PRX Life

The actin cortex is a dynamic biopolymer network whose mechanical rigidity, while relying critically on tensioned filaments, is robustly sustained amid constant architectural changes through the assembly and disassembly of filaments and crosslinkers. Yet the role of such remodeling processes in rigidity homeostasis remains essentially unexplored in computational models. As a result, we still lack proper understanding of the biological rationale for remodeling, which is energetically expensive, or of the microscopic mechanisms through which collective rigidity is maintained. To address this, we develop two complementary elastic network models in which rigidity homeostasis with complete turnover emerges as a result of mechanosensitive dynamics of filaments (edges) and crosslinkers (nodes), respectively. Both models require the following minimal ingredients: (1) preferential disassembly of edges or nodes under small tension or force, (2) a small but nonzero rate of random disassembly, and (3) energy injection upon assembly. Our models are robust to variations in random disassembly rates and can recover from drastic structural disruption. Remarkably, nodes and edges undergo diffusion even while elastic moduli and structural correlations reach steady states, showing that the models display representational drift similar to that found in neuronal activities and physical learning circuits. We propose that the cortex is an example of "tunable matter," i.e., its mechanosensitive remodeling dynamics tune its edges and nodes so that the cortex as a whole can maintain robust but flexible rigidity in fluctuating mechanical environments, creating survival advantages that justify its energy consumption.

Cells sense and respond to the mechanical properties of their environment, yet the minimal physical principles sufficient to reproduce mechanotransduction and durotaxis remain debated. This work introduces FraCeMM, a physics-first mechanochemical simulation framework coupling stochastic ligand-integrin-talin binding to a deformable soft-body cell model on an elastic substrate. Without imposed polarity, directional cues, or migration rules, the model reproduces hallmark mechanobiological behaviors including stiffness-dependent spreading, traction reinforcement, focal adhesion asymmetry, and directed durotaxis. A finite pool of adhesion molecules, mechanically coupled through elastic linkages, drives emergent force asymmetry and polarization via self-consistent feedback between stochastic binding, molecular availability, and substrate stiffness. Despite minimal assumptions and a coarse-grained molecular representation, resulting traction forces, adhesion loads, and migration speeds fall within experimentally reported ranges. These results support the view that local force balance, limited adhesion resources, and mechanically binding are sufficient to generate adaptive mechanosensing and directed migration, establishing a transparent and extensible foundation for computational mechanobiology.

Mechanical interactions among cells in a growing microbial colony can significantly influence the colonys spatial genetic structure and, thus, evolutionary outcomes such as the fates of rare mutations. Here, we computationally investigate how this spatial genetic structure changes as a result of heritable phenotypic variations in cell shape. By modeling rod-like bacterial cells as lengthening and dividing circo-rectangles in a 2D Brownian dynamics framework, we simulate the growth of a colony containing two populations with different aspect ratios. Compared to monodisperse colonies, such bidisperse colonies exhibit diminished intermixing between sub-populations when the less elongated cells are too short to nematically order, instead forming large clusters. We find that the cells with longer aspect ratio gradually segregate to the colony periphery. We present evidence that this demixing is related to nematic order in the bulk and to active nematic mixing dynamics near the periphery. These findings are qualitatively robust across different growth rate protocols and initial conditions. Because the periphery is often an advantageous position when nutrients are limited, our results suggest a possible evolutionary selective pressure of mechanical origin that favors large cell aspect ratio.

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

Quantifying how cooperative, many-body relationships drive allostery in protein networks remains a major challenge. To address this, we develop the Laplacian minor hierarchy, a mathematical framework that characterizes the geometric invariants of a protein network. Lower-order minors yield standard metrics including the partition function and effective distances, whereas higher-order minors define novel topological measures: cooperation indices, each bounded between zero and one, that characterize pathway correlations at increasing levels of complexity, the third-order minor determines whether allosteric pathways are correlated or uncorrelated, and the fourth-order minor quantifies how distinct pathways communicate through intermediary residues. We apply this framework to analyze the evolutionary adaptation of the PSD95pdz3 domain from Class I to Class II ligand specificity via mutations G330T and H372A. The cooperation index demonstrates a distinct evolutionary hierarchy: the G330T mutation establishes distributed pathway couplings that the H372A mutation subsequently exploits, whereas H372A alone produces minimal global changes. Furthermore, the fourth-order analysis identifies His317 as a critical intermediary node bridging the class-switching (330-372) and class-bridging (330-400) allosteric pathways. These results demonstrate that allosteric dependencies emerge only when mutations accumulate in specific combinations, with a hierarchical organization of pathways structured around position 330 and intermediary nodes His317 and Phe400. Rather than predicting allosteric mechanisms, this framework provides a mechanistic explanation for why and how allostery emerges during protein evolution.

