental set-up to monitor the growth and oscillations of a hollow tissue spheroid growing freely or when confined. A simple generalization of our theory to account for irreversible deformations allows us to explain the time scales and the amplitudes of oscillations in terms of the geometry and mechanical properties of the tissue shells. Taken together, our theory and experimental observations show how soft hydraulics can regulate the size of growing tissue shells.
Morphogenesis one century after On Growth and Form  Thomas Lecuit and L. Mahadevan,  Development  144, 4197-4198, 2017.
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Morphogenesis, the study of how forms arise in biology, has attracted scientists for aeons. A century ago, D’Arcy Wentworth Thompson crystallized this question in his opus On Growth and Form (Thompson, 1917) using a series of biological examples and geometric and physical analogies to ask how biological forms arise during development and across evolution. In light of the advances in molecular and cellular biology since then, a succinct modern view of the question states: how do genes encode geometry?

Active elastohydrodynamics of vesicles in narrow blind constrictions T. G. Fai, R. Kusters, J. Harting, C. H. Rycroft, and L. Mahadevan,  Physical Review Fluids  2 113601, 2017.
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Fluid-resistance limited transport of vesicles through narrow constrictions is a recurring theme in many biological and engineering applications. Inspired by the motor-driven movement of soft membrane-bound vesicles into closed neuronal dendritic spines, here we study this problem using a combination of passive three-dimensional simulations and a simplified semianalytical theory for the active transport of vesicles forced through constrictions by molecular motors. We show that the motion of these objects is characterized by two dimensionless quantities related to the geometry and to the strength of forcing relative to the vesicle elasticity. We use numerical simulations to characterize the transit time for a vesicle forced by fluid pressure through a constriction in a channel and find that relative to an open channel, transport into a blind end leads to the formation of a smaller forward-flowing lubrication layer that strongly impedes motion. When the fluid pressure forcing is complemented by forces due to molecular motors that are responsible for vesicle trafficking into dendritic spines, we find that the competition between motor forcing and fluid drag results in multistable dynamics reminiscent of the real system. Our study highlights the role of nonlocal hydrodynamic effects in determining the kinetics of vesicular transport in constricted geometries.

Growth patterns for shape-shifting elastic bilayers W. M. van Rees, E. Vouga, and L. Mahadevan,  Proceedings of the National Academy of Sciences , 2017.
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Inspired by the differential-growth-driven morphogenesis of leaves, flowers, and other tissues, there is increasing interest in artificial analogs of these shape-shifting thin sheets made of active materials that respond to environmental stimuli such as heat, light, and humidity. But how can we determine the growth patterns to achieve a given shape from another shape? We solve this geometric inverse problem of determining the growth factors and directions (the metric tensors) for a given isotropic elastic bilayer to grow into a target shape by posing and solving an elastic energy minimization problem. A mathematical equivalence between bilayers and curved monolayers simplifies the inverse problem considerably by providing algebraic expressions for the growth metric tensors in terms of those of the final shape. This approach also allows us to prove that we can grow any target surface from any reference surface using orthotropically growing bilayers. We demonstrate this by numerically simulating the growth of a flat sheet into a face, a cylindrical sheet into a flower, and a flat sheet into a complex canyon-like structure.

Excitable dynamics and yap-dependent mechanical cues drive the segmentation clock A. Hubaud, I. Regev, L. Mahadevan, O. Pourquié,  Cell  171, 1-15, 2017.
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In vitro system supporting stable segmentation clock oscillations d A cell-density effect controls the onset of oscillations in vitro d Yap-dependent mechanical signal acts as a control parameter for oscillations d Segmentation clock has properties of an excitable system

Solar-powered ventilation of African termite mounds S. A. Ocko, H. King, D. Andreen, P. Bardunias, J. S. Turner, R. Soar, and L. Mahadevan,  Journal of Experimental Biology  220, 3260-3269, 2017.
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How termite mounds function to facilitate climate control is still only partially understood. Recent experimental evidence in the mounds of a single species, the south Asian termite Odontotermes obesus, suggests that the daily oscillations of radiant heating associated with diurnal insolation patterns drive convective flow within them. How general this mechanism is remains unknown. To probe this, we consider the mounds of the African termite Macrotermes michaelseni, which thrives in a very different environment. By directly measuring air velocities and temperatures within the mound, we see that the overall mechanisms and patterns involved are similar to that in the south Asian species. However, there are also some notable differences between the physiology of these mounds associated with the temporal variations in radiant heating patterns and CO2 dynamics. Because of the difference between direct radiant heating driven by the position of the sun in African conditions, and the more shaded south Asian environments, we see changes in the convective flows in the two types of mounds. Furthermore, we also see that the south Asian mounds show a significant overturning of stratified gases, once a day, while the African mounds have a relatively uniform concentration of CO2. Overall, our observations show that despite these differences, termite architectures can harness periodic solar heating to drive ventilation inside them in very different environments, functioning as an external lung, with clear implications for human engineering.

Controllable biomimetic birdsong A. Mukherjee, S. Mandre and L. Mahadevan,  Journal Royal Society Interface  14: 20170002, 2017.
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Birdsong is the product of the controlled generation of sound embodied in a neuromotor system. From a biophysical perspective, a natural question is that of the difficulty of producing birdsong. To address this, we built a biomimetic syrinx consisting of a stretched simple rubber tube through which air is blown, subject to localized mechanical squeezing with a linear actuator. A large static tension on the tube and small dynamic variations in the localized squeezing allow us to control transitions between three states: a quiescent state, a periodic state and a solitary wave state. The static load brings the system close to threshold for spontaneous oscillations, while small dynamic loads allow for rapid transitions between the states. We use this to mimic a variety of birdsongs via the slow– fast modulated nonlinear dynamics of the physical substrate, the syrinx, regulated by a simple controller. Finally, a minimal mathematical model of the system inspired by our observations allows us to address the problem of song mimicry in an excitable oscillator for tonal songs

Wrinkling instability of an inhomogeneously stretched viscous sheet S. Srinivasan, Z. Wei, L. Mahadevan,  Physical Review Fluids  2, 074103, 2017.
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Motivated by the redrawing of hot glass into thin sheets, we investigate the shape and stability of a thin viscous sheet that is inhomogeneously stretched in an imposed nonuniform temperature field. We first determine the associated base flow by solving the long-time-scale stretching flow of a flat sheet as a function of two dimensionless parameters: the normalized stretching velocity α and a dimensionless width of the heating zone β. This allows us to determine the conditions for the onset of an out-of-plane wrinkling instability stated in terms of an eigenvalue problem for a linear partial differential equation governing the displacement of the midsurface of the sheet. We show that the sheet can become unstable in two regions that are upstream and downstream of the heating zone where the minimum in-plane stress is negative. This yields the shape and growth rates of the most unstable buckling mode in both regions for various values of the stretching velocity and heating zone width. A transition from stationary to oscillatory unstable modes is found in the upstream region with increasing β, while the downstream region is always stationary. We show that the wrinkling instability can be entirely suppressed when the surface tension is large enough relative to the magnitude of the in-plane stress. Finally, we present an operating diagram that indicates regions of the parameter space that result in a required outlet sheet thickness upon stretching while simultaneously minimizing or suppressing the out-of-plane buckling, a result that is relevant for the glass redraw method used to create ultrathin glass sheets.

Rotation of an immersed cylinder sliding near a thin elastic coating B. Rallabandi, B. Saintyves, T. Jules, T. Salez, C. Schönecker, L. Mahadevan, and H.A. Stone,  Physical Review Fluids  2074102, 2017.
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It is known that an object translating parallel to a soft wall in a viscous fluid produces hydrodynamic stresses that deform the wall, which in turn results in a lift force on the object. Recent experiments with cylinders sliding under gravity near a soft incline, which confirmed theoretical arguments for the lift force, also reported an unexplained steady-state rotation of the cylinders [B. Saintyves et al., Proc. Natl. Acad. Sci. USA 113, 5847 (2016)]. Motivated by these observations, we show, in the lubrication limit, that an infinite cylinder that translates in a viscous fluid parallel to a soft wall at constant speed and separation distance must also rotate in order to remain free of torque. Using the Lorentz reciprocal theorem, we show analytically that for small deformations of the elastic layer, the angular velocity of the cylinder scales with the cube of the sliding speed. These predictions are confirmed numerically. We then apply the theory to the gravity-driven motion of a cylinder near a soft incline and find qualitative agreement with the experimental observa

Avian egg shape: Form, function, and evolution M.C. Stoddard, E.H. Yong, D. Akkaynak, C. Sheard, J.A. Tobias, L. Mahadevan,  Science  356, 1249-1254, 2017.
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components that are required to assemble chromosomes in a test tube (9). Three components were found to be essential: histones, together with assembly factors that they require to load onto DNA; condensin; and topoisomerase II. The latter is an enzyme that allows DNA strands to pass each other, thereby preventing DNA from getting hopelessly tangled up.

Optimal strategies for throwing accurately M. Venkadesan and L. Mahadevan,  Royal Society Open Science  , 4: 170136. 2017.
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Growing plant stems and shoots exhibit a variety of shapes that embody growth in response to various stimuli. Building on experimental observations, we provide a quantitative biophysical theory for these shapes by accounting for the inherent observed passive and active effects: (i) the active controllable growth response of the shoot in response to its orientation relative to gravity, (ii) proprioception, the shoot’s growth response to its own observable current shape, and (iii) the passive elastic deflection of the shoot due to its own weight, which determines the current shape of the shoot. Our theory separates the sensed and actuated variables in a growing shoot and results in a morphospace diagram in terms of two dimensionless parameters representing a scaled local active gravitropic sensitivity, and a scaled passive elastic sag. Our computational results allow us to explain the variety of observed transient and steady morphologies with effective positive, negative and even oscillatory gravitropic behaviours, without the need for ad hoc complex spatio-temporal control strategies in terms of these parameters. More broadly, our theory is applicable to the growth of soft, floppy organs where sensing and actuation are dynamically coupled through growth processes via shape.

On the growth and form of shoots R. Chelakkot and L. Mahadevan,  Journal of the Royal Society Interface , 14, 20170001, 2017.
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Growing plant stems and shoots exhibit a variety of shapes that embody growth in response to various stimuli. Building on experimental observations, we provide a quantitative biophysical theory for these shapes by accounting for the inherent observed passive and active effects: (i) the active controllable growth response of the shoot in response to its orientation relative to gravity, (ii) proprioception, the shoot’s growth response to its own observable current shape, and (iii) the passive elastic deflection of the shoot due to its own weight, which determines the current shape of the shoot. Our theory separates the sensed and actuated variables in a growing shoot and results in a morphospace diagram in terms of two dimensionless parameters representing a scaled local active gravitropic sensitivity, and a scaled passive elastic sag. Our computational results allow us to explain the variety of observed transient and steady morphologies with effective positive, negative and even oscillatory gravitropic behaviours, without the need for ad hoc complex spatio-temporal control strategies in terms of these parameters. More broadly, our theory is applicable to the growth of soft, floppy organs where sensing and actuation are dynamically coupled through growth processes via shape.

Controlled growth and form of precipitating microsculptures C. N. Kaplan, W. L. Noorduin, L. Li, R. Sadza, L. Folkertsma, J. Aizenberg, L. Mahadevan,  Science  355, 1395-99, 2017.
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Controlled self-assembly of three-dimensional shapes holds great potential for fabrication of functional materials. Their practical realization requires a theoretical framework to quantify and guide the dynamic sculpting of the curved structures that often arise in accretive mineralization. Motivated by a variety of bioinspired coprecipitation patterns of carbonate and silica, we develop a geometrical theory for the kinetics of the growth front that leaves behind thin-walled complex structures. Our theory explains the range of previously observed experimental patterns and, in addition, predicts unexplored assembly pathways. This allows us to design a number of functional base shapes of optical microstructures, which we synthesize to demonstrate their light-guiding capabilities. Overall, our framework provides a way to understand and control the growth and form of functional precipitating microsculptures.

BMP signaling controls buckling forces to modulate looping morphogenesis of the gut N. L. Nerurkar, L. Mahadevan, and C.J. Tabin,  Proceedings of the National Academy of Sciences  (USA), 114, 2277-82, 2017.
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Looping of the initially straight embryonic gut tube is an essential aspect of intestinal morphogenesis, permitting proper placement of the lengthy small intestine within the confines of the body cavity. The formation of intestinal loops is highly stereotyped within a given species and results from differential-growth–driven mechanical buckling of the gut tube as it elongates against the constraint of a thin, elastic membranous tissue, the dorsal mesentery. Although the physics of this process has been studied, the underlying biology has not. Here, we show that BMP signaling plays a critical role in looping morphogenesis of the avian small intestine. We first exploited differences between chicken and zebra finch gut morphology to identify the BMP pathway as a promising candidate to regulate differential growth in the gut. Next, focusing on the developing chick small intestine, we determined that Bmp2 expressed in the dorsal mesentery establishes differential elongation rates between the gut tube and mesentery, thereby regulating the compressive forces that buckle the gut tube into loops. Consequently, the number and tightness of loops in the chick small intestine can be increased or decreased directly by modulation of BMP activity in the small intestine. In addition to providing insight into the molecular mechanisms underlying intestinal development, our findings provide an example of how biochemical signals act on tissue-level mechanics to drive organogenesis, and suggest a possible mechanism by which they can be modulated to achieve distinct morphologies through evolution.

Grasping with a soft glove: intrinsic impedance control in pneumatic actuators P. Paoletti, G. W. Jones and L. Mahadevan,  Journal of the Royal Society Interface  14, 20160867, 2017.
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The interaction of a robotic manipulator with unknown soft objects represents a significant challenge for traditional robotic platforms because of the difficulty in controlling the grasping force between a soft object and a stiff manipulator. Soft robotic actuators inspired by elephant trunks, octopus limbs and muscular hydrostats are suggestive of ways to overcome this fundamental difficulty. In particular, the large intrinsic compliance of soft manipulators such as ‘pneu-nets’—pneumatically actuated elastomeric structures—makes them ideal for applications that require interactions with an uncertain mechanical and geometrical environment. Using a simple theoretical model, we show how the geometric and material nonlinearities inherent in the passive mechanical response of such devices can be used to grasp soft objects using force control, and stiff objects using position control, without any need for active sensing or feedback control. Our study is suggestive of a general principle for designing actuators with autonomous intrinsic impedance control.

2016

Spontaneous exfoliation of a drying gel J. Y. Chung, I. Regev and L. Mahadevan,  Soft Matter , 12, 7855-62, 2016.
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Wet starch cracks when it dries inhomogeneously, while hot glass cracks when it cools non-uniformly. In both cases, differential shrinkage induced by drying/cooling from the surface causes superficial cracks to grow perpendicular to the surface in different patterns. In contrast with these observations of bulk cracking in brittle materials, when a soft and homogeneously swollen polymer gel dries, differential strains lead to the peeling of a thin layer that spontaneously tears away from the bulk. Continued drying leads to the process repeating itself, forming a peeled-layered structure. The emergent thickness of the exfoliated layer is a function of both the geometry of the original gel and the physical parameters associated with the drying rate and external temperature. We characterize the experimental conditions under which layer peeling can arise, and use simulations to corroborate these observations. Finally, a minimal theory explains the scaling of the peel thickness, consistent with our experiments

Bending and buckling of wet paper M. Lee, S. Kim, H-Y. Kim, and L. Mahadevan  Physics of Fluids  28, 042101, 2016.
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Flat paper stained with water buckles and wrinkles as it swells and deforms out of the original plane. Here we quantify the geometry and mechanics of a strip of paper that swells when it imbibes water from a narrow capillary. Characterizing the hygroexpansive nature of paper shows that thickness-wise swelling is much faster than in-plane water imbibition, leading to a simple picture for the process by which the strip of paper bends out of the plane. We model the out-of-plane deformation using a quasi-static theory and show that our results are consistent with quantitative experiments. C

Similarity and singularity in adhesive elastohydrodynamic touchdown A. Carlson and L. Mahadevan  Physics of Fluids  28, 011702, 2016.
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We consider the dynamics of an elastic sheet as it starts to adhere to a wall, a process that is limited by the viscous squeeze flow of the intervening liquid. Elastohydrodynamic lubrication theory allows us to derive a partial di↵erential equation coupling the elastic deformation of the sheet, the microscopic van der Waals adhesion, and viscous thin film flow. We use a combination of numerical simulations of the governing equation and a scaling analysis to describe the self-similar touchdown of the sheet as it approaches the wall. An analysis of the equation in terms of similarity variables in the vicinity of the touchdown event shows that only the fundamental similarity solution is observed in the time-dependent numerical simulations, consistent with the fact that it alone is stable. Our analysis generalizes similar approaches for rupture in capillary thin film hydrodynamics and suggests experimentally verifiable predictions for a new class of singular flows linking elasticity, hydrodynamics, and adhesion

Self-sustained lift and low friction via soft lubrication B. Saintyves, T. Jules, T. Saleza, and L. Mahadevan  Proceedings of the National Academy of Sciences  (USA) 113:21 5847–5849, 2016.
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Relative motion between soft wet solids arises in a number of applications in natural and artificial settings, and invariably couples elastic deformation fluid flow. We explore this in a minimal setting by considering a fluid-immersed negatively buoyant cylinder moving along a soft inclined wall. Our experiments show that there is an emergent robust steady-state sliding regime of the cylinder with an effective friction that is significantly reduced relative to that of rigid fluid-lubricated contacts. A simple scaling approach that couples the cylinder-induced flow to substrate deformation allows us to explain the elastohydrodynamic lift that underlies the self-sustained lubricated motion of the cylinder, consistent with recent theoretical predictions. Our results suggest an explanation for a range of effects such as reduced wear in animal joints and long-runout landslides, and can be couched as a design principle for low-friction interfaces.

Optimal switching between geocentric and egocentric strategies in navigation O. Peleg and L. Mahadevan  Royal Society Open Science  3: 160128, 2016.
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Animals use a combination of egocentric navigation driven by the internal integration of environmental cues, interspersed with geocentric course correction and reorientation. These processes are accompanied by uncertainty in sensory acquisition of information, planning and execution. Inspired by observations of dung beetle navigational strategies that show switching between geocentric and egocentric strategies, we consider the question of optimal reorientation rates for the navigation of an agent moving along a preferred direction in the presence of multiple sources of noise. We address this using a model that takes the form of a correlated random walk at short time scales that is punctuated by reorientation events leading to a biased random walks at long time scales. This allows us to identify optimal alternation schemes and characterize their robustness in the context of noisy sensory acquisition as well as performance errors linked with variations in environmental conditions and agent–environment interactions.

Recovery of locomotion after injury in Drosophila melanogaster depends on proprioception A. Isakov, S. M. Buchanan, B. Sullivan, A. Ramachandran, J. K. S. Chapman, E. S. Lu, L. Mahadevan, and B. de Bivort  Journal of Experimental Biology,  219, 1760-1771, 2016.
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Locomotion is necessary for survival in most animal species. However, injuries to the appendages mediating locomotion are common. We assess the recovery of walking in Drosophila melanogaster following leg amputation. Whereas flies preamputation explore open arenas in a symmetric fashion on average, foreleg amputation induces a strong turning bias away from the side of the amputation. However, we find that unbiased walking behavior returns over time in wild-type flies, while recovery is significantly impaired in proprioceptive mutants. To identify the biomechanical basis of this locomotor impairment and recovery, we then examine individual leg motion (gait) at a fine scale. A minimal mathematical model that links neurodynamics to body mechanics during walking shows that redistributing leg forces between the right and left side enables the observed recovery. Altogether, our study suggests that proprioceptive input from the intact limbs plays a crucial role in the behavioral plasticity associated with locomotor recovery after injury.

Integrative neuromechanics of crawling in D. melanogaster larvae C. Pehlevan, P. Paoletti, L Mahadevan  eLife,  5:e11031,  2016.
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Locomotion in an organism is a consequence of the coupled interaction between brain, body and environment. Motivated by qualitative observations and quantitative perturbations of crawling in Drosophila melanogaster larvae, we construct a minimal integrative mathematical model for its locomotion. Our model couples the excitation-inhibition circuits in the nervous system to force production in the muscles and body movement in a frictional environment, thence linking neural dynamics to body mechanics via sensory feedback in a heterogeneous environment. Our results explain the basic observed phenomenology of crawling with and without proprioception, and elucidate the stabilizing role that proprioception plays in producing a robust crawling phenotype in the presence of biological perturbations. More generally, our approach allows us to make testable predictions on the effect of changing body-environment interactions on crawling, and serves as a step in the development of hierarchical models linking cellular processes to behavior.

Phototactic guidance of a tissue-engineered soft-robotic ray S-J Park, M. Gazzola, K. S. Park, S. Park, V. Di Santo, E. L. Blevins, J. U. Lind, P. H. Campbell, S. Dauth, A. K. Capulli, F. S. Pasqualini, S. Ahn, A. Cho, H. Yuan, B. M. Maoz, R. Vijaykumar, J-W Choi, K. Deisseroth, G. V. Lauder, L. Mahadevan, K. K. Parker, Science , 353, 158-62, 2016.
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Inspired by the relatively simple morphological blueprint provided by batoid fish such as stingrays and skates, we created a biohybrid system that enables an artificial animal—a tissue-engineered ray—to swim and phototactically follow a light cue. By patterning dissociated rat cardiomyocytes on an elastomeric body enclosing a microfabricated gold skeleton, we replicated fish morphology at 1=10 scale and captured basic fin deflection patterns of batoid fish. Optogenetics allows for phototactic guidance, steering, and turning maneuvers. Optical stimulation induced sequential muscle activation via serpentinepatterned muscle circuits, leading to coordinated undulatory swimming. The speed and direction of the ray was controlled by modulating light frequency and by independently eliciting right and left fins, allowing the biohybrid machine to maneuver through an obstacle course.

Elastic instability-mediated actuation by a supra-molecular polymer A. Levin, T. C. T. Michaels, L. Adler-Abramovich, T. O. Mason, T. Müller, B. Zhang, L. Mahadevan, E. Gazit, and T. P. J. Knowles.  Nature Physics , 12, 926-30, 2016.
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In nature, fast, high-power-density actuation can be achieved through the release of stored elastic energy by exploiting mechanical instabilities in systems including the closure of the Venus flytrap1 and the dispersal of plant or fungal spores2. Here, we use droplet microfluidics to tailor the geometry of a nanoscale self-assembling supra-molecular polymer to create a mechanical instability. We show that this strategy allows the build-up of elastic energy as a result of peptide selfassembly, and its release within milliseconds when the buckled geometry of the nanotube confined within microdroplets becomes unstable with respect to the straight form. These results overcome the inherent limitations of self-assembly for generating large-scale actuation on the sub-second timescale and illuminate the possibilities and performance limits of irreversible actuation by supra-molecular polymers.

On the growth and form of cortical convolutions T. Tallinen, J.Y. Chung, F. Rousseau, N. Girard, J. Lefèvre, and L. Mahadevan,  Nature Physics , 12, 588-93, 2016.
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The rapid growth of the human cortex during development is accompanied by the folding of the brain into a highly convoluted structure1,2,3. Recent studies have focused on the genetic and cellular regulation of cortical growth4,5,6,7,8, but understanding the formation of the gyral and sulcal convolutions also requires consideration of the geometry and physical shaping of the growing brain9,10,11,12,13,14,15. To study this, we use magnetic resonance images to build a 3D-printed layered gel mimic of the developing smooth fetal brain; when immersed in a solvent, the outer layer swells relative to the core, mimicking cortical growth. This relative growth puts the outer layer into mechanical compression and leads to sulci and gyri similar to those in fetal brains. Starting with the same initial geometry, we also build numerical simulations of the brain modelled as a soft tissue with a growing cortex, and show that this also produces the characteristic patterns of convolutions over a realistic developmental course. All together, our results show that although many molecular determinants control the tangential expansion of the cortex, the size, shape, placement and orientation of the folds arise through iterations and variations of an elementary mechanical instability modulated by early fetal brain geometry.

Programming curvature using origami tessellations L.H. Dudte, E. Vouga, T. Tachi and L. Mahadevan,  Nature Materials , 15, 583-88, 2016.
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Origami describes rules for creating folded structures from patterns on a flat sheet, but does not prescribe how patterns can be designed to fit target shapes. Here, starting from the simplest periodic origami pattern that yields one-degree-of-freedom collapsible structures—we show that scale-independent elementary geometric constructions and constrained optimization algorithms can be used to determine spatially modulated patterns that yield approximations to given surfaces of constant or varying curvature. Paper models confirm the feasibility of our calculations. We also assess the diculty of realizing these geometric structures by quantifying the energetic barrier that separates the metastable flat and folded states. Moreover, we characterize the trade-o between the accuracy to which the pattern conforms to the target surface, and the eort associated with creating finer folds. Our approach enables the tailoring of origami patterns to drape complex surfaces independent of absolute scale, as well as the quantification of the energetic and material cost of doing so.

Biomimetic 4D printing A. S. Gladman, E. A. Matsumoto, R.G. Nuzzo, L. Mahadevan, and J.A. Lewis,  Nature Materials , 15, 413-19, 2016.
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Shape-morphing systems can be found in many areas, including smart textiles1 , autonomous robotics2 , biomedical devices3 , drug delivery4 and tissue engineering5 . The natural analogues of such systems are exemplified by nastic plant motions, where a variety of organs such as tendrils, bracts, leaves and flowers respond to environmental stimuli (such as humidity, light or touch) by varying internal turgor, which leads to dynamic conformations governed by the tissue composition and microstructural anisotropy of cell walls6–10. Inspired by these botanical systems, we printed composite hydrogel architectures that are encoded with localized, anisotropic swelling behaviour controlled by the alignment of cellulose fibrils along prescribed four-dimensional printing pathways. When combined with a minimal theoretical framework that allows us to solve the inverse problem of designing the alignment patterns for prescribed target shapes, we can programmably fabricate plant-inspired architectures that change shape on immersion in water, yielding complex three-dimensional morphologies.

Directional memory arises from long-lived cytoskeletal asymmetries in polarized chemotactic cells H.V. Prentice-Mott, Y. Meroz, A. Carlson, M.A. Levine, M.W. Davidson, D. Irimia, G.T. Charras, L. Mahadevan, and J.V. Shah,  Proceedings of the National Academy of Sciences  (USA) 113, 1267-72, 2016.
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Chemotaxis, the directional migration of cells in a chemical gradient, is robust to fluctuations associated with low chemical concentrations and dynamically changing gradients as well as high saturating chemical concentrations. Although a number of reports have identified cellular behavior consistent with a directional memory that could account for behavior in these complex environments, the quantitative and molecular details of such a memory process remain unknown. Using microfluidics to confine cellular motion to a 1D channel and control chemoattractant exposure, we observed directional memory in chemotactic neutrophil-like cells. We modeled this directional memory as a long-lived intracellular asymmetry that decays slower than observed membrane phospholipid signaling. Measurements of intracellular dynamics revealed that moesin at the cell rear is a longlived element that when inhibited, results in a reduction of memory. Inhibition of ROCK (Rho-associated protein kinase), downstream of RhoA (Ras homolog gene family, member A), stabilized moesin and directional memory while depolymerization of microtubules (MTs) disoriented moesin deposition and also reduced directional memory. Our study reveals that long-lived polarized cytoskeletal structures, specifically moesin, actomyosin, and MTs, provide a directional memory in neutrophil-like cells even as they respond on short time scales to external chemical cues.

A geometric model for the periodic undulation of a confined adhesive crack Z. Wei and L. Mahadevan,  Soft Matter , 12, 1778-82 , 2015.
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Inspired by experiments on the instability of confined interfacial cracks, we construct a minimal mathematical model based on symmetry arguments that can reproduce the form of the crack front in a confined domain. We show that the model can be interpreted in terms of the buckling and postbuckling response of a compressed elastica with a nonuniform bending stiffness that is adhered to a linearly elastic substrate. The model has three parameters that allow us to capture the primary wavelength associated with the onset of an undulatory instability of a straight crack front, as well as the finger amplitudes and finger widths in the nonlinear development of the instability. We determine these parameters using an optimization procedure that minimizes the square error between the computed profile and experimental observations. The results of this procedure yield numerical solutions that agree well with the finger profiles experimentally observed in films of different thicknesses. Our approach shows the efficacy of simple models based on symmetry in explaining interfacial instabilities governed by different physical mechanisms.

