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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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, 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?

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.