During vertebrate development, the flat surface of the gut epithelium undergoes a dramatic transformation into densely packed arrays of finger-like projections called intestinal villi. Recent studies show that the villus formation relies on a tissue dewetting process, in which mesenchymal tissues buckle the overlying epithelial layer into periodic folds. However, the mechanisms driving subsequent elongation of these folds into finger-like villi remain largely unexplored. Here, we propose a simple mechanism for villus elongation that couples tissue dewetting to cell differentiation, which emerged as a repeated outcome of multiple independent simulations of an evolutionary-developmental Cellular Potts Model. In this mechanism, a liquid-like mesenchymal tissue continuously differentiates into a solid-like mesenchymal tissue at the interface between them. This differentiation drives the liquid-like tissue to continuously retract from the solid-like tissue in the opposite direction of the interface through dewetting, ultimately creating a finger-like projection. A merit of our proposed mechanism is that it only requires two tissues with different viscosities, high surface tension, and cell differentiation. We develop a simplified phase-field model to determine exactly how villus morphology depends on these three requirements. Since these requirements are satisfied not only in intestinal villi but also in many other developing tissues, we propose that the same mechanism could also drive the elongation of other tissues.

Sparse mesenchymal cellular networks are ubiquitous across animals, shaping both embryonic and adult structures through dynamic interactions with epithelia. Yet, the physical principles underlying their collective behaviors remain elusive, as their stellate cells and large extracellular spaces--filled with matrix or interstitial fluid--pose significant experimental and computational challenges. Here, we demonstrate that the avian presomitic mesoderm (PSM), a canonical embryonic mesenchymal tissue, behaves as a fluid under tension, exhibiting structural organization that cannot be explained by simple Brownian-like cell motion. Through quantitative modeling, we identify contact inhibition of locomotion (CIL)--where cells actively retract and move away upon contact--as a key mechanism that enables sparse mesenchymal networks to sustain macroscopic tension while flowing like a fluid. Simple continuum equations relate observable cell-scale parameters to the emergent remodeling dynamics observed in both experiments and simulations. Together, these findings put forward an unrecognized mechanical role for CIL, extending its influence beyond collective migration, and establish the fluid-under-tension state as a distinct class of tissue behavior that describes key developing embryonic tissues and may illuminate how matrix-rich adult tissues become fluidized during tumorigenesis.

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

Single cells confined by the extracellular matrix can exhibit persistent rotational motion, yet the physical mechanisms underlying this chiral symmetry breaking remain unclear. Here, we address this gap with a cellular phase field model that couples cell deformation, cell polarization governed by stochastic excitable dynamics, and confinement. We identify the confinement strength as a bifurcation parameter determining three regimes: strong confinement prevents rotation through spatial constraints, intermediate confinement induces stochastic transitions between chiral and non-chiral states, and weak confinement allows persistent rotational motion. For the intermediate regime, we develop a semi-Markovian renewal process framework that characterizes the stochastic dynamics through dwell time statistics, transition probabilities and first-passage times. For the weak confinement regime, we reveal that a mechanochemical feedback enables coherent rotations despite internal noise through the reduction of local excitability mediated by mechanical contraction. We formalize this feedback analytically using Kramers escape theory. Experiments on epithelial MCF10A cells in Matrigel validate predictions for the weak confinement regime. Our results establish a theoretical approach for understanding single-cell chiral symmetry breaking under confinement, with implications for controlling single-cell dynamics by tuning extracellular matrix properties.

