Nature Physics

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.

Biological tissues require branched cellular architectures to maximize spatial coverage while minimizing redundancy. Yet, how cells decode local spatial information to collectively tile territories without a global blueprint remains a key open question. Here, we develop a biophysical theory of interacting branched cells, and show that coupling their growth to short-range repulsion drives efficient tiling with minimal territorial overlap. Our model predicts that the same local mechanism simultaneously suppresses long-range density fluctuations, driving the cellular collective toward hyperuniformity. We confirm these theoretical predictions with experiments on microglial patterning in the developing retina, and show that perturbations resulting in limited cell growth disrupt both tiling and fluctuation suppression. Our results reveal that two seemingly distinct optimization principles of biological patterning, large-scale regularity and efficient tiling, are intimately linked and can arise from a single growth-repulsion feedback, suggesting a general principle for self-organized tissue coverage.

The classical model of bacterial flagellar motility posits a rotary engine driven by proton motive force (pmf), with torque generated by stator-rotor interactions and transmitted through a flexible hook to a helical filament. Despite decades of acceptance, this model faces fundamental challenges in thermodynamics, structural mechanics, evolutionary parsimony, and direct observational evidence. We develop and quantitatively test the murburn model, a new paradigm for bacterial motility in which water, produced as an inevitable byproduct of metabolic redox activity, is ejected via the basal secretory module and channelled along the spiral grooves of the flagellar filament. The ejected flow creates a local shear field that induces a transverse bending wave; the precession of this wave is observed as apparent rotation and generates thrust through anisotropic viscous drag, without any rotary motor, ion gradient, or axial rotation. The principal contribution of this work is a self-contained, first-principles treatment of this mechanism: for a unipolar flagellated cell we derive the governing low-Reynolds-number elastohydrodynamic relations from slender-body theory and show that physiologically realistic rates of metabolic water production reproduce the observed swimming speeds and apparent-rotation frequencies at a small fraction of the cellular energy budget, while direct jet propulsion is quantitatively excluded. Building on this derivation, we provide a force-balance comparison of the competing propulsion mechanisms, obtain a set of falsifiable predictions that distinguish the murburn model from the rotary motor, and report a structural analysis of cryo-EM flagellar-hook architectures that reveals solvent-accessible radial canals consistent with lateral water transport. The same single principle accounts for swimming, tumbling, gliding, spirochete undulation, and archaeal motility, without requiring rotating shafts, ion-gradient coupling, or complex switching mechanisms.

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.

In non-equilibrium (active) systems, increased driving is commonly assumed to amplify energy dissipation. This frames the efficiency of protein-based machines as a fixed or monotonically decreasing function with driving. Using picowatt-sensitive calorimetry and advanced entropy production metrics in reconstituted actomyosin networks, we show that energy dissipation depends non-monotonically on myosin-generated stress (driving). At low driving, dissipation increases proportionally with stress, consistent with near-equilibrium linear response. At high driving, however, dissipation decreases, revealing a far-from-equilibrium regime in which excessive load suppresses motor ATPase activity. This non-monotonicity reflects a transition from spatially localized stress at low driving to delocalized stress at high driving, where force per motor, and thus ATPase suppression, is maximized. Crosslinker mechanics tune this transition as fascin (slip bonds) amplifies stress localization and shifts the dissipation peak to higher driving, whereas -actinin (catch bonds) stabilizes under load, delocalizes stress, and shifts the peak to lower driving. Thus, enhanced mechanochemical coupling causes additional driving to restructure rather than amplify dissipation, revealing how material system organization (bonding), and not driving alone, governs energy flow far from equilibrium.

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.

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.

Transcription factors organize into liquid-like condensates to facilitate gene expression, yet the physical mechanisms governing their formation and properties remain poorly understood. We study the size statistics of transcriptional condensates in human HAP1 cells using widefield and super-resolution microscopy tagging the epigenetic reader BRD4. We find that hubs that appear monolithic in widefield resolve into clusters of smaller droplets that resist coarsening. We link this size control to Active Model B+, a non-equilibrium field theory that captures a regime of reverse Ostwald ripening out of thermal equilibrium. In this regime, chemically driven currents cause larger droplets to transfer mass back to smaller ones, stabilizing a state of microphase segregation. The observed exponential size distribution of BRD4 foci quantitatively matches our numerical simulations, suggesting a universal physical picture for the non-equilibrium self-limitation of cellular condensates.

