Nature Physics

Dense active materials, from cellular tissues to jammed and glassy systems, must continuously relieve internal mechanical stress to remain structurally stable as they are driven far from equilibrium. In epithelial tissues, this relief occurs through cell division, yet what sets the geometry of this structural remodeling event has, for over a century, been attributed to a purely geometric principle: Hertwigs rule, whereby cells divide along their long axis. We show that as epithelial tissues densify and cell shape anisotropy collapses, this geometric rule is superseded by a mechanical one in which dense epithelia relieve anisotropic stress by cells dividing along their principal axis, independent of the tissues isotropic stress state. Using direct force measurement and stress inference, we show that stress orientation, rather than cell shape, governs the axis of cell division across mechanically distinct systems, from fluid-like to jammed monolayers and structurally heterogeneous organoids, remaining predictive precisely where the classical geometric rule fails. This stress-oriented remodeling is reciprocally coupled to the materials mechanical state: anisotropic stress accelerates the underlying remodeling rate, while each remodeling event locally dissipates the stress that triggered it, closing a negative feedback loop. This "principal-stress rule" recasts epithelial cell division as a stress-relief mechanism intrinsic to dense active matter, providing a general mechanical framework linking internal stress, structural remodeling, and homeostasis in living materials.

Rigidity transitions govern tissue organization in ways reminiscent of inert materials. Yet, living tissues are composed of active units with autonomous timing mechanisms, raising the question whether microscopic cellular timing distribution influences collective mechanical states. Here we identify heterogeneity in cellular timescales as a heritable parameter, regulating rigidity transitions in embryonic tissues. Lineage tracking and quantitative mechanical analysis reveal that zebrafish morphogenesis starts with a tissue rigidity collapse occurring at maximal cell cycle length heterogeneity. This heterogeneity arises from size-dependent stochastic differences in resource allocation, with resource availability defining the cell cycle length. Such differences are inherited across generations, amplifying and structuring tissue-wide cell cycle length heterogeneity. Experiments and large-scale 3D simulations identify an optimum level of cellular timing variability at which cell-cell contact remodelling is spatially coordinated driving timely and robustly the rigidity transition. These findings demonstrate that embryos exploit microscopic temporal disorder for timing and tuning tissue morphogenesis.

Surface curvature is a fundamental geometric cue in tissue morphogenesis, yet its role in guiding collective cell organization has remained elusive. Here, we show that curvature acts as a geometric control parameter that shapes supracellular alignment and chirality while modulating myogenic differentiation in myoblast tissues. Cells cultured on curved substrates self-organize into robust helical assemblies whose handedness is set, and can be reversed, by the sign of curvature: convex fibers produce right-handed helices, whereas concave channels invert the chirality. We identify a previously hidden clockwise bias in single-cell motion associated with the helical actin cytoskeleton. A minimal continuum theory coupling an effective chiral drive to curvature quantitatively captures the emergence and reversal of tissue-scale chiral alignment. On substrates with spatially varying curvature, local curvature gradients organize patterned multicellular architectures while preserving a global handedness. Curvature is also associated with myogenic state, with higher curvature linked to reduced or delayed differentiation. Together, these findings reveal how complex geometries shape the alignment, symmetry, and cellular state of living tissues.

The cytoplasm of eukaryotic cells is populated by dense disordered suspensions of filamentous and granular endomembranes, yet how they contribute to the mechanical behavior of the cell interior remains unknown. We combined active micro-rheology, cell-like encapsulation and simulations to study the material properties of marine egg extract fractions enriched in distinct endomembrane components. We characterized the cytoplasm as a composite suspension made of yolk granules interspaced by sheets and tubules of endoplasmic reticulum (ER) bathed in cytosolic fluid, that occupies [~]38% of cell volume. Remarkably, while isolated cytosol, yolk or ER fractions had characteristics of Newtonian fluids, their combination yielded the emergence of viscoelasticity and glass-like dynamics closely resembling that of in vivo cytoplasm. Our data suggest that the ER acts as a sterically excluding backbone that drives the formation of load-bearing yolk flocculation structures to endow the cytoplasm with solid-like properties at volume fractions far below random close packing. This work establishes a generic framework to understand the material properties of composite endomembrane suspensions, and delineates a novel strategy by which eukaryotic cells may tune the physical state of their cytoplasm.

