Nature Physics

Most animals coordinate behaviour using neural computations. Yet, single-celled organisms also exhibit stimulus-responsive, even cognitive, actions. To understand how a single cell can coordinate and drive complex behaviours without any neural encoding, we study an algal protist - a motile cell with four extremely long cilia. The organism displays a surprisingly rich locomotor repertoire, emerging from the intricate dynamics of the cilia, which form a tight bundle when swimming. We leverage high-speed quantitative live imaging to extract the spectrum of possible ciliary beating patterns, and derive a dispersion relation coupling the temporal frequency and spatial wavelength of cilia oscillations. We further reconstruct the attractor manifold embedded in the behavioural space, showing that despite the range and complexity of ciliary beating modes, the underlying behavioural manifold is intrinsically low-dimensional with elaborate topological structure. Dynamic and excitable transitions in motility behaviour are encoded as trajectories in this space.

Thin shells buckle and wrinkle when compressed. While this behavior is generally detrimental in engineering, it has been widely implicated in epithelial morphogenesis and patterning during development. Yet the rules governing buckling of active viscoelastic shells like epithelia remain unclear. Here we delineate those rules by combining an experimental system that allows us to sculpt epithelial shells and subject them to controlled deflation with a 3D computational model linking cytoskeletal dynamics to tissue mechanics. Experiments and simulations across several orders of magnitude in time and space reveal that buckling emerges for fast deflation relative to the cortexs relaxation time, and is suppressed by high contractility. We show, further, that the tissue develops wrinkle patterns with different degrees of symmetry breaking that depend on its size and viscous confinement. Strikingly, we find that epithelial buckling is a multiscale phenomenon involving long-lived supracellular folds but also short-lived subcellular wrinkles in the actin cortex. Finally, by forming epithelial shells with anisotropic curvature we rationally direct buckling into predictable wrinkle patterns. Our study shows that epithelial tissues can be understood as hierarchical materials with mechanical instabilities that can be harnessed to engineer epithelial morphogenesis.

Self-tuning--the ability of disordered systems to develop desired collective behaviors by tuning internal couplings in response to feedback--has recently emerged as a powerful framework for understanding adaptation in amorphous solids, mechanical metamaterials, and electrical networks. These systems can learn desired responses, encode memory, and robustly reorganize under repeated stimuli, much like artificial neural networks but without requiring processors to adjust their weights. Here, we extend this paradigm to morphogenesis and show that the epithelium can be viewed as tunable matter and that epithelial convergent extension (CE) can be understood as a self-tuning process. Using a vertex model with active interfacial tensions, we systematically compare distinct tension-update strategies, including externally imposed shear, global gradient descent optimization, and decentralized local feedback rules. We find that while all methods can generate tissue elongation, only local orientation- and length-sensitive rules reproduce key experimental features of CE, such as supracellular actomyosin pattern formation, cell shape changes, and junctional alignment. In contrast, global optimization produces homogeneous tension patterns and mechanically fragile states. By interpreting CE through the lens of tuning, our framework bridges the physics of tunable matter with developmental biology, revealing how simple, local rules enable tissues to efficiently orchestrate complex morphogenetic outcomes through decentralized mechanical adaptation.

Microbes across species and environments form biofilms, living materials composed of cells and extracellular polymers. Biofilm-dwelling cells benefit from emergent soft matter physics that sculpts three-dimensional morphologies and osmotically absorbs nutrients. Although biofilms are modeled as viscoelastic gels, the physical origins of the phase transition underlying their conversion from groups of cells to living gels have not been systematically investigated. Here, we show that Bacillus subtilis biofilms use polymer composition to tune their physical properties and drive gel formation. Using imaging and water immersion experiments with matrix knockout strains, we demonstrate the complementary roles of two polymers in this developmental transition: hydrophilic poly-{gamma}-glutamate swells colonies by absorbing water and exopolysaccharides serve as effective cross-linkers, causing a sol-gel-like phase transition that imparts structural integrity. With matrix knockout co-culture biofilms, we independently modulate the production of each polymer and reveal a phase space of biofilm morphologies. Colonies that produce both polymers develop macroscopic wrinkles. A thin-film model predicts biofilm wrinkling from swelling-generated internal strain coupled to elasticity. The model reproduces the shape of our observed morphological phase diagram. Our results demonstrate that bacteria leverage gelation to vary their material properties and morphologies, with implications for microbial ecology and engineering living matter.

