PRX Life

During the expansion of a cell collective, such as the development of microbial colonies and tumor progression, the local cell growth increases the local pressure, which in turn suppresses cell growth. How this pressure-growth coupling affects the expansion of a cell collective remains unclear. Here, we answer this question using a continuum model of cell collective. We find that a fast-growing leading front and a slow-growing interior of the cell collective emerge due to the pressure-dependent growth rate. The leading front can exhibit fingering instability and we confirm the predicted instability criteria numerically with the leading front explicitly simulated. Intriguingly, we find that fingering instability is not only a consequence of local cell growth but also enhances the entire populations growth rate as positive feedback. Our work unveils the fitness advantage of fingering formation quantitatively and suggests that the ability to form protrusion can be evolutionarily selected.

Biomolecular condensates play a crucial role in regulating gene expression, but their behavior in chromatin remains poorly understood. Classical theories of phase separation are limited to thermal equilibrium, and traditional methods can only simulate a limited number of condensates. In this paper, we introduce a novel mean-field-like method that allows us to simulate millions of condensates in a heterogeneous elastic medium to model the dynamics of transcriptional condensates in chromatin. Using this method, we unveil an elastic ripening process in which the average condensate radius exhibits a unique temporal scaling, [<]R[>] [~] t1/5, different from the classical Ostwald ripening, and we theoretically derive the exponent based on energy conservation and scale invariance. We also introduce active dissolution to model the degradation of transcriptional condensates upon RNA accumulation. Surprisingly, three different kinetics of condensate growth emerge, corresponding to constitutively expressed, transcriptional-bursting, and silenced genes. Notably, multiple distributions of transcriptional-bursting kinetics from simulations, e.g., the burst frequency, agree with transcriptome-wide experimental data. Furthermore, the timing of growth initiation can be synchronized among bursting condensates, with power-law scaling between the synchronization period and dissolution rate. Our results shed light on the complex interplay between biomolecular condensates and the elastic medium, with important implications for gene expression regulation.

Biomolecular condensates are viscoelastic, and their mechanical properties are intimately related to their biological functions. However, the connection between microscopic networks formed by intermolecular crosslinks and viscoelasticity is still elusive. Here, we model biomolecular condensates as random crosslinked polymer solutions to elucidate how random connectivity fundamentally alters their viscoelasticity. We decompose the entire solution into multiple tree networks and demonstrate that for networks with size n, their spectra of relaxation rates{lambda} exhibit a power-law scaling pn({lambda}) [~]{lambda} -1/3 with a lower cutoff{lambda} min [~] n-3/2. By integrating all networks, we show that for the entire solution, random crosslinks generate an abundance of soft modes involving multiple linear polymers with a flat spectrum of relaxation rates. The soft modes cause anomalous linear frequency scaling of the dynamic modulus, in particular, they significantly boost the low-frequency storage modulus relative to uncrosslinked systems. Our predictions agree quantitatively with the experimental data from distinct biomolecular condensates.

Mechanical adaptation underlies mechanical homeostasis by allowing living systems to restore characteristic mechanical variables under sustained perturbations. Across biological scales, turnover-mediated remodeling enables mechanical adaptation by continuously renewing internal structures under load. Despite extensive progress in this field, it remains to be established what closed-loop mathematical structure of mechanics-turnover coupling is sufficient to guarantee homeostasis and how the characteristic adaptation timescale emerges from this coupling. Here, we identify the minimal mathematical structure of closed-loop mechanics-turnover coupling, providing a unifying description of mechanically adaptive remodeling across scales. We derive an analytical expression for the adaptation timescale as a function of the coupling between internal mechanical parameters and turnover kinetics, enabling direct cross-system comparison. To isolate this structure, we formulate a dynamical model linking mechanics and turnover, and establish conditions under which the closed-loop dynamics exhibit integral action. Specifically, our model describes how deviations in the mechanical state modulate the turnover of an internal structural state, and the renewed structure feeds back onto mechanics in a negative-feedback direction, driving recovery toward a reference state. We define systems satisfying this structure as Feedback Adaptive Turnover-mediated Environment-Dependent (FATED) systems. As an experimental example, we formulate mechanical adaptation in terms of mechanically regulated actin turnover. With the generalization of this architecture, we evaluate cross-system consistency by comparing reported adaptation and turnover timescales across representative remodeling systems.