Pressure-driven occlusive flow of a confined red blood cell T. Savin, M. M. Bandi and L. Mahadevan,  Soft Matter , 12, 562-573, 2015.
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When red blood cells (RBCs) move through narrow capillaries in the microcirculation, they deform as they flow. In pathophysiological processes such as sickle cell disease and malaria, RBC motion and flow are severely restricted. To understand this threshold of occlusion, we use a combination of experiment and theory to study the motion of a single swollen RBC through a narrow glass capillary of varying inner diameter. By tracking the movement of the squeezed cell as it is driven by a controlled pressure drop, we measure the RBC velocity as a function of the pressure gradient as well as the local capillary diameter, and find that the effective blood viscosity in this regime increases with both decreasing RBC velocity and tube radius by following a power-law that depends upon the length of the confined cell. Our observations are consistent with a simple elasto-hydrodynamic model and highlight the role of lateral confinement in the occluded pressure-driven slow flow of soft confined objects.

2015

The Monge–Ampère constraint: Matching of isometries, density and regularity, and elastic theories of shallow shells
M. Lewicka, L. Mahadevan, M. R. Pakzad,  Ann. I. H. Poincare - AN , 2015. 
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The main analytical ingredients of the first part of this paper are two independent results: a theorem on approximation of W2,2 solutions of the Monge–Ampère equation by smooth solutions, and a theorem on the matching (in other words, continuation) of second order isometries to exact isometric embeddings of 2d surface in R3. In the second part, we rigorously derive the -limit of 3-dimensional nonlinear elastic energy of a shallow shell of thickness h, where the depth of the shell scales like hα and the applied forces scale like hα+2, in the limit when h → 0. We offer a full analysis of the problem in the parameter range α ∈ (1/2, 1). We also complete the analysis in some specific cases for the full range α ∈ (0, 1), applying the results of the first part of the paper. © 2015 Elsevier Masson SAS. All rights reserved.

Elastohydrodynamics and kinetics of protein patterning in the immunological synapse
A. Carlson, L. Mahadevan,  PLoS Comput Biol  11(12): e1004481, 2015. 
[View PDF] [Download PDF] Abstract
We propose a minimal mathematical model for the physical basis of membrane protein patterning in the immunological synapse (IS), which encompass membrane mechanics, protein binding kinetics and motion, and fluid flow in the synaptic cleft. Our theory leads to simple predictions for the spatial and temporal scales of protein cluster formation, growth and arrest as a function of membrane stiffness, rigidity and kinetics of the adhesive proteins, and the fluid flow in the synaptic cleft. Numerical simulations complement these scaling laws by quantifying the nucleation, growth and stabilization of proteins domains on the size of the cell. Direct comparison with experiment shows that passive elastohydrodynamics and kinetics of protein binding in the synaptic cleft can describe the short-time formation and organization of protein clusters, without evoking any active processes in the cytoskeleton. Despite the apparent complexity of the process, our analysis shows that just two dimensionless parameters characterize the spatial and temporal evolution of the protein pattern: a ratio of membrane elasticity to protein stiffness, and the ratio of a hydrodynamic time scale for fluid flow relative to the protein binding rate. A simple phase diagram encompasses the variety of patterns that can arise

Elastic cheerios effect: Self-assembly of cylinders on a soft solid
A. Chakrabarti, L. Ryan, M. K. Chaudhury and L. Mahadevan,  Europhysics Letters , 112, 54001, 2015. 
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A rigid cylinder placed on a soft gel deforms its surface. When multiple cylinders are placed on the surface, they interact with each other via the topography of the deformed gel which serves as an energy landscape; as they move, the landscape changes which in turn changes their interaction. We use a combination of experiments, simple scaling estimates and numerical simulations to study the self-assembly of cylinders in this elastic analog of the “Cheerios Effect”, which describes capillary interactions on a fluid interface. Our results show that the effective two-body interaction can be well described by an exponential attraction potential as a result of which the dynamics also show an exponential behavior with respect to the separation distance. When many cylinders are placed on the gel, the cylinders cluster together if they are not too far apart; otherwise their motion gets elastically arrested.

Dynamics of evaporative colloidal patterning
C. N. Kaplan, N. Wu, S. Mandre, J.Aizenberg, and L. Mahadevan,  Physics of Fluids  27, 092105, 2015. 
[DOI] [View PDF] [Download PDF] Abstract
Drying suspensions often leave behind complex patterns of particulates, as might be seen in the coffee stains on a table. Here, we consider the dynamics of periodic band or uniform solid film formation on a vertical plate suspended partially in a drying colloidal solution. Direct observations allow us to visualize the dynamics of band and film deposition, where both are made of multiple layers of close packed particles. We further see that there is a transition between banding and filming when the colloidal concentration is varied. A minimal theory of the liquid meniscus motion along the plate reveals the dynamics of the banding and its transition to the filming as a function of the ratio of deposition and evaporation rates. We also provide a complementary multiphase model of colloids dissolved in the liquid, which couples the inhomogeneous evaporation at the evolving meniscus to the fluid and particulate flows and the transition from a dilute suspension to a porous plug. This allows us to determine the concentration dependence of the bandwidth and the deposition rate. Together, our findings allow for the control of drying-induced patterning as a function of the colloidal concentration and evaporation rate.

Evaporation-driven ring and film deposition from colloidal droplets
C. N. Kaplan and L. Mahadevan,  J. Fluid Mech . 781, R2 , 2015. 
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Evaporating suspensions of colloidal particles lead to the formation of a variety of patterns, ranging from a left-over ring of a dried coffee drop to uniformly distributed solid pigments left behind wet paint. To characterize the transition between rings and uniform deposits, we investigate the dynamics of a drying droplet via a multiphase model of colloidal particles in a solvent. Our theory couples the inhomogeneous evaporation at the evolving droplet interface to the dynamics inside the drop. This includes the liquid flow, local variations of the particle concentration leading to a cross-over between dilute and dense suspensions, and the resulting propagation of the deposition front. A dimensionless parameter combining the capillary number and the droplet aspect ratio captures the formation conditions of different pattern types while correctly accounting for the transition from Stokes flow to Darcy flow at high solute concentrations.

Termite mounds harness diurnal temperature oscillations for ventilation
H. King, S. Ocko, and L. Mahadevan,  Proceedings of the National Academy of Sciences  112, 37, 11589–11593, 2015. 
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Many species of millimetric fungus-harvesting termites collectively build uninhabited, massive mound structures enclosing a network of broad tunnels that protrude from the ground meters above their subterranean nests. It is widely accepted that the purpose of these mounds is to give the colony a controlled microclimate in which to raise fungus and brood by managing heat, humidity, and respiratory gas exchange. Although different hypotheses such as steady and fluctuating external wind and internal metabolic heating have been proposed for ventilating the mound, the absence of direct in situ measurement of internal air flows has precluded a definitive mechanism for this critical physiological function. By measuring diurnal variations in flow through the surface conduits of the mounds of the species Odontotermes obesus, we show that a simple combination of geometry, heterogeneous thermal mass, and porosity allows the mounds to use diurnal ambient temperature oscillations for ventilation. In particular, the thin outer flutelike conduits heat up rapidly during the day relative to the deeper chimneys, pushing air up the flutes and down the chimney in a closed convection cell, with the converse situation at night. These cyclic flows in the mound flush out CO2 from the nest and ventilate the colony, in an unusual example of deriving useful work from thermal oscillations.

Elastohydrodynamics of a sliding, spinning and sedimenting cylinder near a soft wall T. Salez and L. Mahadevan,  J. Fluid Mech . 779, 181-196 2015.
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Optimal control of plates using incompatible strains G.W. Jones and L. Mahadevan,  Nonlinearity  28, 3153–3174, 2015.
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A flat plate will bend into a curved shell if it experiences an inhomogeneous growth field or if constrained appropriately at a boundary. While the forward problem associated with this process is well studied, the inverse problem of designing the boundary conditions or growth fields to achieve a particular shape is much less understood. We use ideas from variational optimization theory to formulate a well posed version of this inverse problem to determine the optimal growth field or boundary condition that will give rise to an arbitrary target shape, optimizing for both closeness to the target shape and for smoothness of the growth field. We solve the resulting system of PDE numerically using finite element methods with examples for both the fully non-symmetric case as well as for simplified one-dimensional and axisymmetric geometries. We also show that the system can also be solved semi-analytically by positing an ansatz for the deformation and growth fields in a circular disk with given thickness profile, leading to paraboloidal, cylindrical and saddle-shaped target shapes, and show how a soft mode can arise from a non-axisymmetric deformation of a structure with axisymmetric material properties.

The organization and control of an evolving interdependent population D.C. Vural, A. Isakov, L. Mahadevan,  J. R. Soc. Interface  12: 20150044, 2015.
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Starting with Darwin, biologists have asked how populations evolve from a low fitness state that is evolutionarily stable to a high fitness state that is not. Specifically of interest is the emergence of cooperation and multicellularity where the fitness of individuals often appears in conflict with that of the population. Theories of social evolution and evolutionary game theory have produced a number of fruitful results employing two-state two-body frameworks. In this study, we depart from this tradition and instead consider a multi-player, multi-state evolutionary game, in which the fitness of an agent is determined by its relationship to an arbitrary number of other agents. We show that populations organize themselves in one of four distinct phases of interdependence depending on one parameter, selection strength. Some of these phases involve the formation of specialized large-scale structures. We then describe how the evolution of independence can be manipulated through various external perturbations.

Protein mediated membrane adhesion A. Carlson and L. Mahadevan,  Physics of Fluids  27, 051901, 2015.
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Adhesion in the context of mechanical attachment, signaling, and movement in cellular dynamics is mediated by the kinetic interactions between membraneembedded proteins in an aqueous environment. Here, we present a minimal theoretical framework for the dynamics of membrane adhesion that accounts for the kinetics of protein binding, the elastic deformation of the membrane, and the hydrodynamics of squeeze flow in the membrane gap. We analyze the resulting equations using scaling estimates to characterize the spatiotemporal features of the adhesive patterning and corroborate them using numerical simulations. In addition to characterizing aspects of cellular dynamics, our results might also be applicable to a range of phenomena in physical chemistry and materials science where flow, deformation, and kinetics are coupled to each other in slender geometries.

Fluid-driven fingering instability of a confined elastic meniscus J.S. Biggins, Z. Wei and L. Mahadevan,  Europhysics Letters , 110, 34001, 2015.
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When a fluid is pumped into a cavity in a confined elastic layer, at a critical pressure, destabilizing fingers of fluid invade the elastic solid along its meniscus (Saintyves B. et al., Phys. Rev. Lett., 111 (2013) 047801). These fingers occur without fracture or loss of adhesion and are reversible, disappearing when the pressure is decreased. We develop an asymptotic theory of pressurized highly elastic layers trapped between rigid bodies in both rectilinear and circular geometries, with predictions for the critical fluid pressure for fingering, and the finger wavelength. Our results are in good agreement with recent experimental observations of this elastic interfacial instability in a radial geometry. Our theory also shows that, perhaps surprisingly, this lateral-pressure–driven instability is analogous to a transverse-displacement–driven instability of the elastic layer. We verify these predictions by using non-linear finite-element simulations on the two systems which show that in both cases the fingering transition is first order (sudden) and hence has a region of bistability.

Bending gradients: how the intestinal stem cell gets its home  A. Shyer, T. Huycke, C-H Lee, L. Mahadevan, and C. Tabin,  Cell  , 161, 569-80, 201, 2015.
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In animal embryos, morphogen gradients determine tissue patterning and morphogenesis. Shyer et al. provide evidence that, during vertebrate gut formation, tissue folding generates graded activity of signals required for subsequent steps of gut growth and differentiation, thereby revealing an intriguing link between tissue morphogenesis and morphogen gradient formation.

Feedback-nduced phase transitions in active heterogeneous conductors S.A. Ocko and L. Mahadevan,  Physical Review Letters  114, 134501, 2015.
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An active conducting medium is one where the resistance (conductance) of the medium is modified by the current (flow) and in turn modifies the flow, so that the classical linear laws relating current and resistance, e.g., Ohm’s law or Darcy’s law, are modified over time as the system itself evolves. We consider a minimal model for this feedback coupling in terms of two parameters that characterize the way in which addition or removal of matter follows a simple local (or nonlocal) feedback rule corresponding to either flow-seeking or flow-avoiding behavior. Using numerical simulations and a continuum mean field theory, we show that flow-avoiding feedback causes an initially uniform system to become strongly heterogeneous via a tunneling (channel-building) phase separation; flow-seeking feedback leads to an immuring (wallbuilding) phase separation. Our results provide a qualitative explanation for the patterning of active conducting media in natural systems, while suggesting ways to realize complex architectures using simple rules in engineered systems.

Gait and speed selection in slender inertial swimmers M. Gazzolaa, M. Argentina and L. Mahadevan,  Proceedings of the National Academy of Sciences  112, 13, 2015.
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Inertial swimmers use flexural movements to push water and generate thrust. We quantify this dynamical process for a slender body in a fluid by accounting for passive elasticity and hydrodynamics and active muscular force generation and proprioception. Our coupled elastohydrodynamic model takes the form of a nonlinear eigenvalue problem for the swimming speed and locomotion gait. The solution of this problem shows that swimmers use quantized resonant interactions with the fluid environment to enhance speed and efficiency. Thus, a fish is like an optimized diode that converts a prescribed alternating transverse motion to forward motion. Our results also allow for a broad comparative view of swimming locomotion and provide a mechanistic basis for the empirical relation linking the swimmer’s speed U, length L, and tail beat frequency f, given by U=L ∼ f [Bainbridge R (1958) J Exp Biol 35:109–133]. Furthermore, we show that a simple form of proprioceptive sensory feedback, wherein local muscle activation is function of body curvature, suffices to drive elastic instabilities associated with thrust production and leads to a spontaneous swimming gait without the need for a central pattern generator. Taken together, our results provide a simple mechanistic view of swimming consistent with natural observations and suggest ways to engineer artificial swimmers for optimal performance.

Solid friction between soft filaments A. Ward, F. Hilitski, W. Schwenger, D. Welch, A.W.C. Lau, V. Vitelli, L. Mahadevan and Z. Dogic,  Nature Materials , 2015.
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Any macroscopic deformation of a filamentous bundle is necessarily accompanied by local sliding and/or stretching of the constituent filaments1,2. Yet the nature of the sliding friction between two aligned filaments interacting through multiple contacts remains largely unexplored. Here, by directly measuring the sliding forces between two bundled F-actin filaments, we show that these frictional forces are unexpectedly large, scale logarithmically with sliding velocity as in solid-like friction, and exhibit complex dependence on the filaments’ overlap length. We also show that a reduction of the frictional force by orders of magnitude, associated with a transition from solid-like friction to Stokes’s drag, can be induced by coating F-actin with polymeric brushes. Furthermore, we observe similar transitions in filamentous microtubules and bacterial flagella. Our findings demonstrate how altering a filament’s elasticity, structure and interactions can be used to engineer interfilament friction and thus tune the properties of fibrous composite materials.

Oscillation of the velvet worm slime jet by passive hydrodynamic instability A. Concha, P. Mellado, B. Morera-Brenes, C.S. Costa, L. Mahadevan and J. Monge-Najera,  Nature Communications  6, 6292, 2015.
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The rapid squirt of a proteinaceous slime jet endows velvet worms (Onychophora) with a unique mechanism for defence from predators and for capturing prey by entangling them in a disordered web that immobilizes their target. However, to date, neither qualitative nor quantitative descriptions have been provided for this unique adaptation. Here we investigate the fast oscillatory motion of the oral papillae and the exiting liquid jet that oscillates with frequencies fB30–60 Hz. Using anatomical images, high-speed videography, theoretical analysis and a physical simulacrum, we show that this fast oscillatory motion is the result of an elastohydrodynamic instability driven by the interplay between the elasticity of oral papillae and the fast unsteady flow during squirting. Our results demonstrate how passive strategies can be cleverly harnessed by organisms, while suggesting future oscillating microfluidic devices, as well as novel ways for micro and nanofibre production using bioinspired strategies.

Elastocapillary coalescence of plates and pillars Z. Wei, T. M. Schneider, J. Kim, H.-Y. Kim, J. Aizenberg and L. Mahadevan,  Proceedings of the Royal Society (A)  471,20140593, 2015.
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When a fluid-immersed array of supported plates or pillars is dried, evaporation leads to the formation of menisci on the tips of the plates or pillars that bring them together to form complex patterns. Building on prior experimental observations, we use a combination of theory and computation to understand the nature of this instability and its evolution in both the two- and three-dimensional setting of the problem. For the case of plates, we explicitly derive the interaction torques based on the relevant physical parameters associated with pillar deformation, contact-line pinning/depinning and fluid volume changes. A Bloch-wave analysis for our periodic mechanical system captures the window of volumes where the two-plate eigenvalue characterizes the onset of the coalescence instability. We then study the evolution of these binary clusters and their eventual elastic arrest using numerical simulations that account for evaporative dynamics coupled to capillary coalescence. This explains both the formation of hierarchical clusters and the sensitive dependence of the final structures on initial perturbations, as seen in our experiments. We then generalize our analysis to treat the problem of pillar collapse in three dimensions, where the fluid domain is completely connected and the interface is a minimal surface with the uniform mean curvature. Our theory and simulations capture the salient features of experimental observations in a range of different situations and may thus be useful in controlling the ensuing patterns.

2014

Exactly isochoric deformations of soft solids John S. Biggins, Z. Wei and L. Mahadevan,  Europhysics Letters  108, 64001, 2014.
[View PDF] [Download PDF] Abstract
Many materials of contemporary interest, such as gels, biological tissues and elastomers, are easily deformed but essentially incompressible. Traditional linear theory of elasticity implements incompressibility only to first order and thus permits some volume changes, which become problematically large even at very small strains. Using a mixed coordinate transformation originally due to Gauss, we enforce the constraint of isochoric deformations exactly to develop a linear theory with perfect volume conservation that remains valid until strains become geometrically large. We demonstrate the utility of this approach by calculating the response of an infinite soft isochoric solid to a point force that leads to a nonlinear generalization of the Kelvin solution. Our approach naturally generalizes to a range of problems involving deformations of soft solids and interfaces in two-dimensional and axisymmetric geometries, which we exemplify by determining the solution to a distributed load that mimics muscular contraction within the bulk of a soft solid.

Neuromimetic Circuits with Synaptic Devices Based on Strongly Correlated Electron Systems Sieu D. Ha, Jian Shi, Yasmine Meroz, L. Mahadevan, and Shriram Ramanathan,  Physical Review Applied 2 , 064003, 2014.
[DOI] [View PDF] [Download PDF] Abstract
Many materials of contemporary interest, such as gels, biological tissues and elastomers, are easily deformed but essentially incompressible. Traditional linear theory of elasticity implements incompressibility only to first order and thus permits some volume changes, which become problematically large even at very small strains. Using a mixed coordinate transformation originally due to Gauss, we enforce the constraint of isochoric deformations exactly to develop a linear theory with perfect volume conservation that remains valid until strains become geometrically large. We demonstrate the utility of this approach by calculating the response of an infinite soft isochoric solid to a point force that leads to a nonlinear generalization of the Kelvin solution. Our approach naturally generalizes to a range of problems involving deformations of soft solids and interfaces in two-dimensional and axisymmetric geometries, which we exemplify by determining the solution to a distributed load that mimics muscular contraction within the bulk of a soft solid.

Drops can bounce from perfectly hydrophilic surfaces J. M. Kolinski, L. Mahadevan and S. M. Rubinstein,  Europhysics Letters  108, 24001, 2014.
[DOI] [View PDF] [Download PDF] Abstract
Drops are well known to rebound from superhydrophobic surfaces and from liquid surfaces. Here, we show that drops can also rebound from a superhydrophilic solid surface such as an atomically smooth mica sheet. However, the coefficient of restitution CR associated with this process is significantly lower than that associated with rebound from superhydrophobic surfaces. A direct imaging method allows us to characterize the dynamics of the deformation of the drop in entering the vicinity of the surface. We find that drop bouncing occurs without the drop ever touching the solid and there is a nanometer-scale film of air that separates the liquid and solid, suggesting that shear in the air film is the dominant source of dissipation during rebound. Furthermore, we see that any discrete nanometer-height defects on an otherwise hydrophilic surface, such as treated glass, completely inhibits the bouncing of the drop, causing the liquid to wet the surface. Our study adds a new facet to the dynamics of droplet impact by emphasizing that the thin film of air can play a role not just in the context of splashing but also bouncing, while highlighting the role of rare surface defects in inhibiting this response.

Evaporative microclimate driven hygrometers and hygromotors J.Y. Chung, H. King and L. Mahadevan,  Europhysics Letters  107, 64002, 2014.
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A strip of paper placed on a hand spontaneously curls upwards. This simple observation illustrates the ability of a relatively homogeneous hygroscopic structural material, paper, to sense and respond to the microclimate near a non-equilibrium system, a moist evaporative boundary layer. We quantify this interaction using a simple experiment and show that it can be understood in terms of a minimal model. A small modification of this paper hygrometer that makes one or another surface partly hydrophobic using a crayon or tape allows us to create a hygro-oscillator or a hygromotor that converts transverse moisture gradients into lateral oscillations or directed motion. Our study shows how treating paper as a responsive structural material allows us to extract information and work from a microclimatic boundary layer, transforming a messenger to a machine.

Scaling macroscopic aquatic locomotion M. Gazzola, M. Argentina and L. Mahadevan,  Nature Physics , 10, 758-61, 2014.
[ONLINE ARTICLE] [View PDF] [Download PDF] Abstract
Inertial aquatic swimmers that use undulatory gaits range in length L from a few millimetres to 30 metres, across a wide array of biological taxa. Using elementary hydrodynamic arguments, we uncover a unifying mechanistic principle characterizing their locomotion by deriving a scaling relation that links swimming speed U to body kinematics (tail beat amplitude A and frequency ω) and fluid properties (kinematic viscosity ν). This principle can be simply couched as the power law Re ∼ Swα, where Re = UL/ν ≫ 1 and Sw = ω AL/ν, with α = 4/3 for laminar flows, and α = 1 for turbulent flows. Existing data from over 1,000 measurements on fish, amphibians, larvae, reptiles, mammals and birds, as well as direct numerical simulations are consistent with our scaling. We interpret our results as the consequence of the convergence of aquatic gaits to the performance limits imposed by hydrodynamics.

Gyrification from constrained cortical expansion T. Tallinen, J.Y. Chung, J.S. Biggins, and L. Mahadevan,  Proceedings of the National Academy of Sciences (USA) , 111, 35:12667-12672, 2014.
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The exterior of the mammalian brain—the cerebral cortex—has a conserved layered structure whose thickness varies little across species. However, selection pressures over evolutionary time scales have led to cortices that have a large surface area to volume ratio in some organisms, with the result that the brain is strongly convoluted into sulci and gyri. Here we show that the gyrification can arise as a nonlinear consequence of a simple mechanical instability driven by tangential expansion of the gray matter constrained by the white matter. A physical mimic of the process using a layered swelling gel captures the essence of the mechanism, and numerical simulations of the brain treated as a soft solid lead to the formation of cusped sulci and smooth gyri similar to those in the brain. The resulting gyrification patterns are a function of relative cortical expansion and relative thickness (compared with brain size), and are consistent with observations of a wide range of brains, ranging from smooth to highly convoluted. Furthermore, this dependence on two simple geometric parameters that characterize the brain also allows us to qualitatively explain how variations in these parameters lead to anatomical anomalies in such situations as polymicrogyria, pachygyria, and lissencephalia

The dynamics of sperm cooperation in a competitive environment H.S. Fisher, L. Giomi, H.E. Hoekstra and L. Mahadevan,  Proceedings of the Royal Society (B) , 281, 20140296, 2014.
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Sperm cooperation has evolved in a variety of taxa and is often considered a response to sperm competition, yet the benefit of this form of collective movement remains unclear. Here, we use fine-scale imaging and a minimal mathematical model to study sperm aggregation in the rodent genus Peromyscus. We demonstrate that as the number of sperm cells in an aggregate increase, the group moves with more persistent linearity but without increasing speed. This benefit, however, is offset in larger aggregates as the geometry of the group forces sperm to swim against one another. The result is a nonmonotonic relationship between aggregate size and average velocity with both a theoretically predicted and empirically observed optimum of six to seven sperm per aggregate. To understand the role of sexual selection in driving these sperm group dynamics, we compared two sister-species with divergent mating systems. We find that sperm of Peromyscus maniculatus (highly promiscuous), which have evolved under intense competition, form optimal-sized aggregates more often than sperm of Peromyscus polionotus (strictly monogamous), which lack competition. Our combined mathematical and experimental study of coordinated sperm movement reveals the importance of geometry, motion and group size on sperm velocity and suggests how these physical variables interact with evolutionary selective pressures to regulate cooperation in competitive environments.

A proprioceptive neuromechanical theory of crawling P. Paoletti and L. Mahadevan,  Proceedings of the Royal Society (B) , 281, 20141092, 2014.
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The locomotion of many soft-bodied animals is driven by the propagation of rhythmic waves of contraction and extension along the body. These waves are classically attributed to globally synchronized periodic patterns in the nervous system embodied in a central pattern generator (CPG). However, in many primitive organisms such as earthworms and insect larvae, the evidence for a CPG is weak, or even non-existent. We propose a neuromechanical model for rhythmically coordinated crawling that obviates the need for a CPG, by locally coupling the local neuro-muscular dynamics in the body to the mechanics of the body as it interacts frictionally with the substrate. We analyse our model using a combination of analytical and numerical methods to determine the parameter regimes where coordinated crawling is possible and compare our results with experimental data. Our theory naturally suggests mechanisms for how these movements might arise in developing organisms and how they are maintained in adults, and also suggests a robust design principle for engineered motility in soft systems.

Continuum dynamics of elastocapillary coalescence and arrest Z. Wei and L. Mahadevan,  Europhysics Letters  106, 14002, 2014.
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The surface-tension–driven coalescence of wet hair, nano-pillars and supported lamellae immersed in an evaporating liquid is eventually arrested elastically. To characterize this at a continuum level, we start from a discrete microscopic model of the process and derive a mesoscopic theory that couples the inhomogeneous dynamics of drying to the capillary forcing and elastic bending of the lamellae. Numerical simulations of the resulting partial differential equation capture the primary unstable mode seen in experiments, and the dynamic coalescence of the lamellae into dimers and quadrimers. Our theory also predicts the elastic arrest of the pattern or the separation of lamellar bundles into their constituents as a function of the amount of liquid left at the end of the process.

Density-gradient-free microfluidic centrifugation for analytical and preparative separation of nanoparticles P. Arosio, T. Müller, L. Mahadevan, and T.P.J. Knowles,  Nano Letters , 14, 2365-71, 2014.
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Sedimentation and centrifugation techniques are widely applied for the separation of biomolecules and colloids but require the presence of controlled density gradients for stable operation. Here we present an approach for separating nanoparticles in free solution without gradients. We use microfluidics to generate a convective flow perpendicular to the sedimentation direction. We show that the hydrodynamic Rayleigh−Taylor-like instability, which, in traditional methods, requires the presence of a density gradient, can be suppressed by the Poiseuille flow in the microchannel. We illustrate the power of this approach by demonstrating the separation of mixtures of particles on the nanometer scale, orders of magnitude smaller than the micrometer-sized objects separated by conventional inertial microfluidic approaches. This technique exhibits a series of favorable features including short analysis time, small sample volume, limited dilution of the analyte, limited interactions with surfaces as well as the possibility to tune easily the separation range by adjusting the geometry of the system. These features highlight the potential of gradient-free microfluidic centrifugation as an attractive route toward a broad range of nanoscale applications
Models for elastic shells with incompatible strains M. Lewicka, L. Mahadevan and M.R. Pakzad,  Proceedings of the Royal Society (A) , 470, 20130604, 2014.
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The three-dimensional shapes of thin lamina, such as leaves, flowers, feathers, wings, etc., are driven by the differential strain induced by the relative growth. The growth takes place through variations in the Riemannian metric given on the thin sheet as a function of location in the central plane and also across its thickness. The shape is then a consequence of elastic energy minimization on the frustrated geometrical object. Here, we provide a rigorous derivation of the asymptotic theories for shapes of residually strained thin lamina with non-trivial curvatures, i.e. growing elastic shells in both the weakly and strongly curved regimes, generalizing earlier results for the growth of nominally flat plates. The different theories are distinguished by the scaling of the mid-surface curvature relative to the inverse thickness and growth strain, and also allow us to generalize the classical Föppl–von Kármán energy to theories of prestrained shallow shells.