Many living cells actively migrate in their environment to perform key biological functions - from unicellular organisms looking for food to single cells such as fibroblasts, leukocytes or cancer cells that can shape, patrol or invade tissues. Cell migration results from complex intracellular processes that enable cell self-propulsion 1,2, and has been shown to also integrate various chemical or physical extracellular signals 3,4,5. While it is established that cells can modify their environment by depositing biochemical signals or mechanically remodeling the extracellular matrix, the impact of such self-induced environmental perturbations on cell trajectories at various scales remains unexplored. Here, we show that cells remember their path: by confining cells on 1D and 2D micropatterned surfaces, we demonstrate that motile cells leave long-lived physicochemical footprints along their way, which determine their future path. On this basis, we argue that cell trajectories belong to the general class of self-interacting random walks, and show that self-interactions can rule large scale exploration by inducing long-lived ageing, subdiffusion and anomalous first-passage statistics. Altogether, our joint experimental and theoretical approach points to a generic coupling between motile cells and their environment, which endows cells with a spatial memory of their path and can dramatically change their space exploration.

Many bacteria live in polymeric fluids, such as mucus, environmental polysaccharides, and extracellular polymers in biofilms. However, lab studies typically focus on cells in polymer-free fluids. Here, we show that interactions with polymers shape a fundamental feature of bacterial life--how they proliferate in space in multicellular colonies. Using experiments, we find that when polymer is sufficiently concentrated, cells generically and reversibly form large serpentine "cables" as they proliferate. By combining experiments with biophysical theory and simulations, we demonstrate that this distinctive form of colony morphogenesis arises from an interplay between polymer-induced entropic attraction between neighboring cells and their hindered ability to diffusely separate from each other in a viscous polymer solution. Our work thus reveals a pivotal role of polymers in sculpting proliferating bacterial colonies, with implications for how they interact with hosts and with the natural environment, and uncovers quantitative principles governing colony morphogenesis in such complex environments.

Biological materials, like epithelial tissues, exhibit remarkable adaptability to mechanical stresses, dynamically remodeling their structure in response to external and internal forces. A key challenge is understanding how these tissues store a memory of past mechanical stimuli. Here, we investigate this memory using an active Vertex Model of epithelial sheets incorporating a local, mechanosensitive tension-remodeling rule where junctional tension updates depend on strain, acting as a slow, history-dependent variable. We demonstrate three hallmark mechanical consequences of this memory mechanism. First, a localized, short contractile cue permanently reprograms the global shear modulus, with the direction of change (stiffening or softening) controlled by the tension remodeling rate. Second, the tissue stores a long-range mechanical memory: a prior stimulus at one site modulates the tissues response to a subsequent, distant stimulus, mediated by coupling across the entire junctional network. Finally, we show that simple cyclic bulk deformation acts as a training protocol that autonomously tunes the tissues constitutive properties, including programming the Poisson ratio to auxetic (negative) values. These findings position epithelial mechanics within the framework of unsupervised physical learning, identifying the mechanosensitive remodeling rates as powerful control parameters for designing programmable tissue-scale rheology.

Destructive mechanical breakdowns and fractures are ubiquitous events in driven physical matter; living tissues, by contrast, can rupture repeatedly while restoring integrity. Here we study rupture-repair interplay in regenerating Hydra tissues, which cycle through osmotic inflation, pressure release by rupture, and resealing. We utilize bright-field imaging of the tissues projected area as a readout of the rupture magnitude before it is arrested. Analyzing these event statistics, we find that the tail of the area-drop distribution is controlled by Ca2+-dependent repair efficiency. When the Ca2+ response is weakened, either by partially blocking gap-junctions mediating the intercellular communication, or by inhibiting stretch-activated Ca2+ channels, the actomyosin force that arrests the rupture process is delayed or reduced. Under these conditions, rare large pressure releases become more likely, and the tail of the distribution crosses over from an exponential behavior, exhibiting a characteristic scale, to a power-law one consistent with a critical-like regime reflecting intermittent rupture propagation. These results identify mechanically evoked Ca2+ activity as a control axis linking repair to rupture statistics in a living tissue. It supports a picture of rupture front advancing by stick-slip-like dynamics as it encounters a heterogeneous mechanical landscape, akin to failure-front propagation in disordered materials.

