Nature Physics

Branching epithelia build supracellular networks that must simultaneously ensure connectivity, mechanical integrity, and efficient space partitioning, yet a general framework for how such networks form beyond the endothelial lineage has been lacking. Here we show that epithelial cells from multiple branching organs spontaneously self-organize into extended reticulate networks in simplified environments, revealing a conserved network-forming capacity. Combining wide-field lensless holographic imaging, deep-learning segmentation (EpiNet), and graph-theoretic analysis, we resolve a reproducible assembly sequence - contact initiation, clustering, percolation, and post-percolation relaxation - and quantify its geometry across scales. Actomyosin contractility controls both the growth of connectivity and the relaxation dynamics that set network geometry, tuning the effective cost of forming connections and thereby selecting between tree-like and reticulate topologies. After percolation, epithelial networks behave as active tension networks that progressively refine space partitioning toward centroidal, near-optimal configurations while maintaining a characteristic mesh size through continuous edge nucleation. These findings establish epithelial network formation as a generic, physically regulated mode of tissue self-organization and provide a quantitative framework linking single-cell mechanics, network topology, and space-partitioning dynamics, with implications for branching morphogenesis, organoid models, and tissue engineering.

At the ocean-land interface lies a critical yet largely ignored ecosystem of tidal flats[1]. These habitats are colonized by diatoms that form thin surface biofilms, creating ecosystem-scale cellular collectives stretching meters to kilometers[2-4]. How these collectives coordinate functions across vast spatiotemporal scales remains poorly understood. This task requires both long-distance transfer and long-term storage of information[5, 6]. In cellular collectives, trigger waves have been known to provide rapid, non-attenuating signaling[7-9], while extracellular matrices allow cells to externalize structural memory[10-12]. Yet, how propagating signals and structural memory integrate to shape collective functions remains elusive. Combining field observations with laboratory reconstitution, we show that tidal-flat diatoms assemble active nematic circuits that physically wire trigger-wave routing into structural memory. Here, trigger waves recruit resting diatoms into polarized motion steered by the nematic director, and topological defects act as gates that focus or bifurcate propagating wave fronts. Memory follows a fast-read, slow-write rule: rapid signals deform the cellular nematic, while slowly evolving cell-deposited mucilage retains a hidden orientational template that guides alignment recovery. Strikingly, recurrent waves progressively remodel the nematic architecture, letting the collective reshape its future routing. Coupling rapid wave propagation to extracellular memory allows collectives to resolve the stability-plasticity dilemma, maintaining structural cohesion while adapting to recurrent stimuli. Our work reveals previously hidden adaptive nematic circuits that self-organize at ecological scales, establishing a physical framework for time-programmable active materials.

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.

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.

Cell density is a fundamental biophysical property of living cells, yet the dynamical architecture underlying density homeostasis remains unknown. Here, we reconstruct the geometry, dynamics, and control structure governing cellular density regulation from single-cell mass-volume measurements acquired during recovery from osmotic perturbation. We identify a persistent anisotropic attractor in mass-volume state space that permits coordinated density-preserving fluctuations while strongly suppressing density-changing deviations. Optimal transport analysis reveals directed recovery trajectories confined to this attractor, enabling inference of an effective density-restoring control law. Density deviations are associated with coordinated changes in biomass accumulation and volume expansion that together generate an effective density-restoring control law. Moreover, density error contains significant predictive information regarding future corrective behavior, revealing an information-rich component of cellular regulation. Together, these findings establish cellular density homeostasis as an emergent dynamical control process and demonstrate how attractor reconstruction, optimal transport, and information theory can be combined to uncover the organizing principles of biological homeostasis.

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.

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.

Neuronal dendrites form highly branched morphologies supported by spatially patterned microtubule arrays that are essential for intracellular transport and structural stability, yet how this organization is established and maintained remains unclear. Here we analyze microtubule behavior in Drosophila sensory neurons using live-cell imaging, deep learning-based analysis, and genetic perturbations. We find that microtubules are shorter and fewer in thin distal branches and progressively longer and more abundant in thicker proximal branches. Locally, polymerization slows in narrow branches due to soluble tubulin depletion, while catastrophe frequency increases near branch points upon cortical encounter. A physical model incorporating these morphology-dependent constraints reproduces both local microtubule dynamics and global organization. Inverting the textbook view that microtubule dynamics shape cell morphology, our results demonstrate that, on short timescales, cell morphology instead constrains microtubule dynamics, thereby determining large-scale cytoskeletal organization.

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.

