Physical Review X

Contact inhibition of proliferation (CIP) enables epithelial tissues to self-regulate growth and maintain tissue homeostasis. However, how cell-level mechanical contact, tissue-scale structural order, and proliferation kinetics interplay remains a fundamental open question in living matter physics. Here, we present a particle-based model of a confluent epithelial monolayer governed by overdamped dynamics, where individual cells interact via a two-dimensional hard core- soft shoulder potential. By comparing structural evolution during quasistatic densification with previously reported experimental division kinetics, we find that the dynamics of proliferation arrest mimics the onset of direct steric contacts between the hard cores of the shell. Identifying hard core contacts as the physical driver of CIP, we couple our mechanical model with a stochastic Monte Carlo division scheme in which the instantaneous division rate decreases to zero from an intrinsic value as the number of hard core contact increases to six from zero. We demonstrate that for high intrinsic division rates, the cellular densification outpaces mechanical relaxation. This kinetic mismatch drives premature hard-core contact formation, shifts the onset of jamming and contact inhibition to lower packing fractions, and induces increasingly disordered transient configurations before the tissue universally converges to a hexagonal close-packed limit. Our model's predicted division kinetics and structural order evolution are consistent with epithelial monolayer experiments, both reported and our own. This minimal physical framework links single-cell steric contact mechanics directly to tissue-scale growth regulation and structural evolution.

Radiation-induced DNA double-strand breaks (DSBs) drive cellular mortality, mutagenesis, and severe evolutionary bottlenecks. While classical phenomenological models, such as the Linear-Quadratic (LQ) framework, reliably predict macroscopic population survival, they obscure the intrinsic single-cell stochasticity that governs critical rare events like tumor recurrence or the emergence of radioresistant persisters. To bridge this divide, we develop a mathematically exact stochastic differential equation (SDE) framework that models continuous DSB induction and repair as a Feller square-root process. By deriving exact closed-form expressions for the foci moments, we establish a highly efficient Maximum Likelihood Estimation (MLE) pipeline that circumvents computationally exhaustive Monte Carlo simulations, allowing the direct extraction of deterministic repair velocities and intrinsic molecular noise from empirical single-cell $\gamma$-H2AX data. Integrating this kinetic model with a cumulative damage hazard via the Feynman-Kac formalism, our framework seamlessly recovers the classic macroscopic LQ survival topology from microscopic first principles. Furthermore, systematic sensitivity analysis uncovers a fundamental evolutionary duality: while initial physical damage operates additively, ultimate cellular fate is driven by a nonlinear survival response governed by the trade-off between the damage hazard rate and intrinsic molecular noise strength. Crucially, we demonstrate that this molecular noise inherently enhances population survival. Governed by Jensen's inequality, stochastic variance acts as a non-genetic bet-hedging mechanism that buffers the population by favoring cells with transiently low damage loads. Ultimately, this exact stochastic framework bridges microscopic biophysics and macroscopic demographics, offering deep mechanistic insights into the evolutionary roots of radioresistance.

The collective spatial phenomenon of complement protein opsonization on nanoparticle surfaces is a key component of the immune response to viruses, engineered nanoparticles, and diseased cells. Recent work showed this opsonization follows a sharp, percolation-like transition versus the spacing d between surface-bound attachment sites, leaving two open questions: 1) whether the transition exhibits hallmarks of true criticality, such as diverging susceptibility, and 2) whether it can be distinguished from an alternative first-order cooperative (Hill-type) process producing an equally sharp threshold without true criticality. Here, we resolve both questions using a hierarchical statistical-mechanics treatment spanning stochastic, mean-field, and spatial reaction-diffusion models. The variance of two order parameters, peak complement activity and activation lifetime, diverges near threshold and sharpens systematically with system size, the defining signature of a critical point rather than a smooth cooperative response. Extending the analysis across site spacing and intrinsic kinetic rate constants traces a two-dimensional locus of critical points with consistent critical exponents throughout, establishing a single, robust universality class. The mean-field dynamic exponent for activation lifetime agrees quantitatively with the exact value predicted for the general epidemic process. Finally, a reaction-diffusion model of the nanoparticle surface shows the critical locus is set by a diffusion-limited length scale, establishing complement percolation as a fundamentally transport-limited surface reaction. These results place complement activation within the percolation universality class and identify the physical parameters, diffusion, catalysis, and decay, that govern its critical threshold, with direct implications for rational design of complement-evading nanomaterials, immunology, and evolutionary biology.

