1. 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.
    [DOI] [View PDF] [Download PDF] 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.
  2. 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.
    [DOI] [View PDF] [Download PDF] 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.
  3. Programming shape using kirigami tessellations G. P. T. Choi, L. H. Dudte and L. Mahadevan, Nature Materials 18, 999–1004. 2019.
    [DOI] [View PDF] [Download PDF] 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.
  4. 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.
    [DOI] [View PDF] [Download PDF] 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.
  5. 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.
    [DOI] [View PDF] [Download PDF] Diversity in the shapes of avian eggs has intrigued biologists for centuries, and recent studies at a range of taxonomic scales suggest that egg shape can be a powerful lens through which to view morphological adaptation. At a broad taxonomic level, we previously examined egg shape in 1400 species (Stoddard et al. 2017). Our study, which contained a detailed analysis of the egg shape morphospace and a new biophysical model of egg shape formation, included a broad-scale phylogenetic comparative analysis of egg shape across more than 1200 species representing 34 orders and 143 families. We found that, at this global scale, most variation in egg shape is correlated with phylogenetic history, an adult bird's body mass and egg size. We also found a significant correlation between egg shape and hand-wing index, a measure of wing shape that provides a general estimate of flight ability, prompting us to consider the possibility that adaptations for flight might be important drivers of egg shape variation.
  6. Molecular control of macroscopic forces drives formation of the vertebrate hindgut N.L. Nerurkar, CH Lee, L. Mahadevan & C.J., Nature 565, 2019.
    [DOI] [View PDF] [Download PDF] 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.
  7. Collective ventilation in honeybee nests J.M. Peters, O. Peleg, L. Mahadevan, J. R. Soc, Interface 16: 20180561. 2019.
    [DOI] [View PDF] [Download PDF] 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.
  8. Morphogenesis of termite mounds S. A. Ocko , A. Heyde, and L. Mahadevan, PNAS 116(9) 3379-3384; published ahead of print February 11, 2019.
    [View PDF] [Download PDF] 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.
  9. Rigidity percolation and geometric information in floppy origami S. Chen, L. Mahadevan, PNAS 116 (17) 8119-8124, 2019.
    [ONLINE ARTICLE] [View PDF] [Download PDF] 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.
  10. A multiphase theory for spreading microbial swarms and films
    S. Srinivasan, N.C. Kaplan, L. Mahadevan, eLife 8:e42697, 2019.
    [DOI] [View PDF] [Download PDF] 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.
  11. Spatial control of irreversible protein aggregation C. Weber, T.C. Michaels and L. Mahadevan, eLife 8:e42315, 2019.
    [DOI] [View PDF] [Download PDF] 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.
  12. Spatio-temporal integration in plant tropisms Y. Meroz, R. Bastien and L. Mahadevan Interface 16, 20190038, 2019.
    [DOI] [View PDF] [Download PDF] 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.
  13. 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] 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.
  14. Optimal strategies for inhibition of protein aggregation T.C. Michaels, C. Weber and L. Mahadevan, PNAS 116 (29) 14593-14598, 2019.
    [View PDF] [Download PDF] 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.
  15. Dynamics of growth and form in prebiotic vesicles T. Herrero-Ruiz, T. Fai, L. Mahadevan, Physical Review Letters 123, 038102, 2019.
    [DOI] [View PDF] [Download PDF] 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.
  16. 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.
    [View PDF] [Download PDF] 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.
  17. 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
    [View PDF] [Download PDF] 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.
  18. 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.
    [View PDF] [Download PDF] 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.
  19. Localized patterns in crushed conical shells O. Gottesman, E. Vouga, S. M. Rubinstein and L. Mahadevan  EPL , 124:14005, 2018.
    [View PDF] [Download PDF] 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.
  20. 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] 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.
  21. Meniscus instabilities in thin elastic layers John S. Biggins and L. Mahadevan,  Soft Matter , 14, 7680-7689, 2018.
    [View PDF] [Download PDF] 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
  22. Planar morphometrics using Teichmüller maps Gary P. T. Choi and L. Mahadevan,  Proceedings of the Royal Society  A 474:20170905, 2018.
    [View PDF] [Download PDF] 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.
  23. Collective mechanical adaptation of honeybee swarms O. Peleg, J. M. Peters, M. K. Salcedo and L. Mahadevan,  Nature Physics Letters , 2018.
    [View PDF] [Download PDF] 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.
  24. Generalized Erdös numbers for network analysis Greg Morrison, Levi H. Dudte and L. Mahadevan,  Royal Society Open Science , 172281, 2018.
    [View PDF] [Download PDF] 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.
