The Emergence of Sequential Buckling in Reconfigurable Hexagonal Networks Embedded into Soft Matrix

The extreme and unconventional properties of mechanical metamaterials originate in their sophisticated internal architectures. Traditionally, the architecture of mechanical metamaterials is decided on in the design stage and cannot be altered after fabrication. However, the phenomenon of elastic instability, usually accompanied by a reconfiguration in periodic lattices, can be harnessed to alter their mechanical properties. Here, we study the behavior of mechanical metamaterials consisting of hexagonal networks embedded into a soft matrix. Using finite element analysis, we reveal that under specific conditions, such metamaterials can undergo sequential buckling at two different strain levels. While the first reconfiguration keeps the periodicity of the metamaterial intact, the secondary buckling is accompanied by the change in the global periodicity and formation of a new periodic unit cell. We reveal that the critical strains for the first and the second buckling depend on the metamaterial geometry and the ratio between elastic moduli. Moreover, we demonstrate that the buckling behavior can be further controlled by the placement of the rigid circular inclusions in the rotation centers of order 6. The observed sequential buckling in bulk metamaterials can provide additional routes to program their mechanical behavior and control the propagation of elastic waves.     

Prototypical model for tensional wrinkling in thin sheets

The buckling and wrinkling of thin films has recently seen a surge of interest among physicists, biologists, mathematicians, and engineers. This activity has been triggered by the growing interest in developing technologies at ever-decreasing scales and the resulting necessity to control the mechanics of tiny structures, as well as by the realization that morphogenetic processes, such as the tissue-shaping instabilities occurring in animal epithelia or plant leaves, often emerge from mechanical instabilities of cell sheets. Although the most basic buckling instability of uniaxially compressed plates was understood by Euler more than two centuries ago, recent experiments on nanometrically thin (ultrathin) films have shown significant deviations from predictions of standard buckling theory. Motivated by this puzzle, we introduce here a theoretical model that allows for a systematic analysis of wrinkling in sheets far from their instability threshold. We focus on the simplest extension of Euler buckling that exhibits wrinkles of finite length--a sheet under axisymmetric tensile loads. The first study of this geometry, which is attributed to Lamé, allows us to construct a phase diagram that demonstrates the dramatic variation of wrinkling patterns from near-threshold to far-from-threshold conditions. Theoretical arguments and comparison to experiments show that the thinner the sheet is, the smaller is the compressive load above which the far-from-threshold regime emerges. This observation emphasizes the relevance of our analysis for nanomechanics applications.     

Hierarchical transitions and fractal wrinkling drive bacterial pellicle morphogenesis

Bacterial cells can self-organize into structured communities at fluid–fluid interfaces. These soft, living materials composed of cells and extracellular matrix are called pellicles. Cells residing in pellicles garner group-level survival advantages such as increased antibiotic resistance. The dynamics of pellicle formation and, more generally, how complex morphologies arise from active biomaterials confined at interfaces are not well understood. Here, using Vibrio cholerae as our model organism, a custom-built adaptive stereo microscope, fluorescence imaging, mechanical theory, and simulations, we report a fractal wrinkling morphogenesis program that differs radically from the well-known coalescence of wrinkles into folds that occurs in passive thin films at fluid–fluid interfaces. Four stages occur: growth of founding colonies, onset of primary wrinkles, development of secondary curved ridge instabilities, and finally the emergence of a cascade of finer structures with fractal-like scaling in wavelength. The time evolution of pellicle formation depends on the initial heterogeneity of the film microstructure. Changing the starting bacterial seeding density produces three variations in the sequence of morphogenic stages, which we term the bypass, crystalline, and incomplete modes. Despite these global architectural transitions, individual microcolonies remain spatially segregated, and thus, the community maintains spatial and genetic heterogeneity. Our results suggest that the memory of the original microstructure is critical in setting the morphogenic dynamics of a pellicle as an active biomaterial.