Cell proliferation plays a crucial role in regulating tissue homeostasis and development. However, our understanding of how cell proliferation is controlled in densely packed tissues is limited. Here we develop a computational framework to predict the patterns of cell proliferation in growing tissues, connecting single-cell behaviors and cell-cell interactions to tissue-level growth. Our model incorporates probabilistic rules governing cell growth, division, and elimination, while also taking into account their feedback with tissue mechanics. In particular, cell growth is suppressed and apoptosis is enhanced in regions of high cell density. With these rules and model parameters calibrated using experimental data, we predict how tissue confinement influences cell size and proliferation dynamics, and how single-cell physical properties influence the spatiotemporal patterns of tissue growth. Our findings indicate that mechanical feedback between tissue confinement and cell growth leads to enhanced cell proliferation at tissue boundaries, whereas cell growth in the bulk is arrested. By tuning cellular elasticity and contact inhibition of proliferation we can regulate the emergent patterns of cell proliferation, ranging from uniform growth at low contact inhibition to localized growth at higher contact inhibition. Furthermore, mechanical state of the tissue governs the dynamics of tissue growth, with cellular parameters affecting tissue pressure playing a significant role in determining the overall growth rate. Our computational study thus underscores the impact of cell mechanical properties on the spatiotemporal patterns of cell proliferation in growing tissues.

Foraging is a central decision-making behavior performed by all animals, essential to garnishing enough energy for an organism to survive. Similarly, mating is crucial for evolutionary continuity and offspring production. Mate choice is one of the central tenets of sexual selection, driving major evolutionary processes, and can be regarded as a decision-making process between potential mating partners. Often researchers have used coarse-grained models to describe macroscopic phenomenology pertaining to mate choice without detailed quantitative mechanisms of how animals use individual and environmental signals to guide their mating decisions. In this letter, we show that mate choice can be cast as a foraging problem, and we present an analytically tractable optimal foraging-inspired mechanistic theory of decision-making underlying mate choice. We begin from the premise that deciding upon which partner with which to mate is at its core a stochastic decision-making process. Agents adopt a variety of decision strategies, tuned by decision thresholds for leaving or committing to a mate. We find that sensitive leaving thresholds are favored independently of signal availability in the population. By contrast, optimal thresholds for committing to a mate depend upon signal availability in the population, with signal-rich populations generally favoring less eager strategies compared to signal-poor populations.

The geometry of the brain imposes fundamental constraints on its activity and function. However, the mechanisms linking its shape to neuronal dynamics remain elusive. Here, we investigate how geometric eigenmodes relate to functional connectivity gradients within three-dimensional structures using numerical simulations and calcium imaging experiments in larval zebrafish. We show that functional connectivity gradients arising from network activity closely match the geometric eigenmodes of the networks spatial embedding when neurons are locally connected. By systematically varying network parameters such as the connectivity radius and the prevalence of long-range connections introduced via edge swaps, we reveal a robust geometry-function correspondence that progressively deteriorates as local connectivity is disrupted. Additionally, we demonstrate that spatial filtering can artificially imprint geometric patterns on functional gradients. To support our computational results, we conduct volumetric calcium imaging experiments at cellular resolution in the optic tectum of zebrafish larvae, uncovering functional gradients that closely align with geometric eigenmodes. Furthermore, the eigenmode-gradient mapping exhibits a cutoff at a spatial wavelength that precisely reflects the size of neuronal arborizations measured from single-neuron reconstructions, as predicted by our simulations. Our findings demonstrate how short-range anatomical connectivity anchors large-scale functional connectivity gradients to the brains geometry.