  25. 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] 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.
  26. 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] 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.
  27. 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.
    [View PDF] [Download PDF] 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.
  28. Differential activity-driven instabilities in biphasic active matter C. A. Weber, C. H. Rycroft, and L. Mahadevan,  Physical Review Letters  120, 248003, 2018.
    [DOI] [View PDF] [Download PDF] 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.
  29. 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.
    [View PDF] [Download PDF] 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.
  30. 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.
    [DOI] [View PDF] [Download PDF] 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.
  31. Deep-reinforcement learning for gliding and perching G. Novati, L. Mahadevan, P. Koumoutsakos, arXiv
    [ONLINE ARTICLE]
  32. Competing failure modes in finite adhesive pads T. Cohen, C.U. Chan, L. Mahadevan, Soft Matter 2018.
    [DOI] [View PDF] [Download PDF] 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.
  33. Topology, geometry, and mechanics of z-plasty E.A. Matsumoto, H. Liang and L. Mahadevan,  Physical Review Letters  120, 068101, 2018.
    [View PDF] [Download PDF] 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.
  34. Mechanics and statistics of the worm-like chain A. Marantan and L Mahadevan,  American Journal of Physics 86 (2), 86-94, 2018.
    [View PDF] [Download PDF] 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
  35. 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.
    [View PDF] [Download PDF] 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.
  36. Morphogenesis one century after On Growth and Form  Thomas Lecuit and L. Mahadevan,  Development  144, 4197-4198, 2017.
    [View PDF] [Download PDF] 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?
  37. 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.
    [View PDF] [Download PDF] 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.
  38. Growth patterns for shape-shifting elastic bilayers W. M. van Rees, E. Vouga, and L. Mahadevan,  Proceedings of the National Academy of Sciences , 2017.
    [DOI] [View PDF] [Download PDF] 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.
  39. Excitable dynamics and yap-dependent mechanical cues drive the segmentation clock A. Hubaud, I. Regev, L. Mahadevan, O. Pourquié,  Cell  171, 1-15, 2017.
    [View PDF] [Download PDF] 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
  40. 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.
    [View PDF] [Download PDF] 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.
  41. Controllable biomimetic birdsong A. Mukherjee, S. Mandre and L. Mahadevan,  Journal Royal Society Interface  14: 20170002, 2017.
    [View PDF] [Download PDF] 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
  42. Wrinkling instability of an inhomogeneously stretched viscous sheet S. Srinivasan, Z. Wei, L. Mahadevan,  Physical Review Fluids  2, 074103, 2017.
    [View PDF] [Download PDF] 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.
  43. 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.
    [View PDF] [Download PDF] 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
  44. 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.
    [View PDF] [Download PDF] 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.
  45. Optimal strategies for throwing accurately M. Venkadesan and L. Mahadevan,  Royal Society Open Science  , 4: 170136. 2017.
    [View PDF] [Download PDF] 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.
  46. On the growth and form of shoots R. Chelakkot and L. Mahadevan,  Journal of the Royal Society Interface , 14, 20170001, 2017.
    [View PDF] [Download PDF] 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.
  47. 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.
    [View PDF] [Download PDF] 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.
  48. BMP signaling controls buckling forces to modulate looping morphogenesis of the gut N. L. Nerurkar, L. Mahadevan, and C.J.,  Proceedings of the National Academy of Sciences  (USA), 114, 2277-82, 2017.
    [View PDF] [Download PDF] 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.
  49. 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.
    [View PDF] [Download PDF] 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.
  50. Motility-gradient induced elongation of the vertebrate embryo I Regev, K Gevourkian, O Pourquie, L Mahadevan, BioRxiv
    [DOI] [View PDF] [Download PDF] The body of vertebrate embryos forms by posterior elongation from a terminal growth zone called the Tail Bud (TB). The TB produces highly motile cells forming the presomitic mesoderm (PSM), a tissue playing an important role in elongation movements. PSM cells establish an anterior-posterior cell motility gradient which parallels the degradation of a specific cellular signal (Fgf8) known to be implicated in cell motility. Here, we combine electroporation of fluorescent reporters in the PSM to time-lapse imaging in the chicken embryo to quantify cell diffusive movements along the motility gradient. We show that simple microscopic and macroscopic mechano-chemical models for tissue extension that couple Fgf activity, cell motility and tissue rheology at both the cellular and continuum levels suffice to capture the speed and extent of elongation. These observations explain how the continuous addition of cells that exhibit a gradual reduction in motility combined with lateral confinement can be converted into an oriented movement that drives body elongation. The results of the models compare well with our experimental results, with implications for other elongation processes in the embryo.
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