Spontaneous folding, wrinkling, and curling of soft tissues and active materials are ubiquitous in nature. For example, during the development of mammalian organs and plant leaves, collections of many cells self-organize into ordered morphological structures far larger than the size of the individual cells. Nontrivial geometric patterns and architectures often link form to function, such as the fractal branching and size scaling of leaf veins (1), the gyrification of the cerebral cortex (2–4), and the curving of villi in the gut (5, 6). Bacterial cells can also self-organize into communities known as biofilms and pellicles at interfaces. These multicellular communities are crucial in contexts such as medical infections and industrial biofouling because cells in biofilms and pellicles display enhanced resilience to antibiotics, immune clearance, and physical perturbations compared to their isogenic planktonic counterparts (7–9). Analogous to eukaryotic systems, bacterial biofilms and pellicles develop striking macroscopic morphologies including wrinkles and delaminations that are driven by combined biological, material-physics, and mechanical determinants (10–14). Studies of biofilms at the single-cell level show the emergence of internal cell ordering (15–17) and collective cellular flow (18). However, the dynamics of self-organization and the sequence of mechanical instabilities that direct morphogenesis for expanding active soft materials at fluid–fluid interfaces, such as bacterial pellicles, are undefined. Critically, overarching principles connecting microscopic cell organization to macroscopic structures, while potentially common to morphogenesis across different biological systems, are not well understood.Here, we report the sequence of architectural transitions that occur during pellicle maturation for the pathogen Vibrio cholerae. We discover a morphogenic transition characterized by a cascade of wrinkles with fractal scaling in wavelength, which is distinct from the classic wrinkle-to-fold transition widely observed in physical systems such as thin polymer films on fluid baths (19), nanoparticle thin sheets (20), and thin epitaxial layers of gold and elastomers (21, 22). In classic wrinkle-to-fold transitions, as compression increases beyond the linear regime, the initial wrinkles coalesce and localize into folds with large amplitudes. During such transitions, the shape evolution of passive films can be characterized by the minimization of the system’s total energy for different conformations (20, 23–25). In particular, elastic bending energies contained in small wavelength undulations are lost in favor of energies associated with large-scale folds. By contrast, as we demonstrate below, the opposite length-scale progression occurs for actively growing V. cholerae pellicles, in which finer wrinkles and creases continue to emerge following initial morphogenic transitions. The length scales of wrinkles in a mature V. cholerae pellicle follow fractal order, achieving a pattern with fractal dimension of ∼1.6. The additional dimensionality conferred by the fractal geometry could promote nutrient access and enhance signal transduction compared to a smooth structure (26). The fractal progression toward small length scales, as opposed to coalescence toward larger folds, stems from heterogeneous growth in the initial film. We find that the original distribution of microcolonies is preserved during pellicle architectural transitions, and, importantly, it determines the exact sequence of morphogenesis events that will occur. Indeed, changing the initial colony seeding density enabled us to identify a total of four morphogenic routes, which we termed the standard, bypass, crystalline, and incomplete modes. Our results demonstrate a direct connection between microscopic structure and macroscopic morphology for an active, growing soft biomaterial.     

Nanoscale buckling deformation in layered copolymer materials

In layered materials, a common mode of deformation involves buckling of the layers under tensile deformation in the direction perpendicular to the layers. The instability mechanism, which operates in elastic materials from geological to nanometer scales, involves the elastic contrast between different layers. In a regular stacking of "hard" and "soft" layers, the tensile stress is first accommodated by a large deformation of the soft layers. The inhibited Poisson contraction results in a compressive stress in the direction transverse to the tensile deformation axis. The hard layers sustain this transverse compression until buckling takes place and results in an undulated structure. Using molecular simulations, we demonstrate this scenario for a material made of triblock copolymers. The buckling deformation is observed to take place at the nanoscale, at a wavelength that depends on strain rate. In contrast to what is commonly assumed, the wavelength of the undulation is not determined by defects in the microstructure. Rather, it results from kinetic effects, with a competition between the rate of strain and the growth rate of the instability.     