A colony migrating into a passage narrower than itself but wider than individuals must adapt its density distribution to pass. Powders, colloids and crowds driven through such an opening jam, since contact interactions provide no pathway for constituents to respond to the constriction before reaching it. Exploring whether a cohesive living tissue can reorganize in advance, we image MDCK epithelial monolayers migrating through microchannels in which a wide channel narrows, and locate response at the taper mouth, a transition zone in which we identify upstream responses. At locations where the local channel width is still unchanged, the monolayer detaches from the side walls and reduces its lateral extent. Particle image velocimetry shows that this is not passive compression; the axial velocity alternates aperiodically in sign, velocity divergence is positive in the transition zone, and tracking the positions of cell nuclei confirms that cells leave the crowded inlet region in both directions. Fluorescence imaging shows a belt of co-enriched E-cadherin, F-actin, and myosin-II at the edges that detach before the inlet, which laser ablation shows to be under elevated tension but dissolves once the tissue passes into the narrow inlet; {beta}-catenin is not co-enriched, indicating that junctions differ in composition in the core and at the edge of colony. This advance proceeds over hours, far more slowly than the viscoelastic reorganization reported for MDCK monolayers, and switches in sign repeatedly, which a linear viscoelastic sheet under sustained constraint cannot do. E-cadherin knockdown abolishes narrowing, flow reversal, density redistribution, and belt assembly.

How mesoscale cargos such as biomolecular condensates are transported and spatially positioned within cells remains a fundamental question in cell biology. During Caenorhabditis elegans zygote polarization, a substantial fraction of P granules undergoes persistent anterior-to-posterior motion that cannot be fully explained by dissolution-recondensation. Here, combining microfluidic reconstitution, quantitative micropipette aspiration and live-cell imaging, we show that a MEG-3 concentration gradient generates interfacial-tension asymmetry and drives the directed transport of PGL-3-RNA co-condensates in vitro and P granules in vivo through the Marangoni effect. This framework enables parameter-free quantitative predictions of condensate transport. Orthogonal molecular perturbations abolish or reverse directional migration, directly linking interfacial properties to transport behavior and establishing the specificity of this mechanism. Together, our findings identify the Marangoni effect as a previously unrecognized mechanism for intracellular transport of biomolecular condensates and provide direct causal evidence that condensate emergent properties can contribute to physiological organization.

The emergence of treatment resistant mutants is one of the primary contributors to therapy failure in cancer. Evolution-based adaptive therapies aim to exploit the competition between sensitive and resistant cells to prolong therapeutic control. However, in the densely packed tissues of solid tumors, competition is not only determined by cell-intrinsic factors but also a result of local physical interactions between neighboring cells. The successful development of physics-informed adaptive therapies therefore hinges upon the bottom-up integration of tissue mechanics and experimentally grounded models of tumor evolution. Here, we show how population-level treatment response emerges from mechanical interactions between individual cells. Combining genetically tailored therapy-mimicry experiments in spatially structured 2D melanoma colonies with mechanistic, particle-based tissue simulations as digital twins in a real-to-sim-to-real framework, we reveal how treatment-induced changes in mechanical crowding shape a cascade of resistance expansion, spatial competitive escape, and consequent therapy failure. We then link these underlying physical mechanisms to population-level observables in an abstracted mathematical model for reinforcement-learning-based therapy optimization and a distilled treatment-decision-heuristic, which we test experimentally. Together, our results identify mechanical crowding and escape as governing principles of resistance-mediated therapy failure in solid tumours and provide a basis for mechanistically informed, evolution-based treatment strategies.

Epithelial cell shape plays a fundamental role in tissue dynamics. Numerous studies have established how cells drastically change their shape to promote epithelial tissue morphogenesis. However, the mechanisms enabling cells to maintain their shape remain far less understood. Here, leveraging live imaging in Drosophila epithelial tissue and theoretical modeling, we identify an emergent mechano-chemical feedback that ensures junction length and cell shape stability, without requiring a dedicated molecular force sensor. We find that an increase in junction length is associated with a passive dilution of E-Cadherin, followed by an increase in Myosin-II-dependent contractility that reduces junction length. Theoretically, we show that this regulation of junction length generically emerges when negative and positive regulators of contractility have distinct kinetics. Experiments confirm that E-Cadherin acts as a negative regulator with slow turnover. Mechanistically, local dilution of E-Cadherin passively lifts an inhibition on lateral apicobasal polarity components, allowing the RhoGEF Cyst -- with its fast turnover -- to accumulate and increase contractility. Perturbing this feedback results in aberrant cell junction and shape regulation, thereby compromising the ability of the tissue to buffer local mechanical fluctuations and global mechanical stresses. Altogether, we propose that differential turnover between apical and lateral polarity complexes provides an emergent mechano-response for junction length and cell shape homeostasis.