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

During development, embryonic tissues experience mechanical stresses ranging from cellular to supracellular length scales. In response, cells generate active forces that drive rearrangements, allowing the tissue to relax accumulated stresses. The nature of these responses depends strongly on the magnitude and duration of the deformation, giving rise to the tissues characteristic viscoelastic behavior. Although experiments have characterized tissue rheology in various contexts, simpler theoretical approaches that directly connect cellular activity to emergent rheological behavior are still limited. In this study, we employ a vertex-based model of epithelial tissue incorporating active force fluctuations in cell vertices to represent cell motility. We capture distinct rounding dynamics and motility-dependent timescales by benchmarking against experimental observations such as the bulging of presomitic mesoderm (PSM) explants driven by Fibroblast Growth Factor(FGF) gradients. Stress relaxation tests reveal rapid short-timescale relaxation alongside persistent longtimescale residual stresses that decrease from anterior to posterior (AP) region of the PSM. By applying oscillatory shear, we analyzed the resulting elastic and viscous responses, revealing motility dependence of storage and loss modulus. Finally, we introduce spatially patterned cues applied in a temporally pulsed manner, mimicking dynamic biochemical or mechanical signals during development. Our results show that while higher motility promotes tissue remodeling in response to these cues, this response is constrained by spatial scale; cellular-scale perturbations are relaxed irrespective of motility strength, preventing complete morphological adaptation.

Biomolecular condensates are dynamic assemblies whose functions depend on continuous exchange of molecular components with the surrounding environment. While scaffold molecules drive phase separation and condensate architecture, many functional components are clients that are recruited through interactions with the scaffold-rich environment. Despite their prevalence, how client-scaffold interactions shape client exchange dynamics remains poorly understood. Here, we develop a reaction-diffusion model for client exchange in scaffold-driven condensates, in which clients switch between a scaffold-bound state and an unbound state. Bound clients exchange through scaffold-mediated transport, whereas unbound clients diffuse through the pore space of the condensate. Using the fluorescence recovery of fully photobleached condensates as a measure of client exchange, we compare transport through these two pathways with bound-unbound conversion and identify three limiting regimes. In the slow-conversion regime, bound and unbound clients recover through distinct scaffold- and pore-mediated pathways. In the intermediate-conversion regime, recovery of bound clients becomes limited by client unbinding. In the fast-conversion regime, local equilibrium between bound and unbound clients produces an effective single-state recovery. We further propose a unifying description that connects these regimes and quantitatively captures the apparent recovery timescales extracted from numerical simulations across condensate sizes. Our results provide a framework for interpreting component-specific exchange dynamics, and highlight client size, client-scaffold binding, and condensate porosity as key regulators of client turnover in multicomponent condensates.

Homologous proteins have similar three-dimensional structures and biological functions that shape their sequences. The resulting coevolution-driven correlations underlie methods from Potts models to AlphaFold, which infer protein structure and function from sequences. Using a minimal model, we show that fluctuating selection strength and the onset of new selection pressures improve coevolutionbased inference of structural contacts. Our conclusions extend to realistic synthetic data and to the inference of interaction partners. Out-of-equilibrium noise arising from ubiquitous variations in natural selection thus enhances, rather than hinders, the success of inference from protein sequences.

In natural biological systems, cells organize into tissues through interactions of several processes, including cellular signaling, collective migration, contractile activity of cytoskeletal elements and interactions with their surroundings. In recent decades, advancements in microscopy, genetic engineering, biochemistry, and computational modeling have enabled a more quantitative understanding of these processes. In this article, we present an integrated computational framework that couples various physical mechanisms such as: cell-cell adhesion, strength and persistence of cellular motility, and the background stiffness, to study how they collectively interact to determine the selforganization starting from a pseudo-random structure as well as the migration behavior. Notably, our simulations predict that motility has a two-way effect on cellular self-assembly: it promotes aggregation at moderate levels but disrupts clusters when excessively strong, yielding an optimal motility for formation of multicellular clusters. On the other hand, adhesion shows a two-stage effect: At lower value it self-assembles the structure, at higher value it compacts it. Furthermore, We experimentally demonstrate the motility-assisted self-aggregation of cells using cancer cells in a granular mechanical milieu. Finally we show that cell-cell adhesion and background medium tune the strength and persistence of cellular migration. Altogether, this work presents a computational framework that allows us to design phase behavior of collective of cells tuning their interaction, motility, and the background mechanics.