Lift-off instability during the impact of a drop on a solid surface J.M. Kolinski, L. Mahadevan, and S.M. Rubinstein,  Physical Review Letters  112, 1334501, 2014.
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We directly measure the rapid spreading dynamics succeeding the impact of a droplet of fluid on a solid, dry surface. Upon impact, the air separating the liquid from the solid surface fails to drain and wetting is delayed as the liquid rapidly spreads outwards over a nanometer thin film of air. We show that the approach of the spreading liquid front toward the surface is unstable and the spreading front lifts off away from the surface. Lift-off ensues well before the liquid contacts the surface, in contrast with prevailing paradigm where lift-off of the liquid is contingent on solid-liquid contact and the formation of a viscous boundary layer. Here we investigate the dynamics of liquid spreading over a thin film of air and its lift-off away from the surface over a large range of fluid viscosities and find that the lift-off instability is dependent on viscosity and occurs at a time that scales with the viscosity to the power of one half.

Aging in complex interdependency networks D.C. Vural, G. Morrison, and L. Mahadevan,  Physical Review E  89, 022811, 2014.
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Although species longevity is subject to a diverse range of evolutionary forces, the mortality curves of a wide variety of organisms are rather similar. Here we argue that qualitative and quantitative features of aging can be reproduced by a simple model based on the interdependence of fault-prone agents on one other. In addition to fitting our theory to the empiric mortality curves of six very different organisms, we establish the dependence of lifetime and aging rate on initial conditions, damage and repair rate, and system size. We compare the size distributions of disease and death and see that they have qualitatively different properties. We show that aging patterns are independent of the details of interdependence network structure, which suggests that aging is a many-body effect, and that the qualitative and quantitative features of aging are not sensitively dependent on the details of dependency structure or its formation.

Dynamics of a nanodroplet under a transmission electron microscope F.Y. Leong, U.M. Mirsaidov, P. Matsudaira, and L. Mahadevan,  Physics of Fluids  26, 012003, 2014.
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We investigate the cyclical stick-slip motion of water nanodroplets on a hydrophilic substrate viewed with and stimulated by a transmission electron microscope. Using a continuum long wave theory, we show how the electrostatic stress imposed by nonuniform charge distribution causes a pinned convex drop to deform into a toroidal shape, with the shape characterized by the competition between the electrostatic stress and the surface tension of the drop, as well as the charge density distribution which follows a Poisson equation. A horizontal gradient in the charge density creates a lateral driving force, which when sufficiently large, overcomes the pinning induced by surface heterogeneities in the substrate disjoining pressure, causing the drop to slide on the substrate via a cyclical stick-slip motion. Our model predicts steplike dynamics in drop displacement and surface area jumps, qualitatively consistent with experimental observations.

Statistical mechanics and shape transitions in microscopic plates E.H. Yong and L. Mahadevan,  Physical Review Letters  112, 048101, 2014.
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Unlike macroscopic multistable mechanical systems such as snap bracelets or elastic shells that must be physically manipulated into various conformations, microscopic systems can undergo spontaneous conformation switching between multistable states due to thermal fluctuations. Here we investigate the statistical mechanics of shape transitions in small elastic elliptical plates and shells driven by noise. By assuming that the effects of edges are small, which we justify exactly for plates and shells with a lenticular section, we decompose the shapes into a few geometric modes whose dynamics are easy to follow. We use Monte Carlo simulations to characterize the shape transitions between conformational minimal as a function of noise strength, and corroborate our results using a Fokker-Planck formalism to study the stationary distribution and the mean first passage time problem. Our results are applicable to objects such as graphene flakes or protein β sheets, where fluctuations, geometry, and finite size effects are important.

Intermittent locomotion as an optimal control strategy P. Paoletti and L. Mahadevan,  Proceedings of the Royal Society (A) , 470, 20130535, 2014.
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Birds, fish and other animals routinely use unsteady effects to save energy by alternating between phases of active propulsion and passive coasting. Here, we construct a minimal model for such behaviour that can be couched as an optimal control problem via an analogy to travelling with a rechargeable battery. An analytical solution of the optimal control problem proves that intermittent locomotion has lower energy requirements relative to steady-state strategies. Additional realistic hypotheses, such as the assumption that metabolic cost at a given power should be minimal (the fixed gear hypothesis), a nonlinear dependence of the energy storage rate on propulsion and/or a preferred average speed, allow us to generalize the model and demonstrate the flexibility of intermittent locomotion with implications for biological and artificial systems.

Bacillus spores as building blocks for stimuli-responsive materials and nanogenerators X. Chen, L. Mahadevan, A. Driks and O. Sahin,  Nature Nanotechnology , 9, 137-141, 2014.
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Materials that respond mechanically to external chemical stimuli have applications in biomedical devices, adaptive architectural systems, robotics and energy harvesting1–5. Inspired by biological systems, stimuli-responsive materials have been created that can oscillate2, transport fluid3, provide homeostasis4 and undergo complex changes in shape5. However, the effectiveness of synthetic stimuli-responsive materials in generating work is limited when compared with mechanical actuators6. Here, we show that the mechanical response of Bacillus spores to water gradients exhibits an energy density of more than 10 MJ m23 , which is two orders of magnitude higher than synthetic water-responsive materials7,8. We also identified mutations that can approximately double the energy density of the spores and found that they can self-assemble into dense, submicrometre-thick monolayers on substrates such as silicon microcantilevers and elastomer sheets, creating bio-hybrid hygromorph actuators9,10. To illustrate the potential applications of the spores, we used them to build an energy-harvesting device that can remotely generate electrical power from an evaporating body of water

Collective thermoregulation in bee clusters S. Ocko and L. Mahadevan,  Journal of the Royal Society - Interface  11, 20131033, 2014.
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Swarming is an essential part of honeybee behaviour. When a fertilized queen leaves the hive she takes a swarm of bees with her to start a new colony. Up to 20000 bees might accompany a newly fertilised queen bee on her quest. These bees usually form a cluster and cling to each other for several days whilst scouts leave to search for a new home to relocate to. The bees, exposed to the outside temperature, are at risk of getting too cold but in their tightly packed cluster they may also become too hot.

Flagellar dynamics of a connected chain of active, polar, Brownian particles R. Chelakkot, A. Gopinath, L. Mahadevan and M.F. Hagan,  Journal of the Royal Society - Interface  11, 20130884, 2014.
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We show that active, self-propelled particles that are connected together to form a single chain that is anchored at one end can produce the graceful beating motions of flagella. Changing the boundary condition from a clamp to a pivot at the anchor leads to steadily rotating tight coils. Strong noise in the system disrupts the regularity of the oscillations. We use a combination of detailed numerical simulations, mean-field scaling analysis and first passage time theory to characterize the phase diagram as a function of the filament length, passive elasticity, propulsion force and noise. Our study suggests minimal experimental tests for the onset of oscillations in an active polar chain.

2013

How a blister heals J.E. Longley, L. Mahadevan and M.K. Chaudhury  Europhysics Letters , 104, 46002, 2013.
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We use experiments to study the dynamics of the healing of a blister, a localized bump in a thin elastic layer that is adhered to a soft substrate everywhere except at the bump. We create a blister by gently placing a glass cover slip on a PDMS substrate. The pressure jump across the elastic layer drives fluid flow through micro-channels that form at the interface between the layer and the substrate; these channels coalesce at discrete locations as the blister heals and eventually disappear at a lower critical radius. The spacing of the channel follows a simple scaling law that can be theoretically justified, and the kinetics of healing is rate limited by fluid flow, but with a non-trivial dependence on the substrate thickness that likely arises due to channelization. Our study is relevant to a variety of soft adhesion scenarios.

Biased migration of confined neutrophil-like cells in asymmetric hydraulic environments H.V. Prentice-Mott, C-H Chang, L. Mahadevan, T.J. Mitchison, D. Irimia, and J.V. Shah  Proceedings of the National Academy of Sciences (USA) , 110, 21006-21110, 2013.
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Cells integrate multiple measurement modalities to navigate their environment. Soluble and substrate-bound chemical gradients and physical cues have all been shown to influence cell orientation and migration. Here we investigate the role of asymmetric hydraulic pressure in directional sensing. Cells confined in microchannels identified and chose a path of lower hydraulic resistance in the absence of chemical cues. In a bifurcating channel with asymmetric hydraulic resistances, this choice was preceded by the elaboration of two leading edges with a faster extension rate along the lower resistance channel. Retraction of the “losing” edge appeared to precipitate a final choice of direction. The pressure differences altering leading edge protrusion rates were small, suggesting weak force generation by leading edges. The response to the physical asymmetry was able to override a dynamically generated chemical cue. Motile cells may use this bias as a result of hydraulic resistance, or “barotaxis,” in concert with chemotaxis to navigate complex environments.

Quantifying cell-generated mechanical forces within living embryonic tissues O. Campàs, T. Mammoto, S. Hasso, R.A. Sperling, D. O’Connell, A.G. Bischof, R. Maas, D.A. Weitz, L. Mahadevan & D.E. Ingber  Nature Methods , 183-189, 2013.
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Cell-generated mechanical forces play a critical role during tissue morphogenesis and organ formation in the embryo. Little is known about how these forces shape embryonic organs, mainly because it has not been possible to measure cellular forces within developing three-dimensional (3D) tissues in vivo. We present a method to quantify cell-generated mechanical stresses exerted locally within living embryonic tissues, using fluorescent, cell-sized oil microdroplets with defined mechanical properties and coated with adhesion receptor ligands. After a droplet is introduced between cells in a tissue, local stresses are determined from droplet shape deformations, measured using fluorescence microscopy and computerized image analysis. Using this method, we quantified the anisotropic stresses generated by mammary epithelial cells cultured within 3D aggregates, and we confirmed that these stresses (3.4 nN mm−2) are dependent on myosin II activity and are more than twofold larger than stresses generated by cells of embryonic tooth mesenchyme, either within cultured aggregates or in developing whole mouse mandibles.

Elastic platonic shells E.H. Yong, D.R. Nelson, and L. Mahadevan  Physical Review Letters , 111, 177801, 2013.
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On microscopic scales, the crystallinity of flexible tethered or cross-linked membranes determines their mechanical response. We show that by controlling the type, number, and distribution of defects on a spherical elastic shell, it is possible to direct the morphology of these structures. Our numerical simulations show that by deflating a crystalline shell with defects, we can create elastic shell analogs of the classical platonic solids. These morphologies arise via a sharp buckling transition from the sphere which is strongly hysteretic in loading or unloading. We construct a minimal Landau theory for the transition using quadratic and cubic invariants of the spherical harmonic modes. Our approach suggests methods to engineer shape into soft spherical shells using a frozen defect topology

How ticks get under your skin: insertion mechanics of the feeding apparatus of Ixodes ricinus ticks D. Richter, F-R. Matuschka, A. Spielman, and L. Mahadevan  Proceedings of the Royal Society B,  280, 20131758, 2013.
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The tick Ixodes ricinus uses its mouthparts to penetrate the skin of its host and to remain attached for about a week, during which time Lyme disease spirochaetes may pass from the tick to the host. To understand how the tick achieves both tasks, penetration and attachment, with the same set of implements, we recorded the insertion events by cinematography, interpreted the mouthparts’ function by scanning electron microscopy and identified their points of articulation by confocal microscopy. Our structural dynamic observations suggest that the process of insertion and attachment occurs via a ratchet-like mechanism with two distinct stages. Initially, the two telescoping chelicerae pierce the skin and, by moving alternately, generate a toehold. Subsequently, a breaststroke-like motion, effected by simultaneous flexure and retraction of both chelicerae, pulls in the barbed hypostome. This combination of a flexible, dynamic mechanical ratchet and a static holdfast thus allows the tick to solve the problem of how to penetrate skin and also remain stuck for long periods of time.

Villification: how the gut gets its villi A. Shyer, T. Tallinen, N. Nerurkar, Z. Wei, E. Kim, D. Kaplan, C. Tabin and L. Mahadevan  Science,  342, 212-218, 2013.
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The villi of the human and chick gut are formed in similarstepwise progressions, wherein the mesenchyme and attached epithelium first fold into longitudinal ridges, then a zigzag pattern, and lastly individual villi. We find that these steps of villification depend on the sequential differentiation of the distinct smooth muscle layers of the gut, which restrict the expansion of the growing endoderm and mesenchyme, generating compressive stresses that lead to their buckling and folding. A quantitative computational model, incorporating measured properties of the developing gut, recapitulates the morphological patterns seen during villification in a variety of species. These results provide a mechanistic understanding of the formation of these elaborations of the lining of the gut, essential for providing sufficient surface area for nutrient absorption.

Digital instability of a confined elastic meniscus J.S. Biggins, B. Saintyves, Z. Wei, E. Bouchard, and L. Mahadevan  Proceedings of the National Academy of Sciences (USA) , 110, 12545-12548, 2013.
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Thin soft elastic layers serving as joints between relatively rigid bodies may function as sealants, thermal, electrical, or mechanical insulators, bearings, or adhesives. When such a joint is stressed, even though perfect adhesion is maintained, the exposed free meniscus in the thin elastic layer becomes unstable, leading to the formation of spatially periodic digits of air that invade the elastic layer, reminiscent of viscous fingering in a thin fluid layer. However, the elastic instability is reversible and rate-independent, disappearing when the joint is unstressed. We use theory, experiments, and numerical simulations to show that the transition to the digital state is sudden (first-order), the wavelength and amplitude of the fingers are proportional to the thickness of the elastic layer, and the required separation to trigger the instability is inversely proportional to the in-plane dimension of the layer. Our study reveals the energetic origin of this instability and has implications for the strength of polymeric adhesives; it also suggests a method for patterning thin films reversibly with any arrangement of localized fingers in a digital elastic memory, which we confirm experimentally.

A pendulum in a flowing soap film M.M. Bandi, A. Concha, R. Wood, and L. Mahadevan, Physics of Fluids, 25, 041702, 2013.
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We consider the dynamics of a pendulum made of a rigid ring attached to an elastic filament immersed in a flowing soap film. The system shows an oscillatory instability whose onset is a function of the flow speed, length of the supporting string, the ring mass, and ring radius. We characterize this system and show that there are different regimes where the frequency is dependent or independent of the pendulum length depending on the relative magnitude of the added-mass. Although the system is an infinite-dimensional, we can explain many of our results in terms of a one degree-of-freedom system corresponding to a forced pendulum. Indeed, using the vorticity measured via particle imaging velocimetry allows us to make the model quantitative, and a comparison with our experimental results shows we can capture the basic phenomenology of this system.

Geometric mechanics of periodic pleated origami Z.Y. Wei, Z.V. Guo, L. Dudte, H.Y. Liang, and L. Mahadevan, Physical Review Letters, 110, 215501, 2013 .
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Origami structures are mechanical metamaterials with properties that arise almost exclusively from the geometry of the constituent folds and the constraint of piecewise isometric deformations. Here we characterize the geometry and planar and nonplanar effective elastic response of a simple periodically folded Miura-ori structure, which is composed of identical unit cells of mountain and valley folds with four-coordinated ridges, defined completely by two angles and two lengths. We show that the in-plane and out-of-plane Poisson’s ratios are equal in magnitude, but opposite in sign, independent of material properties. Furthermore, we show that effective bending stiffness of the unit cell is singular, allowing us to characterize the two-dimensional deformation of a plate in terms of a one-dimensional theory. Finally, we solve the inverse design problem of determining the geometric parameters for the optimal geometric and mechanical response of these extreme structures

Rationally designed complex, hierarchical microarchitectures W.L. Noorduin, A. Grinthal, L. Mahadevan, J. Aizenberg. Science, 340, 832-837.
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The emergence of complex nano- and microstructures is of fundamental interest, and the ability to program their form has practical ramifications in fields such as optics, catalysis, and electronics. We developed carbonate-silica microstructures in a dynamic reaction-diffusion system that allow us to rationally devise schemes for precisely sculpting a great variety of elementary shapes by diffusion of carbon dioxide (CO2) in a solution of barium chloride and sodium metasilicate. We identify two distinct growth modes and show how continuous and discrete modulations in CO2 concentration, pH, and temperature can be used to deterministically switch between different regimes and create a bouquet of hierarchically assembled multiscale microstructures with unprecedented levels of complexity and precision. These results outline a nanotechnology strategy for “collaborating” with self-assembly processes in real time to build arbitrary tectonic architectures.

Adaptive fluid-infused porous films with tunable transparency and wettability X. Yao, Y. Hu, A. Grinthal, T-S. Wong, L. Mahadevan and J. Aizenberg, Nature Materials, 12, 529-34, 2013 .
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Materials that adapt dynamically to environmental changes are currently limited to two-state switching of single properties, and only a small number of strategies that may lead to materials with continuously adjustable characteristics have been reported1–3 . Here we introduce adaptive surfaces made of a liquid film supported by a nanoporous elastic substrate. As the substrate deforms, the liquid flows within the pores, causing the smooth and defect-free surface to roughen through a continuous range of topographies. We show that a graded mechanical stimulus can be directly translated into finely tuned, dynamic adjustments of optical transparency and wettability. In particular, we demonstrate simultaneous control of the film’s transparency and its ability to continuously manipulate various low-surface-tension droplets from freesliding to pinned. This strategy should make possible the rational design of tunable, multifunctional adaptive materials for a broad range of applications.

Hydrodynamics of hemostasis in sickle-cell disease S.I.A. Cohen and L. Mahadevan,  Physical Review Letters 110, 138104, 2013.
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Vaso-occlusion, the stoppage of blood flow in sickle-cell disease, is a complex dynamical process spanning multiple time and length scales. Motivated by recent ex vivo microfluidic measurements of hemostasis using blood from sickle-cell patients, we develop a multiphase model that couples the kinetics and hydrodynamics of a flowing suspension of normal and sickled cells in a fluid. We use the model to derive expressions for the cell velocities and concentrations that quantify the hydrodynamics of hemostasis, and provide simple criteria as well as a phase diagram for occlusion, consistent with our simulations and earlier observations.

Planar morphometry, shear and optimal quasi-conformal mappings G.W. Jones and L. Mahadevan,  Proceedings of the Royal Society (A) , 469, 20120653, 2013.
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To characterize the diversity of planar shapes in such instances as insect wings and plant leaves, we present a method for the generation of a smooth morphometric mapping between two planar domains which matches a number of homologous points. Our approach tries to balance the competing requirements of a descriptive theory which may not reflect mechanism and a multi-parameter predictive theory that may not be well constrained by experimental data. Specifically, we focus on aspects of shape as characterized by local rotation and shear, quantified using quasi-conformal maps that are defined precisely in terms of these fields. To make our choice optimal, we impose the condition that the maps vary as slowly as possible across the domain, minimizing their integrated squared-gradient. We implement this algorithm numerically using a variational principle that optimizes the coefficients of the quasi-conformal map between the two regions and show results for the recreation of a sample historical grid deformation mapping of D’Arcy Thompson. We also deploy our method to compare a variety of Drosophila wing shapes and show that our approach allows us to recover aspects of phylogeny as marked by morphology

Dissolution-driven convection in a Hele-Shaw cell A.C. Slim, M.M. Bandi, J.C. Miller, and L. Mahadevan,  Physics of Fluids , 25, 024101, 2013.
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Motivated by convection in the context of geological carbon-dioxide (CO2) storage, we present an experimental study of dissolution-driven convection in a Hele–Shaw cell for Rayleigh numbers R in the range 100 < R < 1700. We use potassium permanganate (KMnO4) in water as an analog for CO2 in brine and infer concentration profiles at high spatial and temporal resolution and accuracy from transmitted light intensity. We describe behavior from first contact up to 65% average saturation and measure several global quantities including dissolution flux, average concentration, amplitude of perturbations away from pure one-dimensional diffusion, and horizontally averaged concentration profiles. We show that the flow evolves successively through distinct regimes starting with a simple one-dimensional diffusional profile. This is followed by linear growth in which fingers are initiated and grow quasiexponentially, independently of one-another. Once the fingers are well-established, a flux-growth regime begins as fresh fluid is brought to the interface and contaminated fluid removed, with the flux growing to a local maximum. During this regime, fingers still propagate independently. However, beyond the flux maximum, fingers begin to interact and zip together from the root down in a merging regime. Several generations of merging occur before only persistent primary fingers remain. Beyond this, the reinitiation regime begins with new fingers created between primary existing ones before merging into them. Through appropriate scaling, we show that the regimes are universal and independent of layer thickness (equivalently R) until the fingers hit the bottom. At this time, progression through these regimes is interrupted and the flow transitions to a saturating regime. In this final regime, the flux gradually decays in a manner well described by a Howard-style phenomenological model.

Swarming, swirling and stasis in sequestered bristle-bots. L. Giomi, N. Hawley-Weld and L. Mahadevan,  Proceedings of the Royal Society (A), (2012),  469, 20120637.
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The collective ability of organisms to move coherently in space and time is ubiquitous in any group of autonomous agents that can move and sense each other and the environment. Here, we investigate the origin of collective motion and its loss using macroscopic self-propelled bristle-bots, simple automata made from a toothbrush and powered by an onboard cell phone vibrator-motor, that can sense each other through shape-dependent local interactions, and can also sense the environment nonlocally via the effects of confinement and substrate topography. We show that when bristle-bots are confined to a limited arena with a soft boundary, increasing the density drives a transition from a disordered and uncoordinated motion to organized collective motion either as a swirling cluster or a collective dynamical stasis. This transition is regulated by a single parameter, the relative magnitude of spinning and walking in a single automaton. We explain this using quantitative experiments and simulations that emphasize the role of the agent shape, environment and confinement via boundaries. Our study shows how the behavioural repertoire of these physically interacting automatons controlled by one parameter translates into the mechanical intelligence of swarms.

Surface sulci in squeezed soft solids T. Tallinen, J.S. Biggins, and L. Mahadevan,  Physical Review Letters , 110, 024302, 2013.
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The squeezing of soft solids, the constrained growth of biological tissues, and the swelling of soft elastic solids such as gels can generate large compressive stresses at their surfaces. This causes the otherwise smooth surface of such a solid to become unstable when its stress exceeds a critical value. Previous analyses of the surface instability have assumed two-dimensional plane-strain conditions, but in experiments isotropic stresses often lead to complex three-dimensional sulcification patterns. Here we show how such diverse morphologies arise by numerically modeling the lateral compression of a rigidly clamped elastic layer. For incompressible solids, close to the instability threshold, sulci appear as I-shaped lines aligned orthogonally with their neighbors; at higher compressions they are Y-shaped and prefer a hexagonal arrangement. In contrast, highly compressible solids when squeezed show only one sulcified phase characterized by a hexagonal sulcus network.

The cytoplasm of living cells behaves as a poroelastic material E. Moeendarbary, L. Valon, M. Fritzsche, A.R. Harris, D.A. Moulding, A.J. Thrasher, E. Stride, L. Mahadevan, and G.T. Charras,  Nature Materials , 12, 253-261, 2013.
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The cytoplasm is the largest part of the cell by volume and hence its rheology sets the rate at which cellular shape changes can occur. Recent experimental evidence suggests that cytoplasmic rheology can be described by a poroelastic model, in which the cytoplasm is treated as a biphasic material consisting of a porous elastic solid meshwork (cytoskeleton, organelles, macromolecules) bathed in an interstitial fluid (cytosol). In this picture, the rate of cellular deformation is limited by the rate at which intracellular water can redistribute within the cytoplasm. However, direct supporting evidence for the model is lacking. Here we directly validate the poroelastic model to explain cellular rheology at short timescales using microindentation tests in conjunction with mechanical, chemical and genetic treatments. Our results show that water redistribution through the solid phase of the cytoplasm (cytoskeleton and macromolecular crowders) plays a fundamental role in setting cellular rheology at short timescales.

2012

Watching paint dry L. Mahadevan, Op-Ed,  The Harvard Undergraduate Research Journal , 5, 64, 2012.
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“Vulgar and inactive minds confound familiarity with knowledge .... The scientist, who is not content with super!cial views, harasses himself with fruitless curiosity; and still, as he inquires more, perceives only that he knows less...”
And the Ignobel goes to …. Joe Keller,  L. Mahadevan,  SIAM News , Dec. 2012.
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Slicing softly with shear E. Reyssat, T. Tallinen, M. Le Merrer, and L. Mahadevan,  Physical Review Letters , 109, 244301, 2012.
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Experienced chefs know that to make a neat cut in a boiled egg or a piece of cheese, a thin wire, or even a fine piece of thread, can work better than a knife. But even a blunt knife can cut soft solids well if it is rocked back and forth while applying a gentle pressure. Understanding the balance of forces needed to make a clean cut into deformable materials could be important for developing highly efficient techniques in industrial-scale food processing, or new tools for cutting biological tissue for analysis or during surgery. Writing in Physical Review Letters[1], Etienne Reyssat, at Harvard University, and colleagues provide an intriguing analysis of the cutting of soft solids, applying a combination of theory and experiments to pinpoint the role played by shear in facilitating the fracture of a highly deformable material.

Elastic configurations of self-supported oxide membranes for fuel cells K. Kerman, T. Tallinen, S. Ramanathan, L. Mahadevan,  Journal of Power Sources , 222, 359-366, 2012.
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Ultra-thin oxide films are of interest in energy conversion technologies such as low temperature solid oxide fuel cells and permeation membranes. Understanding their thermo-mechanical stability is an important problem. Edge clamped, self-supported thin film membranes show hierarchical wrinkles; with the largest wavelengths in the center, while smaller ones arise near the clamped boundary; correspondingly the largest strains, with tensile stress comparable to the residual stress, are in the vicinity of the clamped boundary. Our results can be understood by simple scaling arguments and are valid for membranes in the post-buckling regime far from threshold. We confirm the validity of our analysis by quantitative experimental comparison to self-supported, square micro-machined yttria-stabilized zirconia membranes of edge length 160 mm fabricated by lithography. The modeling and experiments combined provide a foundation for designing failure resistant self-supported membranes of interest to energy conversion. We show this by utilizing such membranes to fabricate thin film solid oxide fuel cells and demonstrate power generation utilizing natural gas as fuel at w400
C.

The size, shape, and dynamics of cellular blebs F.Y. Lim, K-H. Chiam, L. Mahadevan,  Europhysics Letters , 100, 28004, 2012.
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A cellular bleb grows when a portion of the cell membrane detaches from the underlying cortex under the influence of a cytoplasmic pressure. We develop a quantitative model for the growth and dynamics of these objects in a simple two-dimensional setting. In particular, we first find the minimum cytoplasmic pressure and minimum unsupported membrane length for a stationary bleb to nucleate and grow as a function of the membrane-cortex adhesion. We next show how a bleb may travel around the periphery of the cell when the cytoplasmic pressure varies in space and time in a prescribed way and find that the traveling speed is governed by the speed of the pressure change induced by local cortical contraction while the shape of the traveling bleb is governed by the speed of cortical healing. Finally, we relax the assumption that the pressure change is prescribed and couple it hydrodynamically to the cortical contraction and membrane deformation. By quantifying the phase space of bleb formation and dynamics, our framework serves to delineate the range and scope of bleb-associated cell motility.