Epithelial tissues maintain mechanical integrity through a balance between cell-cell adhesion and cortical contractility. Disruption of E-cadherin-mediated adhesion is a hallmark of epithelial-mesenchymal transition and cancer progression; yet how local adhesion defects propagate to tissue-scale mechanical changes remains poorly understood. Here, we use a two-dimensional vertex model (varying mutant cell fraction, spatial arrangement, and initial tissue disorder) to investigate how adhesion-deficient cells regulate epithelial mechanics. We show that increasing the fraction of mutant cells drives the tissue towards geometric signatures associated with reduced mechanical rigidity, characterised by elevated cellular shape index and increased prevalence of non-hexagonal cells. Crucially, spatial organisation acts as an independent structural variable that modulates tissue mechanics beyond mutant fraction alone. For identical mutant fractions, randomly distributed mutants undergo rapid, spatially isolated T2-mediated removal events producing only transient shape-index perturbations. Clustered mutants, by contrast, undergo sequential boundary removal, delaying elimination and sustaining elevated shape index in the surrounding tissue. This persistent elevation induces topological disorder within the local neighbourhood that outlasts mutant clearance itself. Our results establish spatial organisation as a key determinant of epithelial rigidity transitions, with implications for understanding early-stage cancer 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.

In cells, cytoskeletal filaments such as microtubules are dissipative polymers that switch stochastically between growth and rapid collapse, a behaviour known as dynamic instability. This switching is coupled to nucleotide hydrolysis, so a filament's fate depends on the chemical state of its subunits and the free-monomer pool. Previously reported synthetic assemblies can be cycled between assembled and disassembled states, but the switch is typically set by the global fuel level rather than by a state stored within each monomer. Here we demonstrate a DNA/RNA hybrid polymer in which every monomer holds a one-bit internal state, assembly-competent or inactivated, flipped irreversibly by cleavage of an internal RNA linkage. The bit is written by two routes sharing the same transesterification chemistry: a slow spontaneous cleavage giving each monomer an intrinsic lifetime, and a fast, site-specific write by a programmable DNAzyme. Because inactivation is irreversible, sustained cycling requires continuous regeneration of active monomer, holding the system in a non-equilibrium steady state in which filaments undergo repeated depolymerization and rescue at frequencies near 0.2 (min)-1. We also find that the filaments form meshes auto-catalytically. Because each crosslink recruits filaments from the pool, crosslinking accelerates autocatalytically, driving a percolation transition to a system-spanning network that continuously remodels as its filaments turn over. Thus the timing of switching can be stored within individual monomers rather than imposed as a global threshold -providing a route to autonomously remodelling active materials.

How can simple organisms lacking nervous systems encode and transmit environmental signals to generate complex, adaptive behaviours? Using the unicellular organism Physarum polycephalum as a model, we identify a unifying mechanochemical mechanism that links intracellular calcium oscillations to large-scale behavioural coordination. We first demonstrate experimentally that local perturbation of the actomyosin cortex is sufficient to induce symmetry breaking and directed migration, even in the absence of nutrient cues. Building on evidence linking calcium concentration to actin depolymerization and contractile relaxation, we develop a mechanochemical tubule model in which self-sustained calcium oscillations are coupled to pressure-driven mechanics. We show that environmental cues, encoded through the local modulation of these oscillations, give rise to directed transport and the redistribution of biomass. By extending this framework to a two-dimensional phase-field model, we demonstrate that this mechanism is sufficient to generate a diverse set of slime mould behaviours, including chemotaxis, network formation, and balancing exploration-exploitation trade-offs. In doing so, we provide a single mechanistic framework linking intracellular dynamics to organism-scale behaviour across spatial and temporal scales. Our work shows that these sophisticated behaviours can emerge from the modulation of self-sustained oscillations coupled by diffusion, providing a physically grounded mechanism for information processing in non-neural organisms and offering insight into the evolutionary origins of coordinated behaviour.