Fluid-filled biological cavities are ubiquitous, but their collective dynamics has remained largely unexplored from a physical perspective. Based on experimental observations in early embryos, we propose a model where a cavity forms through the coarsening of myriad of pressurized micrometric lumens, that interact by ion and fluid exchanges through the intercellular space. Performing extensive numerical simulations, we find that hydraulic fluxes lead to a self-similar coarsening of lumens in time, characterized by a robust dynamic scaling exponent. The collective dynamics is primarily controlled by hydraulic fluxes, which stem from lumen pressures differences and are dampened by water permeation through the membrane. Passive osmotic heterogeneities play, on the contrary, a minor role on cavity formation but active ion pumping can largely modify the coarsening dynamics: it prevents the lumen network from a collective collapse and gives rise to a novel coalescence-dominated regime exhibiting a distinct scaling law. Interestingly, we prove numerically that spatially biasing ion pumping may be sufficient to position the cavity, suggesting a novel mode of symmetry breaking to control tissue patterning. Providing generic testable predictions, our model forms a comprehensive theoretical basis for hydro-osmotic interaction between biological cavities, that shall find wide applications in embryo and tissue morphogenesis. Author summaryThe formation of a single biological cavity, or lumen, in tissues and embryos has been widely studied experimentally but the collective dynamics of multiple lumens has received much less attention. Here, we focus on a particular type of lumens, which are located at the adhesive side of cells and can therefore interact directly through the intercellular space, as recently observed in the very first stages of embryogenesis. We propose a generic model to describe the hydraulic and osmotic exchanges between lumens themselves, and with the surrounding cellular medium. Lumens are pressurized by a surface tension, which leads naturally to their coarsening into a single final cavity through hydraulic exchanges. With extensive numerical simulations and mean-field theory we predict that such coarsening dynamics follows a robust scaling law, that barely depends on concentration heterogeneities between lumens. On the contrary, active osmotic pumping largely influences the collective dynamics by favoring lumen coalescence and by biasing the position of the final cavity. Our theoretical work highlights the essential role of hydraulic and osmotic flows in morphogenesis.

Cells dynamically remodel their internal structures by modulating the arrangement of actin filaments (AFs). In this process, individual AFs exhibit stochastic behavior without knowing macroscopic higher-order structures they are meant to create or disintegrate. Cellular adaptation to environmental cues is accompanied with this type of self-assembly and disassembly, but the mechanism allowing for the stochastic process-driven remodeling of the cell structure remains incompletely understood. Here we employ percolation theory to explore how AFs interacting only with neighboring ones without recognizing the overall configuration can nonetheless construct stress fibers (SFs) at particular locations. To achieve this, we determine the binding and unbinding probabilities of AFs undergoing cellular tensional homeostasis, a fundamental property maintaining intracellular tension. We showed that the duration required for the assembly of SFs is shortened by the amount of preexisting actin meshwork, while the disassembly occurs independently of the presence of actin meshwork. This asymmetry between the assembly and disassembly, consistently observed in actual cells, is explained by considering the nature of intracellular tension transmission. Thus, our percolation analysis provides insights into the role of coexisting higher-order actin structures in their flexible responses during cellular adaptation.

Local stresses in a tissue, a collective property, regulate cell division and apoptosis. In turn, cell growth and division induce active stresses in the tissue. As a consequence, there is a feed-back between cell growth and local stresses. However, how the cell dynamics depend on local stress-dependent cell division and the feedback strength is not fully understood. Here, we probe the consequences of stress-mediated growth and cell division on cell dynamics using agent-based simulations of a two-dimensional growing tissue. We discover a rich dynamical behavior of individual cells, ranging from jamming (mean square displacement, {Delta}(t) [~] t with less than unity), to hyperdiffusion ( > 2) depending on cell division rate and the strength of the mechanical feedback. Strikingly, {Delta}(t) is determined by the tissue growth law, which quantifies cell proliferation (number of cells N (t) as a function of time). The growth law (N (t) [~] t{lambda} at long times) is regulated by the critical pressure that controls the strength of the mechanical feedback and the ratio between cell division-apoptosis rates. We show that{lambda} [~] , which implies that higher growth rate leads to a greater degree of cell migration. The variations in cell motility are linked to the emergence of highly persistent forces extending over several cell cycle times. Our predictions are testable using cell-tracking imaging techniques.