Structural network representations of metastatic dissemination typically focus on static topology without resolving transport dynamics, relaxation timescales, or steady-state behaviour. Here, we formulate a discrete Markovian transport model on a directed higher-order network with transition rates derived from qualitative clinical affinity classes. By constructing a non-Hermitian row-stochastic transfer operator, we characterise the relaxation dynamics through its spectral decomposition. The system exhibits a fast-mixing regime characterised by a spectral gap of {gamma} {approx} 0.67, corresponding to a characteristic relaxation timescale of {tau} {approx} 1.49 discrete steps, with the influence of the primary tumour origin progressively attenuated during dissemination. Convergence towards a non-equilibrium steady state (NESS) is accompanied by a reduction in Shannon entropy, concentrating probability mass within specific topological sinks. This spectral relaxation delineates two distinct dynamical regimes: early transient dissemination (n < {tau}), dominated by local organ-specific transition probabilities (organotropism), and the asymptotic regime (n > {tau}), determined increasingly by the global transport architecture of the network. Comparison with independent clinical and autopsy observations across 21 primary tumours and 23 target organs indicates that the predicted stationary distribution is consistent with the observed hierarchy of metastatic organ involvement.

Biomolecular condensates (BMCs) organize cellular biochemistry by concentrating selected molecules into dynamic membrane-free compartments. Yet the molecular parameters that determine not only whether condensates form, but also how they behave and what they do, remain poorly defined. Here we show that scaffold binding affinity (Kd) is a quantitative determinant of condensate phase behavior, internal dynamics and biochemical output. Using a modular SUMO-SIM system in which scaffold valency was held constant while binding affinity was systematically varied, we found that affinity governs the phase boundary, resistance to chemical perturbation, and molecular mobility of condensates in vitro and in human cells. In multicomponent mixtures, the highest-affinity scaffold dominated dense-phase composition and dynamics, revealing a hierarchical rule for condensate organization. Finally, affinity-dependent changes in condensate dynamics translated into tunable enzyme activity, establishing binding energetics as an engineerable parameter for programming condensate biochemistry.

Eukaryotic organisms rely on post-translational modifications to chromatin to maintain stable patterns of gene silencing. These modifications include trimethylation at histone H3 lysine 27 (H3K27me3), which is deposited by Polycomb Repressive Complex 2 (PRC2) and accumulates on the genome during embryogenesis. While this process underlies the proper specification of cell types, we lack the ability to quantitatively predict the de novo establishment of Polycomb states. The kinetics of H3K27 methylation is difficult to quantify in vivo, and further, the network of molecular interactions that influences Polycomb states is complex. Here, leveraging the Drosophila embryonic system, we measure H3K27me3 dynamics with ChIP-seq and extract the rate the modification spreads along chromatin in vivo. To provide a mechanistic explanation for this rate, we build a reaction-diffusion framework that models how PRC2 establishes states of gene silencing de novo. The reaction-diffusion system recapitulates experimental observations in wild-type and mutant embryos, and suggests that PRC2 can diffuse in 1D along chromatin at a rate enhanced by Polycomb Repressive Complex 1. Through this work, we define a minimal set of parameters that dictate in vivo Polycomb dynamics, and provide evidence that the early embryo creates a super-charged environment for epigenetic modification.

Enzymatic reactions in biomolecular condensates are often assumed to be regulated through local enrichment of reactants. However, condensates also reshape molecular transport and reaction kinetics, making it unclear how phase separation controls catalysis in living cells. Here, we develop a quantitative theory of biomolecular catalysis in phase-separated systems and find that liquid condensates can act as tunable catalytic switches, transitioning between regimes of enhanced and suppressed enzymatic activity, exhibiting optimal responses at biologically relevant condensate sizes. We show that condensate-mediated catalysis cannot be understood from reactant enrichment alone, but instead emerges from the coupled interplay of molecular partitioning, diffusive transport, and phase-dependent reaction kinetics. The strongest regulatory effects occur under rapid interphase exchange, where the spatially heterogeneous catalytic network admits a system-level Michaelis-Menten description governed by system-averaged concentrations and reaction kinetics. Our framework predicts that micron-sized condensates can either enhance or suppress enzymatic activity by up to two orders of magnitude, and that optimal catalytic regulation can emerge at condensate sizes comparable to many biomolecular condensates. These results provide experimentally testable predictions for condensate-mediated catalysis and establish quantitative principles for understanding and engineering enzyme-catalysed reactions in biomolecular condensates.