Macroscopic magnetic frustration P. Mellado, A. Concha, L. Mahadevan,  Physical Review Letters , 109, 257203, 2012.
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A cellular bleb grows when a portion of the cell membrane detaches from the underlying cortex under the influence of a cytoplasmic pressure. We develop a quantitative model for the growth and dynamics of these objects in a simple two-dimensional setting. In particular, we first find the minimum cytoplasmic pressure and minimum unsupported membrane length for a stationary bleb to nucleate and grow as a function of the membrane-cortex adhesion. We next show how a bleb may travel around the periphery of the cell when the cytoplasmic pressure varies in space and time in a prescribed way and find that the traveling speed is governed by the speed of the pressure change induced by local cortical contraction while the shape of the traveling bleb is governed by the speed of cortical healing. Finally, we relax the assumption that the pressure change is prescribed and couple it hydrodynamically to the cortical contraction and membrane deformation. By quantifying the phase space of bleb formation and dynamics, our framework serves to delineate the range and scope of bleb-associated cell motility.

Geometric mechanics of curved crease origami M.A. Dias, L.H. Dudte, L. Mahadevan, C.D. Santangelo,  Physical Review Letters , 109, 114301, 2012.
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Folding a sheet of paper along a curve can lead to structures seen in decorative art and utilitarian packing boxes. Here we present a theory for the simplest such structure: an annular circular strip that is folded along a central circular curve to form a three-dimensional buckled structure driven by geometrical frustration. We quantify this shape in terms of the radius of the circle, the dihedral angle of the fold, and the mechanical properties of the sheet of paper and the fold itself. When the sheet is isometrically deformed everywhere except along the fold itself, stiff folds result in creases with constant curvature and oscillatory torsion. However, relatively softer folds inherit the broken symmetry of the buckled shape with oscillatory curvature and torsion. Our asymptotic analysis of the isometrically deformed state is corroborated by numerical simulations that allow us to generalize our analysis to study structures with multiple curved creases.

Strategies for cell shape control in the tip-growing cells O. Campas, E. Rojas, J. Dumais, and L. Mahadevan,  American Journal of Botany  99(9):1577–1582, 2012.
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Despite the large diversity in biological cell morphology, the processes that specify and control cell shape are not yet fully understood. Here we study the shape of tip-growing, walled cells, which have evolved a polar mode of cell morphogenesis leading to characteristic fi lamentous cell morphologies that extend only apically.

How the cucumber tendril coils and overwinds S.J. Gerbode, J.R. Puzey, A.G. McCormick, L. Mahadevan,  Science  337, 1087, 2012.
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The helical coiling of plant tendrils has fascinated scientists for centuries, yet the underlying mechanism remains elusive. Moreover, despite Darwin’s widely accepted interpretation of coiled tendrils as soft springs, their mechanical behavior remains unknown. Our experiments on cucumber tendrils demonstrate that tendril coiling occurs via asymmetric contraction of an internal fiber ribbon of specialized cells. Under tension, both extracted fiber ribbons and old tendrils exhibit twistless overwinding rather than unwinding, with an initially soft response followed by strong strain-stiffening at large extensions. We explain this behavior using physical models of prestrained rubber strips, geometric arguments, and mathematical models of elastic filaments. Collectively, our study illuminates the origin of tendril coiling, quantifies Darwin’s original proposal, and suggests designs for biomimetic twistless springs with tunable mechanical responses.

Physical basis for the adaptive flexibility of bacillus spore coats O. Sahin, E-H Yong, A. Driks and L. Mahadevan,  Journal of the Royal Society - Interface,  9, 3156-3160, 2012.
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Bacillus spores are highly resistant dormant cells formed in response to starvation. The spore is surrounded by a structurally complex protein shell, the coat, which protects the genetic material. In spite of its dormancy, once nutrient is available (or an appropriate physical stimulus is provided) the spore is able to resume metabolic activity and return to vegetative growth, a process requiring the coat to be shed. Spores dynamically expand and contract in response to humidity, demanding that the coat be flexible. Despite the coat’s critical biological functions, essentially nothing is known about the design principles that allow the coat to be tough but also flexible and, when metabolic activity resumes, to be efficiently shed. Here, we investigated the hypothesis that these apparently incompatible characteristics derive from an adaptive mechanical response of the coat. We generated a mechanical model predicting the emergence and dynamics of the folding patterns uniformly seen in Bacillus spore coats. According to this model, spores carefully harness mechanical instabilities to fold into a wrinkled pattern during sporulation. Owing to the inherent nonlinearity in their formation, these wrinkles persist during dormancy and allow the spore to accommodate changes in volume without compromising structural and biochemical integrity. This characteristic of the spore and its coat may inspire design of adaptive materials.

Deformation and capillary self-repair of carbon nanotube brushes V. Pushparaj, L. Mahadevan, S. Sreekala, L. Ci, R. Nalamasu, P.M. Ajayan.  Carbon , 50, 5618-5630, 2012.
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Brushes with nanoscale bristles, such as nanotube arrays held together by van der Waals forces, have applications as compliant electrical switches, probes and micro-scale cleaning tools. Repeated use exposes the brushes to contact and impact at high strains resulting in the bristles undergoing exfoliation, deformation and damage. We show that the damages incurred can be nearly recovered by capillary evaporation of solvents from the free standing aligned nanotube brushes.

Discovering communities through friendship G. Morrison, L. Mahadevan.  PLoS ONE  7(7): e38704. 2012.
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We introduce a new method for detecting communities of arbitrary size in an undirected weighted network. Our approach is based on tracing the path of closest-friendship between nodes in the network using the recently proposed Generalized Erdo¨s Numbers. This method does not require the choice of any arbitrary parameters or null models, and does not suffer from a system-size resolution limit. Our closest-friend community detection is able to accurately reconstruct the true network structure for a large number of real world and artificial benchmarks, and can be adapted to study the multi-level structure of hierarchical communities as well. We also use the closeness between nodes to develop a degree of robustness for each node, which can assess how robustly that node is assigned to its community. To test the efficacy of these methods, we deploy them on a variety of well known benchmarks, a hierarchal structured artificial benchmark with a known community and robustness structure, as well as real-world networks of coauthorships between the faculty at a major university and the network of citations of articles published in Physical Review. In all cases, microcommunities, hierarchy of the communities, and variable node robustness are all observed, providing insights into the structure of the network.

Banding, excitability and chaos in active nematic suspensions L. Giomi, L Mahadevan, B. Chakraborty and M. F. Hagan.  Nonlinearity  25, 2245–2269, 2012.
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Motivated by the observation of highly unstable flowing states in suspensions of microtubules and kinesin, we analyse a model of mutually propelled filaments suspended in a solvent. The system undergoes a mean-field isotropic–nematic transition for large enough filament concentrations when the nematic order parameter is allowed to vary in space and time. We analyse the model in two contexts: a quasi-one-dimensional channel with no-slip walls and a two-dimensional box with periodic boundaries. Using stability analysis and numerical calculations we show that the interplay between non-uniform nematic order, activity, and flow results in a variety of complex scenarios that include spontaneous banded laminar flow, relaxation oscillations and chaos

Scale and nature of sulcification patterns E. Hohlfeld and L. Mahadevan,  Physical Review Letters , 109, 025701, 2012.
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Sulci are surface folds commonly seen in strained soft elastomers and form via a strongly subcritical, yet scale-free, instability. Treating the threshold for nonlinear instability as a nonlinear critical point, we explain the nature of sulcus patterns in terms of the scale and translation symmetries which are broken by the formation of an isolated, small sulcus. Our perturbative theory and simulations show that sulcus formation in a thick, compressed slab can arise either as a supercritical or as a weakly subcritical bifurcation relative to this nonlinear critical point, depending on the boundary conditions. An infinite number of competing, equilibrium patterns simultaneously emerge at this critical point, but the one selected has the lowest energy. We give a simple, physical explanation for the formation of these sulcification patterns using an analogy to a solid-solid phase transition with a finite energy of transformation.

Flow induced channelization in a porous medium A. Mahadevan, A.V. Orpe, A. Kudrolli, and L. Mahadevan,  Europhysics Letters , 98, 58003, 2012.
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Flow through a saturated, granular, porous medium can lead to internal erosion, preferential flow enhancement, and the formation of channels within the bulk of the medium. We examine this phenomenon using a combination of experimental observations, continuum theory and numerical simulations in a minimal setting. Our experiments are carried out by forcing water through a Hele-Shaw cell packed with bidisperse grains. When the local flow-induced stress exceeds a critical threshold, the smaller grains are dislodged and transported. This changes the porosity of the medium, thence, the local hydraulic conductivity, and leads to the development of erosional channels. Erosion is ultimately arrested due to the drop in the mean pressure gradient, while most of the flow occurs through the channels. We describe this using a minimal multiphase description of erosion where the volume fraction of the fluid, mobile, and immobile, grains change in space and time. Numerical solutions of the resulting initial boundary value problem yield results for the dynamics and morphology that are in qualitative agreement with our experiments. In addition to providing a basis for channelization in porous media, our study highlights how heterogeneity in porous media may arise from flow as a function of the erosion threshold.

How things get stuck: kinetics, elastohydrodynamics, and soft adhesion M. Mani, A. Gopinath, and L. Mahadevan,  Physical Review Letters , 108, 226104, 2012.
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We consider the sticking of a fluid-immersed colloidal particle with a substrate coated by polymeric tethers, a model for soft, wet adhesion in many natural and artificial systems. Our theory accounts for the kinetics of binding, the elasticity of the tethers, and the hydrodynamics of fluid drainage between the colloid and the substrate, characterized by three dimensionless parameters: the ratio of the viscous drainage time to the kinetics of binding, the ratio of elastic to thermal energies, and the size of the particle relative to the height of the polymer brush. For typical experimental parameters and discrete families of tethers, we find that adhesion proceeds via punctuated steps, where rapid transitions to increasingly bound states are separated by slow aging transients, consistent with recent observations. Our results also suggest that the bound particle is susceptible to fluctuation-driven instabilities parallel to the substrate.

Geometric control of rippling in supported polymer nanolines V.R. Tirumala, C.M. Stafford, L.E. Ocola, J.F. Douglas, and L. Mahadevan,  Nanoletters , 12, 1516-1521, 2012.
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We study the swelling behavior of finlike polymer line gratings supported on a rigid substrate and show that the edge-supported polymer laminae undergo a rippling instability with a well-defined ripple wavelength λ transverse to the plane of the solid supporting substrate and a ripple amplitude that monotonically decreases from its maximum at the free-edge. These ripple patterns develop due to inhomogeneous compressive strains that arise from the geometric constraints that progressively suppress swelling near the supporting substrate where the laminae are clamped. By experimentally examining the influence of swelling strain and pattern geometry on the observed rippling instability, we find that the ripple wavelength λ scales with line width w for sufficiently long gratings, which is consistent with a simple theory. These trends were validated for polymer nanoline test patterns having w between (50 to 250) nm and a height-to-width aspect-ratio in the range 0.5 to 5. Our results suggest that line geometry, rather than material properties, governs the onset of rippling and suggest simple rules for their control.

A method for tensile tests of biological tissues at the mesoscale T. Savin, A. E. Shyer, and L. Mahadevan,  Journal of Applied Physics  111, 074704, 2012.
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We describe a new technique for determining the tensile properties of biological tissues at the mesoscale. The procedure uses a calibrated magnetic interaction between a steel bead attached to the sample and a permanent magnet to apply a uniaxial tensile force, along with a simple video assay to monitor the sample extension and thus the strain. Our method fills a significant gap in the accessible range of both forces and strains and is useful for forces in the micro and milliNewton range, and displacements in the range of hundreds of microns with strains of up to 200%. We give two examples of the mechanical characterization of tissues using our technique, employing it to characterize the elastic modulus of tubular and membraneous embryonic tissues from the chick.

Balancing on tightropes and slacklines P. Paoletti and L. Mahadevan,  Journal of the Royal Society - Interface , 9, 2097-2108, 2012.
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Balancing on a tightrope or a slackline is an example of a neuromechanical task where the whole body both drives and responds to the dynamics of the external environment, often on multiple timescales. Motivated by a range of neurophysiological observations, here we formulate a minimal model for this system and use optimal control theory to design a strategy for maintaining an upright position. Our analysis of the open and closed-loop dynamics shows the existence of an optimal rope sag where balancing requires minimal effort, consistent with qualitative observations and suggestive of strategies for optimizing balancing performance while standing and walking. Our consideration of the effects of nonlinearities, potential parameter coupling and delays on the overall performance shows that although these factors change the results quantitatively, the existence of an optimal strategy persists.

Skating on a film of air: drops impacting on a surface J. M. Kolinski, S. M. Rubinstein, S. Mandre, M. P. Brenner, D. A. Weitz, and L. Mahadevan,  Physical Review Letters , 108, 074503, 2012.
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The commonly accepted description of drops impacting on a surface typically ignores the essential role of the air that is trapped between the impacting drop and the surface. Here we describe a new imaging modality that is sensitive to the behavior right at the surface. We show that a very thin film of air, only a few tens of nanometers thick, remains trapped between the falling drop and the surface as the drop spreads. The thin film of air serves to lubricate the drop enabling the fluid to skate on the air film laterally outward at surprisingly high velocities, consistent with theoretical predictions. Eventually this thin film of air breaks down as the fluid wets the surface via a spinodal-like mechanism. Our results show that the dynamics of impacting drops are much more complex than previously thought, with a rich array of unexpected phenomena that require rethinking classic paradigms

Twisting graphene nanoribbons into carbon nanotubes O.O. Kit, T. Tallinen, L. Mahadevan, J. Timonen, P. Koskinen,  Physical Review B , 85, 085428, 2012.
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Although carbon nanotubes consist of honeycomb carbon, they have never been fabricated from graphene directly. Here, it is shown by quantum molecular-dynamics simulations and classical continuum-elasticity modeling, that graphene nanoribbons can, indeed, be transformed into carbon nanotubes by means of twisting. The chiralities of the tubes thus fabricated can be not only predicted but also externally controlled. This twisting route is an opportunity for nanofabrication, and is easily generalizable to ribbons made of other planar nanomaterials.

A biophysical indicator of vaso-occlusive risk in sickle cell disease D.K. Wood, A. Soriano, L. Mahadevan, J.M. Higgins, S.N. Bhatia,  Science Translational Medicin e, 4:123, 123ra26, 2012.
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The search for predictive indicators of disease has largely focused on molecular markers. However, biophysical markers, which can integrate multiple pathways, may provide a more global picture of pathophysiology. Sickle cell disease affects millions of people worldwide and has been studied intensely at the molecular, cellular, tissue, and organismal level for a century, but there are still few, if any, markers quantifying the severity of this disease. Because the complications of sickle cell disease are largely due to vaso-occlusive events, we hypothesized that a physical metric characterizing the vaso-occlusive process could serve as an indicator of disease severity. Here, we use a microfluidic device to characterize the dynamics of “jamming,” or vaso-occlusion, in physiologically relevant conditions, by measuring a biophysical parameter that quantifies the rate of change of the resistance to flow after a sudden deoxygenation event. Our studies show that this single biophysical parameter could be used to distinguish patients with poor outcomes from those with good outcomes, unlike existing laboratory tests. This biophysical indicator could therefore be used to guide the timing of clinical interventions, to monitor the progression of the disease, and to measure the efficacy of drugs, transfusion, and novel small molecules in an ex vivo setting.

Actin network growth under load O. Campàs, L. Mahadevan, and J-F. Joanny,  Biophysical Journal , 102, 1049-1058, 2012.
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Many processes in eukaryotic cells, including the crawling motion of the whole cell, rely on the growth of branched actin networks from surfaces. In addition to their well-known role in generating propulsive forces, actin networks can also sustain substantial pulling loads thanks to their persistent attachment to the surface from which they grow. The simultaneous network elongation and surface attachment inevitably generate a force that opposes network growth. Here, we study the local dynamics of a growing actin network, accounting for simultaneous network elongation and surface attachment, and show that there exist several dynamical regimes that depend on both network elasticity and the kinetic parameters of actin polymerization. We characterize this in terms of a phase diagram and provide a connection between mesoscopic theories and the microscopic dynamics of an actin network at a surface. Our framework predicts the onset of instabilities that lead to the local detachment of the network and translate to oscillatory behavior and waves, as observed in many cellular phenomena and in vitro systems involving actin network growth, such as the saltatory dynamics of actin-propelled oil drops.

Minimal surfaces bounded by elastic lines L. Giomi and L. Mahadevan, Proceedings of the Royal Society of London (A) , 468, 1851-1864, 2012.
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In mathematics, the classical Plateau problem consists of finding the surface of least area that spans a given rigid boundary curve. A physical realization of the problem is obtained by dipping a stiff wire frame of some given shape in soapy water and then removing it; the shape of the spanning soap film is a solution to the Plateau problem. But what happens if a soap film spans a loop of inextensible but flexible wire? We consider this simple query that couples Plateau’s problem to Euler’s Elastica: a special class of twist-free curves of given length that minimize their total squared curvature energy. The natural marriage of two of the oldest geometrical problems linking physics and mathematics leads to a quest for the shape of a minimal surface bounded by an elastic line: the Euler–Plateau problem. We use a combination of simple physical experiments with soap films that span soft filaments and asymptotic analysis combined with numerical simulations to explore some of the richness of the shapes that result. Our study raises questions of intrinsic interest in geometry and its natural links to a range of disciplines, including materials science, polymer physics, architecture and even art.

Soft catenaries K. Kamrin and L. Mahadevan,  Journal of Fluid Mechanics  691, 165-177, 2012.
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The branch with the furthest reach Z. Wei, S. Mandre and L. Mahadevan,  Europhysics Letters , 97, 14005, 2012.
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How should a given amount of material be moulded into a cantilevered beam clamped at one end, so that it will have the furthest horizontal reach? Here, we formulate and solve this variational problem for the optimal variation of the cross-section area of a heavy cantilevered beam with a given volume V , Young’s modulus E, and density ρ, subject to gravity g. We find that the cross-sectional area should vary according a universal profile that is independent of material parameters, with both the length and maximum reach-out distance of the branch that scale as (EV /ρg) 1/4 , with a universal self-similar shape at the tip with the area of cross-section a ∼ s 3 , s being the distance from the tip, consistent with earlier observations of tree branches, but with a different local interpretation than given before. A simple experimental realization of our optimal beam shows that our result compares favorably with that of our observations. Our results for the optimal design of slender structures with the longest reach are valid for cross-sections of arbitrary shape that can be solid or hollow and thus relevant for a range of natural and engineered systems.

2011

The Foppl-von Karman equations for plates with incompatible strains M. Lewicka, L. Mahadevan, and M. Pakzad,  Proceedings of the Royal Society, Lond. (A) , 467, 402-426, 2011.
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We provide a derivation of the Föppl-von Kármán equations for the shape of and stresses in an elastic plate with incompatible or residual strains. These might arise from a range of causes: inhomogeneous growth, plastic deformation, swelling or shrinkage driven by solvent absorption. Our analysis gives rigorous bounds on the convergence of the threedimensional equations of elasticity to the low-dimensional description embodied in the plate-like description of laminae and thus justifies a recent formulation of the problem to the shape of growing leaves. It also formalizes a procedure that can be used to derive other low-dimensional descriptions of active materials with complex non-Euclidean geometries

Hydrodynamics of writing with ink
J. Kim, M-W. Moon, K-R. Lee, L. Mahadevan, and H-Y. Kim, Physical Review Letters,  107, 264502, 2011. 
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Evolution of spur-length diversity in Aquilegia petals is achieved solely through cell-shape anisotropy J. R. Puzey, S.J. Gerbode, S.A. Hodges, E.M. Kramer and L. Mahadevan,  Proceedings of the Royal Society (B) , 279, 1640-1645, 2011.
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The role of petal spurs and specialized pollinator interactions has been studied since Darwin. Aquilegia petal spurs exhibit striking size and shape diversity, correlated with specialized pollinators ranging from bees to hawkmoths in a textbook example of adaptive radiation. Despite the evolutionary significance of spur length, remarkably little is known about Aquilegia spur morphogenesis and its evolution. Using experimental measurements, both at tissue and cellular levels, combined with numerical modelling, we have investigated the relative roles of cell divisions and cell shape in determining the morphology of the Aquilegia petal spur. Contrary to decades-old hypotheses implicating a discrete meristematic zone as the driver of spur growth, we find that Aquilegia petal spurs develop via anisotropic cell expansion. Furthermore, changes in cell anisotropy account for 99 per cent of the spur-length variation in the genus, suggesting that the true evolutionary innovation underlying the rapid radiation of Aquilegia was the mechanism of tuning cell shape.

Forced tearing of ductile and brittle thin sheets T. Tallinen and L. Mahadevan,  Physical Review Letters , 107, 245502, 2011.
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Tearing a thin sheet by forcing a rigid object through it leads to complex crack morphologies; a single oscillatory crack arises when a tool is driven laterally through a brittle sheet, while two diverging cracks and a series of concertinalike folds forms when a tool is forced laterally through a ductile sheet. On the other hand, forcing an object perpendicularly through the sheet leads to radial petallike tears in both ductile and brittle materials. To understand these different regimes we use a combination of experiments, simulations, and simple theories. In particular, we describe the transition from brittle oscillatory tearing via a single crack to ductile concertina tearing with two tears by deriving laws that describe the crack paths and wavelength of the concertina folds and provide a simple phase diagram for the morphologies in terms of the material properties of the sheet and the relative size of the tool.

A simple model for nanofiber formation by rotary jet-spinning P. Mellado, H.A. McIlwee, M.R. Badrossamay, J.A. Goss, L. Mahadevan, and K.K. Parker,  Applied Physics Letters ., 99, 203107, 2011.
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Nanofibers are microstructured materials that span a broad range of applications from tissue engineering scaffolds to polymer transistors. An efficient method of nanofiber production is rotary jet-spinning (RJS), consisting of a perforated reservoir rotating at high speeds along its axis of symmetry, which propels a liquid, polymeric jet out of the reservoir orifice that stretches, dries, and eventually solidifies to form nanoscale fibers. We report a minimal scaling framework complemented by a semi-analytic and numerical approach to characterize the regimes of nanofiber production, leading to a theoretical model for the fiber radius consistent with experimental observations. In addition to providing a mechanism for the formation of nanofibers, our study yields a phase diagram for the design of continuous nanofibers as a function of process parameters with implications for the morphological quality of fibers.

New encoding schemes with infofuses K.M. Park, C. Kim, S.W. Thomas III, H.J. Yoon, G. Morrison, L. Mahadevan, and G.M. Whitesides,  Advanced Matererials , 23, 4851-4856, 2011.
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Information technology is an area of such broad importance that almost all new methodologies fi nd uses. [1] Most information derived from chemistry, and especially from some form of analysis, proceeds by a path in which a sensor (e.g., an analytical instrument) using electrical power generates information, which is then encoded and transmitted in a separate step, again using electrical power, to a separate unit, which may be local or distant, for processing and interpretation. We [2,3] and others [4–7] are exploring schemes in which information is transmitted directly, without using electrical energy. Such schemes have the potential to be useful where electrical power is not reliably available or where other constraints (e.g., size) argue for other types of solutions.

Robust error correction in info fuses G. Morrison, S.W. Thomas III, C. N. LaFratta, J. Guo, M.A. Palacios, S. Sonkusale, D.R. Walt, G.M. Whitesides and L. Mahadevan,  Proceedings of the Royal Society (A) , 468, 361-377, 2011.
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An infofuse is a combustible fuse in which information is encoded through the patterning of metallic salts, with transmission in the optical range simply associated with burning. The constraints, advantages and unique error statistics of physical chemistry require us to rethink coding and decoding schemes for these systems. We take advantage of the non-binary nature of our signal with a single bit representing one of N = 7 states to produce a code that, using a single or pair of intensity thresholds, allows the recovery of the intended signal with an arbitrarily high recovery probability, given reasonable assumptions about the distribution of errors in the system. An analysis of our experiments with infofuses shows that the code presented is consistent with these schemes, and encouraging for the field of chemical communication and infochemistry given the vast permutations and combinations of allowable nonbinary signals

Shock driven jamming and periodic fracture of particulate rafts M. M. Bandi, T. Tallinen, L. Mahadevan,  Europhysics Letters Journal , 96, 36008, 2011.
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A tenuous monolayer of hydrophobic particles at the air-water interface often forms a scum or raft. When such a monolayer is disturbed by the localized introduction of a surfactant droplet, a radially divergent surfactant shock front emanates from the surfactant origin and packs the particles into a jammed, compact, annular band with a packing fraction that saturates at a peak packing fraction φ ∗ . As the resulting two-dimensional, disordered elastic band grows with time and is driven radially outwards by the surfactant, it fractures to form periodic triangular cracks with robust geometrical features. We find that the number of cracks N and the compaction band radius R ∗ at fracture onset vary monotonically with the initial packing fraction (φinit). However, the compaction band’s width W∗ is constant for all φinit. A simple geometric theory that treats the compaction band as an elastic annulus, and accounts for mass conservation allows us to deduce that N ≃ 2πR∗ /W∗ ≃ 4πφRCP /φinit, a result we verify both experimentally and numerically. We show that the essential ingredients for this phenomenon are an initially low enough particulate packing fraction that allows surfactant-driven advection to cause passive jamming and eventual fracture of the hydrophobic particulate interface.

Multistability of spontaneously curved anisotropic strips L. Giomi, L. Mahadevan,  Proceedings of the Royal Society (A) , 468, 511-530, 2011.
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Multi-stable structures are objects with more than one stable conformation, exemplified by the simple switch. Continuum versions are often elastic composite plates or shells, such as the common measuring tape or the slap bracelet, both of which exhibit two stable configurations: rolled and unrolled. Here, we consider the energy landscape of a general class of multi-stable anisotropic strips with spontaneous Gaussian curvature. We show that while strips with non-zero Gaussian curvature can be bistable, and strips with positive spontaneous curvature are always bistable, independent of the elastic moduli, strips of spontaneous negative curvature are bistable only in the presence of spontaneous twist and when certain conditions on the relative stiffness of the strip in tension and shear are satisfied. Furthermore, anisotropic strips can become tristable when their bending rigidity is small. Our study complements and extends the theory of multi-stability in anisotropic shells and suggests new design criteria for these structures.

Buckling of a thin-layer Couette flow
A. Slim, J. Teichman, L. Mahadevan,  Journal of Fluid Mechanics,  1-24, 2011. 
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Planar controlled gliding, tumbling and descent.
P. Paoletti and L. Mahadevan,  Journal of Fluid Mechanics,  698, 489-516, 2011. 
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Probability, geometry and dynamics in the toss of a thick coin. E-H. Yong, L. Mahadevan,   American Journal of Physics  79(12):1195-1201, 2011.
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When a thick cylindrical coin is tossed in the air and lands without bouncing on an inelastic substrate, it ends up on its face or its side. We account for the rigid body dynamics of spin and precession and calculate the probability distribution of heads, tails, and sides for a thick coin as a function of its dimensions and the distribution of its initial conditions. Our theory yields a simple expression for the aspect ratio of homogeneous coins with a prescribed frequency of heads or tails compared to sides, which we validate using data from the results of tossing coins of different aspect ratios.

On the growth and form of the gut T. Savin, N.A. Kurpios, A.E. Shyer, P. Florescu, H. Liang, L. Mahadevan & C.J. Tabin,  Nature  476:57-62, 2011.
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The developing vertebrate gut tube forms a reproducible looped pattern as it grows into the body cavity. Here we use developmental experiments to eliminate alternative models and show that gut looping morphogenesis is driven by the homogeneous and isotropic forces that arise from the relative growth between the gut tube and the anchoring dorsal mesenteric sheet, tissues that grow at different rates. A simple physical mimic, using a differentially strained composite of a pliable rubber tube and a soft latex sheet is consistent with this mechanism and produces similar patterns. We devise a mathematical theory and a computational model for the number, size and shape of intestinal loops based solely on the measurable geometry, elasticity and relative growth of the tissues. The predictions of our theory are quantitatively consistent with observations of intestinal loops at different stages of development in the chick embryo. Our model also accounts for the qualitative and quantitative variation in the distinct gut looping patterns seen in a variety of species including quail, finch and mouse, illuminating how the simple macroscopic mechanics of differential growth drives the morphology of the developing gut.