In morphogenesis and disease, biological tissues may exhibit diverse mechanical properties due to their capacity to switch between fluid-like to solid-like states through the (un)jamming transition. Here, we introduce a novel foam model to investigate how active mechanical properties and cellular interactions govern this transition in active cell monolayers. This model explicitly represents 3D cell shapes and describes cell-cell interactions via discrete interacting surfaces. Simulations reveal that cell-cell adhesive tension promotes tissue fluidization in high adhesive tissues, where it mainly promotes cell deformability, while it induces solidification in the low adhesive regime, where it prevents cell-cell debonding. Moreover, we study the dynamic role of adhesive ligand turnover through an effective intercellular friction. Through simulated shear experiments, we find that intercellular friction strongly suppresses neighbor exchanges, but does not lead to solid-like tissue properties. We discuss the implications of our results for understanding the relationship between unjamming and partial epithelial-mesenchymal transition, highlighting how differences in adhesion dynamics and intercellular friction may reconcile conflicting observations in tissue mechanics and cancer metastasis.

Efficient absorption of signaling molecules and carbohydrates through receptors on cell surfaces is crucial for various biological processes. While ubiquitous patterns of receptor distributions, including polar localization in rod-shaped cells, have been widely observed experimentally, their underlying evolutionary advantage is unclear. In this work, we study how spatial distributions of receptors on cell surfaces affect the total flux entering the cell. We innovate a method by which one can calculate the fluxes through all receptors using linear equations, which applies to arbitrarily shaped cells. Our theories recover previous results for spherical cells and further show that the flux through each receptor is spatially dependent in non-spherical cells. In particular, the fluxes are the highest near the poles in rod-shaped cells and the highest near the invagination in defective spherical cells. Surprisingly, we prove that the optimal receptor distribution on an arbitrarily shaped cell maximizing the total flux is precisely the charge density distribution on an ideal conductor of the same shape, which agrees with numerical simulations. Our work unveils the evolutionary origin of receptor localizations.

Understanding how the collective physical processes drive robust morphological transitions in animal development requires the characterization of the relevant fields underlying morphogenesis. Calcium (Ca2+) is known to be such a field. Here we show that the Ca2+ spatial fluctuations, in whole-body Hydra regeneration, exhibit universal properties captured by a field-theoretic model describing fluctuations in a tilted double-well potential. We utilize an external electric field and Heptanol, a drug blocking gap junctions, as two separate controls affecting the Ca2+ activity and pausing the regeneration process in a reversible way. Subjecting the Hydra tissue to an electric field increases the calcium activity and its spatial correlations, while applying Heptanol inhibits the activity and weakens the spatial correlations. The statistical characteristics of the Ca2+ spatial fluctuations - i.e., the coefficient of variation and the skewness - exhibit universal shape distributions across tissue samples and conditions, demonstrating the existence of global constraints over this field. Our analysis shows that the Hydras tissue resides near the onset of bistability; the local Ca2+ activity in different regions fluctuates between low and high excited states. The controls modulate the dynamics near that onset, preserving the universal characteristics of the Ca2+ fluctuations and, by that, maintaining the tissues ability to regenerate.