The cytoskeleton organizes the cellular interior using cytoskeletal filaments that rely on bundling, usually executed by stable and ordered crosslinking proteins. Bundling often requires protein complexes with at least two defined microtubule binding regions, as present in many molecular motors. Here, we establish a mechanism of microtubule bundling based on capillary forces, analogous to how wet hair sticks together. We show using in vitro experiments and theory that condensates can bundle microtubules through capillary forces, wherein liquid-like capillary bridges form between microtubules and adhere them together through interfacial and wetting forces. We quantify the structure and dynamics of these capillary bundles using total internal reflection fluorescence microscopy, and directly measure the charge-dependent interfacial tensions of condensates on microtubules using atomic force microscopy. Lastly, we show that these capillary bridges provide viscous resistance to motor-driven microtubule sliding that is insensitive to the bulk protein concentration. Taken together, we provide a novel mechanism for how cytoskeletal filaments bundle: through condensate-mediated capillary forces.

Cellular activity drives epithelial fluidization -- a widespread phenomenon observed during tissue development, remodeling, and repair both in vivo and in vitro. Yet the physical origins and spatial organization of active forces vary widely across biological systems and are often represented by a single generic mechanism in theoretical models. Here, using an active vertex model, we systematically compare four modes of epithelial activity spanning subcellular to tissue scales: apolar motility, polar motility, fluctuating contractility, and mechanochemical regulation. Although all four mechanisms drive the same global transition from a solid-like rectangular tissue to a fluid-like circular morphology, they reach this state through distinct pathways -- differing in the rates and topology of junctional rearrangements, cell elimination, and collective motion and leave distinguishable signatures in tissue architecture, cell dynamics, and mechanical relaxation. Among these observables, spatial velocity correlations directly capture the spatial organization of activity: their correlation length and functional form together resolve all four mechanisms. The robustness of these signatures across activity strengths suggests that spatial velocity correlations offer an experimentally accessible means of identifying the physical origin of epithelial activity from live-cell imaging alone.

Navigation near boundaries under strong flow is central to microswimmer transport in active matter. Using microfluidics, we track rolling bovine sperm near planar walls in Poiseuille flow with near-wall shear rates up to 50 s-1. As flow increases, we observe a universal dynamical transition: circular surface swimming at zero flow, upstream rheotaxis at weak flow, and a novel near-surface oscillation (NSO) state at high shear, characterized by large-angle oscillations and periodic lifting from the wall. Surprisingly, sperm remain concentrated in a near-wall layer even when downstream advection dominates. A minimal mechanistic model combining hydrodynamic wall interactions, shear-driven Jeffery rotation, and steric flagellar-wall collisions reproduces these transitions and reveals a hydrodynamic buffer zone--a range of shear rates where the mean wall distance remains nearly constant. This buffering arises from a competition between wall-attracted and bulk-oscillatory states, providing a robust physical mechanism for surface navigation in fluctuating environments.

Although topological defects in cell monolayers have been recognized as mechanical organizing centers in morphogenetic processes, the mechanism by which cells coordinate their motion at such defects and self-organize into higher-order structures remains elusive. Here, we report the formation of three-dimensional (3D) multicellular mounds in unconfined myoblast monolayers, at well-controlled vortex topological defects. Prior to the onset of bilayering, the vortex structure induces millimeter-scale cell flows converging toward the defect center. As a result, 3D cell mounds form at the defect core, layer-by-layer. These mounds grow by interlayer permeation sustained by the converging cell flows. At late stages, the bell shape of the structured mounds can be modeled with a dynamics driven by these converging flows. Our results therefore highlight the crucial role of integer topological defects in driving large-scale cell flows yielding the formation of highly ordered 3D tissues from a monolayer. We propose that similar mechanisms may be at play in certain morphogenetic and tumorigenic events.

Collective cell behaviors emerge from mechanical interactions with the extracellular matrix (ECM), yet the physical principles governing long-range cell-cell communication remain elusive. Existing models assume that neighboring cells couple by strain-stiffening the ECM between them, amplifying contractility through positive feedback. Here we show that pairwise interactions are insufficient. Instead, stable mechanical communication requires opposing mechanical anchors that allow a cell to strain-stiffen the matrix on both sides. Combining ECM strain mapping, direct cell-force measurements, and live-cell imaging, we find that isolated cell pairs generate only weak, stochastic matrix strains without persistent interactions. In contrast, cells supported by opposing neighbors, or rigid beads acting as mechanical anchors, generate large bilateral matrix strains, increase effective matrix stiffness, align collagen fibers, and form stable multicellular networks. To explain these observations, we develop a predictive mechanosensitive theory introducing effective matrix stiffness and a critical contractile force governing the transition from stochastic to persistent interaction. The theory predicts, and experiments confirm, that opposing mechanical anchorage enables cells to exceed the critical force, trigger collective matrix remodeling, and compact the matrix through collagen-fiber buckling. Together, these findings provide a unifying framework for understanding collective force generation in development, wound repair, fibrosis, and tumor progression.