Gradients of extracellular signals organise cells in tissues. Although there are several models for how gradients can pattern cell behaviour, it is not clear how cells react to gradients when the population is undergoing 3D morphogenesis, in which cell-cell and cell-signal interactions are continually changing. Dictyostelium cells follow gradients of their nutritional source to feed and maintain their undifferentiated state. Using light sheet imaging to simultaneously monitor signaling, single cell and population dynamics, we show that the cells migrate towards nutritional gradients in swarms. As swarms advance, they deposit clumps of cells at the rear, triggering differentiation. Clump deposition is explained by a physical model in which cell swarms behave as active droplets: cells proliferate within the swarm, with clump shedding occurring at a critical population size, at which cells at the rear no longer perceive the gradient and are not retained by the emergent surface tension of the swarm. The droplet model predicts vortex motion of the cells within the swarm emerging from the local transfer of propulsion forces, a prediction validated by 3D tracking of single cells. This active fluid behaviour reveals a developmental mechanism we term "musical chairs" decision-making, in which the decision to proliferate or differentiate is determined by the position of a cell within the group as it bifurcates.

How are bacterial communities altered by changes in their microenvironment? Evidence from homogeneous liquid or flat plate cultures implicates biochemical cues -- such as variation in nutrient composition 1,2, response to chemoattractants and toxins 3,4, and inter-species signalling 5,6 -- as the primary modes of bacterial interaction with their microenvironment. However, these systems fail to capture the effect of physical confinement on bacteria in their natural habitats. Bacterial niches like the pores of soil, mucus, and infected tissues are disordered microenvironments with material properties defined by their internal pore sizes and shear moduli7-11. Here, using three-dimensional matrices that match the viscoelastic properties of gut mucus, we test how altering the physical properties of their microenvironment influences bacterial growth under confinement. We find that low aspect-ratio bacteria form compact, spherical colonies under confinement while high aspect-ratio bacteria push their progenies further outwards to create elongated colonies with a higher surface area, enabling increased access to nutrients. As a result, the population level growth of high aspect-ratio bacteria is more robust to increased physical confinement compared to that of low aspect-ratio bacteria. Thus, our results capture experimental evidence showing that physical constraints can play a selective role in bacterial growth based on cell shape.

The active regulation of tissue material properties via phase transitions is central in morphogenesis. Transitions abruptly occur at critical points in diverse control parameters, including cell density, shape or adhesion. Whether these parameters are interdependent, performing redundant or distinct functions, is unknown. Here we show that co-regulation of multiple control parameters impacts not only tissue deformability, but also cell polarization. We theoretically define a new phase diagram capturing the material states of zebrafish pluripotent tissues and show that they cross simultaneously critical points in cell density, connectivity and adhesion strength. Combining optogenetics, biophysical measurements and quantitative morphometrics, we independently modulate each parameter, identifying adhesion as the main determinant of tissue rheology. Unexpectedly, uncoupling adhesion-driven from density-driven rigidification in amorphous tissues triggers epithelial organization via tricellular junction formation, followed by luminogenesis and apicobasal polarization. Altogether, this work reveals the non-linear dynamics of emergent tissue mechanics as instructive mechanisms of tissue organization.

Sheets of confluent cells are often considered as active nematics, with accumulation at [Formula] topological defects and escape from [Formula] defects being widely recognized. However, collective dynamics surrounding integer-charge defects remain poorly understood, despite its biological importance. By using microfabricated patterns, we induce diverse +1 topological defects (aster, spirals, and target) within monolayers of neural progenitor cells. Remarkably, cells are consistently attracted to the core of +1 defects regardless of their type, challenging existing theories and the conventional extensile/contractile dichotomy. We trace back the origin of this accumulation behavior to previously overlooked nonlinear active forces using a combination of experiments and a continuous theory derived from a cell-level model. Our findings demonstrate that +1 topological defects can reveal key features of active nematic systems and offer a new way to characterize and classify cell layers.