Epithelial monolayers perform a variety of mechanical functions, which include maintaining a cohesive barrier or developing 3D shapes, while undergoing stretches over a wide range of magnitudes and loading rates. To perform these functions, they rely on a hierarchical organization, which spans molecules, cytoskeletal networks, adhesion complexes and junctional networks up to the tissue scale. While the molecular understanding and ability to manipulate cytoskeletal components within cells is rapidly increasing, how these components integrate to control tissue mechanics is far less understood, partly due to the disconnect between theoretical models of sub-cellular dynamics and those at a tissue scale. To fill this gap, here we propose a formalism bridging active-gel models of the actomyosin cortex and 3D vertex-like models at a tissue scale. We show that this unified framework recapitulates a number of seemingly disconnected epithelial time-dependent phenomenologies, including stress relaxation following stretch/unstretch maneuvers, active flattening after buckling, or nonreciprocal and non-affine pulsatile contractions. We further analyze tissue dynamics probed by a novel experimental setup operating in a pressure-controlled ensemble. Overall, the proposed framework systematically connects sub-cellular cortical dynamics and tissue mechanics, and ties a variety of epithelial phenomenologies to a common sub-cellular origin.

While biomolecular condensates are often liquid-like, many experiments found that condensates also exhibit solid-like behaviors, making them indissoluble in conditions liquid condensates dissolve. Despite the biological significance of indissoluble condensates to cellular fitness, the mechanisms underlying the indissolubility of solid-like condensates are still unclear. In this work, we study the effects of elasticity on the dissolution of biomolecular condensates. We demonstrate that the bulk stress inside condensates may prevent the condensates from dissolution and obtain a new mechanical equilibrium condition of elastic condensates. Moreover, we theoretically predict a phase diagram of indissolubility for biomolecular condensates and identify a minimum bulk modulus for the condensates to be indissoluble. To verify our theories, we simulate the two-fluid model in which the slow component corresponding to biomolecules generates elastic stress. Our theoretical predictions are nicely confirmed and independent of microscopic details. Our works show that elasticity makes biomolecular condensates less prone to dissolution.

In cortical neurons, spontaneous membrane potential fluctuations affect the likelihood of firing an action potential. Yet despite retaining sensitivity to random electrical noise in gating signaling outcomes, these cells achieve highly accurate computations with extraordinary energy efficiency. A new approach models the inherently probabilistic nature of cortical neuron firing as a thermodynamic process of non-deterministic computation. Typically, the cortical neuron is modeled as a binary computational unit, in either an off-state or an on-state, but here, the cortical neuron is modeled as a two-state quantum system, with some probability of switching from an off-state to an on-state. This approach explicitly takes into account the contribution of random electrical noise in gating signaling outcomes, particularly during cortical up-states. In this model, the membrane potential is described as the mixed sum of all component microstates, or the quantity of von Neumann entropy encoded by the computational unit. This distribution of macrostates is given by a density matrix, which undergoes a unitary change of basis as each unit, System A, interacts with its surrounding environment, System B. Any linear correlations reduce the number of distinguishable pure states, leading to the selection of an optimal system state in the present context. This process of information compression is shown to be equivalent to the extraction of predictive value from a thermodynamic quantity of information. Calculations demonstrate that estimated coulomb scattering profiles and decoherence timescales in cortical neurons are consistent with a quantum system, with random electrical noise driving signaling outcomes.

Bacteria and cancer cells inhabit spatially heterogeneous environments, where migration shapes microhabitat structures critical for colonization and metastasis. The interplay between growth, migration, and spatial structure complicates the prediction of population responses to drug treatment--such as clearance or persistence--even under the same spatially averaged growth rate. Accurately predicting these responses is essential for designing effective treatment strategies. Here, we propose a minimal growth-migration model to study population dynamics on discrete microhabitat structures under spatial drug heterogeneity. By applying a kernel transformation, we map the original structure to an effective fully connected graph and derive a new exact criterion for population response based on a regularized Laplacian kernel reweighted by local growth rates. This criterion connects to forest closeness centrality and yields analytical bounds and sufficient conditions for population growth or decline. We find that higher structural connectivity--like increased migration--generally promotes decline. Our framework also informs optimal spatial drug assignments, which reduce to selecting interconnected subcores in the effective complete graph. For partially controllable microhabitats or unknown drug distributions, we identify strategies that ensure population decline. Overall, our results offer a new theoretical perspective on drug response in spatially structured populations and provide practical guidance for optimizing spatially explicit dosing strategies in heterogeneous environments.