Digital instability of a confined elastic meniscus

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

Microtubule bundling and nested buckling drive stripe formation in polymerizing tubulin solutions

Various mechanisms govern pattern formation in chemical and biological reaction systems, giving rise to structures with distinct morphologies and physical properties. The self-organization of polymerizing microtubules (MTs) is of particular interest because of its implications for biological function. We report a study of the microscopic structure and properties of the striped patterns that spontaneously form in polymerizing tubulin solutions and propose a mechanism driving this assembly. Microscopic observations reveal that the pattern comprises wave-like MT bundles. The retardance of the solution and the fluorescence intensity of labeled MTs vary periodically in space, suggesting a coincident periodic variation in MT alignment and density. This wave-like structure forms through the development and coordinated buckling of initially aligned MT bundles. Both static magnetic fields and convective flow can induce the initial alignment. The nesting of the buckled MT bundles gives rise to density variations that are in quantitative accord with the data. We further propose that the buckling wavelength is selected by a balance between the bending energy of the bundles and the elastic energy of the MT network surrounding them. These studies reveal a unique physical chemical mechanism by which mechanical buckling couples with protein polymerization to produce macroscopic patterns. Self-organization of this type may be important to the formation of certain biological structures.     

Design for Additive Manufacturing and Investigation of Surface-Based Lattice Structures for Buckling Properties Using Experimental and Finite Element Methods

Additive Manufacturing (AM) is rapidly evolving due to its unlimited design freedom to fabricate complex and intricate light-weight geometries with the use of lattice structure that have potential applications including construction, aerospace and biomedical applications, where mechanical properties are the prime focus. Buckling instability in lattice structures is one of the main failure mechanisms that can lead to major failure in structural applications that are subjected to compressive loads, but it has yet to be fully explored. This study aims to investigate the effect of surface-based lattice structure topologies and structured column height on the critical buckling load of lattice structured columns. Four different triply periodic minimal surface (TPMS) lattice topologies were selected and three design configurations (unit cells in x, y, z axis), i.e., 2 × 2 × 4, 2 × 2 × 8 and 2 × 2 × 16 column, for each structure were designed followed by printing using HP MultiJet fusion. Uni-axial compression testing was performed to study the variation in critical buckling load due to change in unit cell topology and column height. The results revealed that the structured column possessing Diamond structures shows the highest critical buckling load followed by Neovius and Gyroid structures, whereas the Schwarz-P unit cell showed least resistance to buckling among the unit cells analyzed in this study. In addition to that, the Diamond design showed a uniform decrease in critical buckling load with a column height maximum of 5193 N, which makes it better for applications in which the column’s height is relatively higher while the Schwarz-P design showed advantages for low height column maximum of 2271 N. Overall, the variations of unit cell morphologies greatly affect the critical buckling load and permits the researchers to select different lattice structures for various applications as per load/stiffness requirement with different height and dimensions. Experimental results were validated by finite element analysis (FEA), which showed same patterns of buckling while the numerical values of critical buckling load show the variation to be up to 10%.     

Buckling-induced encapsulation of structured elastic shells under pressure

We introduce a class of continuum shell structures, the Buckliball, which undergoes a structural transformation induced by buckling under pressure loading. The geometry of the Buckliball comprises a spherical shell patterned with a regular array of circular voids. In order for the pattern transformation to be induced by buckling, the possible number and arrangement of these voids are found to be restricted to five specific configurations. Below a critical internal pressure, the narrow ligaments between the voids buckle, leading to a cooperative buckling cascade of the skeleton of the ball. This ligament buckling leads to closure of the voids and a reduction of the total volume of the shell by up to 54%, while remaining spherical, thereby opening the possibility of encapsulation. We use a combination of precision desktop-scale experiments, finite element simulations, and scaling analyses to explore the underlying mechanics of these foldable structures, finding excellent qualitative and quantitative agreement. Given that this folding mechanism is induced by a mechanical instability, our Buckliball opens the possibility for reversible encapsulation, over a wide range of length scales.     