In linear polysomes, excluded-volume interactions among ribosomes can induce dimensional reduction of mRNA. Yet linear architectures allow steric stress to relax at open ends-- limiting how strongly crowding can remodel the mRNA's structure and dynamics. Using coarse-grained molecular-dynamics simulations, we compare circular and linear polysomes over a range of ribosome densities. Circular closure selects a predominantly quasi-planar global conformational ensemble, as indicated by a shape dimensionality dshape {approx} 2 over a range of ribosome densities. Crucially, circular topology and ribosome crowding act cooperatively to suppress structural fluctuations. While closure alone or linear crowding reduces relative global size fluctuations ({Delta}Rg/Rg) only to {approx} 0.16, their combined effect drives this fluctuation down to {approx} 0.07. Within this stabilized architecture, increasing ribosome density drives a distinct in-plane reorganization: the ring becomes more isotropic, global size fluctuations are strongly suppressed, and the scaling exponent increases toward {nu} [~=] 0.74 - 0.77, consistent with two-dimensional self-avoiding walk-like value over the accessible finite-size window, 1000 [&le;] N [&le;] 4969. Closure shortens the radius-of-gyration decorrelation time of circular polysomes by 40-fold relative to matched linear systems, reflecting the topological elimination of free ends. Within this closureselected ensemble, ribosome crowding further reduces the decorrelation time by up to 20% at the highest density. A fluctuation-informed crossover model links the density dependence of the global scaling exponent to inter-ribosomal subchain statistics. These results distinguish the geometric role of circular closure from the density-dependent steric response that it enables, revealing a confined yet dynamically responsive conformational regime for circular polysomes.

The shared trade-off in microbial resource-utilization strategies has been proposed to resolve the paradox of the plankton, which states that the diversity observed in nature greatly exceeds the theoretically predicted upper bound that limits the number of coexisting species to the number of available resources. However, three important aspects remain unaddressed in this line of work. First, trade-offs have been quantified not only for phenotypes associated with alternative resource utilization, but also for other modes of microbial interaction. Second, in natural systems, not all taxa are subjected to the same trade-offs. Third, existing trade-off-based models do not explain the empirically observed clustering of taxa according to functional similarity. Here, we extend the trade-off-based framework to incorporate multiple types of resources. We assume that different subsets of taxa are constrained by distinct sets of trade-offs. Under this framework, our model predicts the emergence of clusters: while taxa with similar strategies can belong to the same cluster, each cluster is sustained by taxa with substantially different strategies. The resulting system supports high diversity with an effectively unlimited number of coexisting taxa, yet can still be described as a low-diversity community in which the number of coexisting functional clusters does not exceed the theoretical upper bound.

Information is fundamental to biological survival, but the amount of information and its biological value are not equivalent. Shannon information quantifies uncertainty reduction, whereas Volkenstein's value of information measures how information changes the probability of a biologically relevant outcome. Although originally developed for molecular biology contexts, the latter concept has rarely been applied to environmental sensing and ecological interactions. Here we develop a value-of-information framework for microbial predator-prey interactions based on hydrodynamic sensing, in which prey detect fluid disturbances generated by approaching predators. Using a mechanistic model that incorporates sensory thresholds, memory, false alarms, biological benefits and costs, and predator encounter probability, we characterize mutual information from three hierarchical measures of biological value: encounter-conditional value, ecological value, and lifetime fitness value. The framework reveals how small amounts of sensory information can produce disproportionately large survival benefits during predator encounters, generating encounter-level value amplification in which biological value exceeds Shannon information. However, although global sensitivity analysis shows that such amplification is common, it is not universal and becomes progressively diluted at broader ecological and lifetime scales by encounter rarity, background noise, and sensory costs. Across most parameter combinations, the encounter-conditional value exceeded the ecological value, which in turn exceeded the lifetime fitness value. These results demonstrate that environmental sensing should be evaluated not only by how accurately it represents the external world, but by how strongly it changes biologically relevant outcomes. More broadly, the framework extends Volkenstein's concept of information value to ecological interactions and provides a quantitative framework for predicting when environmental information enhances survival and fitness, thereby providing a platform for explaining the evolution, maintenance, diversification, and loss of sensory systems.