Microtubules (MTs) and their motor proteins collectively harness chemical energy to generate mechanical work, driving some of the most coordinated self-organized dynamics in living cells. The unique properties of these molecules also make them versatile building blocks of cytoskeletal active matter and biomimetic nanomachines that recapitulate cellular motility, emergent pattern formation, and motor-driven transport. However, these canonical systems use MTs of fixed length and do not incorporate the natural ability of MTs to grow and regenerate. Here, we go beyond these limits by using dynamic self-amplifying branched MT networks. Driven by kinesin-1 and cytoplasmic dynein activity, surface-gliding branched MT bundles undergo swarming that yields large-scale collective MT architectures with several sought-after features. They are polar and orientationally aligned, dense, span millimeter scales, and persist over hours. We then show that these features enable molecular transport along the swarm at unprecedented capacities, with up to six million motor complexes walking in parallel across millimeter-scale distances over hours. Our results introduce a new regime in cytoskeletal active matter in which the interplay between motor-driven activity and filament generation via branching leads to emergent polar order in proliferating swarms. Such emergent polarity makes these swarms suitable for engineering scalable transport nanotechnologies and programmable soft materials.

Directed migration along chemical gradients controls immune surveillance, development, and cancer invasion. However, the same chemical cue can produce different responses depending on its concentration and whether cells move alone or in groups. For example, in steep gradients, isolated malignant lymphocyte cells migrate away from the chemoattractant source, whereas clusters of the same cells continue to migrate toward it. Here, combining computational modeling and experimental observations, we show that this reversal is governed by coupled mechanisms acting across molecular, cellular, and collective scales. At the single-cell level, our model predicts that receptor endocytosis generates a feedback that produces a nonmonotonic surface receptor density with increasing chemoattractant concentration. Above a critical concentration that depends on the cell's volume-to-sensing-area ratio, receptor depletion reverses cell polarity and drives chemorepulsion. However, in clusters, cell-cell contacts reduce the membrane area exposed to ligand, increasing the volume-to-sensing-area ratio, thus increasing the critical concentration and preserving chemotaxis. An agent-based model incorporating these mechanisms quantitatively reproduces the sign reversal of the migration index across gradient steepness and cluster size. We show that collective rearrangements further stabilize chemoattraction with exchanges between the cluster rim and core helping remove chemorepulsive cells from the leading edge, keeping their fraction below the threshold required to reverse cluster migration. The model further predicts, and experiments confirm, that increasing ambient ligand concentration while keeping the gradient fixed reduces cluster chemoattraction. Our results identify receptor trafficking, cell geometry, and cluster fluidity as physical determinants of collective directional decision-making, with implications for immune cell homing, tissue morphogenesis, and cancer dissemination.

Biomolecules self-organize into membrane-less organelles known as condensates that compartmentalize essential biochemical processes, such as ribosome biogenesis in the nucleolus1-3. Molecular dynamics within condensates are governed by chemical preferences and interaction networks that can imbue nanoscale structure4-7. Such organization is typically inferred from ensemble-averaged measurements, such as scattering and electron microscopy, which reveal molecular arrangements8-14. However, the complexity of cells obscures the interpretability of these techniques, limiting insight into condensate internal structure and roles in macromolecular assembly and transport. Here, we develop an approach to quantify the average microenvironment surrounding specific proteins within condensates in live cells, using thermodynamic principles to interpret the partitioning of designed protein probes. Using this approach, we find that condensates in cells, including the nucleolus, stress granule, and nuclear pore, exhibit spatial inhomogeneity, aligning with emerging views of condensates as networked fluids5,6,15-18. Within the nucleolus, we link spatial inhomogeneity to ribosome biogenesis, which progressively loosens the average local meshwork, facilitating transport of assembled ribosomal subunits. Within the nuclear pore, we find that transporters experience a weaker local meshwork than nucleoporins, consistent with the selective phase model19,20. Together, our approach uncovers a distinct mode of biomolecular control arising from nanoscale structure, which we term microenvironment coupling, whereby internal interaction landscapes shape transport to enable regulation and proofreading.