Morphogenesis and cell ordering in confined bacterial biofilms

Biofilms are aggregates of bacterial cells surrounded by an extracellular matrix. Much progress has been made in studying biofilm growth on solid substrates; however, little is known about the biophysical mechanisms underlying biofilm development in three-dimensional confined environments in which the biofilm-dwelling cells must push against and even damage the surrounding environment to proliferate. Here, combining single-cell imaging, mutagenesis, and rheological measurement, we reveal the key morphogenesis steps of Vibrio cholerae biofilms embedded in hydrogels as they grow by four orders of magnitude from their initial size. We show that the morphodynamics and cell ordering in embedded biofilms are fundamentally different from those of biofilms on flat surfaces. Treating embedded biofilms as inclusions growing in an elastic medium, we quantitatively show that the stiffness contrast between the biofilm and its environment determines biofilm morphology and internal architecture, selecting between spherical biofilms with no cell ordering and oblate ellipsoidal biofilms with high cell ordering. When embedded in stiff gels, cells self-organize into a bipolar structure that resembles the molecular ordering in nematic liquid crystal droplets. In vitro biomechanical analysis shows that cell ordering arises from stress transmission across the biofilm–environment interface, mediated by specific matrix components. Our imaging technique and theoretical approach are generalizable to other biofilm-forming species and potentially to biofilms embedded in mucus or host tissues as during infection. Our results open an avenue to understand how confined cell communities grow by means of a compromise between their inherent developmental program and the mechanical constraints imposed by the environment.

The growth of living organisms is critically influenced by the external environment. One form of such environmental influence is the transmission of mechanical stress, which can instruct morphogenesis in systems ranging from stem cells to tissues to the entire organisms (1, 2). In the prokaryotic domain, bacteria commonly live in complex communities encased by an extracellular matrix (3) known as biofilms (4). Biofilm formation is a morphogenetic process whereby a single founder cell develops into a three-dimensional (3D) aggregate in which bacterial cells interact with each other and with the environment (4–8). Recent work has revealed biophysical mechanisms underlying biofilm morphogenesis on solid substrates, which is controlled by cell–substrate adhesion and the resulting shear stress (9–15). In addition to those living on surfaces, bacterial communities are also commonly found inside soft, structured environments, such as hydrogels. Examples include biofilms growing in mucus layers and host tissues during an infection or food contamination (16). Indeed, many common biofilm formers including Pseudomonas aeruginosa and Vibrio cholerae encounter biological hydrogels as their niche during infection (17, 18). Under these conditions, embedded biofilms must grow against 3D confinement and potentially damage the surrounding environment—a process that is fundamentally different from how surface-attached biofilms expand against friction with the surface (10, 13, 15, 19). However, little is known about how biofilms develop under such 3D mechanical constraints, including how cells collectively organize in response to the confinement and how the confining environment, in turn, is modified by cell proliferation. This is in stark contrast to the accumulating knowledge on the growth dynamics of mammalian cell aggregates and tumors under confinement (20, 21).In this study, we integrate single-cell live imaging, mutagenesis, in vitro mechanical testing, and numerical modeling to investigate how the 3D confinement determines the morphodynamics and cell ordering of an embedded biofilm. A model system is established by embedding V. cholerae, the causal agent of the cholera pandemic and a model biofilm former (22, 23), inside agarose gels (24). By using 3D visualization techniques with high spatiotemporal resolution, we reveal that embedded biofilms undergo a shape transition and a series of self-organization events that are distinct from those in surface-attached biofilms. We first show that the stiffness contrast between the biofilm and the confining hydrogels controls a transition between spherical and ellipsoidal biofilms. Furthermore, we discover that embedded biofilms display a core-shell structure with intricate ordering similar to nematic liquid crystal (LC) droplets (25). Finally, we demonstrate that Vibrio polysaccharide (VPS) and cell-to-surface adhesion proteins effectively transmit stress between the environment and the biofilm, giving rise to distinct cell ordering patterns in embedded biofilms.     