The shape of density-dependence governs species persistence, and ecosystem stability. Yet, whether per-capita growth declines sublinearily, or superlinearily with density remains hotly debated. Growth rates across the tree of life have been shown to decline sublinearly with density, whereas theory founded on resource competition predicts the opposite. Here, we resolve this discrepancy and show that sublinearity can readily emerge from geometric constraints on consumer interactions. By linking inter individual spacing, movement and interference rates, we derive two limiting-interference regimes, one of which the well-mixed limit recovers the form of classic Beddington DeAngelis interference response. We then developed an individual-based model from first principles which reproduces the derived sublinearity response, and further use empirical data from published consumer-resource experiments that also bears the signature of sublinear density-dependence. Further, embedding the interference mechanisms underlying the emergence of sublinear density-dependence in coexistence theory opens a new regime for species coexistence where classical theory fails to predict. Our framework indicates that non-consumptive interactions are not merely a correction to resource competition but might be a distinct axis along which diverse communities may potentially coexist.

Biological aging is accompanied by systematic changes in epigenetic modifications and chromatin organization. The reversal of the effects of aging, rejuvenation, is experimentally achieved by the transient induction of factors that modify these marks in cells and organisms. Here, we show that key features of rejuvenation experiments emerge from the biophysical interplay between dynamic epigenetic marks and the three-dimensional conformation of chromatin. Using a minimal field theory and molecular dynamics simulations, we show that the system responds in three distinct temporal regimes. The intermediary regime fulfills necessary conditions for successful rejuvenation. In this regime, the system spends time near a separatrix, allowing for high epigenetic plasticity, while memory retained in the chromatin conformation enables restoration of the original epigenetic correlations. Analysis of sequencing data further supports the predicted coupling between chromatin compaction and epigenetic correlations. Our results provide a physical explanation for how rejuvenation may remodel age-associated epigenetic states without irreversibly erasing cellular identity. We identify a general mechanism by which memory stored in a slow structural variable permits reversible remodeling of a faster internal state.

Decision formation is commonly described as the accumulation of noisy evidence in a low-dimensional decision variable, but it remains unclear how this latent computation is implemented by heterogeneous neural responses. Here, we propose that ramping and sequentially firing neurons form complementary population codes for the same decision variable. Inspired by Laplace-domain neural representations of time, exponential receptive fields in a ramping population give rise to a translatable edge-like activity profile; localized receptive fields in a sequential population give rise to an aligned bump-like profile. We construct a continuous attractor neural network that dynamically maintains these complementary representations while implementing evidence accumulation along a shared latent manifold. At the behavioral level, simulations show that the circuit closely reproduces the single-trial trajectories, choice probabilities, and reaction-time statistics of a standard diffusion decision model while generating heterogeneous ramping and sequential neural responses. Our framework connects latent behavioral dynamics, population geometry, and recurrent circuit mechanisms. More broadly, it provides a circuit-level realization of computation in the Laplace domain that may support the representation and updating of continuous cognitive variables across decision making, timing, memory, and spatial cognition.

High-dimensional population balance equations (PBEs) provide a natural framework for modeling heterogeneous cell populations, but their direct numerical solution becomes computationally prohibitive when the internal state space contains many molecular variables. We propose a hybrid mechanistic-machine learning framework for reducing and simulating PBEs defined over high-dimensional intracellular coordinates. The cell population is described by a number density n(x, t), where x [isin] [R]N represents gene and protein states associated with macrophage activation. A dynamics-preserving autoencoder maps this state space to a low-dimensional latent coordinate z [isin] [R]d, with d << N, while retaining key qualitative features of the underlying gene regulatory network, including attractor structure and multistability. Mechanistic information from the original regulatory dynamics is used to construct interpretable drift and diffusion terms for the reduced latent-space PBE. The reduced PBE is solved using a stochastic Lagrangian particle representation, in which particles evolve according to stochastic differential equations (SDEs) corresponding to the latent drift and diffusion fields. The resulting latent-space solution is subsequently decoded and propagated back into the original state space to recover physically interpretable cellular dynamics. We demonstrate the framework on macrophage polarization under cytokine-dependent regulation, including gene knockout perturbations. Overall, the proposed framework provides a computationally tractable and mechanistically interpretable route for integrating single-cell genomic data with population balance models of cell-state dynamics.

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.