Dynamic instability of a growing adsorbed polymorphic filament S. Zapperi and L. Mahadevan,  Biophysical Journal  101:267-275, 2011.
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The intermittent transition between slow growth and rapid shrinkage in polymeric assemblies is termed ‘‘dynamic instability’’, a feature observed in a variety of biochemically distinct assemblies including microtubules, actin, and their bacterial analogs. The existence of this labile phase of a polymer has many functional consequences in cytoskeletal dynamics, and its repeated appearance suggests that it is relatively easy to evolve. Here, we consider the minimal ingredients for the existence of dynamic instability by considering a single polymorphic filament that grows by binding to a substrate, undergoes a conformation change, and may unbind as a consequence of the residual strains induced by this change. We identify two parameters that control the phase space of possibilities for the filament: a structural mechanical parameter that characterizes the ratio of the bond strengths along the filament to those with the substrate (or equivalently the ratio of longitudinal to lateral interactions in an assembly), and a kinetic parameter that characterizes the ratio of timescales for growth and conformation change. In the deterministic limit, these parameters serve to demarcate a region of uninterrupted growth from that of collapse. However, in the presence of disorder in either the structural or the kinetic parameter the growth and collapse phases can coexist where the filament can grow slowly, shrink rapidly, and transition between these phases, thus exhibiting dynamic instability. We exhibit the window for the existence of dynamic instability in a phase diagram that allows us to quantify the evolvability of this labile phase.

Probability, physics, and the coin toss
L. Mahadevan and E-H. Yong,  Physics Today  July 2011 66-67. 
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Painting with drops, jets, and sheets
A. Herczynski, C. Cernuschi, and L. Mahadevan,  Physics Today  June 2011, 31-36. 
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Excitable patterns in active nematics L. Giomi, L. Mahadevan, B. Chakraborty, and M. F. Hagan,  Physical Review Letters , 106, 218101, 2011.
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We analyze a model of mutually propelled filaments suspended in a two-dimensional solvent. The system undergoes a mean-field isotropic-nematic transition for large enough filament concentrations, and the nematic order parameter is allowed to vary in space and time. We show that the interplay between nonuniform nematic order, activity, and flow results in spatially modulated relaxation oscillations, similar to those seen in excitable media. In this regime the dynamics consists of nearly stationary periods separated by ‘‘bursts’’ of activity in which the system is elastically distorted and solvent is pumped throughout. At even higher activity, the dynamics becomes chaotic

The shallow turn of a worm D. Kim, S. Park, L. Mahadevan and J. Shin,  Journal of Experimental Biology , 214, 1554-1559, 2011.
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When crawling on a solid surface, the nematode Caenorhabditis elegans (C. elegans) moves forward by propagating sinusoidal dorso-ventral retrograde contraction waves. A uniform propagating wave leads to motion that undulates about a straight line. When C. elegans turns as it forages or navigates its environment, it uses several different strategies of reorientation. These modes include the well-known omega turn, in which the worm makes a sharp angle turn forming an -shape, and the reversal, in which the worm draws itself backwards. In these two modes of reorientation, C. elegans strongly disrupts its propagating sinusoidal wave, either in form or in direction, leading to abrupt directional change. However, a third mode of reorientation, the shallow turn, involves a gentler disruption of the locomotory gait. Analyzing the statistics of locomotion suggests that the shallow turn is by far the most frequent reorienting maneuver in navigation in the absence of food. We show that the worm executes a shallow turn by modulating the amplitude and wavelength of its curvature during forward movement, and provide a minimal description of the process using a three-parameter mathematical model. The results of our study augment the understanding of how these parameters are controlled at the neuromotor circuit level.

Unfolding the sulcus E. Hohlfeld and L. Mahadevan,  Physical Review Letters , 106, 105702, 2011.
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Sulci are localized furrows on the surface of soft materials that form by a compression-induced instability. We unfold this instability by breaking its natural scale and translation invariance, and compute a limiting bifurcation diagram for sulcfication showing that it is a scale-free, subcritical nonlinear instability. In contrast with classical nucleation, sulcification is continuous, occurs in purely elastic continua and is structurally stable in the limit of vanishing surface energy. During loading, a sulcus nucleates at a point with an upper critical strain and an essential singularity in the linearized spectrum. On unloading, it quasistatically shrinks to a point with a lower critical strain, explained by breaking of scale symmetry. At intermediate strains the system is linearly stable but nonlinearly unstable with no energy barrier. Simple experiments confirm the existence of these two critical strains.

How wet paper curls E. Reyssat and L. Mahadevan,  Europhysics Letters , 93, 54001, 2011.
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When a piece of tracing paper is placed gently on the surface of a bath of water, it rapidly curls up from one edge and rolls up due to the swelling of the side in contact with water. With time, as the swelling front propagates through the thickness of the paper, the paper gradually uncurls itself and eventually straightens out. We analyze the experimental dynamics of rolling and unrolling of the paper and complement these with a minimal theory that explains the basic observations. Our study might be useful in the context of designing biomimetic devices that work as actuators or harness energy from humidity variations.

Asymmetric network connectivity using weighted harmonic averages G. Morrison and L. Mahadevan,  Europhysics Letters , 93, 40002, 2011.
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We propose a non-metric measure of the “closeness” felt between two nodes in an undirected, weighted graph using a simple weighted harmonic average of connectivity, that is a realvalued Generalized Erd¨os Number (GEN). While our measure is developed with a collaborative network in mind, the approach can be of use in a variety of artificial and real-world networks. We are able to distinguish between network topologies that standard distance metrics view as identical, and use our measure to study some simple analytically tractable networks. We show how this might be used to look at asymmetry in authorship networks such as those that inspired the integer Erd¨os numbers in mathematical coauthorships. We also show the utility of our approach to devise a ratings scheme that we apply to the data from the NetFlix prize, and find a significant improvement using our method over a baseline

Growth, geometry and mechanics of the blooming lily H-Y. Liang and L. Mahadevan,  Proceedings of the National Academy of Sciences , 108, 5516-21, 2011.
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Despite the common use of the blooming metaphor, its floral inspiration remains poorly understood. Here we study the physical process of blooming in the asiatic lily Lilium casablanca. Our observations show that the edges of the petals wrinkle as the flower opens, suggesting that differential growth drives the deployment of these laminar shell-like structures. We use a combination of surgical manipulations and quantitative measurements to confirm this hypothesis and provide a simple theory for this change in the shape of a doubly curved thin elastic shell subject to differential growth across its planform. Our experiments and theory overturn previous hypotheses that suggest that blooming is driven by differential growth of the inner layer of the petals and in the midrib by providing a qualitatively different paradigm that highlights the role of edge growth. This functional morphology suggests new biomimetic designs for deployable structures using boundary or edge actuation rather than the usual bulk or surface actuation.

Structural dynamics of an actin spring L. Mahadevan, C. Riera and J. Shin  Biophysical Journal , 100, 839-44, 2011.
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Actin-based motility in cells is usually associated with either polymerization/depolymerization in the presence of cross-linkers or contractility in the presence of myosin motors. Here, we focus on a third distinct mechanism involving actin in motility, seen in the dynamics of an active actin spring that powers the acrosomal reaction of the horseshoe crab (Limulus polyphemus) sperm. During this process, a 60-mm bent and twisted bundle of cross-linked actin uncoils and becomes straight in a few seconds in the presence of Ca2þ. This straightening, which occurs at a constant velocity, allows the acrosome to forcefully penetrate the egg. Synthesizing ultrastructural information with the kinetics, energetics, and imaging of calcium binding allows us to construct a dynamical theory for this mechanochemical engine consistent with our experimental observations. It also illuminates the general mechanism by which energy may be stored in conformational changes and released cooperatively in ordered macromolecular assemblies

Elastohydrodynamics of wet bristles, carpets and brushes. A. Gopinath and L. Mahadevan,  Proceedings of the Royal Society of London (A) , 467, 1665-1685, 2011.
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Surfaces covered by bristles, hairs, polymers and other filamentous structures arise in a variety of natural settings in science such as the active lining of many biological organs, e.g. lungs, reproductive tracts, etc., and have increasingly begun to be used in technological applications. We derive an effective field theory for the elastohydrodynamics of ordered brushes and disordered carpets that are made of a large number of elastic filaments grafted on to a substrate and interspersed in a fluid. Our formulation for the elastohydrodynamic response of these materials leads naturally to a set of constitutive equations coupling bed deformation to fluid flow, accounts for the anisotropic properties of the medium, and generalizes the theory of poroelasticity to these systems. We use the effective medium equations to study three canonical problems—the normal settling of a rigid sphere onto a carpet, the squeeze flow in a carpet and the tangential shearing motion of a rigid sphere over the carpet, all problems of relevance in mechanosensation in biology with implications for biomimetic devices.

2010

A generalized theory of viscous and inviscid flutter S. Mandre and L. Mahadevan,  Proceedings of the Royal Society of London (A) , 466, 141-156, 2010.
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We present a unified theory of flutter in inviscid and viscous flows interacting with flexible structures based on the phenomenon of 1 : 1 resonance. We show this by treating four extreme cases corresponding to viscous and inviscid flows in confined and unconfined flows. To see the common mechanism clearly, we consider the limit when the frequencies of the first few elastic modes are closely clustered and small relative to the convective fluid time scale. This separation of time scales slaves the hydrodynamic force to the instantaneous elastic displacement and allows us to calculate explicitly the dependence of the critical flow speed for flutter on the various problem parameters. We show that the origin of the instability lies in the coincidence of the real frequencies of the first two modes at a critical flow speed beyond which the frequencies become complex, thus making the system unstable to oscillations. This critical flow speed depends on the difference between the frequencies of the first few modes and the nature of the hydrodynamic coupling between them. Our generalized framework applies to a range of elastohydrodynamic systems and further extends the Benjamin–Landahl classification of fluid–elastic instabilities.

Control of shape and size of nanopillar assembly by adhesion-mediated elastocapillary interaction S. Kang, B. Pokroy, L. Mahadevan and J. Aizenberg,  ACS-Nano , 4, 11, 6323-31, 2010.
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Control of self-organization of nanofibers into regular clusters upon evaporation-induced assembly is receiving increasing attention due to the potential importance of this process in a range of applications including particle trapping, adhesives, and structural color. Here we present a comprehensive study of this phenomenon using a periodic array of polymeric nanopillars with tunable parameters as a model system to study how geometry, mechanical properties, as well as surface properties influence capillary-induced self-organization. In particular, we show that varying the parameters of the building blocks of self-assembly provides us with a simple means of controlling the size, chirality, and anisotropy of complex structures. We observe that chiral assemblies can be generated within a narrow window for each parameter even in the absence of chiral building blocks or a chiral environment. Furthermore, introducing anisotropy in the building blocks provides a way to control both the chirality and the size of the assembly. While capillary-induced self-assembly has been studied and modeled as a quasi-static process involving the competition between only capillary and elastic forces, our results unequivocally show that both adhesion and kinetics are equally important in determining the final assembly. Our findings provide insight into how multiple parameters work together in capillary-induced self-assembly and provide us with a diverse set of options for fabricating a variety of nanostructures by self-assembly.

Physiological and pathological population dynamics of circulating human red blood cells J. Higgins and L. Mahadevan,  Proceedings of the National Academy of Sciences , 107, 20587-92, 2010.
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The systems controlling the number, size, and hemoglobin concentrations of populations of human red blood cells (RBCs), and their dysregulation in anemia, are poorly understood. After release from the bone marrow, RBCs undergo reduction in both volume and total hemoglobin content by an unknown mechanism [Lew VL, et al. (1995) Blood 86:334–341; Waugh RE, et al. (1992) Blood 79:1351–1358]; after ∼120 d, responding to an unknown trigger, they are removed. We used theory from statistical physics and data from the hospital clinical laboratory [d’Onofrio G, et al. (1995) Blood 85:818–823] to develop a master equation model for RBC maturation and clearance. The model accurately identifies patients with anemia and distinguishes thalassemia-trait anemia from irondeficiency anemia. Strikingly, it also identifies many pre-anemic patients several weeks before anemia becomes clinically detectable. More generally we illustrate how clinical laboratory data can be used to develop and to test a dynamic model of human pathophysiology with potential clinical utility.

Why subduction zones are curved L. Mahadevan, R. Bendick and H-Y. Liang,  Tectonics , 29,TC6002, 2010.
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We give an explanation for the polarity, localization, shape, size, and initiation of subduction zones on Earth. By considering a soft, thin, curved lithospheric cap with either elastic or viscous rheology supported by a thick, nearly incompressible mantle, we find two different characteristic subduction geometries arise depending on boundary conditions: (1) plate boundaries where subduction results primarily from the gravitational body force (free subduction) have characteristic plate lengths and form arc‐shaped dimpled segments resulting from the competition between bending and stretching in edge buckling modes of thin spherical shells, and (2) subduction zones due to localized applied loads that push one slab of thin, positively buoyant lithosphere beneath an overriding plate (forced subduction) form localized straight segments, consistent with the deformation of indented spherical shells. Both types of subduction are nonlinear subcritical instabilities, so small perturbations in the mechanical properties of the lithosphere have pronounced effects on subduction initiation and evolution. Yet in both cases, geometric relationships determined by the shape of the Earth itself play the most critical role in controlling the basic morphology and characteristic length scales of subduction zones

Geometry, mechanics and electronics of singular structures in graphene V. Pereira, H-Y Liang, A. Castro-Neto and L. Mahadevan,  Physical Review Letters , 105, 156603, 2010.
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As the thinnest atomic membrane, graphene presents an opportunity to combine geometry, elasticity, and electronics at the limits of their validity. We describe the transport and electronic structure in the neighborhood of conical singularities, the elementary excitations of the ubiquitous wrinkled and crumpled graphene. We use a combination of atomistic mechanical simulations, analytical geometry, and transport calculations in curved graphene, and exact diagonalization of the electronic spectrum to calculate the effects of geometry on electronic structure, transport, and mobility in suspended samples, and how the geometry-generated pseudomagnetic and pseudoelectric fields might disrupt Landau quantization.

Cooperative adhesion and friction of compliant nanohairs  L. Ge, A. Goyal, R. Shi, L. Mahadevan, P. Ajayan and A. Dhinojwala,  Nanoletters , 10, 4509, 2010.
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The adhesion and friction behavior of soft materials, including compliant brushes and hairs, depends on the temporal and spatial evolution of the interfaces in contact. For compliant nanofibrous materials, the actual contact area individual fibers make with surfaces depends on the preload applied upon contact. Using in situ microscopy observations of preloaded nanotube hairs, we show how nanotubes make cooperative contact with a surface by buckling and conforming to the surface topography. The overall adhesion of compliant nanohairs increases with increasing preload as nanotubes deform and continuously add new side-wall contacts with the surface. Electrical resistance measurements indicate significant hysteresis in the relative contact area. Contact area increases with preload (or stress) and decreases suddenly during unloading, consistent with strong adhesion observed for these complaint nanohairs.

Nanopottery: coiling of electrospun polymer nanofibers H-Y. Kim, M. Lee, K-J. Park, S. Kim and L. Mahadevan,  Nanoletters , 10, 2138, 2010.
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The buckling, folding, and coiling of thin sheets and filaments of solids and fluids take place on length scales spanning several orders of magnitude, in phenomena ranging from orogenesis in geophysics to materials processing and soft-matter physics. For example, when an elastic rope is fed uniformly toward a horizontal plane, it first buckles and eventually coils into a spool that is deposited onto the plane.1 A similar phenomenon also occurs when a slender viscous fluid jet impinges onto a horizontal plane and leads to the deposition of a liquid rope coil.2 In either case, although the scale of the coil and the speed of coiling are determined by the balance between the internal elastic or viscous forces that resist deformation and a combination of inertia and gravity, the basic phenomenology is a consequence of geometry which favors bending deformations over stretching modes. Here, we consider the spon

Statistical mechanics of developable ribbons L. Giomi and L. Mahadevan,  Physical Review Letters , 104, 238104, 2010.
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We investigate the statistical mechanics of long developable ribbons of finite width and very small thickness. The constraint of isometric deformations in these ribbonlike structures that follows from the geometric separation of scales introduces a coupling between bending and torsional degrees of freedom. Using analytical techniques and Monte Carlo simulations, we find that the tangent-tangent correlation functions always exhibit an oscillatory decay at any finite temperature implying the existence of an underlying helical structure even in the absence of a preferential zero-temperature twist. In addition, the persistence length is found to be over 3 times larger than that of a wormlike chain having the same bending rigidity. Our results are applicable to many ribbonlike objects in polymer physics and nanoscience that cannot be described by the classical wormlike chain model.

Influence of feedback on the stochastic evolution of simple climate systems L. Mahadevan and J. Deutch,  Proceedings of the Royal Society of London (A) , 466, 993, 2010.
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We consider the dynamical evolution of a simple climate system that describes the average temperature of the Earth’s atmosphere owing to radiative forcing and coupling to a positive feedback variable such as the concentration of greenhouse gases in the presence of fluctuations. Analysing the resulting stochastic dynamical system shows that, if the temperature relaxes rapidly relative to the concentration, the time-dependent and stationary probability density functions (pdfs) for the temperature rise possess a fat tail. In contrast, if the feedback variable relaxes rapidly relative to the temperature, the pdf has no fat tail, and, instead, the system shows critical slowing down as the singular limit of positive feedback is approached. However, if there is uncertainty in the feedback variable itself, a fat tail can reappear. Our analysis may be generalized to more complex models with similar qualitative results. Our results have policy implications: although fat tails imply that the expectation of plausible damage functions is infinite, the pdfs permit an examination of the trade-off between reducing emissions and reducing the positive feedback gain.

2009

Shape and dynamics of tip-growing cells O. Campas and L. Mahadevan,  Current Biology , 19, 2102, 2009.
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Walled cells have the ability to remodel their shape while sustaining an internal turgor pressure that can reach values up to 10 atmospheres [1–7]. Although it is undisputed that this requires a tight and simultaneous regulation of cell wall assembly and mechanics, previous theoretical studies on tip growth focused either on the mechanical behavior of the cell wall or on its assembly [8–14]. To study the interplay between growth and mechanics in shaping a walled cell, we examine the particularly simple geometry of tip-growing cells [1, 3, 15, 16], which elongate via the assembly and expansion of cell wall in the apical region of the cell. We describe the observed irreversible expansion of the cell wall during growth as the extension of an inhomogeneous viscous fluid shell under the action of turgor pressure, fed by a material source in the neighborhood of the growing tip. This allows us to determine theoretically the radius of the cell and its growth velocity in terms of the turgor pressure and the secretion rate and rheology of the cell wall material. We derive simple scaling laws for the geometry of the cell and find that a single dimensionless parameter, which characterizes the relative roles of cell wall assembly and expansion, is sufficient to explain the observed variability in shapes of tip-growing cells. More generally, our description provides a framework to understand cell growth and remodeling in plants (pollen tubes [17], root hairs, etc. [18]), fungi (hyphal growth [19, 20] and fission and budding yeast [3]), and some bacteria [21], in the context of both tip growth and diffuse growth.

The shape of a long leaf H. Liang and L. Mahadevan,  Proceedings of the National Academy of Sciences (USA) ,106, 22049, 2009.
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Long leaves in terrestrial plants and their submarine counterparts, algal blades, have a typical, saddle-like midsurface and rippled edges. To understand the origin of these morphologies, we dissect leaves and differentially stretch foam ribbons to show that these shapes arise from a simple cause, the elastic relaxation via bending that follows either differential growth (in leaves) or differential stretching past the yield point (in ribbons). We quantify these different modalities in terms of a mathematical model for the shape of an initially flat elastic sheet with lateral gradients in longitudinal growth. By using a combination of scaling concepts, stability analysis, and numerical simulations, we map out the shape space for these growing ribbons and find that as the relative growth strain is increased, a long flat lamina deforms to a saddle shape and/or develops undulations that may lead to strongly localized ripples as the growth strain is localized to the edge of the leaf. Our theory delineates the geometric and growth control parameters that determine the shape space of finite laminae and thus allows for a comparative study of elongated leaf morphology.

Flip-flop-induced relaxation of bending energy: implications for membrane remodeling R. Bruckner, S. Mansy, A. Ricardo, L. Mahadevan, and J. Szostak,  Biophysical Journal , 97, 3113, 2009
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Cellular and organellar membranes are dynamic materials that underlie many aspects of cell biology. Biological membranes have long been thought of as elastic materials with respect to bending deformations. A wealth of theory and experimentation on pure phospholipid membranes provides abundant support for this idea. However, biological membranes are not composed solely of phospholipids—they also incorporate a variety of amphiphilic molecules that undergo rapid transbilayer flip-flop. Here we describe several experimental systems that demonstrate deformation-induced molecular flip-flop. First we use a fluorescence assay to track osmotically controlled membrane deformation in single component fatty acid vesicles, and show that the relaxation of the induced bending stress is mediated by fatty acid flip-flop. We then look at two-component phospholipid/cholesterol composite vesicles. We use NMR to show that the steady-state rate of interleaflet diffusion of cholesterol is fast relative to biological membrane remodeling. We then use a Fo¨rster resonance energy transfer assay to detect the transbilayer movement of cholesterol upon deformation. We suggest that our results can be interpreted by modifying the area difference elasticity model to account for the time-dependent relaxation of bending energy. Our findings suggest that rapid interleaflet diffusion of cholesterol may play a role in membrane remodeling in vivo. We suggest that the molecular characteristics of sterols make them evolutionarily preferred mediators of stress relaxation, and that the universal presence of sterols in the membranes of eukaryotes, even at low concentrations, reflects the importance of membrane remodeling in eukaryotic cells.
Controlling the orientation and synaptic differentiation of myotubes with micropatterned substrates J. Gingras, R. Rioux, D. Cuvelier, N. Geisse, J. Lichtman, G. Whitesides, L. Mahadevan, and J. Sanes,  Biophysical Journa l, 97, 2771, 2009.
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Micropatterned poly(dimethylsiloxane) substrates fabricated by soft lithography led to large-scale orientation of myoblasts in culture, thereby controlling the orientation of the myotubes they formed. Fusion occurred on many chemically identical surfaces in which varying structures were arranged in square or hexagonal lattices, but only a subset of patterned surfaces yielded aligned myotubes. Remarkably, on some substrates, large populations of myotubes oriented at a reproducible acute angle to the lattice of patterned features. A simple geometrical model predicts the angle and extent of orientation based on maximizing the contact area between the myoblasts and patterned topographic surfaces. Micropatterned substrates also provided short-range cues that influenced higher-order functions such as the localization of focal adhesions and accumulation of postsynaptic acetylcholine receptors. Our results represent what we believe is a new approach for musculoskeletal tissue engineering, and our model sheds light on mechanisms of myotube alignment in vivo.

The shape and motion of a ruck in a rug J. Kolinski, P. Aussillous and L. Mahadevan,  Physical Review Letters , 103, 174302, 2009.
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The motion of a ruck in a rug is used as an analogy to explain the role of dislocations in crystalline solids. We take literally one side of this analogy and study the shape and motion of a bump, wrinkle or ruck in a thin sheet in partial contact with a rough substrate in a gravitational field. Using a combination of experiments, scaling analysis and numerical solutions of the governing equations, we quantify the static shape of a ruck on a horizontal plane. When the plane is inclined, the ruck becomes asymmetric and moves by rolling only when the inclination of the plane reaches a critical angle, at a speed determined by a simple power balance. We find that the angle at which rolling starts is larger than the angle at which the ruck stops; i.e., static rolling friction is larger than dynamic rolling friction. We conclude with a generalization of our results to wrinkles in soft adherent extensible films.

Infochemistry: encoding information as optical pulses using droplets in a microfluidic device M. Hashimoto, J. Feng, R. York, A. Ellerbee, G. Morrison, S. Thomas,  L. Mahadevan, and G. Whitesides,  Journal of the American Chemical Society , 131, 12420, 2009.
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This article describes a new procedure for generating and transmitting a messagesa sequence of optical pulsessby aligning a mask (an opaque sheet containing transparent “windows”) below a microfluidic channel in which flows an opaque continuous fluid containing transparent droplets. The optical mask encodes the message as a unique sequence of windows that can transmit or block light; the flow of transparent droplets in the channel converts this message into a sequence of optical pulses. The properties of the windows on the mask (e.g., their size, wavelength of transmittance, orientation of polarization) determine the information carried in these optical pulses (e.g., intensity, color, polarization). The structure of a transmitted signal depends on the number and spacing of droplets in the channel. Fourier transformation can deconvolve superimposed signals created by the flow of multiple droplets into the message that a single droplet would transmit. The research described in this contribution explores a new field at the intersection of chemistry, materials science, and information technology: infochemistry.

Animal cell hydraulics G. Charras, T. Mitchison and L. Mahadevan,  Journal of Cell Science , 122, 3233, 2009.
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Water is the dominant ingredient of cells and its dynamics are crucial to life. We and others have suggested a physical picture of the cell as a soft, fluid-infiltrated sponge, surrounded by a water-permeable barrier. To understand water movements in an animal cell, we imposed an external, inhomogeneous osmotic stress on cultured cancer cells. This forced water through the membrane on one side, and out on the other. Inside the cell, it created a gradient in hydration, that we visualized by tracking cellular responses using natural organelles and artificially introduced quantum dots. The dynamics of these markers at short times were the same for normal and metabolically poisoned cells, indicating that the cellular responses are primarily physical rather than chemical. Our finding of an internal gradient in hydration is inconsistent with a continuum model for cytoplasm, but consistent with the sponge model, and implies that the effective pore size of the sponge is small enough to retard water flow significantly on time scales (~10–100 seconds) relevant to cell physiology. We interpret these data in terms of a theoretical framework that combines mechanics and hydraulics in a multiphase poroelastic description of the cytoplasm and explains the experimentally observed dynamics quantitatively in terms of a few coarse-grained parameters that are based on microscopically measurable structural, hydraulic and mechanical properties. Our fluid-filled sponge model could provide a unified framework to understand a number of disparate observations in cell morphology and motility.

Calcium regulation of an actin spring B. Tam, J. Shin, E. Pfeiffer, P. Matsudaira and L. Mahadevan,  Biophysical Journal , 97, 1125, 2009.
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Calcium is essential for many biological processes involved in cellular motility. However, the pathway by which calcium influences motility, in processes such as muscle contraction and neuronal growth, is often indirect and complex. We establish a simple and direct mechanochemical link that shows how calcium quantitatively regulates the dynamics of a primitive motile system, the actin-based acrosomal bundle of horseshoe crab sperm. The extension of this bundle requires the continuous presence of external calcium. Furthermore, the extension rate increases with calcium concentration, but at a given concentration, we find that the volumetric rate of extension is constant. Our experiments and theory suggest that calcium sequentially binds to calmodulin molecules decorating the actin filaments. This binding leads to a collective wave of untwisting of the actin filaments that drives bundle extension.

Strain induced alignment in collagen gels D. Vader, A. Kabla, D. Weitz and L. Mahadevan,  PLoS One , 4 (6), e5902, 2009.
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Collagen is the most abundant extracellular-network-forming protein in animal biology and is important in both natural and artificial tissues, where it serves as a material of great mechanical versatility. This versatility arises from its almost unique ability to remodel under applied loads into anisotropic and inhomogeneous structures. To explore the origins of this property, we develop a set of analysis tools and a novel experimental setup that probes the mechanical response of fibrous networks in a geometry that mimics a typical deformation profile imposed by cells in vivo. We observe strong fiber alignment and densification as a function of applied strain for both uncrosslinked and crosslinked collagenous networks. This alignment is found to be irreversibly imprinted in uncrosslinked collagen networks, suggesting a simple mechanism for tissue organization at the microscale. However, crosslinked networks display similar fiber alignment and the same geometrical properties as uncrosslinked gels, but with full reversibility. Plasticity is therefore not required to align fibers. On the contrary, our data show that this effect is part of the fundamental non-linear properties of fibrous biological networks.