BslA is a self-assembling bacterial hydrophobin that coats the Bacillus subtilis biofilm

Biofilms represent the predominant mode of microbial growth in the natural environment. Bacillus subtilis is a ubiquitous Gram-positive soil bacterium that functions as an effective plant growth-promoting agent. The biofilm matrix is composed of an exopolysaccharide and an amyloid fiber-forming protein, TasA, and assembles with the aid of a small secreted protein, BslA. Here we show that natively synthesized and secreted BslA forms surface layers around the biofilm. Biophysical analysis demonstrates that BslA can self-assemble at interfaces, forming an elastic film. Molecular function is revealed from analysis of the crystal structure of BslA, which consists of an Ig-type fold with the addition of an unusual, extremely hydrophobic “cap” region. A combination of in vivo biofilm formation and in vitro biophysical analysis demonstrates that the central hydrophobic residues of the cap are essential to allow a hydrophobic, nonwetting biofilm to form as they control the surface activity of the BslA protein. The hydrophobic cap exhibits physiochemical properties remarkably similar to the hydrophobic surface found in fungal hydrophobins; thus, BslA is a structurally defined bacterial hydrophobin. We suggest that biofilms formed by other species of bacteria may have evolved similar mechanisms to provide protection to the resident bacterial community.     

Synthesis,Characterization and Testing of Antimicrobial Activity of Composites of Unsaturated Polyester Resins with Wood Flour and Silver Nanoparticles

This paper presents the properties of the wood-resin composites. For improving their antibacterial character, silver nanoparticles were incorporated into their structures. The properties of the obtained materials were analyzed in vitro for their anti-biofilm potency in contact with aerobic Gram-positive Staphylococcus aureus and Staphylococcus epidermidis; and aerobic Gram-negative Escherichia coli and Pseudomonas aeruginosa. These pathogens are responsible for various infections, including those associated with healthcare. The effect of silver nanoparticles incorporation on mechanical and thermomechanical properties as well as gloss were investigated for the samples of composites before and after accelerating aging tests. The results show that bacteria can colonize in various wrinkles and cracks on the composites with wood flour but also the surface of the cross-linked unsaturated polyester resin. The addition of nanosilver causes the death of bacteria. It also positively influences mechanical and thermomechanical properties as well as gloss of the resin.     

Modelling Strategies for Reinforced Concrete Elements under Corrosion Degradation

Aging and corrosion of reinforced concrete structures (RCS) is becoming a global problem, thus proper procedures for simulating the structural performance of corroded RCS should be assessed. Among the main corrosion effects, concrete cover cracking and reinforcement cross-section reduction may influence the materials’ constitutive laws, moreover the confinement contribution and the lateral instability of the longitudinal rebars can be modified. In the present paper, the predictive models available in the scientific literature to assess the materials’ mechanical properties of corroded RCS are recalled and employed into a novel model to derive the theoretical moment–curvature relationships for the cross-section of square and rectangular corroded reinforced concrete elements. The model accounts for cover spalling, buckling of longitudinal reinforcing bars, reduction in confinement pressures, reduction in concrete constitutive law due to the concrete cracking induced by rust formation and decay of mechanical properties for corroded reinforcements. The obtained results are compared with the classical simplified models for corroded RCS, highlighting that buckling and confinement variations cannot be disregarded into a reliable modelling strategy, especially when local ductility plays a key role in the performed investigations.     