Cellular respiration depends on the rapid, lateral flow of protons along the inner mitochondrial membrane to drive ATP synthesis. The precise nanoscale thermodynamic forces confining protons to this local circuit remain highly debated. Previous attempts to model macroscopic interfacial proton diffusion have been hindered by parameter equifinality and geometric artifacts, preventing the deconvolution of structural water networks from lipid electrostatics. Here, we resolve this ambiguity using a constrained, high-resolution two-dimensional continuum model. By incorporating experimentally validated buffer proton consumption rates as strict biological priors, we break mathematical degeneracy and isolate the specific thermodynamic components of planar lipid bilayers. Calibrating our model against time-resolved DOPG fluorescence kinetics, we decouple a universal structural water barrier (5.7 kBT) from the specific -1e electrostatic trap (4.3 kBT). Extrapolating these first principles, we predict the confinement architecture of cardiolipin, the signature -2e dimeric lipid of mitochondria. Our simulations reveal a deep kBT thermodynamic well. Crucially, this massive barrier confines protons within 1 to 2 nanometres of the membrane surface, virtually abolishing vertical leakage into the bulk aqueous phase of the inter-membrane space. We demonstrate that this spatial confinement triggers dimensional squeezing, preserving a robust lateral concentration gradient that actively accelerates radial proton wave propagation. Biologically, these findings reveal that cardiolipin does not merely prevent proton dissipation, it functions as a highly efficient, quasi-two-dimensional nanoscale antenna that captures and rapidly channels protons directly to ATP synthase, ensuring the kinetic viability of eukaryotic energy production.

Scaling laws are powerful tools in material science to relate geometric and mechanical properties of materials. The actin cortex, a dynamic network beneath the plasma membrane, is essential for cellular morphogenesis, force generation, and tissue organization. Despite its critical role, the mechanical properties of the cortex itself remain poorly understood. Using the magnetic pincher, a new technique we recently developed, we directly measure the thickness (h) and elastic modulus (E) of the actin cortex in live cells, uncovering a universal scaling (E ~ h-2) across multiple cell types. Drawing an analogy to cellular solids, common in nature and material science, we identified an origin for this scaling: the volume fraction of actin filaments varies concomitantly with the cortex thickness, due to a conservation of filamentous actin quantity. Thus thinner cortices exhibit higher actin density and stiffness, while thicker cortices are sparser and softer. The relationship holds under diverse perturbations targeting myosin contractility, actin nucleation, and turnover, but is lost upon actin disassembly, highlighting its dependence on the intact actin network. Our results establish that cells, across cell types, function within a rather limited range of quantity of cortical actin filaments and primarily modulate cortex thickness to tune mechanical properties, with profound implications for cell shape regulation, tissue mechanics, and the interpretation of indentation-based mechanical measurements.

Liquid-liquid phase separation (LLPS) widely organizes the cellular interior, yet how third-party macromolecules modulate LLPS remains a puzzle. While one would expect that macromolecules can either promote or suppress phase separation, empirical observations show that a small dosage of macromolecules virtually always promotes phase separation. To resolve this paradox, we study the linear response of phase separation to macromolecule addition. We prove that for macromolecules significantly larger than the solvent molecule, their addition essentially always promotes phase separation, regardless of how they interact with the scaffold protein. Crucially, in the biologically relevant scenario of dilute condensates, the linear responses, including the saturation volume fraction, scale proportionally to [1-v2(1+{chi}12)2], where v2 is the macromolecule size and {chi}12 is the scaffold-macromolecule interaction parameter. Importantly, this universal behavior extends to multicomponent solutions in which the effective interaction parameter is composition-dependent. Our work shifts macromolecular modulation of LLPS from empirical observation to predictable design.

The actin cytoskeleton drives shape changes and transport in cells and supports mechanical signal transmission. However, how cells control and use active cytoskeletal flows at the mesoscale is not well understood. We reconstituted an active cytoskeleton in water-in-oil emulsion droplets of Xenopus laevis egg extract and observed, above a critical droplet size, the emergence of a 3D radially convergent steady-state flow of polymeric actin, maintained by continuous actin turnover. The flow condensed lipid-rich cellular debris into a centered inclusion. Steady-state F-actin density and flow velocity profiles roughly collapse onto scale-invariant master curves. This behavior can be explained by a physical model representing the network as an isotropic active viscous fluid with a percolation threshold. The contracting network behaves as an active swimmer with complex internal dynamics that centers itself and the central inclusion inside the droplets without physical boundary attachment. Active contraction, crosslinking and polymerization dynamics in an actin network can thus generate cell-scale flow patterns that sense the confining geometry and external signals and exert forces that are likely sufficient to move and localize organelles in cells.

Delamination within stratified epithelia like the skin epidermis describes the detachment and upward motion of cells originating from the basal layer. Despite its fundamental importance for tissue development, homeostatic regeneration and repair, the mechanisms that drive delamination remain a longstanding open question. Upward motion follows cell shape changes, which are inherently driven by physical forces, but their role is elusive. Here, we investigate delamination in stratifying keratinocytes by combining imaging, force measurements and theoretical modeling. We identify a local change in force balance between differentiating cells and their environment as the key step initiating delamination. Within a homogeneous cell layer with apically polarized contractility, differentiation leads to actomyosin remodeling, redistributing cellular force exertion to the basal side. Such mechanical heterogeneity then results in differentiating cells experiencing and inward basal and outward apical forces that manifest in the formation of a +1 force defect and promote shape changes culminating in upward motion. Simultaneously, delaminating cells actively pull on their underlying neighbors, generating convergent tissue flows which close the basal layer below. Together, we propose a general physical description of delamination initiation, which may act across various multilayered epithelia.