Termite mounds harness diurnal temperature oscillations for ventilation

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

Solid friction between soft filaments

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

Bending gradients: how the intestinal stem cell gets its home

We address the mechanism by which adult intestinal stem cells (ISCs) become localized to the base of each villus during embryonic development. We find that, early in gut development, proliferating progenitors expressing ISC markers are evenly distributed throughout the epithelium, in both the chick and mouse. However, as the villi form, the putative stem cells become restricted to the base of the villi. This shift in the localization is driven by mechanically influenced reciprocal signaling between the epithelium and underlying mesenchyme. Buckling forces physically distort the shape of the morphogenic field, causing local maxima of epithelial signals, in particular Shh, at the tip of each villus. This induces a suite of high-threshold response genes in the underlying mesenchyme to form a signaling center called the "villus cluster." Villus cluster signals, notably Bmp4, feed back on the overlying epithelium to ultimately restrict the stem cells to the base of each villus.

Feedback-induced phase transitions in active heterogeneous conductors

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

Elastocapillary coalescence of plates and pillars

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

Gyrification from constrained cortical expansion

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

Density-gradient-free microfluidic centrifugation for analytical and preparative separation of nanoparticles

Sedimentation and centrifugation techniques are widely applied for the separation of biomolecules and colloids but require the presence of controlled density gradients for stable operation. Here we present an approach for separating nanoparticles in free solution without gradients. We use microfluidics to generate a convective flow perpendicular to the sedimentation direction. We show that the hydrodynamic Rayleigh-Taylor-like instability, which, in traditional methods, requires the presence of a density gradient, can be suppressed by the Poiseuille flow in the microchannel. We illustrate the power of this approach by demonstrating the separation of mixtures of particles on the nanometer scale, orders of magnitude smaller than the micrometer-sized objects separated by conventional inertial microfluidic approaches. This technique exhibits a series of favorable features including short analysis time, small sample volume, limited dilution of the analyte, limited interactions with surfaces as well as the possibility to tune easily the separation range by adjusting the geometry of the system. These features highlight the potential of gradient-free microfluidic centrifugation as an attractive route toward a broad range of nanoscale applications.

Models for elastic shells with incompatible strains

The three-dimensional shapes of thin lamina, such as leaves, flowers, feathers, wings, etc., are driven by the differential strain induced by the relative growth. The growth takes place through variations in the Riemannian metric given on the thin sheet as a function of location in the central plane and also across its thickness. The shape is then a consequence of elastic energy minimization on the frustrated geometrical object. Here, we provide a rigorous derivation of the asymptotic theories for shapes of residually strained thin lamina with non-trivial curvatures, i.e. growing elastic shells in both the weakly and strongly curved regimes, generalizing earlier results for the growth of nominally flat plates. The different theories are distinguished by the scaling of the mid-surface curvature relative to the inverse thickness and growth strain, and also allow us to generalize the classical Föppl-von Kármán energy to theories of prestrained shallow shells.

Intermittent locomotion as an optimal control strategy

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

Lift-off instability during the impact of a drop on a solid surface

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

Collective thermoregulation in bee clusters

Swarming is an essential part of honeybee behaviour, wherein thousands of bees cling onto each other to form a dense cluster that may be exposed to the environment for several days. This cluster has the ability to maintain its core temperature actively without a central controller. We suggest that the swarm cluster is akin to an active porous structure whose functional requirement is to adjust to outside conditions by varying its porosity to control its core temperature. Using a continuum model that takes the form of a set of advection-diffusion equations for heat transfer in a mobile porous medium, we show that the equalization of an effective 'behavioural pressure', which propagates information about the ambient temperature through variations in density, leads to effective thermoregulation. Our model extends and generalizes previous models by focusing the question of mechanism on the form and role of the behavioural pressure, and allows us to explain the vertical asymmetry of the cluster (as a consequence of buoyancy-driven flows), the ability of the cluster to overpack at low ambient temperatures without breaking up at high ambient temperatures, and the relative insensitivity to large variations in the ambient temperature. Our theory also makes testable hypotheses for the response of the cluster to external temperature inhomogeneities and suggests strategies for biomimetic thermoregulation.

Aging in complex interdependency networks

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

Bacillus spores as building blocks for stimuli-responsive materials and nanogenerators

Materials that respond mechanically to external chemical stimuli have applications in biomedical devices, adaptive architectural systems, robotics and energy harvesting. Inspired by biological systems, stimuli-responsive materials have been created that can oscillate, transport fluid, provide homeostasis and undergo complex changes in shape. However, the effectiveness of synthetic stimuli-responsive materials in generating work is limited when compared with mechanical actuators. Here, we show that the mechanical response of Bacillus spores to water gradients exhibits an energy density of more than 10 MJ m(-3), which is two orders of magnitude higher than synthetic water-responsive materials. We also identified mutations that can approximately double the energy density of the spores and found that they can self-assemble into dense, submicrometre-thick monolayers on substrates such as silicon microcantilevers and elastomer sheets, creating bio-hybrid hygromorph actuators. To illustrate the potential applications of the spores, we used them to build an energy-harvesting device that can remotely generate electrical power from an evaporating body of water.

Quantifying cell-generated mechanical forces within living embryonic tissues

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

Statistical mechanics and shape transitions in microscopic plates

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

Flagellar dynamics of a connected chain of active, polar, Brownian particles

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

How ticks get under your skin: insertion mechanics of the feeding apparatus of Ixodes ricinus ticks

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

Elastic platonic shells

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

Villification: how the gut gets its villi

The villi of the human and chick gut are formed in similar stepwise progressions, wherein the mesenchyme and attached epithelium first fold into longitudinal ridges, then a zigzag pattern, and lastly individual villi. We find that these steps of villification depend on the sequential differentiation of the distinct smooth muscle layers of the gut, which restrict the expansion of the growing endoderm and mesenchyme, generating compressive stresses that lead to their buckling and folding. A quantitative computational model, incorporating measured properties of the developing gut, recapitulates the morphological patterns seen during villification in a variety of species. These results provide a mechanistic understanding of the formation of these elaborations of the lining of the gut, essential for providing sufficient surface area for nutrient absorption.

Adaptive fluid-infused porous films with tunable transparency and wettability

Materials that adapt dynamically to environmental changes are currently limited to two-state switching of single properties, and only a small number of strategies that may lead to materials with continuously adjustable characteristics have been reported. Here we introduce adaptive surfaces made of a liquid film supported by a nanoporous elastic substrate. As the substrate deforms, the liquid flows within the pores, causing the smooth and defect-free surface to roughen through a continuous range of topographies. We show that a graded mechanical stimulus can be directly translated into finely tuned, dynamic adjustments of optical transparency and wettability. In particular, we demonstrate simultaneous control of the film's transparency and its ability to continuously manipulate various low-surface-tension droplets from free-sliding to pinned. This strategy should make possible the rational design of tunable, multifunctional adaptive materials for a broad range of applications.

Geometric mechanics of periodic pleated origami

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

Planar morphometry, shear and optimal quasi-conformal mappings

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