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

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

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

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

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

As the thinnest atomic membrane, graphene presents an opportunity to combine geometry, elasticity, and electronics at the limits of their validity. We describe the transport and electronic structure in the neighborhood of conical singularities, the elementary excitations of the ubiquitous wrinkled and crumpled graphene. We use a combination of atomistic mechanical simulations, analytical geometry, and transport calculations in curved graphene, and exact diagonalization of the electronic spectrum to calculate the effects of geometry on electronic structure, transport, and mobility in suspended samples, and how the geometry-generated pseudomagnetic and pseudoelectric fields might disrupt Landau quantization.

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

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

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

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

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

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

Cellular and organellar membranes are dynamic materials that underlie many aspects of cell biology. Biological membranes have long been thought of as elastic materials with respect to bending deformations. A wealth of theory and experimentation on pure phospholipid membranes provides abundant support for this idea. However, biological membranes are not composed solely of phospholipids—they also incorporate a variety of amphiphilic molecules that undergo rapid transbilayer flip-flop. Here we describe several experimental systems that demonstrate deformation-induced molecular flip-flop. First we use a fluorescence assay to track osmotically controlled membrane deformation in single component fatty acid vesicles, and show that the relaxation of the induced bending stress is mediated by fatty acid flip-flop. We then look at two-component phospholipid/cholesterol composite vesicles. We use NMR to show that the steady-state rate of interleaflet diffusion of cholesterol is fast relative to biological membrane remodeling. We then use a Fo¨rster resonance energy transfer assay to detect the transbilayer movement of cholesterol upon deformation. We suggest that our results can be interpreted by modifying the area difference elasticity model to account for the time-dependent relaxation of bending energy. Our findings suggest that rapid interleaflet diffusion of cholesterol may play a role in membrane remodeling in vivo. We suggest that the molecular characteristics of sterols make them evolutionarily preferred mediators of stress relaxation, and that the universal presence of sterols in the membranes of eukaryotes, even at low concentrations, reflects the importance of membrane remodeling in eukaryotic cells.

Micropatterned poly(dimethylsiloxane) substrates fabricated by soft lithography led to large-scale orientation of myoblasts in culture, thereby controlling the orientation of the myotubes they formed. Fusion occurred on many chemically identical surfaces in which varying structures were arranged in square or hexagonal lattices, but only a subset of patterned surfaces yielded aligned myotubes. Remarkably, on some substrates, large populations of myotubes oriented at a reproducible acute angle to the lattice of patterned features. A simple geometrical model predicts the angle and extent of orientation based on maximizing the contact area between the myoblasts and patterned topographic surfaces. Micropatterned substrates also provided short-range cues that influenced higher-order functions such as the localization of focal adhesions and accumulation of postsynaptic acetylcholine receptors. Our results represent what we believe is a new approach for musculoskeletal tissue engineering, and our model sheds light on mechanisms of myotube alignment in vivo.

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

This article describes a new procedure for generating and transmitting a messagesa sequence of optical pulsessby aligning a mask (an opaque sheet containing transparent “windows”) below a microfluidic channel in which flows an opaque continuous fluid containing transparent droplets. The optical mask encodes the message as a unique sequence of windows that can transmit or block light; the flow of transparent droplets in the channel converts this message into a sequence of optical pulses. The properties of the windows on the mask (e.g., their size, wavelength of transmittance, orientation of polarization) determine the information carried in these optical pulses (e.g., intensity, color, polarization). The structure of a transmitted signal depends on the number and spacing of droplets in the channel. Fourier transformation can deconvolve superimposed signals created by the flow of multiple droplets into the message that a single droplet would transmit. The research described in this contribution explores a new field at the intersection of chemistry, materials science, and information technology: infochemistry.

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

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

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

Drosophila germ-band extension (GBE) is an example of the convergence and extension movements that elongate and narrow embryonic tissues. To understand the collective cell behaviours underlying tissue morphogenesis, we have continuously quantified cell intercalation and cell shape change during GBE. We show that the fast, early phase of GBE depends on cell shape change in addition to cell intercalation. In antero-posterior patterning mutants such as those for the gap gene Krüppel, defective polarized cell intercalation is compensated for by an increase in antero-posterior cell elongation, such that the initial rate of extension remains the same. Spatio-temporal patterns of cell behaviours indicate that an antero-posterior tensile force deforms the germ band, causing the cells to change shape passively. The rate of anteroposterior cell elongation is reduced in twist mutant embryos, which lack mesoderm. We propose that cell shape change contributing to germ-band extension is a passive response to mechanical forces caused by the invaginating mesoderm.

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

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

Ratcheting surfaces are a common motif in nature and appear in plant awns and grasses. They are known to proffer selective advantages for seed dispersion and burial. In two simple model experiments, we show that these anisotropically toothed surfaces naturally serve as motion rectifiers and generically move in a unidirectional manner, when subjected to temporally and spatially symmetric excitations of various origins. Using a combination of theory and experiment, we show that a linear relationship between awn length and ratchet efficiency holds under biologically relevant conditions. Grass awns can thus efficiently transform non-equilibrium environmental stresses from such sources as humidity variations into useful work and directed motion using their length as a fluctuation amplifier, yielding a selective advantage to these organelles in many plant species.