Cyanobacterial macrostructures are ubiquitous in nature. They harbour spatially organised metabolic processes that impact biogeochemistry and enable biotechnologies. How macrostructures form remains unknown due to a lack of tractable model systems. We overcome this limitation using a motile filamentous cyanobacterium that reproducibly forms macrostructures in laboratory conditions. We discover an emergent microparticle collection behaviour, mediated by gliding motility and leading to granular macrostructures. We link collection to filament buckling and entangling, and predict a dependence on filament length and stiffness, using a novel physical model. Shortened filaments and a naturally short Pseudanabaenales filament do not collect particles or form granular macrostructures. These findings link macrostructures to gliding motility and filament physics, giving insight into their formation in nature and design for biotechnologies.

While the physical aging of biomolecular condensates into macroscopic glasses is heavily linked to pathological disease states, the nanoscale topological rules governing this non-equilibrium relaxation remain elusive. Using heterotypic alpha-synuclein-Tau coacervates, we combine variable-stringency dissolution and FLIM-FRET to provide direct experimental mapping of the internal network reorganization over time. Rather than a passive, isotropic kinetic jamming event typical of classic glasses, we demonstrate that this physical aging is driven by continuous rheostatic network consolidation; a progressive, directed topological relaxation toward deeper free-energy minima powered by the cooperative spatial optimization of sticker motifs. We formalize these dynamics into a mesoscale series-resistance model derived from size-resolved kinetics, proving that thermodynamic quench depth dictates the initial network state while clustered sticker patterning introduces configurational frustration that kinetically stalls maturation to preserve liquidity. This multi-scale framework links sequence grammar to non-equilibrium transport laws, revealing how biomolecular assemblies navigate the boundary between physiological utility and pathological arrest.

At sites of active gene expression, dynamic compartments known as transcriptional condensates assemble and dissolve on timescales relevant to RNA synthesis and degradation. Yet how the non-equilibrium dynamics of these condensates emerge from the coupling of RNA concentration and phase separation remains poorly understood. Here we engineer synthetic active condensates in which T7 RNA polymerase transcribes RNA in situ, triggering phase separation with a cationic scaffold protein. By using RNA concentration as a tunable parameter, we drive condensates along defined paths through a characterized phase diagram. This reaction-phase separation coupling gives rise to three emergent dynamic phenomena not accessible in passive systems: a rapid switch-like nucleation burst, RNA-mediated positive and negative feedback regulation of transcription, and oscillatory condensate formation in which RNA degradation spontaneously renucleates condensates. Together, these results show that the dynamic functions of transcriptional condensates emerge from their reaction-driven paths through phase space, providing a quantitative framework for understanding how RNA flux governs condensate dynamics in living cells.

Balancing cellular loss in tissues requires fine balance of cell proliferation and differentiation. In differentiated tissues consisting of a single cell type, a mechanical regulation of proliferation has been proposed to underlie growth-control and homeostatic steady-states. Yet, how tissues containing different cell types with distinct proliferation rates, mechanical interactions, and spatial self-organization retain robust homeostasis of cell proportions remains poorly understood. Here, we combine particle-based mechanical models of proliferative tissues with a classical hierarchy of stem, progenitor, and differentiated cells, undergoing stochastic fate choices, and show that mechanical feedback alone is sufficient to stabilize populations. We derive analytically and computationally a phase diagram of possible stable states, in particular those maintained either via slow and rare stem cells with short-lived progenitors or no stem cells and long-lived progenitors. Our simulations uncover that mechanical control of growth is sufficient, in the absence of any codes of adhesion or extrinsic niche signals, to cause stable spatial structures, with small stem cell clusters forming and maintaining dynamical renewal units. Our results demonstrate how complex spatial structures can emerge in minimal stochastic and mechanical simulations with impact to understand the homeostasis of multi-cellular systems.