Defining a body axis is a central aspect of animal morphogenesis. During regeneration from excised Hydra tissue pieces, the newly formed body axis typically preserves the orientation of the parent body axis and aligns with the inherited nematic organization of the supracellular actomyosin fibers. Here we show that this inherited orientation can be overridden by geometric confinement. Tissue spheroids confined in narrow cylindrical channels in a frustrating configuration, with the inherited axis initially perpendicular to the channel, regenerate with their body axis aligned along the channel. Using high-resolution live imaging we show that this reorientation is accompanied by remodeling of the nematic fiber organization. New fibers form parallel to the channel axis in the initially disordered closure regions, creating sharp domain boundaries with the inherited transverse fibers. These domain boundaries subsequently propagate, with perpendicular fibers dissolving and new fibers forming along the channel axis. The confined tissue behaves as a solid-like active nematic material, storing anisotropic strain over long timescales while allowing nematic reorganization relative to the material frame. Our results suggest that coupling between tissue strain and nematic alignment contributes to fiber reorientation and body-axis patterning, highlighting how external mechanical constraints can redirect the body axis during morphogenesis.

Epithelial gap closure is essential for maintaining tissue integrity during development and wound healing. Previous studies have shown that closure of small gaps is driven by actomyosin purse-string contraction and traction forces generated at the gap edge. Here, we show that millimeter-scale circular gap closure in mouse epicardial (MEC1) monolayers is driven primarily by growth-mediated compressive stresses. Compared with MDCK monolayers, MEC1 cells close gaps more rapidly with reduced undulation near gap edge through coordinated tissue-wide extension-contraction. The collective closing dynamics can be modulated by partial epithelial-mesenchymal transition induction and Rho kinase inhibition. By integrating tissue and cell kinematic analyses, traction-force mapping, and a continuum framework that decomposes tissue strain rates into growth-, elastic-, and fluidity-related contributions, we reveal that growth-generated compression drives inward tissue flow, while elastic cell elongation and fluid-like tissue remodeling through cell-cell intercalation act synergistically to accommodate deformation and promote robust collective gap closure.

Cell states are increasingly conceptualized as attractors of high-dimensional dynamical systems, yet quantitative approaches for integrating phenotypic information into this framework remain limited. Here, we take an image-based approach that combines unsupervised machine learning (ML) with timelapse imaging to extract and characterize the temporal dynamics of morphological features. Using a cell line with endogenously tagged VE-cadherin, we acquired brightfield and fluorescence timelapse images of human induced pluripotent stem cell-derived endothelial cell (hiPSC-EC) monolayers, which adopt distinct phenotypes at two different magnitudes of shear stress in terms of their morphology, behavior, and VE-cadherin organization. To quantify these phenotypic cell states without segmentation, we trained a diffusion autoencoder to predict VE-cadherin signal from brightfield images. We identified interpretable ML-based features representing cell orientation, elongation, and local density. Treating these variables as dimensions of a morphological state space, we estimated a data-driven vector field and found that the two observed phenotypic cell states correspond to stable fixed points of the inferred dynamical system. Mapping measured cell migration coherence onto this space further distinguished the states. Imaging cells across intermediate shear stresses revealed a regime of bistability in which both states coexist, indicating that the shear-stress-dependent transition between endothelial cell states occurs as a bifurcation of the inferred dynamical system. Finally, we applied this method to study an N-terminal truncation of VE-cadherin, finding that mutated cells preserve alignment and coherent migration, but exhibit altered morphology and increased migration speed. This work demonstrates the applicability of a dynamical systems approach to quantitatively characterize morphological aspects of cell state from interpretable ML-based features.

Developmental patterns can scale with size during growth, a phenomenon commonly attributed to morphogen scaling. Although patterning is orchestrated by gene regulatory networks (GRNs) activated by morphogens, how GRN dynamics interact with growth is not understood. We present a theoretical framework that integrates morphogen signalling, GRN dynamics, and tissue growth. We show that pattern scaling emerges from the interplay of GRN dynamics and growth, even in the absence of morphogen scaling. This relies on memory effects encoded in the GRNs, providing a cell-autonomous route to global scaling, and offering a general mechanism for size-invariant patterning beyond morphogen-based models.