Reorganization of columnar architecture in the growing visual cortex

Many cortical areas increase in size considerably during postnatal development, progressively displacing neuronal cell bodies from each other. At present, little is known about how cortical growth affects the development of neuronal circuits. Here, in acute and chronic experiments, we study the layout of ocular dominance (OD) columns in cat primary visual cortex during a period of substantial postnatal growth. We find that despite a considerable size increase of primary visual cortext, the spacing between columns is largely preserved. In contrast, their spatial arrangement changes systematically over this period. Whereas in young animals columns are more band-like, layouts become more isotropic in mature animals. We propose a novel mechanism of growth-induced reorganization that is based on the “zigzag instability,” a dynamical instability observed in several inanimate pattern forming systems. We argue that this mechanism is inherent to a wide class of models for the activity-dependent formation of OD columns. Analyzing one representative of this class, the Elastic Network model, we show that this mechanism can account for the preservation of column spacing and the specific mode of reorganization of OD columns that we observe. We conclude that column width is preserved by systematic reorganization of neuronal selectivities during cortical expansion and that this reorganization is well described by the zigzag instability. Our work suggests that cortical circuits may remain plastic for an extended period in development to facilitate the modification of neuronal circuits to adjust for cortical growth.     

Elasticity Approach to Predict Shape Transformation of Functionally Graded Mechanical Metamaterial under Tension

The re-entrant structures are among the simple unit cell designs that have been widely used in the design of mechanical metamaterials. Changing the geometrical parameters of these unit cell structures, their overall elastic properties (i.e., elastic stiffness and Poisson’s ratio), can be simultaneously tuned. Therefore, different design strategies (e.g., functional gradient) can be implemented to design advanced engineering materials with unusual properties. Here, using the theory of elasticity and finite element modeling, we propose a fast and direct approach to effectively design the microarchitectures of mechanical metamaterials with re-entrant structures that allow predicting complex deformation shapes under uniaxial tensile loading. We also analyze the efficiency of this method by back calculating the microarchitectural designs of mechanical metamaterials to predict the complex 1-D external contour of objects (e.g., vase and foot). The proposed approach has several applications in creating programmable mechanical metamaterials with shape matching properties for exoskeletal and soft robotic devices.     

Emerging Phage Resistance in Pseudomonas aeruginosa PAO1 Is Accompanied by an Enhanced Heterogeneity and Reduced Virulence

Bacterial surface structures of a proteinic nature and glycoconjugates contribute to biofilm formation and provide shields to host defense mechanisms (e.g., the complement system and phagocytosis). A loss or alteration of these molecules, leading to phage resistance, could result in fewer virulent bacteria. In this study, we evaluate the biology and phenotype changes in Pseudomonas aeruginosa PAO1 phage-resistant clones, which emerge in phage-treated biofilms. We characterize these clones for phage-typing patterns, antibiotic resistance, biofilm formation, pathogenicity, and interactions with the innate immune system. Another important question that we address is whether phage-resistant mutants are also generated incidentally, despite the phage treatment-selective pressure, as the natural adaptation of the living biofilm population. It is found that the application of different phages targeting a particular receptor selects similar phage resistance patterns. Nevertheless, this results in a dramatic increase in the population heterogeneity, giving over a dozen phage-typing patterns, compared to one of the untreated PAO1 sessile forms. We also confirm the hypothesis that “phage-resistant bacteria are more susceptible to antibiotics and host-clearance mechanisms by the immune system”. These findings support phage application in therapy, although the overall statement that phage treatment selects the less virulent bacterial population should be further verified using a bigger collection of clinical strains.     

Nipah Virus Infection Generates Ordered Structures in Cellulo

Nipah virus (NiV) is a zoonotic paramyxovirus with a fatality rate of up to 92% in humans. While several pathogenic mechanisms used by NiV to counteract host immune defense responses have been described, all of the processes that take place in cells during infection are not fully characterized. Here, we describe the formation of ordered intracellular structures during NiV infection. We observed that these structures are formed specifically during NiV infection, but not with other viruses from the same Mononegavirales order (namely Ebola virus) or from other orders such as Bunyavirales (Junín virus). We also determined the kinetics of the appearance of these structures and their cellular localization at the cellular periphery. Finally, we confirmed the presence of these NiV-specific ordered structures using structured illumination microscopy (SIM), as well as their localization by transmission electron microscopy (TEM), scanning electron microscopy (SEM), and correlative light and electron microscopy (CLEM). Herein, we describe a cytopathogenic mechanism that provides a new insight into NiV biology. These newly described ordered structures could provide a target for novel antiviral approaches.     