Cell neighbor exchanges are integral to tissue rearrangements in biology, including development and repair. Often these processes occur via topological T1 transitions analogous to those observed in foams, grains and colloids. However, in contrast to in non-living materials the T1 transitions in biological tissues are rate-limited and cannot occur instantaneously due to the finite time required to remodel complex structures at cell-cell junctions. Here we study how this rate-limiting process affects the mechanics and collective behavior of cells in a tissue by introducing this important biological constraint in a theoretical vertex-based model as an intrinsic single-cell property. We report in the absence of this time constraint, the tissue undergoes a motility-driven glass transition characterized by a sharp increase in the intermittency of cell-cell rearrangements. Remarkably, this glass transition disappears as T1 transitions are temporally limited. As a unique consequence of limited rearrangements, we also find that the tissue develops spaitally correlated streams of fast and slow cells, in which the fast cells organize into stream-like patterns with leader-follower interactions, and maintain optimally stable cell-cell contacts. The predictions of this work is compared with existing in-vivo experiments in Drosophila pupal development.

The functional activity of proteins within cells is often unequally distributed: only a small subset of molecules tends to account for the majority of cellular work. This skewed contribution pattern, reminiscent of Paretos principle, often known as the 80/20 rule, has been observed across various protein classes, yet its mechanistic origin remains poorly understood. In this study, we present a statistical mechanics-based framework that explains how such disparities naturally emerge from biologically plausible rules of interaction and regulation. By modeling proteins as elements whose activity levels and outputs evolve through mutual comparison and feedback, we demonstrate that power-law distributions can arise without assuming any intrinsic heterogeneity. The model also captures a recursive feature of disparity: even among highly active proteins, a new skewed distribution reappears when a subpopulation is isolated, reflecting the scale-invariant structure commonly observed in complex adaptive systems. We analytically derive these patterns under both positive and negative feedback scenarios and identify key conditions under which long-term functional dominance is established. Our results offer a mechanistic interpretation for the coexistence of active and inactive molecular populations and suggest that functional inequality may reflect an adaptive organizational principle of cellular systems.

Immune cells, such as macrophages and dendritic cells, can utilize podosomes, actin-rich protrusions, to generate forces, migrate, and patrol for foreign antigens. In these cells, individual podosomes exhibit periodic protrusion and retraction cycles (vertical oscillations) to probe their microenvironment, while multiple podosomes arranged in clusters demonstrate coordinated wave-like spatiotemporal dynamics. However, the mechanisms governing both the individual vertical oscillations and the coordinated oscillation waves in clusters remain unclear. By integrating actin polymerization, myosin contractility, actin diffusion, and mechanosensitive signaling, we develop a chemo-mechanical model for both the oscillatory growth of individual podosomes and wave-like dynamics in clusters. Our model reveals that podosomes show oscillatory growth when the actin polymerization-associated protrusion and the signaling-associated myosin contraction occur at similar rates, while the diffusion of actin monomers within the cluster drives mesoscale coordination of individual podosome oscillations in an apparent wave-like fashion. Our model predicts the influence of different pharmacological treatments targeting myosin activity, actin polymerization, and mechanosensitive pathways, as well as the impact of the microenvironment stiffness on the wavelengths, frequencies, and speeds of the chemo-mechanical waves. Overall, our integrated theoretical and experimental approach reveals how collective wave dynamics arise due to the coupling between chemo-mechanical signaling and actin diffusion, shedding light on the role of podosomes in immune cell mechanosensing within the context of wound healing and cancer immunotherapy.