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.

A variety of connected systems, ranging from the cytoskeleton to human organizations, dynamically rearrange themselves in order to move through physical or abstract space. However, our understanding of how systems-level behaviors arise from local restructuring actions remains limited, necessitating comparison of real-world data to models that predict network structure and dynamics. To understand these systems, we study an accessible example, the branching slime mold Physarum polycephalum, by imaging the organism as it travels and extracting key fundamental quantities from its continuously remodeling tubular network. By using these quantities as input parameters to a traveling network model, we find that with no further fitting, the model quantitatively matches key emergent properties from P. polycephalum dynamics including path length, relocation time, and search efficiency at different spatial resolutions. These findings demonstrate how a traveling network model can capture P. polycephalum behaviors, highlighting the potential to use traveling networks more broadly for understanding and predicting connected dynamic systems by linking local measurements to emergent, system-wide behaviors.

The nuclear lamina, composed of supramolecular structures of lamin proteins, is a two-dimensional protein meshwork that preserves the structural integrity, elasticity, and morphology of the nucleus. Lamins--A/C-type and B-type--assemble into dynamic, individual but interacting networks with distinct structural properties. Lamina meshwork assembly can be disrupted by lamin mutations in diseases known as laminopathies. Despite extensive experimental insights, the biophysical mechanisms that alter the lamina meshwork topology in health and disease remain relatively poorly understood. In this study, we develop a coarse-grained molecular dynamics (MD) model of lamina self-assembly, where lamin dimers are modeled as semiflexible polymers confined within an elastic nuclear shell. By systematically interrogating inter-lamin and lamin-shell association affinities, our simulations reproduce a plethora of experimentally observed lamina architectures, from lattice-like to fibrous meshwork topologies. This elucidates how the interplay between inter-lamin and lamin-nuclear envelope interactions can shape the nuclear lamina. Importantly, inter-lamin interactions can cause a heterogeneous distribution of lamins on the surface and result in large, lamin-free surface domains at sufficiently low lamin-shell affinities. Furthermore, paracrystalline lamin sheets form with increasing propensity for parallel lamin alignment, in addition to the canonical, sticky terminal groups. Overall, our integrative MD and network analysis provide the first explicit polymer physics model of the lamina and demonstrate how lamin interactions may affect the mesoscale architecture of the lamina in disease.

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.

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 are widespread cellular self-assembled structures with essential functions. There are suggestions of condensates formed by different proteins being near criticality. However, systematic investigation of the criticality of condensates is absent, and critical exponents defining their universality class have not been found. Here, using long-time simulations, we show that condensates exhibit typical critical phenomena, including scale-free spatiotemporal correlations, critical slowing down, divergence of correlation length and dynamic scaling. From these scaling behaviors, a set of critical exponents is determined. Based on dynamic critical exponent, diverse condensates can be divided into two distinct universality classes, arising from differences in their molecular components and interaction types.

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.

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.

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.

1Neuronal function requires precise spatial organization of mitochondria to meet localized energetic demand. However, the physical constraints governing mitochondrial transport in axons remain poorly defined. Bidirectional motor-driven trafficking inherently introduces the potential for collisions, but the implications of these interactions for transport failure and structural damage are not understood. Here, we develop an agent-based model that couples mitochondrial motility, morphology, and lifecycle dynamics to a deformable axonal boundary. We show that mitochondrial traffic jams emerge from a force balance between active propulsion and steric interactions, and that their severity is governed by organelle shape and mechanical properties. Elongated, mechanically rigid mitochondria remain aligned and are transported rapidly, whereas flexible, low-aspect-ratio mitochondria are prone to jamming and accumulation. Incorporating fission and fusion dynamics reveals that fission amplifies transport disruption by generating collision-prone populations, while fusion restores transport by producing anisotropic structures that navigate crowded environments more efficiently. Importantly, we find that sustained jamming generates mechanical stress on the axonal membrane, leading to deformation and swelling. Together, these results establish a physical framework linking mitochondrial dynamics to axonal integrity and provide testable predictions for how dysregulated fission-fusion balance can drive transport failure and structural pathology in neurons. 2 SignificanceAxonal deformation is implicated in myriad neurodegenerative conditions. Mitochondrial transport disruption is inextricably linked to axonal deformation and disease progression. Mechanistic understanding of the interplay between mitochondrial transport and axon stability remains opaque. Here, we developed an agent-based model of mitochondrial transport through axons. We found that mitochondria, driven to-ward presynapses for energy supply and toward the soma for repositioning or recycling, can collide, jam, and accumulate within axonal segments. The severity of jamming is sensitive to mitochondrial density as well as mechanical and morphological properties. Further, we found a balance between lifecycle dynamics including fission and fusion is paramount to maintaining homeostatic transport. Lastly, we predict that accumulated mitochondria can deform the axonal membrane, thereby elucidating a direct mechanical link between mitochondrial transport disruption and axonal deformation.

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.

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.

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.

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.