Active tissues exhibit diverse collective dynamics, yet the cell-cell interactions that generate ordered microscopic flows remain poorly understood. Here, we show that antiparallel cell circulation can emerge from self-aligned, polarity-dependent tension gradients. Using a minimal vertex model of confluent tissues, we studied polar cells that align their polarity with their own velocity and impose polarity-dependent tension gradients along cell-cell contacts, without relying on substrate traction. This behavior can be generalized as a minimal interaction in which forces transmitted between cells act with opposite signs, reminiscent of action-reaction forces, organizing cells into stable interlocking antiparallel lanes. In mixtures of motile and nonmotile cells, this circulation drives phase separation, in which motile cells spontaneously form persistent domains. Accordingly, we identified similar antiparallel circulation patterns in two-dimensional aggregates of Dictyostelium discoideum, supporting the biological relevance of the mechanism. Together, these results demonstrate that self-aligned tension gradients provide a robust and underappreciated route to dynamic microscopic pattern formation in multicellular systems.

In growing active matter systems, a large collection of engineered or living autonomous units metabolize free energy and create order at different length scales as they proliferate and migrate collectively. One such example is bacterial biofilms, which are surface-attached aggregates of bacterial cells embedded in an extracellular matrix. However, how bacterial growth coordinates with cell-surface interactions to create distinctive, long-range order in biofilms remains elusive. Here we report a collective cell reorientation cascade in growing Vibrio cholerae biofilms, leading to a differentially ordered, spatiotemporally coupled core-rim structure reminiscent of a blooming aster. Cell verticalization in the core generates differential growth that drives radial alignment of the cells in the rim, while the radially aligned rim in turn generates compressive stresses that expand the verticalized core. Such self-patterning disappears in adhesion-less mutants but can be restored through opto-manipulation of growth. Agent-based simulations and two-phase active nematic modeling reveal the strong interdependence of the driving forces for the differential ordering. Our findings provide insight into the collective cell patterning in bacterial communities and engineering of phenotypes and functions of living active matter.

When a material enters the body, it is immediately attacked by hundreds of proteins, organized into complex networks of binding interactions and reactions. How do such complex systems interact with a material, "deciding" whether to attack? We focus on the "complement" system of [~]40 blood proteins that bind microbes, nanoparticles, and medical devices, initiating inflammation. We show a sharp threshold for complement activation upon varying a fundamental material parameter, the surface density of potential complement attachment points. This sharp threshold manifests at scales spanning single nanoparticles to macroscale pathologies, shown here for diverse engineered and living materials. Computational models show these behaviors arise from a minimal subnetwork of complement, manifesting percolation-type critical transitions in the complement response. This criticality switch explains the "decision" of a complex signaling network to interact with a material, and elucidates the evolution and engineering of materials interacting with the body.

Active nematic liquid crystals are the main structural phase of gliomas, promoting collective migration and aggression. We establish the existence of nematic order and topological defect lines and loops in 3D in vivo mouse and human glioma brain tumors. As predicted by theory, sections through the disclination lines in 3D appear as {+/-}1/2 topological defects in 2D. In 3D, these defects either persist along disclination lines or twist as they interconvert from -1/2 to +1/2. Cell alignment exhibits quasi-long-range order, spreading throughout the tumor over distances between 300-3000 m. In vitro -1/2 and +1/2 defects display changes in apoptosis levels, suggesting topological defects regulate glioma cell density. The large scale order of gliomas correlates with tumors aggressive behavior. The organization of gliomas as active nematic liquid crystals provides a novel physical foundation of complex solid tumors; their deconstruction signposts potential treatments for deadly cancers.