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 appear throughout the cell serving a wide variety of functions. Many condensates appear to form by the assembly of multivalent molecules, which produce phase separated networks with liquid-like properties. These networks then recruit client molecules, with the total composition providing functionality. Here we use a model system of poly-SUMO and poly-SIM proteins to understand client-network interactions and find that the structure of the network plays a strong role in defining client recruitment, and thus functionality. The basic unit of assembly in this system is a zipper-like filament composed of alternating poly-SUMO and poly-SIM molecules. These filaments have defects of unsatisfied bonds that allow for both the formation of a 3D network and the recruitment of clients. The filamentous structure constrains the scaffold stoichiometries and the distribution of client recruitment sites that the network can accommodate. This results in a non-monotonic client binding response that can be tuned independently by the client valence and binding energy. These results show how the interactions within liquid states can be disordered yet still contain structural features that provide functionality to the condensate.

Cellular monolayers often exhibit orientational order, with nematic alignment of cell shape and cytoskeletal structures governing tissue-scale collective dynamics. Despite extensive studies, a unified analysis framework for characterizing active nematics in living systems remains partial, and key discrepancies with theory persist. Here, we present a systematic and comparative analysis of nematic order and tissue flow dynamics across twelve distinct cell types. We quantify the impact of analysis parameters and provide data-driven guidelines to improve reproducibility and cross-study comparability. Across all nematic systems, we uncover remarkably consistent static properties, supporting the universality of nematic behavior in living tissues. By combining orientation-field analysis with velocity-field measurements and numerical simulations, we show that all examined systems display contractile active nematic signatures, with characteristic flow structures around topological defects. However, direct tracking of individual defects reveals subdiffusive dynamics, in stark contrast with the superdiffusive, self-propelled motion predicted by the hydrodynamic theory of active nematics. Our results establish a standardized framework for nematic analysis in biological systems and highlight fundamental limitations of current active nematic models in describing defect dynamics in living tissues.

Keeping a memory of evolving stimuli is ubiquitous in biology, an example of which is immune memory for evolving pathogens. However, learning and memory storage for dynamic patterns still pose challenges in machine learning. Here, we introduce an analytical energy-based framework to address this problem. By accounting for the tradeoff between utility in keeping a high-affinity memory and the risk in forgetting some of the diverse stimuli, we show that a moderate tolerance for risk enables a repertoire to robustly classify evolving patterns, without much fine-tuning. Our approach offers a general guideline for learning and memory storage in systems interacting with diverse and evolving stimuli.

Collagen IV is one of the main components of the basement membrane, a layer of material that lines the majority of tissues in multicellular organisms. Collagen-IV molecules assemble into networks, providing stiffness and elasticity to tissues and informing cell and organ shape, especially during development. In this work, we develop two coarse grained models for collagen-IV molecules that retain biochemical bond specificity and coarse-grain at different length scales. Through molecular dynamics simulations, we test the assembly and mechanics of the resulting networks and measure their response to strain in terms of stress, microscopic alignment, and bond dynamics. Within the basement membrane, collagen-IV networks rearrange by molecule turnover, which affects tissue organisation and can be linked with enzyme activity. Here we explore network rearrangements via bond remodelling -- the process of dynamical breaking and remaking of bonds between network molecules. We then investigate the effects of active (enzymatic) bond remodelling. We find that this non-equilibrium remodelling allows a network to keep its integrity under strain, while relaxing fully over a variety of timescales - a dynamic response that is unavailable to networks undergoing equilibrium remodelling.

How cytoskeletal structures control their assembly while sharing a common pool of their constituent parts is an open question in biology. Experiments indicate that mechanisms promoting the disassembly of these structures and replenishing the pool may play a vital role. Here, we compare the role of two modes of disassembly: monomer loss and loss of fragments (severing), in the assembly of bare filaments and bundles, modeled as a collection of linear filaments. Using analytical calculations and simulations, we show that severing can accelerate the assembly of these structures and ensure their precise size control in a shared pool. We also examine their length fluctuations and find that the decay in the autocorrelation function is faster with severing. Our study identifies parameters that influence assembly kinetics as well as the decay in autocorrelations of length fluctuations. These findings provide a framework for designing experiments that can differentiate between size control mechanisms in cytoskeletal structures.