Cell shape changes indicate a role for extrinsic tensile forces in Drosophila germ-band extension L. Butler, G. Blanchard, A. Kabla, N. Lawrence, D. Welchman, L. Mahadevan, R. Adams and B. Sanson,  Nature Cell Biology , 11(7), 859-64, 2009.
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Drosophila germ-band extension (GBE) is an example of the convergence and extension movements that elongate and narrow embryonic tissues. To understand the collective cell behaviours underlying tissue morphogenesis, we have continuously quantified cell intercalation and cell shape change during GBE. We show that the fast, early phase of GBE depends on cell shape change in addition to cell intercalation. In antero-posterior patterning mutants such as those for the gap gene Krüppel, defective polarized cell intercalation is compensated for by an increase in antero-posterior cell elongation, such that the initial rate of extension remains the same. Spatio-temporal patterns of cell behaviours indicate that an antero-posterior tensile force deforms the germ band, causing the cells to change shape passively. The rate of anteroposterior cell elongation is reduced in twist mutant embryos, which lack mesoderm. We propose that cell shape change contributing to germ-band extension is a passive response to mechanical forces caused by the invaginating mesoderm.

Tissue Tectonics: morphogenetic strain rates, cell shape change and intercalation G. Blanchard, A. Kabla, L. Butler, B. Sanson, N. Gorfinkiel, L. Mahadevan and R. Adams,  Nature Methods , 6(6), 458-64, 2009.
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The dynamic reshaping of tissues during morphogenesis results from a combination of individual cell behaviors and collective cell rearrangements. However, a comprehensive framework to unambiguously measure and link cell behavior to tissue morphogenesis is lacking. Here we introduce such a kinematic framework, bridging cell and tissue behaviors at an intermediate, mesoscopic, level of cell clusters or domains. By measuring domain deformation in terms of the relative motion of cell positions and the evolution of their shapes, we characterized the basic invariant quantities that measure fundamental classes of cell behavior, namely tensorial rates of cell shape change and cell intercalation. In doing so we introduce an explicit definition of cell intercalation as a continuous process. We mapped strain rates spatiotemporally in three models of tissue morphogenesis, gaining insight into morphogenetic mechanisms. Our quantitative approach has broad relevance for the precise characterization and comparison of morphogenetic phenotypes.

Hygromorphs: from pine cones to biomimetic bilayers E. Reyssat and L. Mahadevan,  Journal of the Royal Society, Interface , 6, 951-957, 2009.
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We consider natural and artificial hygromorphs, objects that respond to environmental humidity by changing their shape. Using the pine cone as an example that opens when dried and closes when wet, we quantify the geometry, mechanics and dynamics of closure and opening at the cell, tissue and organ levels, building on our prior structural knowledge. A simple scaling theory allows us to quantify the hysteretic dynamics of opening and closing. We also show how simple bilayer hygromorphs of paper and polymer show similar behaviour that can be quantified via a theory which couples fluid transport in a porous medium and evaporative flux to mechanics and geometry. Our work unifies varied observations of natural hygromorphs and suggests interesting biomimetic analogues, which we illustrate using an artificial flower with a controllable blooming and closing response.

Botanical ratchets I. Kulic, M. Mani, H. Mohrbach, R. Thaokar, L. Mahadevan,  Proceedings of the Royal Society of London (B), Biological Sciences , 276, 2243-47, 2009.
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Ratcheting surfaces are a common motif in nature and appear in plant awns and grasses. They are known to proffer selective advantages for seed dispersion and burial. In two simple model experiments, we show that these anisotropically toothed surfaces naturally serve as motion rectifiers and generically move in a unidirectional manner, when subjected to temporally and spatially symmetric excitations of various origins. Using a combination of theory and experiment, we show that a linear relationship between awn length and ratchet efficiency holds under biologically relevant conditions. Grass awns can thus efficiently transform non-equilibrium environmental stresses from such sources as humidity variations into useful work and directed motion using their length as a fluctuation amplifier, yielding a selective advantage to these organelles in many plant species.

Statistical dynamics of flowing red blood cells by morphological image processing J. Higgins, D. Eddington, S. Bhatia and L. Mahadevan,  PLoS Computational Biology , 5, e1000288, 2009.
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Blood is a dense suspension of soft non-Brownian cells of unique importance. Physiological blood flow involves complex interactions of blood cells with each other and with the environment due to the combined effects of varying cell concentration, cell morphology, cell rheology, and confinement. We analyze these interactions using computational morphological image analysis and machine learning algorithms to quantify the non-equilibrium fluctuations of cellular velocities in a minimal, quasi-two-dimensional microfluidic setting that enables high-resolution spatio-temporal measurements of blood cell flow. In particular, we measure the effective hydrodynamic diffusivity of blood cells and analyze its relationship to macroscopic properties such as bulk flow velocity and density. We also use the effective suspension temperature to distinguish the flow of normal red blood cells and pathological sickled red blood cells and suggest that this temperature may help to characterize the propensity for stasis in Virchow’s Triad of blood clotting and thrombosis.

Self-organization of a mesoscale bristle into ordered hierarchical helical assemblies B. Pokroy, S. Kang, L. Mahadevan, and J. Aizenberg,  Science , 323, 237, 2009.
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Mesoscale hierarchical helical structures with diverse functions are abundant in nature. Here we show how spontaneous helicity can be induced in a synthetic polymeric nanobristle assembling in an evaporating liquid. We use a simple theoretical model to characterize the geometry, stiffness, and surface properties of the pillars that favor the adhesive self-organization of bundles with pillars wound around each other. The process can be controlled to yield highly ordered helical clusters with a unique structural hierarchy that arises from the sequential assembly of self-similar coiled building blocks over multiple length scales. We demonstrate their function in the context of self-assembly into previously unseen structures with uniform, periodic patterns and controlled handedness and as an efficient particle-trapping and adhesive system.

Nonequilibrium scale selection mechanism for columnar jointing L. Goehring L. Mahadevan, and S. Morris,  Proceedings of the National Academy of Sciences (USA) , 106, 387, 2009.
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Crack patterns in laboratory experiments on thick samples of drying cornstarch are geometrically similar to columnar joints in cooling lava found at geological sites such as the Giant’s Causeway. We present measurements of the crack spacing from both laboratory and geological investigations of columnar jointing, and show how these data can be collapsed onto a single master scaling curve. This is due to the underlying mathematical similarity between theories for the cracking of solids induced by differential drying or by cooling. We use this theory to give a simple quantitative explanation of how these geometrically similar crack patterns arise from a single dynamical law rooted in the nonequilibrium nature of the phenomena. We also give scaling relations for the characteristic crack spacing in other limits consistent with our experiments and observations, and discuss the implications of our results for the control of crack patterns in thin and thick solid films.

2008

Elasticity of floppy and stiff random networks M. Wyart, H. Liang, A. Kabla,and L. Mahadevan,  Physical Review Letters , 101, 215501, 2008.
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We study the linear and nonlinear elastic behavior of amorphous systems using a two-dimensional random network of harmonic springs as a model system. A natural characterization of these systems arises in terms of the network coordination (average number of springs per node) relative to that of a marginally rigid network
z: a floppy network has
z < 0, while a stiff network has
z > 0. Under the influence of an externally applied load, we observe that the response of both floppy and stiff networks is controlled by the critical point corresponding to the onset of rigidity. We use numerical simulations to compute the exponents which characterize the shear modulus, the heterogeneity of the response, and the network stiffening as a function of
z and derive these theoretically, thus allowing us to predict aspects of the mechanical response of glasses and fibrous networks.

Quantifying the relation between bond number and myoblast proliferation T. Boontheekul, Hyun-Joon Kong, S. Hsiong, Y-C. Huang, L. Mahadevan, H. Vandenburgh and D. Mooney,  Faraday Discussions , 139, 53, 2008.
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Many functions of the extracellular matrix can be mimicked by small peptide fragments (e.g., arginine–glycine–aspartic acid (RGD) sequence) of the entire molecule, but the presentation of the peptides is critical to their effects on cells. It is likely that some effects of peptide presentation from biomaterials simply relate to the number of bonds formed between cell receptors and the adhesion ligands, but a lack of tools to quantify bond number limits direct investigation of this assumption. The impact of different ligand presentations (density, affinity, and nanoscale distribution) on the proliferation of C2C12 and human primary myoblasts was first examined in this study. Increasing the ligand density or binding affinity led to a similar enhancement in proliferation of C2C12 cells and human primary myoblasts. The nanoscale distribution of clustered RGD ligands also influenced C2C12 cells and human primary myoblast proliferation, but in an opposing manner. A rheological technique and a FRET technique were then utilized to quantify the number of receptor–ligand interactions as a function of peptide presentation. Higher numbers of bonds were formed when the RGD density and affinity were increased, as measured with both techniques, and bond number correlated with cell growth rates. However, the influence of the nanoscale peptide distribution did not appear to be solely a function of bond number. Altogether, these findings provide significant insight to the role of peptide presentation in the regulation of cell proliferation, and the approaches developed in this work may have significant utility in probing how adhesion regulates a variety of other cellular functions and aid in developing design criterion for cell-interactive materials.
Polymer science and biology: structure and dynamics at multiple scales
L. Mahadevan,  Faraday Discussions , 139, 9, 2008. 
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Implications of a poroelastic cytoplasm for the dynamics of animal cell shape T. Mitchison, G. Charras and L. Mahadevan,  Seminars in Cell & Developmental Biology  19, 215, 2008.
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Two views have dominated recent discussions of the physical basis of cell shape change during migration and division of animal cells: the cytoplasm can be modeled as a viscoelastic continuum, and the forces that change its shape are generated only by actin polymerization and actomyosin contractility in the cell cortex. Here, we question both views: we suggest that the cytoplasm is better described as poroelastic, and that hydrodynamic forces may be generally important for its shape dynamics. In the poroelastic view, the cytoplasm consists of a porous, elastic solid (cytoskeleton, organelles, ribosomes) penetrated by an interstitial fluid (cytosol) that moves through the pores in response to pressure gradients. If the pore size is small (30–60 nm), as has been observed in some cells, pressure does not globally equilibrate on time and length scales relevant to cell motility. Pressure differences across the plasma membrane drive blebbing, and potentially other type of protrusive motility. In the poroelastic view, these pressures can be higher in one part of a cell than another, and can thus cause local shape change. Local pressure transients could be generated by actomyosin contractility, or by local activation of osmogenic ion transporters in the plasma membrane. We propose that local activation of Na+/H+ antiporters (NHE1) at the front of migrating cells promotes local swelling there to help drive protrusive motility, acting in combination with actin polymerization. Local shrinking at the equator of dividing cells may similarly help drive invagination during cytokinesis, acting in combination with actomyosin contractility. Testing these hypotheses is not easy, as water is a difficult analyte to track, and will require a joint effort of the cytoskeleton and ion physiology communities.

How kelp produce blade shapes suited to different flow regimes: A new wrinkle M. Koehl, W. Silk, H. Liang and L. Mahadevan,  Integrative and Comparative Biology , 48(6), 834, 2008.
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Synopsis Many species of macroalgae have flat, strap-like blades in habitats exposed to rapidly flowing water, but have wide, ruffled ‘‘undulate’’ blades at protected sites. We used the giant bull kelp, Nereocystis luetkeana, to investigate how these ecomorphological differences are produced. The undulate blades of N. luetkeana from sites with low flow remain spread out and flutter erratically in moving water, thereby not only enhancing interception of light, but also increasing drag. In contrast, strap-like blades of kelp from habitats with rapid flow collapse into streamlined bundles and flutter at low amplitude in flowing water, thus reducing both drag and interception of light. Transplant experiments in the field revealed that shape of the blade in N. luetkeana is a plastic trait. Laboratory experiments in which growing blades from different sites were subjected to tensile forces that mimicked the hydrodynamic drag experienced by blades in different flow regimes showed that change in shape is induced by mechanical stress. During growth experiments in the field and laboratory, we mapped the spatial distribution of growth in both undulate and strap-like blades to determine how these different morphologies were produced. The highest growth rates occur near the proximal ends of N. luetkeana blades of both morphologies, but the rates of transverse growth of narrow, strap-like blades are lower than those of wide, undulate blades. If rates of longitudinal growth at the edges of a blade exceed the rate of longitudinal growth along the midline of the blade, ruffles along the edges of the blade are produced by elastic buckling. In contrast, flat blades are produced when rates of longitudinal growth are similar across the width of a blade. Because ruffles are the result of elastic buckling, a compliant undulate N. luetkeana blade can easily be pushed into different configurations (e.g., the wavelengths of the ruffles along the edges of the blade can change, and the whole blade can twist into left- and right-handed helicoidal shapes), which may enhance movements of the blade in flowing water that reduce self-shading and increase mass exchange along blade surfaces

Dynamics of chromatin decondensation reveals the structural integrity of a mechanically prestressed nucleus  A. Mazumder, T. Roopa, A. Basu, L. Mahadevan, and G. Shivashankar,  Biophysical Journal , 95, 3028, 2008.
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Genome organization within the cell nucleus is a result of chromatin condensation achieved by histone tail-tail interactions and other nuclear proteins that counter the outward entropic pressure of the polymeric DNA. We probed the entropic swelling of chromatin driven by enzymatic disruption of these interactions in isolated mammalian cell nuclei. The large-scale decondensation of chromatin and the eventual rupture of the nuclear membrane and lamin network due to this entropic pressure were observed by fluorescence imaging. This swelling was accompanied by nuclear softening, an effect that we quantified by measuring the fluctuations of an optically trapped bead adhered onto the nucleus. We also measured the pressure at which the nuclear scaffold ruptured using an atomic force microscope cantilever. A simple theory based on a balance of forces in a swelling porous gel quantitatively explains the diffusive dynamics of swelling. Our experiments on decondensation of chromatin in nuclei suggest that its compaction is a critical parameter in controlling nuclear stability

Optimal vein density in artificial and real leaves X. Noblin, L. Mahadevan, I. Coomaraswamy, D. Weitz, N. Holbrook and M. Zwieniecki,  Proceedings of the National Academy of Sciences (USA),  105, 9140, 2008.
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The long evolution of vascular plants has resulted in a tremendous variety of natural networks responsible for the evaporatively driven transport of water. Nevertheless, little is known about the physical principles that constrain vascular architecture. Inspired by plant leaves, we used microfluidic devices consisting of simple parallel channel networks in a polymeric material layer, permeable to water, to study the mechanisms of and the limits to evaporationdriven flow. We show that the flow rate through our biomimetic leaves increases linearly with channel density (1/d) until the distance between channels (d) is comparable with the thickness of the polymer layer (
), above which the flow rate saturates. A comparison with the plant vascular networks shows that the same optimization criterion can be used to describe the placement of veins in leaves. These scaling relations for evaporatively driven flow through simple networks reveal basic design principles for the engineering of evaporation–permeation-driven devices, and highlight the role of physical constraints on the biological design of leaves.

Localized and extended deformations of elastic shells A. Vaziri and L. Mahadevan,  Proceedings of the National Academy of Sciences (USA),  105, 7913, 2008.
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The dried raisin, the crushed soda can, and the collapsed bicycle inner tube exemplify the nonlinear mechanical response of naturally curved elastic surfaces with different intrinsic curvatures to a variety of different external loads. To understand the formation and evolution of these features in a minimal setting, we consider a simple assay: the response of curved surfaces to point indentation. We find that for surfaces with zero or positive Gauss curvature, a common feature of the response is the appearance of faceted structures that are organized in intricate localized patterns, with hysteretic transitions between multiple metastable states. In contrast, for surfaces with negative Gauss curvature the surface deforms nonlocally along characteristic lines that extend through the entire system. These different responses may be understood quantitatively by using numerical simulations and classified qualitatively by using simple geometric ideas. Our ideas have implications for the behavior of small-scale structures.

Signal processing by HOG MAP kinase pathway P. Hersen, M. McClean, L. Mahadevan, and S. Ramanathan,  Proceedings of the National Academy of Sciences (USA),  105, 7165, 2008.
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Signaling pathways relay information about changes in the external environment so that cells can respond appropriately. How much information a pathway can carry depends on its bandwidth. We designed a microfluidic device to reliably change the environment of single cells over a range of frequencies. Using this device, we measured the bandwidth of the Saccharomyces cerevisiae signaling pathway that responds to high osmolarity. This prototypical pathway, the HOG pathway, is shown to act as a low-pass filter, integrating the signal when it changes rapidly and following it faithfully when it changes more slowly. We study the dependence of the pathway’s bandwidth on its architecture. We measure previously unknown bounds on all of the in vivo reaction rates acting in this pathway. We find that the two-component Ssk1 branch of this pathway is capable of fast signal integration, whereas the kinase Ste11 branch is not. Our experimental techniques can be applied to other signaling pathways, allowing the measurement of their in vivo kinetics and the quantification of their information capacity.

Limbless undulatory propulsion on land Z. Guo and L. Mahadevan,  Proceedings of the National Academy of Sciences (USA),  105, 3179, 2008.
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We analyze the lateral undulatory motion of a natural or artificial snake or other slender organism that ‘‘swims’’ on land by propagating retrograde flexural waves. The governing equations for the planar lateral undulation of a thin filament that interacts frictionally with its environment lead to an incomplete system. Closures accounting for the forces generated by the internal muscles and the interaction of the filament with its environment lead to a nonlinear boundary value problem, which we solve using a combination of analytical and numerical methods. We find that the primary determinant of the shape of the organism is its interaction with the external environment, whereas the speed of the organism is determined primarily by the internal muscular forces, consistent with prior qualitative observations. Our model also allows us to pose and solve a variety of optimization problems such as those associated with maximum speed and mechanical efficiency, thus defining the performance envelope of this mode of locomotion.

Equilibrium of an elastically confined liquid drop H-M. Kwon, H-Y. Kim, J. Puell and L. Mahadevan,  Journal of Applied Physics,  103, 093519, 2008.
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When a liquid drop is confined between an elastic plate and a rigid substrate, it spreads spontaneously due to the effects of interfacial forces, eventually reaching an equilibrium shape determined by the balance between elastic and capillary effects. We provide an analytical theory for the static shape of the sheet and the extent of liquid spreading and show that our experiments are quantitatively consistent with the theory. The theory is relevant for the first step of painting when a brush is brought down on to canvas. More mundanely, it allows us to understand the stiction of microcantilevers to wafer substrates occurring in microelectromechanical fabrication processes

A quantitative analysis of contractility in active cytoskeletal protein networks P. Bendix, G. Koenderink, D. Cuvelier, Z. Dogic, B. Koeleman, W. Brieher, C. Field, L. Mahadevan and D. Weitz,  Biophysical Journal,  94, 3126, 2008.
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Cells actively produce contractile forces for a variety of processes including cytokinesis and motility. Contractility is known to rely on myosin II motors which convert chemical energy from ATP hydrolysis into forces on actin filaments. However, the basic physical principles of cell contractility remain poorly understood. We reconstitute contractility in a simplified model system of purified F-actin, muscle myosin II motors, and a-actinin cross-linkers. We show that contractility occurs above a threshold motor concentration and within a window of cross-linker concentrations. We also quantify the pore size of the bundled networks and find contractility to occur at a critical distance between the bundles. We propose a simple mechanism of contraction based on myosin filaments pulling neighboring bundles together into an aggregated structure. Observations of this reconstituted system in both bulk and low-dimensional geometries show that the contracting gels pull on and deform their surface with a contractile force of ;1mN, or ;100 pN per F-actin bundle. Cytoplasmic extracts contracting in identical environments show a similar behavior and dependence on myosin as the reconstituted system. Our results suggest that cellular contractility can be sensitively regulated by tuning the (local) activity of molecular motors and the cross-linker density and binding affinity.

Life and times of a cellular bleb G. Charras, M. Coughlin, T. Mitchison and L. Mahadevan,  Biophysical Journal,  94, 1836, 2008.
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Blebs are spherical cellular protrusions that occur in many physiological situations. Two distinct phases make up the life of a bleb, each of which have their own biology and physics: expansion, which lasts ;30 s, and retraction, which lasts ;2 min. We investigate these phases using optical microscopy and simple theoretical concepts, seeking information on blebbing itself, and on cytomechanics in general. We show that bleb nucleation depends on pressure, membrane-cortex adhesion energy, and membrane tension, and test this experimentally. Bleb growth occurs through a combination of bulk flow of lipids and delamination from the cell cortex via the formation and propagation of tears. In extreme cases, this can give rise to a traveling wave around the cell periphery, known as ‘‘circus movement.’’ When growth stalls, an actin cortex reforms under the bleb membrane, and retraction starts, driven by myosin-II. Using flicker spectroscopy, we find that retracting blebs are fivefold more rigid than expanding blebs, an increase entirely explained by the properties of the newly formed cortical actin mesh. Finally, using artificially nucleated blebs as pressure sensors, we show that cells rounded up in mitosis possess a substantial intracellular pressure.

Power-limited contraction dynamics of Vorticella convallaria: an ultrafast biological spring A. Upadhyaya, M. Baraban, J. Wong, P. Matsudaira, A. van Oudenaarden and L. Mahadevan,  Biophysical Journal , 94, 265, 2008.
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Vorticella convallaria is one of the fastest and most powerful cellular machines. The cell body is attached to a substrate by a slender stalk containing a polymeric structure—the spasmoneme. Helical coiling of the stalk results from rapid contraction of the spasmoneme, an event mediated by calcium binding to a negatively charged polymeric backbone. We use high speed imaging to measure the contraction velocity as a function of the viscosity of the external environment and find that the maximum velocity scales inversely with the square root of the viscosity. This can be explained if the rate of contraction is ultimately limited by the power delivered by the actively contracting spasmoneme. Microscopically, this scenario would arise if the mechanochemical wave that propagates along the spasmoneme is faster than the rate at which the cell body can respond due to its large hydrodynamic resistance. We corroborate this by using beads as markers on the stalk and find that the contraction starts at the cell body and proceeds down the stalk at a speed that exceeds the velocity of the cell body.

2007

Sickle cell vaso-occlusion and rescue in a microfluidic device J. Higgins, D. Eddington, S. Bhatia and L. Mahadevan,  Proceedings of the National Academy of Sciences (USA) , 104, 20496, 2007.
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The pathophysiology of sickle cell disease is complicated by the multiscale processes that link the molecular genotype to the organismal phenotype: hemoglobin polymerization occurring in milliseconds, microscopic cellular sickling in a few seconds or less [Eaton WA, Hofrichter J (1990) Adv Protein Chem 40:63–279], and macroscopic vessel occlusion over a time scale of minutes, the last of which is necessary for a crisis [Bunn HF (1997) N Engl J Med 337:762–769]. Using a minimal but robust artificial microfluidic environment, we show that it is possible to evoke, control, and inhibit the collective vasoocclusive or jamming event in sickle cell disease. We use a combination of geometric, physical, chemical, and biological means to quantify the phase space for the onset of a jamming event, as well as its dissolution, and find that oxygendependent sickle hemoglobin polymerization and melting alone are sufficient to recreate jamming and rescue. We further show that a key source of the heterogeneity in occlusion arises from the slow collective jamming of a confined, flowing suspension of soft cells that change their morphology and rheology relatively quickly. Finally, we quantify and investigate the effects of small-molecule inhibitors of polymerization and therapeutic red blood cell exchange on this dynamical process. Our experimental study integrates the dynamics of collective processes associated with occlusion at the molecular, polymer, cellular, and tissue level; lays the foundation for a quantitative understanding of the rate-limiting processes; and provides a potential tool for optimizing and individualizing treatment, and identifying new therapies.

Settling and swimming of flexible fluid lubricated foils M. Argentina, J. Skotheim and L. Mahadevan,  Physical Review Letters , 99, 224053, 2007.
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We study the dynamics of a flexible foil immersed in a fluid and moving close to a rigid wall. Lubrication theory allows us to derive equations of motion for the foil and thus examine the passive settling and the active swimming of a foil. This also allows us to partly answer the long-standing question in cartoon physics—can carpets fly? Our analysis suggests a region in parameter space where one may realize this dream and move the virtual towards reality.

Mechanosensation and mechanical loads modulate the locomotory gait of swimming C. elegans J. Korta, D. Clark, C. Gabel, L. Mahadevan, and A. Samuel,  Journal of Experimental Biology , 210, 2383, 2007.
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Animals move through their environments by selecting gaits that are adapted to the physical nature of their surroundings. The nematode Caenorhabditis elegans swims through fluids or crawls on surfaces by propagating flexural waves along its slender body and offers a unique opportunity for detailed analysis of locomotory gait at multiple levels including kinematics, biomechanics and the molecular and physiological operation of sensory and motor systems. Here, we study the swimming gait of C. elegans in viscous fluids in the range 0.05–50·Pa s. We find that the spatial form of the swimming gait does not vary across this range of viscosities and that the temporal frequency of the swimming gait only decreases by about 20% with every 10-fold increase in viscosity. Thus, C. elegans swims in low gear, such that its musculature can deliver mechanical force and power nearly 1000-fold higher than it delivers when swimming in water. We find that mutations that disrupt mechanosensation, or the laser killing of specific touch receptor neurons, increase the temporal frequency of the undulating gait, revealing a novel effect of mechanosensory input in regulating the putative central pattern generator that produces locomotion. The adaptability of locomotory gait in C. elegans may be encoded in sensory and motor systems that allow the worm to respond to its own movement in different physical surroundings.

Gravitational stability of suspensions of attractive colloidal particles. C. Kim, Y. Liu, A. Kuhnle, S. Hess, S. Viereck, T. Danner, L. Mahadevan, and D. Weitz,  Physical Review Letters , 99, 028303, 2007.
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Colloidal suspensions are susceptible to gravitationally induced phase separation. This can be mitigated by the formation of a particle network caused by depletion attraction. The effectiveness of this network in supporting the buoyant weight of the suspension can be characterized by its compressional modulus. We measure the compressional modulus for emulsion networks induced by depletion attraction and present a model that quantitatively predicts their gravitational stability. We also determine the relationship between the strength of the depletion attraction and the magnitude of the compressional modulus.

Force of an actin spring J.H. Shin, B.K. Tam, R.R. Brau, M.J. Lang, L. Mahadevan, and Paul Matsudaira,  Biophysical Journal , 92, 3729, 2007.
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Cellular movements are produced by forces. Typically, cytoskeletal proteins such as microtubules and actin filaments generate forces via polymerization or in conjunction with molecular motors. However, the fertilization of a Limulus polyphemus egg involves a third type of actin-based cellular engine—a biological spring. During the acrosome reaction, a 60-mm long coiled and twisted bundle of actin filaments straightens and extends from a sperm cell, penetrating the vitelline layer surrounding the egg. A subtle overtwist of 0.2/subunit underlies the mechanochemical basis for the extension of this actin spring. Upon calcium activation, this conformational strain energy is converted to mechanical work, generating the force required to extend the bundle through the vitelline layer. In this article, we stall the extension of the acrosome bundle in agarose gels of different concentrations. From the stall forces, we estimate a maximum force of 2 nN and a puncturing pressure of 1.6 MPa. We show the maximum force of extension is three times larger than the force required to puncture the vitelline layer. Thus, the elastic strain energy stored in the acrosome bundle is more than sufficient to power the acrosome reaction through the egg envelope.

The universal dynamics of cell spreading D. Cuvelier, M. Thery, Y-S. Chu, S. Dufour, J-P. Thiery, M. Bornens, P. Nassoy, and L. Mahadevan,  Current Biology  , 17, 694, 2007.
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Cell adhesion and motility depend strongly on the interactions between cells and extracellular matrix (ECM) substrates. When plated onto artificial adhesive surfaces, cells first flatten and deform extensively as they spread. At the molecular level, the interaction of membrane-based integrins with the ECM has been shown to initiate a complex cascade of signaling events [1], which subsequently triggers cellular morphological changes and results in the generation of contractile forces [2]. Here, we focus on the early stages of cell spreading and probe their dynamics by quantitative visualization and biochemical manipulation with a variety of cell types and adhesive surfaces, adhesion receptors, and cytoskeleton-altering drugs. We find that the dynamics of adhesion follows a universal power-law behavior. This is in sharp contrast with the common belief that spreading is regulated by either the diffusion of adhesion receptors toward the growing adhesive patch [3–5] or by actin polymerization [6–8]. To explain this, we propose a simple quantitative and predictive theory that models cells as viscous adhesive cortical shells enclosing a less viscous interior. Thus, although cell spreading is driven by well-identified biomolecular interactions, it is dynamically limited by its mesoscopic structure and material properties.