The epithelium undergoes stratification, transitioning from a monolayer to a multilayer structure, across broad phenomena. Recent studies have identified several cell behaviors as triggers, including junctional tension, cell density and geometry, and topological defects. However, how these factors drive stratification throughout the entire epithelium remains poorly understood. Here, we report a mechanism underlying epithelial stratification that mirrors the physics of phase transition. Combining cell culture with three-dimensional vertex modeling, we demonstrate that epithelial stratification is analogous to a structural phase transition driven by the nucleation-growth process, i.e., multilayer origins dispersedly appear and expand across the epithelium via unordered intermediate states. This transition is induced by a mechanical instability inherent in the foam-like geometry of the epithelium. Moreover, the nucleation-growth concept applies to embryonic skin development and intestinal cancer transformation. These findings conceptualize epithelial stratification as a form of a phase transition governed by foam mechanics, offering a physical perspective on various epithelial developments.

Biomolecular condensates, including those formed by prion-like low complexity domains (LCDs) of proteins, are typically maintained by networks of molecular interactions. Such collective interactions give rise to the rich array of material behaviors underlying condensate function. Previous work has uncovered distinct LCD conformations in condensates versus dilute phases, and recently, single-component LCD condensates have been predicted to exhibit microstructures with "small-world" networks--where molecular nodes are highly clustered and connected via short pathlengths. However, a framework linking single-molecule properties, condensate microstructure, and macroscopic material properties remains elusive. Here, we combine molecular simulation and graph-theoretic analysis to reveal how molecular features encode condensate microstructure, which impacts molecule-scale conformations and droplet-scale material properties. Using a residue-resolution coarse-grained model, we probe condensates comprising natural LCD sequences and generalize our findings by varying composition and patterning in binary sequences of hydrophobic and polar residues. We show that non-blocky sequences form condensates with small-world internal networks featuring "hubs"--molecules responsible for global connectivity--and "cliques", molecular clusters bound by persistent short-ranged associations. Cliques localize near interfaces without a secondary phase transition, suggesting a role in mediating molecular partitioning and condensate aging by tuning interfacial material properties. Moreover, we demonstrate that network smallworldness predicts droplet surface tension. We also track single-molecule structure and dynamics inside condensates, revealing that internal heterogeneity at the single-molecule level is systematically encoded by network topology. Collectively, our work establishes multiscale structure-property relationships in LCD condensates, providing general principles for designing and interpreting condensates with complex internal organization and material properties.

Epithelial cortinoids, fluid filled shells formed from induced pluripotent stem cells (iPSCs), must accommodate large deformations during growth and morphogenesis. Using inflation-deflation assays and high-resolution imaging, we find that these fluid-filled shells are weakly-pressurized and achieve extreme deformability through reversible soft modes of deformation accommodated by the cytoskeleton. We show that cytoskeletal elements such as actin localized along lateral cell edges undergo tilt and bend instabilities that buffer mechanical load by decoupling apico-basal stretching from lateral extension. These reversible instabilities act as elastic safety valves, permitting large shape changes without loss of epithelial hydraulic and topological integrity. A minimal theoretical and computational model demonstrates how tilt and bend reduce effective resistance to radial thinning and explains the observed pressure-strain softening. Thus, iPSC shells exploit reversible cytoskeletal instabilities as mechanical buffers, enabling robust tolerance of large deformations in developing epithelia.

While topographical and chemical cues are well known to regulate cell shape and function, the role of stiffness heterogeneity has remained unclear. Here, we demonstrate - for the first time to our knowledge - that cells can be guided solely by the stiffness heterogeneity of their environment. To that end, we engineered a cell-guiding platform with abrupt, subcellular stiff and soft domains, whose flatness and uniform chemistry eliminated confounding cues. Cells elongate and align along stiff regions, sensing soft domains as barriers when wider than 2 microns. Perturbated myosin activity, cortical tension, and elasticity contrast reveal distinct biomechanical contributions, while a probabilistic model integrating adhesion, contractility, and cortical tension extracts key mechanical parameters characterizing the cellular state. Finally, experiments and dissipative particle dynamics demonstrate collective stiffness-based contact guidance. This work identifies stiffness heterogeneity as a fundamental regulator of cell and tissue organization and provides a framework for designing mechanoregulatory biomaterials.