Spatial gradients of signaling molecules pattern multicellular tissues with high precision. The canonical synthesis-diffusion-degradation (SDD) framework imposes a tradeoff on these gradients: ligand-receptor interactions that generate downstream signaling activity are also responsible for consuming the ligand. Correspondingly, at a fixed ligand synthesis rate, raising ligand-receptor affinity increases local signal strength at the expense of spatial range, and lowering it extends range at the expense of strength. Recent live-imaging measurements appear to violate this seemingly fundamental tradeoff, with low-affinity ligands of the epidermal growth factor receptor (EGFR) diffusing farther and driving spatially broader signaling activity compared to high-affinity ligands. Here we explain these observations with a model of multi-step ligand processing at the receptor, and show that the activity-range tradeoff is a consequence of receptor architecture rather than a physical necessity. When receptors process ligand through a multi-step phosphorylation cascade with kinetic-proofreading-like resetting, the states that generate activity decouple from those that consume ligand, and signaling activity and range increase together over a finite window of ligand residence time. This lets cells tune how far a signal travels independently of how strongly it acts through tuning signaling parameters. Realistic EGFR parameters place the low-affinity ligands in this window. Because multi-site phosphorylation and preferential degradation of the active receptor recur across multiple receptor families, kinetic proofreading may be a general strategy for controlling signaling range. Significance StatementCells coordinate by releasing molecules that bind receptors on neighboring cells. For a fixed supply, how strongly a signal acts and how far it spreads are locked together: tight binding gives a strong response but the molecule is captured near its source, while weak binding spreads farther but signals feebly. Yet recent imaging of epidermal growth factor receptor ligands shows the opposite: weak binders activate a broader field of cells. We show this limit reflects how receptors read the signal, not physics. A receptor that processes a bound molecule through several steps, and can release it partway, separates the states that signal from those that destroy it. Cells, and engineers, can then set a signals reach independently of its strength.

Collective cell migration is a fundamental process in morphogenesis, tissue repair, cancer invasion, and frequently occurs under geometric confinement in vivo. However, how confinement interfaces with signaling pathways that coordinate collective motion remains poorly understood. Here, we confine migrating epithelial monolayers within adhesive microstripes of defined width and observe a progressive slow-down of collective migration with increasing spatial confinement. Combining biophysical modeling, live imaging of ERK activity, and pharmacological perturbations, we show that confinement increases tissue crowding while reducing cell and nuclear projected areas, thereby shifting epithelial tissues toward a mechanically compressed state associated with dampened ERK waves. Across conditions, migration speed scales with ERK signaling dynamics, which correlates with EGFR signaling as well as cell and nuclear projected areas, together serving as quantitative proxies for the confinement-imposed mechanical state. Pharmacological inhibition of ROCK restores cell spreading, ERK signaling, and migration under strong confinement, demonstrating that this state is reversible and governed by actomyosin contractility. Together, our results identify geometric confinement as a physical regulator of a contractility-dependent mechanochemical state that controls ERK signaling and collective migration in epithelial tissues.

Enzymatic reactions in biomolecular condensates are often assumed to be regulated through local enrichment of reactants. However, condensates also reshape molecular transport and reaction kinetics, making it unclear how phase separation controls catalysis in living cells. Here, we develop a quantitative theory of biomolecular catalysis in phase-separated systems and find that liquid condensates can act as tunable catalytic switches, transitioning between regimes of enhanced and suppressed enzymatic activity, exhibiting optimal responses at biologically relevant condensate sizes. We show that condensate-mediated catalysis cannot be understood from reactant enrichment alone, but instead emerges from the coupled interplay of molecular partitioning, diffusive transport, and phase-dependent reaction kinetics. The strongest regulatory effects occur under rapid interphase exchange, where the spatially heterogeneous catalytic network admits a system-level Michaelis-Menten description governed by system-averaged concentrations and reaction kinetics. Our framework predicts that micron-sized condensates can either enhance or suppress enzymatic activity by up to two orders of magnitude, and that optimal catalytic regulation can emerge at condensate sizes comparable to many biomolecular condensates. These results provide experimentally testable predictions for condensate-mediated catalysis and establish quantitative principles for understanding and engineering enzyme-catalysed reactions in biomolecular condensates.

Despite substantial variation in adult size, animals within a species maintain consistent tissue patterns and shapes, a core property known as developmental scaling or size invariance. Developmental scaling has predominantly been attributed to the scaling of morphogen gradients and gene patterns to maintain positional information and cell fate specification1,2. However, development also necessitates collective cell flows that reshape tissues and reposition cells3,4. How these flows adapt to body size remains unclear. By combining quantitative live imaging, experimental perturbations, and physical modeling in the Drosophila thorax epithelium, we address this question in the context of a fundamental process: collective cell migration. We find that migration velocity scales linearly with tissue size, accounting for size-invariant cell positioning. While gene patterning scales with tissue size and modulates force generation, it is not sufficient to ensure proper velocity scaling. Instead, tissue mechanical properties govern the dependence of migration velocity on tissue size, enabling developmental scaling within the physiological range of animal sizes. These findings uncover principles and limits of size invariance by revealing how tissue mechanics sets the scaling behavior of collective cell flows with organismal size.