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

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

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

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

Many functions of the extracellular matrix can be mimicked by small peptide fragments (e.g., arginine–glycine–aspartic acid (RGD) sequence) of the entire molecule, but the presentation of the peptides is critical to their effects on cells. It is likely that some effects of peptide presentation from biomaterials simply relate to the number of bonds formed between cell receptors and the adhesion ligands, but a lack of tools to quantify bond number limits direct investigation of this assumption. The impact of different ligand presentations (density, affinity, and nanoscale distribution) on the proliferation of C2C12 and human primary myoblasts was first examined in this study. Increasing the ligand density or binding affinity led to a similar enhancement in proliferation of C2C12 cells and human primary myoblasts. The nanoscale distribution of clustered RGD ligands also influenced C2C12 cells and human primary myoblast proliferation, but in an opposing manner. A rheological technique and a FRET technique were then utilized to quantify the number of receptor–ligand interactions as a function of peptide presentation. Higher numbers of bonds were formed when the RGD density and affinity were increased, as measured with both techniques, and bond number correlated with cell growth rates. However, the influence of the nanoscale peptide distribution did not appear to be solely a function of bond number. Altogether, these findings provide significant insight to the role of peptide presentation in the regulation of cell proliferation, and the approaches developed in this work may have significant utility in probing how adhesion regulates a variety of other cellular functions and aid in developing design criterion for cell-interactive materials.

Two views have dominated recent discussions of the physical basis of cell shape change during migration and division of animal cells: the cytoplasm can be modeled as a viscoelastic continuum, and the forces that change its shape are generated only by actin polymerization and actomyosin contractility in the cell cortex. Here, we question both views: we suggest that the cytoplasm is better described as poroelastic, and that hydrodynamic forces may be generally important for its shape dynamics. In the poroelastic view, the cytoplasm consists of a porous, elastic solid (cytoskeleton, organelles, ribosomes) penetrated by an interstitial fluid (cytosol) that moves through the pores in response to pressure gradients. If the pore size is small (30–60 nm), as has been observed in some cells, pressure does not globally equilibrate on time and length scales relevant to cell motility. Pressure differences across the plasma membrane drive blebbing, and potentially other type of protrusive motility. In the poroelastic view, these pressures can be higher in one part of a cell than another, and can thus cause local shape change. Local pressure transients could be generated by actomyosin contractility, or by local activation of osmogenic ion transporters in the plasma membrane. We propose that local activation of Na+/H+ antiporters (NHE1) at the front of migrating cells promotes local swelling there to help drive protrusive motility, acting in combination with actin polymerization. Local shrinking at the equator of dividing cells may similarly help drive invagination during cytokinesis, acting in combination with actomyosin contractility. Testing these hypotheses is not easy, as water is a difficult analyte to track, and will require a joint effort of the cytoskeleton and ion physiology communities.

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

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

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

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

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

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

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

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

Blebs are spherical cellular protrusions that occur in many physiological situations. Two distinct phases make up the life of a bleb, each of which have their own biology and physics: expansion, which lasts ;30 s, and retraction, which lasts ;2 min. We investigate these phases using optical microscopy and simple theoretical concepts, seeking information on blebbing itself, and on cytomechanics in general. We show that bleb nucleation depends on pressure, membrane-cortex adhesion energy, and membrane tension, and test this experimentally. Bleb growth occurs through a combination of bulk flow of lipids and delamination from the cell cortex via the formation and propagation of tears. In extreme cases, this can give rise to a traveling wave around the cell periphery, known as ‘‘circus movement.’’ When growth stalls, an actin cortex reforms under the bleb membrane, and retraction starts, driven by myosin-II. Using flicker spectroscopy, we find that retracting blebs are fivefold more rigid than expanding blebs, an increase entirely explained by the properties of the newly formed cortical actin mesh. Finally, using artificially nucleated blebs as pressure sensors, we show that cells rounded up in mitosis possess a substantial intracellular pressure.

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

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

We study the dynamics of a flexible foil immersed in a fluid and moving close to a rigid wall. Lubrication theory allows us to derive equations of motion for the foil and thus examine the passive settling and the active swimming of a foil. This also allows us to partly answer the long-standing question in cartoon physics—can carpets fly? Our analysis suggests a region in parameter space where one may realize this dream and move the virtual towards reality.

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

Colloidal suspensions are susceptible to gravitationally induced phase separation. This can be mitigated by the formation of a particle network caused by depletion attraction. The effectiveness of this network in supporting the buoyant weight of the suspension can be characterized by its compressional modulus. We measure the compressional modulus for emulsion networks induced by depletion attraction and present a model that quantitatively predicts their gravitational stability. We also determine the relationship between the strength of the depletion attraction and the magnitude of the compressional modulus.

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

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

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

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

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

Mechanisms for shaping and folding sheets of cells during development are poorly understood. An example is the complex reorganisation of the forebrain neural plate during neurulation, which must fold a sheet into a tube while evaginating two eyes from a single contiguous domain within the neural plate. We, for the first time, track these cell rearrangements to show that forebrain morphogenesis differs significantly from prior hypotheses. We postulate a new model for forebrain neurulation and demonstrate how mutations affecting two signalling pathways can generate cyclopic phenotypes by disrupting normal cell movements or introducing new erroneous behaviours.