Anisotropic growth shapes intestinal tissues during embryogenesis

Embryogenesis offers a real laboratory for pattern formation, buckling, and postbuckling induced by growth of soft tissues. Each part of our body is structured in multiple adjacent layers: the skin, the brain, and the interior of organs. Each layer has a complex biological composition presenting different elasticity. Generated during fetal life, these layers will experience growth and remodeling in the early postfertilization stages. Here, we focus on a herringbone pattern occurring in fetal intestinal tissues. Common to many mammalians, this instability is a precursor of the villi, finger-like projections into the lumen. For avians (chicks’ and turkeys’ embryos), it has been shown that, a few days after fertilization, the mucosal epithelium of the duodenum is smooth, and then folds emerge, which present 2 d later a pronounced zigzag instability. Many debates and biological studies are devoted to this specific morphology, which regulates the cell renewal in the intestine. After reviewing experimental results about duodenum morphogenesis, we show that a model based on simplified hypothesis for the growth of the mesenchyme can explain buckling and postbuckling instabilities. Being completely analytical, it is based on biaxial compressive stresses due to differential growth between layers and it predicts quantitatively the morphological changes. The growth anisotropy increasing with time, the competition between folds and zigzags, is proved to occur as a secondary instability. The model is compared with available experimental data on chick’s duodenum and can be applied to other intestinal tissues, the zigzag being a common and spectacular microstructural pattern of intestine embryogenesis.     

Cell–cell contacts confine public goods diffusion inside Pseudomonas aeruginosa clonal microcolonies

The maintenance of cooperation in populations where public goods are equally accessible to all but inflict a fitness cost on individual producers is a long-standing puzzle of evolutionary biology. An example of such a scenario is the secretion of siderophores by bacteria into their environment to fetch soluble iron. In a planktonic culture, these molecules diffuse rapidly, such that the same concentration is experienced by all bacteria. However, on solid substrates, bacteria form dense and packed colonies that may alter the diffusion dynamics through cell–cell contact interactions. In Pseudomonas aeruginosa microcolonies growing on solid substrate, we found that the concentration of pyoverdine, a secreted iron chelator, is heterogeneous, with a maximum at the center of the colony. We quantitatively explain the formation of this gradient by local exchange between contacting cells rather than by global diffusion of pyoverdine. In addition, we show that this local trafficking modulates the growth rate of individual cells. Taken together, these data provide a physical basis that explains the stability of public goods production in packed colonies.     

Active multistage coarsening of actin networks driven by myosin motors

In cells, many vital processes involve myosin-driven motility that actively remodels the actin cytoskeleton and changes cell shape. Here we study how the collective action of myosin motors organizes actin filaments into contractile structures in a simplified model system devoid of biochemical regulation. We show that this self-organization occurs through an active multistage coarsening process. First, motors form dense foci by moving along the actin network structure followed by coalescence. Then the foci accumulate actin filaments in a shell around them. These actomyosin condensates eventually cluster due to motor-driven coalescence. We propose that the physical origin of this multistage aggregation is the highly asymmetric load response of actin filaments: they can support large tensions but buckle easily under piconewton compressive loads. Because the motor-generated forces well exceed this threshold, buckling is induced on the connected actin network that resists motor-driven filament sliding. We show how this buckling can give rise to the accumulation of actin shells around myosin foci and subsequent coalescence of foci into superaggregates. This new physical mechanism provides an explanation for the formation and contractile dynamics of disordered condensed actomyosin states observed in vivo.