Nonlinear mechanics of soft fibrous networks A. Kabla and L. Mahadevan,  Journal of the Royal Society - Interface , 4, 99, 2007.
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Mechanical networks of fibres arise on a range of scales in nature and technology, from the cytoskeleton of a cell to blood clots, from textiles and felts to skin and collageneous tissues. Their collective response is dependent on the individual response of the constituent filaments as well as density, topology and order in the network. Here, we use the example of a lowdensity synthetic felt of athermal filaments to study the generic features of the mechanical response of such networks including strain stiffening and large effective Poisson ratios. A simple microscopic model allows us to explain these features of our observations, and provides us with a baseline framework to understand active biomechanical networks.

Persistence of a pinch in a pipe L. Mahadevan, A. Vaziri and M. Das,  Europhysics Letters , 77, 40003, 2007.
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The response of low-dimensional solid objects combines geometry and physics in unusual ways, exemplified in structures of great utility such as a thin-walled tube that is ubiquitous in nature and technology. Here we provide a consequence of this confluence of geometry and physics in tubular structures: our analysis shows that the persistence of a localized pinch in an elastic pipe whose effect decays as an oscillatory exponential with a persistence length that diverges as the thickness of the tube vanishes, which we confirm using simulations and simple experiments. The result is more a consequence of geometry than material properties, and is thus equally applicable to carbon nanotubes as it is to oil pipelines.

Curvature condensation and bifurcation in an elastic shell M. Das, A. Vaziri, A. Kudrolli, and L. Mahadevan,  Physical Review Letters,  98, 014301, 2007.
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We study the formation and evolution of localized geometrical defects in an indented cylindrical elastic shell using a combination of experiment and numerical simulation. We find that as a symmetric localized indentation on a semicylindrical shell increases, there is a transition from a global mode of deformation to a localized one which leads to the condensation of curvature along a symmetric parabolic defect. This process introduces a soft mode in the system, converting a load-bearing structure into a hinged, kinematic mechanism. Further indentation leads to twinning wherein the parabolic defect bifurcates into two defects that move apart on either side of the line of symmetry. A qualitative theory captures the main features of the phenomena but leads to further questions about the mechanism of defect nucleation

2006

A dynamic fate map of the forebrain shows how vertebrate eyes form and explains two causes of cyclopia S.J. England, G.B. Blanchard, L. Mahadevan, and R.J. Adams,  Development , 133, 4613, 2006.
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Mechanisms for shaping and folding sheets of cells during development are poorly understood. An example is the complex reorganisation of the forebrain neural plate during neurulation, which must fold a sheet into a tube while evaginating two eyes from a single contiguous domain within the neural plate. We, for the first time, track these cell rearrangements to show that forebrain morphogenesis differs significantly from prior hypotheses. We postulate a new model for forebrain neurulation and demonstrate how mutations affecting two signalling pathways can generate cyclopic phenotypes by disrupting normal cell movements or introducing new erroneous behaviours.

Sensorimotor control during isothermal tracking in Caenorhabditis elegans L. Luo, D.A. Clark, D. Biron, L. Mahadevan, and A.D.T. Samuel,  The Journal of Experimental Biology  209, 4652, 2006.
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In order to purposefully navigate their environments, animals rely on precise coordination between their sensory and motor systems. The integrated performance of circuits for sensorimotor control may be analyzed by quantifying an animal’s motile behavior in defined sensory environments. Here, we analyze the ability of the nematode C. elegans to crawl isothermally in spatial thermal gradients by quantifying the trajectories of individual worms responding to defined spatiotemporal thermal gradients. We show that sensorimotor control during isothermal tracking may be summarized as a strategy in which the worm changes the curvature of its propulsive undulations in response to temperature changes measured at its head. We show that a concise mathematical model for this strategy for sensorimotor control is consistent with the exquisite stability of the worm’s isothermal alignment in spatial thermal gradients as well as its more complex trajectories in spatiotemporal thermal gradients.

Mechanics of Interfacial Composite Materials A.B. Subramaniam, M. Abkarian, L. Mahadevan, and H.A. Stone,  Langmuir , 22, 10204, 2006.
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Recent experiments and simulations have demonstrated that particle-covered fluid/fluid interfaces can exist in stable nonspherical shapes as a result of the steric jamming of the interfacially trapped particles. The jamming confers the interface with solidlike properties. We provide an experimental and theoretical characterization of the mechanical properties of these armored objects, with attention given to the two-dimensional granular state of the interface. Small inhomogeneous stresses produce a plastic response, while homogeneous stresses produce a weak elastic response. Shear-driven particle-scale rearrangements explain the basic threshold needed to obtain the near-perfect plastic deformation that is observed. Furthermore, the inhomogeneous stress state of the interface is exhibited experimentally by using surfactants to destabilize the particles on the surface. Since the interfacially trapped particles retain their individual characteristics, armored interfaces can be recognized as a kind of composite material with distinct chemical,structural,

Fall and rise of a viscoelastic filament A. Roy, L. Mahadevan and J-L Thiffeault,  Journal of Fluid Mechanics  , 563, 283, 2006.
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When a viscoelastic fluid blob is stretched out into a thin horizontal filament, it sags and falls gradually under its own weight, forming a catenary-like structure that evolves dynamically. If the ends are brought together rapidly after stretching, the falling filament tends to straighten by rising. These two effects are strongly influenced by the elasticity of the fluid and yield qualitatively different behaviours from the case of a purely viscous filament analysed previously (Teichman & Mahadevan, J. Fluid Mech. vol. 478, 2003, p. 71). Starting from the bulk equations for the motion of a viscoelastic fluid, we derive a simplified equation for the dynamics of a viscoelastic filament and analyse this equation in some simple settings to explain our observations.

Microtubules can bear enhanced compressive loads in living cells because of lateral reinforcements C. Brangwynne, F. Mackintosh, S. Kumar, N. Geisse, J. Talbot, L. Mahadevan, K. Parker, D. Ingber and D. Weitz,  Journal of Cell Biology  , 173, 733, 2006.
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Cytoskeletal microtubules have been proposed to infl uence cell shape and mechanics based on their ability to resist large-scale compressive forces exerted by the surrounding contractile cytoskeleton. Consistent with this, cytoplasmic microtubules are often highly curved and appear buckled because of compressive loads. However, the results of in vitro studies suggest that microtubules should buckle at much larger length scales, withstanding only exceedingly small compressive forces. This discrepancy calls into question the structural role of microtubules, and highlights our lack of quantitative knowledge of the magnitude of the forces they experience and can withstand in living cells. We show that intracellular microtubules do bear large-scale compressive loads from a variety of physiological forces, but their buckling wavelength is reduced signifi cantly because of mechanical coupling to the surrounding elastic cytoskeleton. We quantitatively explain this behavior, and show that this coupling dramatically increases the compressive forces that microtubules can sustain, suggesting they can make a more signifi cant structural contribution to the mechanical behavior of the cell than previously thought possible

Modeling DNA loops using the theory of elasticity A. Balaeff, L. Mahadevan and K. Schulten,  Physical Review E,  73, 031919, 2006.
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An elastic rod model of a protein-bound DNA loop is adapted for application in multi-scale simulations of protein-DNA complexes. The classical Kirchhoff system of equations which describes the equilibrium structure of the elastic loop is modified to account for the intrinsic twist and curvature, anisotropic bending properties, and electrostatic charge of DNA. The effects of bending anisotropy and electrostatics are studied for the DNA loop clamped by the lac repressor protein. For two possible lengths of the loop, several topologically different conformations are predicted and extensively analyzed over the broad range of model parameters describing DNA bending and electrostatic properties. The scope and applications of the model in already accomplished and in future multi-scale studies of protein-DNA complexes are discussed.

Dynamics of fracture in drying suspensions E. Dufresene, D. Stark, N. Greenblatt, J. Cheng, J. Hutchinson, L. Mahadevan and D. Weitz,  Langmuir , 22, 7144, 2006.
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We investigate the dynamics of fracture in drying films of colloidal silica. Water loss quenches the nanoparticle dispersionsto form a liquid-saturated elastic network of particlesthat relieves drying-induced strain by cracking. These cracks display intriguing intermittent motion originating from the deformation of arrested crack tips and aging of the elastic network. The dynamics of a single crack exhibits a universal evolution, described by a balance of the driving elastic power with the sum of interfacial power and the viscous dissipation rate of flowing interstitial fluid.

Dynamics of surfactant-driven fracture of particle rafts D. Vella, H-Y Kim, P. Aussillous and L. Mahadevan,  Physical Review Letters , 96, 178301, 2006.
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We investigate the dynamic fracture of a close-packed monolayer of particles, or particle raft, floating at a liquid-gas interface induced by the localized addition of surfactant. Unusually for a two-dimensional solid, our experiments show that the speed of crack propagation here is not affected by the elastic properties of the raft. Instead it is controlled by the rate at which surfactant is advected to the crack tip by means of the induced Marangoni flows. Further, the velocity of propagation is not constant in time and the length of the crack scales as t 3=4. More broadly, this surfactant-induced rupture of interfacial rafts suggests ways to manipulate them for applications.

Crack-front instability in a confined elastic film M. Adda Bedia and L. Mahadevan,  Proceedings of the Royal Society of London, series A , 462, 3233, 2006.
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We study the undulatory instability of a straight crack front generated by peeling a flexible elastic plate from a thin elastomeric adhesive film. We show that there is a threshold for the onset of the instability that is dependent on the ratio of two lengthscales that arise naturally in the problem: the thickness of the film and an elastic length defined by the stiffness of the plate and that of the film. A linear stability analysis predicts that the wavelength of the instability scales linearly with the film thickness. Our results are qualitatively and quantitatively consistent with recent experiments, and show how crack fronts may lose stability due to a competition between bulk and surface effects in the presence of multiple length scales.

A simple model for the dynamics of adhesive failure D. Vella and L. Mahadevan,  Langmuir , 22, 163, 2006.
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We consider a microscopic model for the failure of soft adhesives in tension based on ideas of bond rupture under dynamic loading. By focusing on adhesive failure under loading at constant velocity, we demonstrate that bimodal curves of stress against strain may occur due to effects of finite polymer chain or bond length and characterize the loading conditions under which such bimodal behavior is observed. The results of this analysis are in qualitative agreement with experiments performed on unconfined adhesives in which failure does not occur by cavitation.

Superficial wrinkles in stretched, drying gelatin films R. Rizzieri, L. Mahadevan, A. Vaziri and A. Donald,  Langmuir , 22, 3622, 2006.
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When a thin film of initially hydrated gelatin is allowed to dry from the surface, superficial changes in the structure of the material affect the local mechanical properties of the drying region. If the film is simultaneously subjected to large strain deformation (above 20%), a periodic pattern of wrinkles appears on the surface of the gelatin along the length of the sample in the direction of the applied force. These wrinkles are uniformly distributed on the surface of the gelatin with a wavelength that is much smaller than the sample thickness, which changes with sample composition, aging time, and deformation rate. We investigate these patterns via in situ environmentalscanning electron microscopy (ESEM) and provide a theory for their origin.

Capillary rise between elastic sheets H-Y Kim and L. Mahadevan,  Journal of Fluid Mechanics , 548, 141, 2006.
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When a paintbrush is dipped into a pot of paint and pulled out, surface tension forces cause the individual hairs in the brush to coalesce even as the brush becomes impregnated with paint. We study a simple model of this elastocapillary interaction in the context of the surface-tension-driven vertical rise of a liquid between two long flexible hydrophilic sheets that are held a small distance apart at one end. We provide an analytic theory for the static shapes of the sheets as well as the liquid rise height which is different from that of the classical law of Jurin, and show that our experiments are quantitatively consistent with the theory.

Transitions to nematic states in homogeneous suspensions of high aspect ratio magnetic rods A. Gopinath, L. Mahadevan, and R.A. Armstrong,  Physics of Fluids , 18, 028102, 2006.
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Isotropic-nematic and nematic-nematic transitions from a homogeneous suspension of high aspect ratio magnetic rods are studied for both Maier-Saupe and Onsager excluded volume potentials. Asymptotic analysis in the vicinity of critical points yields insight into the stability and type of polarized nematic states emanating from nonpolarized equilibrium states. This, in conjunction with recently published global numerical results, yields a unified picture of the bifurcation diagram and provides a convenient base state to study effects of external orienting fields.

2005

Non-spherical bubbles A. Balasubramaniam, M. Abkarian, L. Mahadevan and H.A. Stone,  Nature , 438, 930, 2005.
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Powerful curves L. Mahadevan and T. Mitchison,  Nature , 435, 895, 2005.
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A cell’s contents are organized by a scaffolding of microtubules. These long, thin polymers continuously grow and shrink, and the structures of two forms of the constituent protein provide clues to how this occurs.

Solenoids and Plectonemes in stretched and twisted elastomeric filaments,  A. Ghatak and L. Mahadevan,  Physical Review Letters  , 95, 057801, 2005.
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We study the behavior of a naturally straight highly extensible elastic filament subjected to large extensional and twisting strains. We find that two different phases can coexist for a range of parameter values: the plectoneme and the solenoid. A simple theory based on a neo-Hookean model for the material of the filament and accounting for the slender geometry suffices to explain these observations, and leads to a phase diagram that is consistent with observations. Extension and relaxation experiments on these phases show the presence of large hysteresis loops and sawtoothlike force-displacement curves which are different for the plectoneme and the solenoid.

Soft lubrication: the elastohydrodynamics of conforming and non-conforming contacts J. Skotheim and L. Mahadevan,  Physics of Fluids , 17, 092101, 2005.
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We study the lubrication of fluid-immersed soft interfaces and show that elastic deformation couples tangential and normal forces and thus generates lift. We consider materials that deform easily, due to either geometry
e.g., a shell or constitutive properties
e.g., a gel or a rubber, so that the effects of pressure and temperature on the fluid properties may be neglected. Four different system geometries are considered: a rigid cylinder moving parallel to a soft layer coating a rigid substrate; a soft cylinder moving parallel to a rigid substrate; a cylindrical shell moving parallel to a rigid substrate; and finally a cylindrical conforming journal bearing coated with a thin soft layer. In addition, for the particular case of a soft layer coating a rigid substrate, we consider both elastic and poroelastic material responses. For all these cases, we find the same generic behavior: there is an optimal combination of geometric and material parameters that maximizes the dimensionless normal force as a function of the softness parameter
= hydrodynamic pressure/elastic stiffness = surface deflection/ gap thickness, which characterizes the fluid-induced deformation of the interface. The corresponding cases for a spherical slider are treated using scaling concepts.

The ‘Cheerios Effect’ D. Vella and L. Mahadevan,  American Journal of Physics , 73, 817-825, 2005.
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Objects that float at the interface between a liquid and a gas interact because of interfacial deformation and the effect of gravity. We highlight the crucial role of buoyancy in this interaction, which, for small particles, prevails over the capillary suction that often is assumed to be the dominant effect. We emphasize this point using a simple classroom demonstration, and then derive the physical conditions leading to mutual attraction or repulsion. We also quantify the force of interaction in particular instances and present a simple dynamical model of this interaction. The results obtained from this model are validated by comparison to experimental results for the mutual attraction of two identical spherical particles. We consider some of the applications of the effect that can be found in nature and the laboratory

Gravitational collapse of colloidal gels S. Manley, J.M. Skotheim, L. Mahadevan, D. Weitz,  Physical Review Letters , 94, 218302, 2005 
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We present a unified framework for understanding the compaction of colloidal gels under their own weight. The dynamics of the collapse are determined by the value of the gravitational stress
g, as compared to the yield stress
Y of the network. For
g <
Y, gels collapse poroelastically, and their rate of compression decays exponentially in time. For
g >
Y, the network eventually yields, leading to rapid settling. In both cases, the rate of collapse is backflow limited, while its overall magnitude is determined by a balance between gravitational stress and network elastic stress.

Physical limits and design principles for plant and fungal movements J. Skotheim and L. Mahadevan,  Science,  308, 1308-10, 2005.
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Non-equilibration of hydrostatic pressure in blebbing cells, G. Charras, J. Yarrow, M. Horton, L. Mahadevan and T. Mitchison,  Nature , 435, 365-69. 2005.
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Current models for protrusive motility in animal cells focus on cytoskeleton-based mechanisms, where localized protrusion is driven by local regulation of actin biochemistry1–3. In plants and fungi, protrusion is driven primarily by hydrostatic pressure4–6. For hydrostatic pressure to drive localized protrusion in animal cells7,8, it would have to be locally regulated, but current models treating cytoplasm as an incompressible viscoelastic continuum9 or viscous liquid10 require that hydrostatic pressure equilibrates essentially instantaneously over the whole cell. Here, we use cell blebs as reporters of local pressure in the cytoplasm. When we locally perfuse blebbing cells with cortex-relaxing drugs to dissipate pressure on one side, blebbing continues on the untreated side, implying non-equilibration of pressure on scales of approximately 10 mm and 10 s. We can account for localization of pressure by considering the cytoplasm as a contractile, elastic network infiltrated by cytosol. Motion of the fluid relative to the network generates spatially heterogeneous transients in the pressure field, and can be described in the framework of poroelasticity11,12.

Self-organized origami, L. Mahadevan and S. Rica,  Science , 307, 1740, 2005.
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The controlled folding and unfolding of maps, space structures, wings, leaves, petals, and other foldable laminae is potentially complicated by the independence of individual folds; as their number increases, there is a combinatorial explosion in the number of folded possibilities. The artificially constructed Miura-ori (1) pattern, with a periodic array of geometrically and elastically coupled mountain and valley folds (Fig. 1A), circumvents this complication by allowing the entire structure to be folded or unfolded simultaneously. Making such a pattern is not easy, so it may be surprising to find an elegant natural counterpart that is a few hundred millennia old. In Fig. 1B, we show the different stages of the opening of a hornbeam leaf that starts life in its bud as a Miura-ori folded pattern (2). Similar structures arise in insect wings (3) and elsewhere in nature (4), suggesting that these origami patterns are a result of convergent design. This raises a question of mechanism: How might this spatial organization of folds be brought about?

Self-similar nested wrinkling patterns in skins K. Efimenko, M. Rackaitis, E. Manias, A. Vaziri, L. Mahadevan and J. Genzer,  Nature — Materials , 4, 293-97, 2005.
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Stiff thin fi lms on soft substrates are both ancient and commonplace in nature; for instance, animal skin comprises a stiff epidermis attached to a soft dermis. Although more recent and rare, artifi cial skins are increasingly used in a broad range of applications, including fl exible electronics1 , tunable diff raction gratings2,3, force spectroscopy in cells4 , modern metrology methods5 , and other devices6–8. Here we show that model elastomeric artifi cial skins wrinkle in a hierarchical pattern consisting of self-similar buckles extending over fi ve orders of magnitude in length scale, ranging from a few nanometres to a few millimetres. We provide a mechanism for the formation of this hierarchical wrinkling pattern, and quantify our experimental fi ndings with both computations and a simple scaling theory. Th is allows us to harness the substrates for applications. In particular, we show how to use the multigeneration-wrinkled substrate for separating particles based on their size, while simultaneously forming linear chains of monodisperse particles.

How the Venus Flytrap snaps Y. Forterre, J. Skotheim, J. Dumais and L. Mahadevan,  Nature,  433, 421-25, 2005.
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The rapid closure of the Venus flytrap (Dionaea muscipula) leaf in about 100 ms is one of the fastest movements in the plant kingdom. This led Darwin to describe the plant as “one of the most wonderful in the world”1 . The trap closure is initiated by the mechanical stimulation of trigger hairs. Previous studies2–7 have focused on the biochemical response of the trigger hairs to stimuli and quantified the propagation of action potentials in the leaves. Here we complement these studies by considering the post-stimulation mechanical aspects of Venus flytrap closure. Using high-speed video imaging, non-invasive microscopy techniques and a simple theoretical model, we show that the fast closure of the trap results from a snap-buckling instability, the onset of which is controlled actively by the plant. Our study identifies an ingenious solution to scaling up movements in non-muscular engines and provides a general framework for understanding nastic motion in plants.

Hydrodynamical models for the chaotic dripping faucet, P. Coullet, L. Mahadevan and C. Riera,  Journal of Fluid Mechanics,  526, 1-17, 2005.
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We give a hydrodynamical explanation for the chaotic behaviour of a dripping faucet using the results of the stability analysis of a static pendant drop and a proper orthogonal decomposition (POD) of the complete dynamics. We find that the only relevant modes are the two classical normal forms associated with a saddle– node–Andronov bifurcation and a Shilnikov homoclinic bifurcation. This allows us to construct a hierarchy of reduced-order models including maps and ordinary differential equations which are able to qualitatively explain prior experiments and numerical simulations of the governing partial differential equations and provide an explanation for the complexity in dripping. We also provide a new mechanical analogue for the dripping faucet and a simple rationale for the transition from dripping to jetting modes in the flow from a faucet.

Confined elastic developable surfaces: cylinders, cones and the elastica E. Cerda and L. Mahadevan,  Proceedings of the Royal Society of London (A),  461, 671-700, 2005.
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We consider two of the simplest problems associated with the packing of a naturally flat thin elastic sheet. Both problems involve packing the sheet into a hollow cylinder; the first considers the partial contact of a cylindrically curved sheet with a cylindrical surface, while the second considers the partial contact of a conically curved sheet with the edge of a cylindrical surface. In each case, we solve the free-boundary problems to determine the shape, response and stability of the confined surfaces. In particular, we show that an exact description of both the cylindrical and conical structures is given by solutions of the Elastica equation, allowing us to present a unified description of a large class of elastic developable surfaces. This includes what is possibly the simplest example of strain localization, occurring at a point and forming one of the constituent elements of a crumpled elastic sheet.

Using the peel test to measure the work of adhesion in a confined elastic film A. Ghatak, L. Mahadevan and M. Chaudhury,  Langmuir,  21, 1277-81, 2005.
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We present a theoretical and experimental study of a method for the determination of the adhesion strength between a thin elastomeric film bonded to a rigid substrate and a flexible plate in a geometry common in the peel test. In particular, we characterize the work of adhesion in terms of the length of an equilibrium crack, generated by a spacer of known thickness wedged between the flexible plate and adhesive film, and the elastic and geometric properties of the film and the plate. We treat both the limit of perfect bonding and that of perfect slippage at the interface of the adhesive film and the flexible plate. A series of experiments allow us to verify the theory quantitatively and thus validate our method, which ought to be of value in many technological situations.

Buckling of drying droplets of colloidal suspensions, N. Tsapsi, E. Dufresne, S. Sinha, C. Riera, J. Hutchinson, L. Mahadevan, D. Weitz,  Physical Review Letters , 94, 018302, 2005.
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Minute concentrations of suspended particles can dramatically alter the behavior of a drying droplet. After a period of isotropic shrinkage, similar to droplets of a pure liquid, these droplets suddenly buckle like an elastic shell. While linear elasticity is able to describe the morphology of the buckled droplets, it fails to predict the onset of buckling. Instead, we find that buckling is coincident with a stress-induced fluid to solid transition in a shell of particles at a droplet’s surface, occurring when attractive capillary forces overcome stabilizing electrostatic forces between particles.

Spontaneous folding of planar surfaces into three-dimensional objects by magnetic self-assembly, M. Boncheva, S. Andreev, L. Mahadevan, A. Winkelman, D. Reichman, M. Prentiss, S. Whitesides and G. Whitesides,  Proceedings of the National Academy of Sciences (USA),  102, 3924-29, 2005.
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This report describes the spontaneous folding of flat elastomeric sheets, patterned with magnetic dipoles, into free-standing, 3D objects that are the topological equivalents of spherical shells. The path of the self-assembly is determined by a competition between mechanical and magnetic interactions. The potential of this strategy for the fabrication of 3D electronic devices is demonstrated by generating a simple electrical circuit surrounding a spherical cavity.

Fluid-flow induced flutter of a flag M. Argentina and L. Mahadevan,  Proceedings of the National Academy of Sciences (USA), 102, 1829-34, 2005.
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We give an explanation for the onset of fluid-flow-induced flutter in a flag. Our theory accounts for the various physical mechanisms at work: the finite length and the small but finite bending stiffness of the flag, the unsteadiness of the flow, the added mass effect, and vortex shedding from the trailing edge. Our analysis allows us to predict a critical speed for the onset of flapping as well as the frequency of flapping. We find that in a particular limit corresponding to a low-density fluid flowing over a soft high-density flag, the flapping instability is akin to a resonance between the mode of oscillation of a rigid pivoted airfoil in a flow and a hinged-free elastic plate vibrating in its lowest mode.

2004

Photo-induced deformation of beams, plates and films Warner, M. and L. Mahadevan,  Physical Review Letters , 92, 134302, 2004.
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Photoresponsive solids such as nematic photoelastomers can undergo large deformations induced by light absorbed into rodlike molecules which bend and disrupt liquid crystal order. Significant variation of photoabsorption through the solid leads to nonuniform elastic deformations such as bending of beams and plates and pitting of layers. Such effects are also found in the presence of inhomogeneous thermal or swelling fields in solids or gels. We analyze the small deflection limit of these problems and show that beams made of these materials can have two elastically neutral planes, and that plates of these materials have a typical saddle shape. We also give a scaling analysis of the elasticity of photoinduced mounds and pits and speculate on their applications.

Soft lubrication Skotheim, J. and L. Mahadevan,  Physical Review Letters , 92, 245509, 2004.
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We consider some basic principles of fluid-induced lubrication at soft interfaces. In particular, we quantify how a soft substrate changes the geometry of and the forces between surfaces sliding past each other. By considering the model problem of a symmetric nonconforming contact moving tangentially to a thin elastic layer, we determine the normal force in the small and large deflection limit, and show that there is an optimal combination of material and geometric properties which maximizes the normal force. Our results can be generalized to a variety of other geometries which show the same qualitative behavior. Thus, they are relevant in the elastohydrodynamic lubrication of soft elastic and poroelastic gels and shells, and in the context of biolubrication in cartilaginous joints.

Peeling, healing and bursting in lubricated elastic sheets, Hosoi, A. and L. Mahadevan,  Physical Review Letters , 93, 137802, 2004.
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We consider the dynamics of an elastic sheet lubricated by the flow of a thin layer of fluid that separates it from a rigid wall. By considering long wavelength deformations of the sheet, we derive an evolution equation for its motion, accounting for the effects of elastic bending, viscous lubrication, and body forces. We then analyze various steady and unsteady problems for the sheet, such as peeling, healing, levitating, and bursting, using a combination of numerical simulation and dimensional analysis. On the macroscale, we corroborate our theory with a simple experiment, and, on the microscale, we analyze an oscillatory valve that can transform a continuous stream of fluid into a series of discrete pulses.

Scaling of F-actin rheology to probe single filament elasticity and dynamics, Gardel, M., J. Shin, F. Mackintosh, L. Mahadevan, P. Matsudaira and D. Weitz,  Physical Review Letters , 93, 188102, 2004.
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The linear and nonlinear viscoelastic response of networks of cross-linked and bundled cytoskeletal filaments demonstrates remarkable scaling with both frequency and applied prestress, which helps elucidate the origins of the viscoelasticity. The frequency dependence of the shear modulus reflects the underlying single-filament relaxation dynamics for 0:1–10 rad=sec. Moreover, the nonlinear strain stiffening of such networks exhibits a universal form as a function of prestress; this is quantitatively explained by the full force-extension relation of single semiflexible filaments.

Peeling from a patterned thin elastic film,  Ghatak, A., L. Mahadevan, J. Yun, M. Chaudhury and V. Shenoy,  Proceedings of the Royal Society of London (A) , 460, 2725-35 (2004).
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Inspired by the observation that many naturally occurring adhesives arise as textured thin films, we consider the displacement-controlled peeling of a flexible plate from an incision-patterned thin adhesive elastic layer. We find that crack initiation from an incision on the film occurs at a load much higher than that required to propagate it on a smooth adhesive surface; multiple incisions thus cause the crack to propagate intermittently. Microscopically, this mode of crack initiation and propagation in geometrically confined thin adhesive films is related to the nucleation of cavitation bubbles behind the incision which must grow and coalesce before a viable crack propagates. Our theoretical analysis allows us to rationalize these experimental observations qualitatively and quantitatively and suggests a simple design criterion for increasing the interfacial fracture toughness of adhesive films

Elastic behavior of cross-linked and bundled actin networks,  Gardel, M., J. Shin, F. Mackintosh, L. Mahadevan, P. Matsudaira and D. Weitz,  Science,  304, 1301-5, 2004.
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Networks of cross-linked and bundled actin filaments are ubiquitous in the cellular cytoskeleton, but their elasticity remains poorly understood. We show that these networks exhibit exceptional elastic behavior that reflects the mechanical properties of individual filaments. There are two distinct regimes of elasticity, one reflectingbendingof single filaments and a second reflectingstretchingof entropic fluctuations of filament length. The mechanical stiffness can vary by several decades with small changes in cross-link concentration, and can increase markedly upon application of external stress. We parameterize the full range of behavior in a state diagram and elucidate its origin with a robust model.