Living matter produces a variety of beautiful spatiotemporal structures and patterns that are not enduringly present in their nonliving counterparts. These ordered, non-equilibrium steady states are often sustained through the consumption of energy. Here, we investigate the energetic cost of assembling an ordered aster from an initially disordered, uniform mixture of cytoskeletal microtubules and kinesin motors. Using a calibrated fluorescent ATP reporter, we measure reproducible radial ATP gradients on scales of tens of microns that establish within, and persist over, tens of minutes, alongside coupled spatial gradients in motor density. These appreciable gradients are predicted by a reaction-diffusion model that acknowledges the localization of ATP consumption to regions where both molecular motors and microtubules are sufficiently abundant to encourage consumption, as confirmed by finite element modeling. With our results, we compare the power per volume required by our cytoskeletal networks with the known power per volume expenditure in cells. Comparison of our measured results with estimates of the dissipative processes available to motor-microtubule mixtures leads to the hypothesis that maintaining spatial motor gradients dominates the energetic demand in this system. Our direct quantification of energetic fluxes across space unlocks future explorations of what steady states are accessible to cells, and how the cytoskeleton drives broad spatial organization. SignificanceHow much energy do organisms pay to form and maintain their organizing biochemical patterns? Existing measurements of cellular metabolism and energy expenditures largely resolve net or supply-side biochemical fluxes, without spatial information, impeding the study of this basic question. Here, we develop an experimental approach to directly measure the distributions of biochemical energy that respond to power expenditures of cytoskeletal motor-microtubule networks as they form aster structures, reminiscent of those found in the mitotic spindle. As these structures self-assemble, calibrated readouts in real molecular units register large, reproducible, and long-lived gradients of ATP. We interpret these measurements by developing theory to account for the functional destinies of energy expenditure. These advances clarify outstanding questions of energy in living matter.

Bacterial propulsion is powered by torque generated by the flagellar motor and transmitted to the flagellum through the hook, a short deformable structure acting as a flexible joint. Despite the hook being essential for propulsion, the physical mechanism governing torque transmission remains poorly characterized. Here, we show that the torque consists of two components: one parallel to the flagellum, responsible for rapid spin, and another along the motor axis, which induces precession of the former component. Evidence of such a two-component torque also emerge in bead assay experiments, where the attached bead can exhibit complex trajectories rather than simple circular motion. We introduce a minimal mechanical model that captures both the spin/precession dynamics and the commonly observed circular orbits.

We introduce a 3D mechanically adaptive viscoelastic cell-network model that links single-cell interactions to emergent tissue rheology. Unlike existing continuum or cell-based models, viscoelasticity is embedded within discrete, mechanically adaptive intercellular connections, allowing tissue-scale rheology and phenomena such as swirling and jamming to arise from single-cell behaviors and connection remodeling. The framework is motivated by recent advances in three-dimensional imaging and structural analysis that resolve single-cell behaviors within aggregates. It is validated against two gold-standard bulk assays performed on spherical aggregates: micropipette aspiration and Hertzian plate compression. Under aspiration, the model demonstrates a transition from elastic deformation to viscous creep governed by localized packing and emergent jamming at the aspirated neck, accompanied by increased mechanically adaptive remodeling. Under compression, core rheology determines deformation mode: liquid-like aggregates exhibit enhanced swirling, consistent with experimental observations, whereas solid-like aggregates exhibit affine, Poisson-like deformation. These results bridge cell-scale dynamics and quantifiable tissue rheology including elastic modulus and vicosity, providing a framework to interpret emerging 3D measurements of multicellular mechanics.

Sea slugs in the Sacoglossa superorder are some of the few animals capable of photosynthesising by isolating and maintaining functional chloroplasts within their body1,2. While this ability allows some species in this superorder, such as Elysia viridis, to appear green, camouflaging themselves within their surroundings3,4, this species is marked by extremely bright, coloured regions. Here, we show that these animals produce a yet undiscovered class of photonic structure consisting of intracellular mixed amorphous CaCO3 and calcite spherical nanoparticles organised in non-closed-packed face-centred cubic (FCC) lattices and photonic glasses5. By mapping the distribution of the cells containing such architectures, we suggest that their colour is linked both to their function and to their biological formation via the animals renal system. Using a combination of different optical methods and cryo-electron microscopy, we reveal that the biomineralisation pathway proceeds through stages of calcium ion concentration in the kidney, transport via internal vessels, and precipitation from a dense liquid-like precursor, culminating in the formation of monodisperse nanoparticles, which are the building blocks of these photonic structures.