Classical neurogeometric models describe the primary visual cortex as a fibered structure in which retinal position and local orientation are coupled through the geometry of the roto-translation group. We extend this approach to the visuomotor cortex by modeling it as an assemblage of visual and motor cortical geometries. The model combines orientation-selective representations, analogous to those of the primary visual cortex, with movement-direction-selective representations, analogous to those of the primary motor cortex, in order to describe the mixed visual and motor selectivity observed in the visuomotor cortex. We introduce a coupled visuomotor structure in which visual orientation and motor direction coexist over a common spatial plane and interact through a relative-orientation constraint. Neural responses are modeled by orientation- and direction-dependent profile functions, and preference maps are obtained from vectorized population responses. Numerical simulations generate visual, motor, and mixed visuomotor response maps. A competition rule between visual and motor responses produces incidence ratios close to experimental observations in macaque visuomotor cortex. This framework provides a first neurogeometric approximation of visuomotor functional architecture and a mathematical setting for studying visually guided action.

Maintaining a prescribed composition in engineered microbial consortia is difficult because small fitness differences can drive competitive exclusion. We study a two-strain consortium in continuous culture and develop a feedback architecture that regulates composition by selectively slowing the fast strain as a function of the population ratio. At the population level, we derive an idealized ratio-feedback law with a tunable positive coexistence equilibrium. We then propose a biomolecular realization using orthogonal quorum sensing, an sRNA-based ratiometric controller, and a ppGpp-mediated growth actuator. Exploiting the separation between slow population growth and faster intracellular controller dynamics, we use singular perturbation theory to show that, for sufficiently fast controller dynamics, the full implementation model inherits the coexistence equilibrium and its local stability properties from the reduced model. Numerical simulations validate the reduction and show how weaker timescale separation or loss of the assumed molecular regime degrades performance.

Biological neurons can perform nonlinear computations within their dendrites and support branch-localized plasticity. This raises the possibility that single cells can store memories more efficiently and with less interference by confining synaptic modifications to specific dendrites. We study a parallel-dendrite model performing online familiarity detection and compare three dendrite-update rules during learning: (i) independent thresholding, (ii) an interacting rule that adapts the target local dendritic activation per item, and (iii) an interacting n-winners-take-all (WTA) rule that constrains the number of updated branches per item. The interacting rules substantially improve capacity by limiting variance in memory responses and decorrelating weights across branches -- even when inputs are strongly correlated. These results suggest that competition among dendrites, consistent with resource-limited plasticity mechanisms, can enhance single-cell memory beyond non-interacting schemes.

Binding of ligands to partially or fully unfolded proteins can play a key role in the mechanism of cellular and pharmacological chaperones, facilitating proper folding. However, it is challenging to quantify the binding affinity of ligands for unfolded states in a protein that is normally folded, as the methods standardly used to destabilize the native fold also affect ligand binding. We used single-molecule force spectroscopy to unfold single protein molecules without altering solution condi-tions and observe interactions of a ligand with unfolded states. Focusing on pentosan polysulfate (PPS), an anti-prion pharmacological chaperone previously shown to interact with both the native and partially or fully unfolded states of the prion protein, we measured the concentration-dependent effects of PPS binding on the conformational dynamics of bank vole prion protein (BvPrP) molecules held in optical tweezers. We found that PPS stabilized certain partially unfolded intermediate states of BvPrP as well as the fully unfolded state. Strikingly, the tendency to bind unfolded states instead of the folded state increased as the PPS concentration was reduced, implying a higher affinity to unfolded states. From the relative amount of binding to unfolded versus folded states, we estimated that PPS bound roughly 100-fold more tightly to unfolded states than to the native state of PrP. These results reinforce the likely importance of unfolded states in prion misfolding and propagation. More generally, they show how binding affinity to transient, unstable states can be estimated.

Microbial populations generally evolve in fluctuating environments under time-varying conditions. These are often described by binary switching models, sometimes seen as coarse-grained feast-famine cycles, in which resource availability switches abruptly between abundant and scarce conditions. However, experimental studies suggest that feast-famine environments actually exhibit more complex temporal dynamics. Here, we study how two strains, one growing slightly slower than the other, compete for the same resources in fluctuating environments comprising a finite number of intermediate states, each having its own carrying capacity. Environmental switching between these states and their carrying capacities represents gradual changes in nutrient availability. This class of multi-state stochastic switching models can be interpreted as a coarse-grained description of feast-famine cycles and allows us to investigate strain competition under the gradual recovery and depletion of resources. By computational and analytical means, we characterise the population dynamics in these multi-state fluctuating environments. In particular, we study how the switching rates and distribution of carrying capacities affect the population-size statistics, fixation probability, and mean fixation time. By comparing these results with their counterparts in binary environments, we clarify how the frequency and amplitude of environmental fluctuations influence population dynamics in coarse-grained feast-famine cycles.