Capillarity-induced zippering of a flexible train floating on an air-water interface, Vella, D., H-Y. Kim and L. Mahadevan,  Journal of Fluid Mechanics , 502, 89-98, 2004.
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We consider the dynamics of capillary attraction between an articulated train of rigid rods floating at a liquid–gas interface and a nearby wall. We then explain some of the phenomena that are a result of the strong anisotropy and the extended nature of the system, such as the lining up next to the walling in a ‘zippering’ motion that is observed and compare our results qualitatively with those of experiments.

Bending stiffness of a crystalline actin bundle,  Shin, J., L. Mahadevan, P.T. So and P. Matsudaira,  Journal of Molecular Biology , 337, 255-61, 2004.
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The acrosomal process of the sperm of the horseshoe crab (Limulus polyphemus) is a unique crystalline actin bundle, consisting of multiple actin filaments cross-linked by the actin-bundling protein, scruin. For successful fertilization, the acrosomal bundle must penetrate through a 30 mm thick jelly coat surrounding the egg and thus it must be sufficiently stiff. Here, we present two measurements of the bending stiffness of a single crystalline bundle of actin. Results from these measurements indicate that the actin:scruin composite bundle has an average elastic modulus of 2 GPa, which is similar to that of a single actin filament, and a bending stiffness that is more than two orders of magnitude larger than that of a bundle of uncross-linked actin filaments due to stiffening by the scruin matrix.

Modeling DNA loops using continuum and statistical mechanics Balaeff, A., C. Koudella, L. Mahadevan and K. Schulten,  Philosophical Transactions of the Royal Society of London (A) , 362, 1355-71, 2004.
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The classical Kirchhoff elastic-rod model applied to DNA is extended to account for sequence-dependent intrinsic twist and curvature, anisotropic bending rigidity, electrostatic force interactions, and overdamped Brownian motion in a solvent. The zero-temperature equilibrium rod model is then applied to study the structural basis of the function of the lac repressor protein in the lac operon of Escherichia coli. The structure of a DNA loop induced by the clamping of two distant DNA operator sites by lac repressor is investigated and the optimal geometries for the loop of length 76 bp are predicted. Further, the mimicked binding of catabolite gene activator protein (CAP) inside the loop provides solutions that might explain the experimentally observed synergy in DNA binding between the two proteins. Finally, a combined Monte Carlo and Brownian dynamics solver for a worm-like chain model is described and a preliminary analysis of DNA loop-formation kinetics is presented.

Biomimetic ratcheting motion of lubricated hydrogel filaments, Mahadevan, L., S. Daniel and M. Chaudhury,  Proceedings of the National Academy of Sciences (USA) , 101, 23-26, 2004.
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Inspired by the locomotion of terrestrial limbless animals, we study the motion of a lubricated rod of a hydrogel on a soft substrate. We show that it is possible to mimic observed biological gaits by vibrating the substrate and by using a variety of mechanisms to break longitudinal and lateral symmetry. Our simple theory and experiments provide a unified view of the creeping, undulating, and inchworming gaits observed in limbless locomotion on land, all of which originate as symmetry-breaking bifurcations of a simple base state associated with periodic longitudinal oscillations of a slender gel. These ideas are therefore also applicable to technological situations that involve moving small, soft solids on substrates.

Elements of Draping Cerda, E., L. Mahadevan and J. Passini,  Proceedings of the National Academy of Sciences (USA) , 101 (7), 1806-10, 2004.
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We consider the gravity-induced draping of a 3D object with a naturally flat, isotropic elastic sheet. As the size of the sheet increases, we observe the appearance of new folded structures of increasing complexity that arise because of the competition between elasticity and gravity. We analyze some of the simpler 3D structures by determining their shape and analyzing their response and stability and show that these structures can easily switch between a number of metastable configurations. For more complex draperies, we derive scaling laws for the appearance and disappearance of new length scales. Our results are consistent with commonplace observations of drapes and complement large-scale computations of draping by providing benchmarks. They also yield a qualitative guide to fashion design and virtual reality animation.

Relating microstructure to rheology of a bundled and cross-linked F-actin network in-vitro Shin, J., M. Gardel, L. Mahadevan, P. Matsudaira and D. Weitz,  Proceedings of the National Academy of Sciences (USA) , 101(26), 9636-41 (2004).
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The organization of individual actin filaments into higher-order structures is controlled by actin-binding proteins (ABPs). Although the biological significance of the ABPs is well documented, little is known about how bundling and cross-linking quantitatively affect the microstructure and mechanical properties of actin networks. Here we quantify the effect of the ABP scruin on actin networks by using imaging techniques, cosedimentation assays, multiparticle tracking, and bulk rheology. We show how the structure of the actin network is modified as the scruin concentration is varied, and we correlate these structural changes to variations in the resultant network elasticity.

Elasticity of interfacial particle rafts, Vella, D., P. Aussillous and L. Mahadevan,  Europhysics Letters , 68 (2), 212-18, 2004.
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We study the collective behaviour of a close-packed monolayer of non-Brownian particles at a fluid-liquid interface. Such a particle raft forms a two-dimensional elastic solid and can support anisotropic stresses and strains, e.g. it buckles in uniaxial compression and cracks in tension. We characterise this solid in terms of Young’s modulus and Poisson ratio derived from simple theoretical considerations and show the validity of these estimates by using an experimental buckling assay to deduce Young’s modulus.

Popliteal instability of bent multi-walled elastic tubes, Mahadevan, L., J. Bico and G. McKinley,  Europhysics Letters , 65 (3), 323-29, 2004.
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Soft slender structures are ubiquitous in natural and artificial systems, in active and passive settings and across scales, from polymers and flagella, to snakes and space tethers. In this paper, we demonstrate the use of a simple and practical numerical implementation based on the Cosserat rod model to simulate the dynamics of filaments that can bend, twist, stretch and shear while interacting with complex environments via muscular activity, surface contact, friction and hydrodynamics. We validate our simulations by solving a number of forward problems involving the mechanics of passive filaments and comparing them with known analytical results, and extend them to study instabilities in stretched and twisted filaments that form solenoidal and plectonemic structures. We then study active filaments such as snakes and other slender organisms by solving inverse problems to identify optimal gaits for limbless locomotion on solid surfaces and in bulk liquids.

Structural model for cooperative DNA binding by CAP and Lac repressor, Balaeff, A., L. Mahadevan and K. Schulten,  Structure , 12, 123-32, 2004.
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Thin adhesive pads used to attach objects to each other often fail catastrophically. Here we consider the nature of failure of such a pad under loading parallel to the adhesive substrate. To determine the modes of failure of the pad and to understand what limits its load bearing capacity, we conduct experiments with finite pads composed of a soft adhesive layer with a stiff backing and load them parallel to the surface of adhesion. We find that two different peeling mechanisms emerge as a function of the slenderness of the adhesive pad: an interfacial peeling mechanism that starts close to the pulling end for very long pads, and an unstable curling mechanism that starts at the opposite end for relatively short pads. A minimal theoretical framework allows us to explain our observations and reveals the adhesive bond stiffness as a dominant parameter in defining the peeling mode. A phase diagram that delineates the different regimes of peeling modes brings our experiments and theory together. Our results suggest that unstable peeling by curling may be more common than previously thought, and could perhaps occur naturally in such examples as the gecko foot.

Multiscale methods for modeling protein-DNA complexes, Villa, E. , Balaeff, A., L. Mahadevan and K. Schulten,  SIAM Multiscale Modeling and Simulation , 2, 527-553 (2004).
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We present a multiresolution approach to modeling complexes between protein and DNA that contain looped or coiled DNA. The approach combines a coarse-grained model of the DNA loop, based on the classical theory of elasticity, with an atom level model of proteins and proteinDNA interfaces based on molecular dynamics. The coarse-grained DNA description is controlled through the atom level protein description and vice versa. The feasibility of the resulting multiscale modeling approach is demonstrated for a protein-DNA complex in which a protein called the E. coli lac repressor forces DNA into a 76 base pair loop. The required simulation involves 230,000 atoms, a number that would triple if both protein and DNA loops were described at the atomic level.
Dynamics of poroelastic filaments,
Skotheim, J. and L. Mahadevan,  Proceedings of the Royal Society of London (A) , 460, 1995-2020 (2004).  
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2003

Stored elastic energy powers the 60-micron extension of the Limulus polyphemus sperm actin bundle, Shin, J., L. Mahadevan, G. Waller, K. Langsmo and P. Matsudaira,  Journal of Cell Biology , 162(7), 1183-88, 2003.
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During the 5 s of the acrosome reaction of Limulus polyphemus sperm, a 60-m-long bundle of scruin-decorated actin filaments straightens from a coiled conformation and extends from the cell. To identify the motive force for this movement, we examined the possible sources of chemical and mechanical energy and show that the coil releases 1013 J of stored mechanical D strain energy, whereas chemical energy derived from calcium binding is 1015 J. These measurements indicate that the coiled actin bundle extends by a spring-based mechanism, which is distinctly different from the better known polymerization or myosin-driven processes, and that calcium initiates but does not power the reaction.

Rings, rackets and kinks in filamentous assemblies, Cohen, A. and L. Mahadevan,  Proceedings of the National Academy of Sciences (USA) , 100, 12141-46, 2003.
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Carbon nanotubes and biological filaments each spontaneously assemble into kinked helices, rings, and ‘‘tennis racket’’ shapes due to competition between elastic and interfacial effects. We show that the slender geometry is a more important determinant of the morphology than any molecular details. Our mesoscopic continuum theory is capable of quantifying observations of these structures and is suggestive of their occurrence in other filamentous assemblies as well

The force-velocity relationship for the actin-based motility of Listeria-Monocytogenes, McGrath, J., J. Eungdamrong, C. Fisher, F. Peng, L. Mahadevan, T. Mitchison and S. Kuo,  Current Biology , 13 (1-20), 1-6, 2003.
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Geometry and physics of wrinkling,  Cerda, E. and L. Mahadevan,  Physical Review Letters , 90 (7) 074302, 2003 (Physical Review Focus Article).
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The wrinkling of thin elastic sheets occurs over a range of length scales, from the fine scale patterns in substrates on which cells crawl to the coarse wrinkles seen in clothes. Motivated by the wrinkling of a stretched elastic sheet, we deduce a general theory of wrinkling, valid far from the onset of the instability, using elementary geometry and the physics of bending and stretching. Our main result is a set of simple scaling laws; the wavelength of the wrinkles

K1=4, where K is the stiffness due to an ‘‘elastic substrate’’ effect with a multitude of origins, and the amplitude of the wrinkle A

. These could form the basis of a highly sensitive quantitative wrinkling assay for the mechanical characterization of thin solid membranes.

The viscous catenary Teichman, J. and L. Mahadevan,  Journal of Fluid Mechanics , 478, pp. 71-80, 2003.
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A filament of an incompressible highly viscous fluid that is supported at its ends sags under the influence of gravity. Its instantaneous shape resembles that of a catenary, but evolves with time. At short times, the shape is dominated by bending deformations. At intermediate times, the effects of stretching become dominant everywhere except near the clamping boundaries where bending boundary layers persist. Finally, the filament breaks off in finite time via strain localization and pinch-off.

Crack street: the cycloidal wake of a cylinder ripping through a thin solid sheet,  Ghatak, A. and L. Mahadevan,  Physical Review Letters . 91, 215507, 2003.
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When a cylindrical tool cuts through a thin sheet of a relatively brittle material, it leaves behind a visually arresting crack street in its wake, reminiscent of a vortex street in the wake of a cylinder moving through a fluid. We show that simple geometrical arguments based on the interplay of in-plane stretching and out-of-plane bending suffice to explain the cycloidal morphology of the curved crack. The coupling between geometry and dynamics also allows us to explain the ‘‘stick-slip’’-like behavior of tearing and suggests that these oscillations should occur generically in the brittle fracture of thin solid films.

2002

Wrinkling of a stretched elastic sheet, Cerda, E., K. Ravi-Chandar and L. Mahadevan,  Nature , 419, 579, 2002.
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The edge of a torn plastic sheet forms a complex three-dimensional fractal shape. We have found that the shape results from a simple elongation of the sheet in the direction along its edge. Natural growth processes in some leaves, flowers and vesicles could lead to a similar elongation and hence to the generation of characteristic wavy shapes. We used rectangular plastic sheets pulled from the sides (in the y-direction) to generate a steadily travelling crack (in the xdirection). The high stresses near the crack tip produce an irreversible plastic deformation of the sheet and, as they are relieved, the deformed sheet is free to relax and to adopt a new shape in space.

How aphids lose their marbles, Pike, N., D. Richard, W. Foster and L. Mahadevan,  Proceedings of the Royal Society of London, Series (B), Biological Sciences , 269, 1211-15, 2002.
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Insects provide examples of many cunning stratagems to cope with the challenges of living in a world dominated by surface forces. Despite being the current masters of the land environment, they are at constant risk of being entrapped in liquids, which they prevent by having waxy and hairy surfaces. The problem is particularly acute in an enclosed space, such as a plant gall. Using secreted wax to efficiently parcel and transport their own excrement, aphids were able to solve this problem 200 Myr ago. Here, we report on the physical and physiological significance of this ingenious solution. The secreted powdery wax has three distinct roles: (i) it is hydrophobic, (ii) it creates a microscopically rough inner gall surface made of weakly compacted wax needles making the gall ultra-hydrophobic, and (iii) it coats the honeydew droplets converting them into liquid marbles, that can be rapidly and efficiently moved.

Four-phase merging in compound drops, Mahadevan, L., M. Adda Bedia and Y. Pomeau,  Journal of Fluid Mechanics , 451, pp. 411-20, 2002.
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We consider the statics of compound droplets made of two immiscible fluids on a rigid substrate, in the limit when gravity is dominated by capillarity. In particular, we show that the merging of four phases along a single contact line is a persistent and robust phenomenon from a mechanical and thermodynamic perspective; it can and does occur for a range of interfacial energies and droplet volumes. We give an interpretation for this in the context of the macroscopic Young–Laplace law and its microscopic counterpart due to van der Waals, and show that the topological transitions that result can be of either a continuous or discontinuous type depending on the interfacial energies in question.

Shocks in sand flowing in a silo, Samadani, A., L. Mahadevan and A. Kudrolli,  Journal of Fluid Mechanics , 452, 293-301, 2002.
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We study the formation of shocks on the surface of a granular material draining through an orifice at the bottom of a quasi-two-dimensional silo. At high flow rates, the surface is observed to deviate strongly from a smooth linear inclined profile, giving way to a sharp discontinuity in the height of the surface near the bottom of the incline, the typical response of a choking flow such as encountered in a hydraulic jump in a Newtonian fluid like water. We present experimental results that characterize the conditions for the existence of such a jump, describe its structure and give an explanation for its occurrence.

1993-2001

Non-stick water,  Mahadevan, L.,  Nature , 411, 895-96, 2001.
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Much to the consternation of adults, a broken mercury thermometer is a source of delight to a curious child absorbed by the spectacle of the silvery beads that elude capture. The epithet ‘quicksilver’ aptly describes the droplets, which seem to roll rapidly on the surface much like a solid marble.This unusual behaviour elicits a host of questions that are relevant to scientists in diverse fields: from chemists and engineers interested in the dynamics of drops, to astronomers interested in the stability of rotating stars and planets. How and when can liquid droplets actually roll on a surface? How fast can they move? Can they be controlled? And to what end?

Folding of viscous filaments and sheets Skorobogatiy, M., and L. Mahadevan,  Europhysics Letters , 52, 532-38, 2000.
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We consider the nonlinear folding behavior of a viscous filament or a sheet under the influence of an external force such as gravity. Everyday examples of this phenomenon are provided by the periodic folding of a sheet of honey as it impinges on toast, or the folding of a stream of shampoo as it falls on one’s hand. To understand the evolution of a fold, we formulate and solve a free-boundary problem for the phenomenon, give scaling laws for the size of the folds and the frequency with which they are laid out, and verify these experimentally

Chaotic dripping from a faucet, Coullet, P., L. Mahadevan and C. Riera,  Progress in Theoretical Physics Supplement , 139, 507-516, 2000.
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We propose a simple model for the chaotic dripping of a faucet in terms of a return map constructed by analyzing the stability of a pendant drop. The return map couples two classical normal forms, an Andronov saddle-node bifurcation, and a Shilnikov homoclinic bifurcation. The former corresponds to the initiation of the instability when the drop volume exceed a critical value set by the balance between surface tension and gravity, while the latter models the global reinjection associated with pinch-off that eventually return the drop to a state close to its original unstable configuration. The results obtained using the return map are consistent with those of numerical simulations of the governing PDEs and prior experiments, and show periodic and quasi-periodic dripping at low and high flow rates, and chaotic behavior at intermediate flow rates.

Motility driven by macromolecular springs and ratchets, Mahadevan, L. and P. Matsudaira,  Science , 288, 95-99, 2000.
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We propose a simple model for the chaotic dripping of a faucet in terms of a return map constructed by analyzing the stability of a pendant drop. The return map couples two classical normal forms, an Andronov saddle-node bifurcation, and a Shilnikov homoclinic bifurcation. The former corresponds to the initiation of the instability when the drop volume exceed a critical value set by the balance between surface tension and gravity, while the latter models the global reinjection associated with pinch-off that eventually return the drop to a state close to its original unstable configuration. The results obtained using the return map are consistent with those of numerical simulations of the governing PDEs and prior experiments, and show periodic and quasi-periodic dripping at low and high flow rates, and chaotic behavior at intermediate flow rates.

Rippling instability of a collapsing Bubble,  da Silveira, R., S. Chaieb and L. Mahadevan,  Science , 287, 1468-71, 2000.
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When a bubble of air rises to the top of a highly viscous liquid, it forms a dome-shaped protuberance on the free surface. Unlike a soap bubble, it bursts so slowly as to collapse under its own weight simultaneously, and folds into a wavy structure. This rippling effect occurs for both elastic and viscous sheets, and a theory for its onset is formulated. The growth of the corrugation is governed by the competition between gravitational and bending (shearing) forces and is exhibited for a range of densities, stiffnesses (viscosities), and sizes—a result that arises less from dynamics than from geometry, suggesting a wide validity. A quantitative expression for the number of ripples is presented, together with experimental results that support the theoretical predictions.

Tumbling cards Mahadevan, L., W. Ryu, and A.D.T. Samuel,  Physics of Fluids , 11, 1-3, 1999.
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The purpose of this Letters section is to provide rapid dissemination of important new results in the fields regularly covered by Physics of Fluids. Results of extended research should not be presented as a series of letters in place of comprehensive articles. Letters cannot exceed three printed pages in length, including space allowed for title, figures, tables, references and an abstract limited to about 100 words. There is a three-month time limit, from date of receipt to acceptance, for processing Letter manuscripts. Authors must also submit a brief statement justifying rapid publication in the Letters section.

Axial instability of a free-surface front in a partially-filled horizontal rotating cylinder,  Hosoi, A.E., and L. Mahadevan,  Physics of Fluids , 11, 97-106, 1999.
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We investigate the axial instability of the free-surface front of a viscous fluid in a horizontal cylinder rotating about its longitudinal axis. A simplified model equation for the evolution of the free surface is derived and includes the effects of gravity, capillarity, inertia, and viscosity. This equation is solved numerically to determine the base state with no axial variation, and a numerical linear stability analysis is carried out to examine the onset of unstable axial modes. Various computational results are presented for the wavelength of the axial instability. Inertia is found to play an important role in the onset of the instability and the wavelength of the instability l satisfies the power law l;g1/3, where g is surface tension. Finally some numerical simulations of the simplified evolution equation are presented to show that they can capture the steady shark-teeth patterns observed in recent experiments @R. E. Johnson, in Engineering Science, Fluid Dynamics: A Symposium to Honor T. Y. Wu ~World Scientific, Singapore, 1990!, pp. 435–449; S. T. Thoroddsen and L. Mahadevan, ‘‘Experimental studies of the instabilities in a partially filled horizontal rotating cylinder,’’ Exp. Fluids 23, 1 ~1997!#.

Propagating fronts on sandpile surfaces, Mahadevan, L. and Y. Pomeau,  Europhysics Letters , 46, 595-601, 1999.
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The flow of granular matter such as sand is often characterized by the motion of a thin superficial layer near the free surface, while the bulk of the solid remains immobile. A pair of equations called the BCRE equations (Bouchaud J-P., Cates M. E., Ravi Prakash J. and Edwards S. F. J. Phys. 4 (1994) 1383) have been proposed to model these flows and account for the dynamic exchange of mass between moving and stationary grains using the simplest kinematic considerations. We uncover a new conservation law for the BCRE equations and its variants that unifies a variety of recent special solutions and show that these equations support simple waves, and are capable of finite time singularities that correspond to propagating erosion fronts.

Elastic model of a DNA loop in the lac operon,  Balaeff, A., L. Mahadevan, and K. Schulten,  Physical Review Letters , 83, 4900-03, 1999.
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We use the theory of elasticity to compute the shape of the DNA loop bridging the gap in the crystal structure of the lac repressor-DNA complex. The Kirchhoff system of equations with boundary conditions derived from the crystal structure is solved using a continuation method. This approach can be applied effectively to find coarse-grained conformational minima of DNA loops.

Rolling droplets Mahadevan, L., and Y. Pomeau,  Physics of Fluids , 11, 2449-53, 1999.
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When a rigid circular cylinder or sphere is placed on a rough inclined plane it will roll down the plane. When the experiment is repeated with a rigid cube it will slide down the plane. If the object is deformable a variety of motions become possible; the motion of elastic bodies and fluid drops depends on the interfacial energies of the materials, the roughness of the interfaces, the size of the objects, etc. This is because a deformable body maintains contact with the surface over a finite area. For a viscous fluid droplet, two possible motions may ensue. If the droplet partially wets the surface it slides along it, while if the droplet is nonwetting, it can roll on the surface, much like an elastic body when viewed from the exterior. Here we consider the motion of a small nonwetting droplet forced by a weak gravitational field. A classic example of this motion is exhibited by a droplet of mercury on an inclined plane and is probably the origin of the name quicksilver, after the Latin Argentum Vivum for the swiftly moving droplet of the silvery liquid.

Conical dislocations in crumpling Cerda, E., S. Chaieb, F. Melo and L. Mahadevan,  Nature , 401, 46-49, 1999.
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A crumpled piece of paper is made up of cylindrically curved or nearly planar regions folded along line-like ridges, which themselves pivot about point-like peaks; most of the deformation and energy is focused into these localized objects. Localization of deformation in thin sheets is a diverse phenomenon1±6, and is a consequence of the fact7 that bending a thin sheet is energetically more favourable than stretching it. Previous studies8±11 considered the weakly nonlinear response of peaks and ridges to deformation. Here we report a quantitative description of the shape, response and stability of conical dislocations, the simplest type of topological crumpling deformation. The dislocation consists of a stretched core, in which some of the energy resides, and a peripheral region dominated by bending. We derive scaling laws for the size of the core, characterize the geometry of the dislocation away from the core, and analyse the interaction between two conical dislocations in a simple geometry. Our results show that the initial stages of crumpling (characterized by the large deformation of a few folds) are dominated by bending only. By considering the response of a transversely forced conical dislocation, we show that it is dynamically unstable above a critical load threshold. A similar instability is found for the case of two interacting dislocations, suggesting that a cascade of related instabilities is responsible for the focusing of energy to progressively smaller scales during crumpling.

Fluid rope trick investigated Mahadevan, L., W. Ryu, and A.D.T. Samuel,  Nature, 391, 140, 1998. Corrigendum; ibid., 403, 502, 2000.
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Buckling instabilities can arise from competition between axial compression and bending in slender objects. These are not restricted to solids, but also occur with fluids with free surfaces1–4, in geophysics5 and in materials processing6 . Here we consider a classic demonstration of fluid buckling7 . When honey is poured from a sufficient height, it approaches one’s toast as a thin filament which whirls steadily around the vertical forming a regular helical coil (illustrated with silicone oil in Fig. 1), a behaviour reminiscent of the coiling of a falling flexible rope8 . We derive a scaling law that predicts the coiling frequency in terms of the filament radius and the flow rate.

Conical surfaces and crescent singularities in crumpled sheets,  Cerda, E., and L. Mahadevan,  Physical Review Letters , 80, 2358-61, 1998.
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We analyze the geometry and elasticity of the crescentlike singularity on a crumpled elastic sheet. We give a physical realization of this in terms of a free-boundary contact problem. An analytical solution is given for the universal shape of a developable cone that characterizes the singularity far from the tip, and some of its predictions are qualitatively verified experimentally. We also give a scaling relation for the core size, defined as the region close to the tip of the cone where the sheet is not developable.

Experimental study of instabilities in a partially-filled horizontally-rotating cylinder, Thoroddsen, S.T., and L. Mahadevan,  Experiments in Fluids , 23, 1-13, 1997.
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We describe a number of different phenomena seen in the free-surface flow inside a partially filled circular cylinder which is rotated about its horizontal axis of symmetry. At low angular velocities the flow settles into a steady two-dimensional flow with a front where the coating film coalesces with the pool at the bottom of the cylinder. This mode becomes unstable at higher angular velocities, initially to a sloshing mode on the rising side of the coating film and then to an axial instability on the front. The undulations that appear on the front grow into large-amplitude stationary patterns with cusp-like features for some parameter values. At still higher angular velocities and volume fractions, a number of different inertial instabilities and patterns appear. We present a phase diagram of the various transitions and characterize some of the more prominent instabilities and patterns in detail, along with some possible mechanisms for the observed behaviour.

Colliding waves in an excitable medium: preservation, annihilation and bifurcation, Argentina, M., P. Coullet, and L. Mahadevan,  Physical Review Letters , 79, 2803-07, 1997.
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We analyze the transition from annihilation to preservation of colliding waves. The analysis exploits the similarity between the local and global phase portraits of the system. The transition is shown to be the infinite-dimensional analog of the creation and annihilation of limit cycles in the plane via a homoclinic Andronov bifurcation, and has parallels to the nucleation theory of first-order phase transitions
Tumbling of a falling card Mahadevan, L. Comptes Rendus de l’Academie des Sciences, Paris, Series II , 323, 729-736, 1996.


Shark-teeth patterns in coating flow inside a horizontally-rotating cylinder Thoroddsen, S.T., and L. Mahadevan,  Physics of Fluids , 8(9), S10, 1996.
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Coiling of flexible ropes Mahadevan, L., and J.B. Keller,  Proceedings of the Royal Society of London, Series A, 1452, 1679-1694, 1996.
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Periodic folding of thin sheets Mahadevan, L., and J.B. Keller,  SIAM Journal on Applied Mathematics , 55(6) , 1609-1624, 1995.
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When a thin sheet of a flexible material such as paper is fed from a horizontal spool towards a rough horizontal plane below it, the sheet folds on itself in a regular manner. We model this phenomenon as a free boundary problem for a nonlinearly elastic sheet, taking into account the stiffness and weight of the sheet and the height of the spool above the plane. By using a continuation scheme we solve the problem numerically and follow the evolution of one period of the fold for various values of the parameters. The results are found to agree well with observations of the folding of paper sheets.
Comment on "Behavior of a falling paper," Mahadevan, L., H. Aref, and S.W. Jones,  Physical Review Letters , 75 , 1420, 1995.
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The shape of a Möbius band Mahadevan, L., and J.B. Keller,  Proceedings of the Royal Society of London, Series A , 1440, 149-162, 1993.
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