PRX Life

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.

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.

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 are dynamic, membrane-free compartments that continuously exchange molecules with their surroundings. The dwell time, defined as the time a molecule remains inside a condensate between entry and exit, determines how extensively the molecule can explore the dense phase and encounter potential binding partners or reaction sites, thereby modulating condensate function. Motivated by our single-molecule measurements of RNA dwell times, we developed an analytical theory to understand dwell-time distributions in biomolecular condensates. Our theory predicts that the dwell-time distributions generally exhibit an early-time power-law regime followed by a late-time exponential tail. The form of the distribution encodes the rate-limiting mechanism of molecular escape: dense-phase diffusion-limited transport feature a -1.5 power law with an exponential tail set by a diffusion timescale, whereas interfacial barrier-crossing-limited transport feature a -0.5 power law with a decay governed by a barrier-crossing timescale. These distinct signatures provide a direct readout of the physical processes that control molecular retention in condensates, with implications for both natural and synthetic condensates.

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

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.

Allosteric communication in biomacromolecules is fundamentally governed by thermal fluctuation gradients, yet standard Gaussian Network Models (GNMs) treat atomic contacts as uniform, binary couplings without differentiating core constraints from solvent-exposed surface flexibility. Here, we present an analytical matrix framework that incorporates continuous distance-dependent weighting into the Kirchhoff matrix L. This formulation captures the steep steric constraints of hydrophobic core packing versus peripheral surface loops while strictly recovering the classic unweighted GNM as a high-temperature limit (T [->]{infty}). Using Schur complements of partitioned joint covariance matrices, we show that conditional fluctuation variances and higher-order entropy-transfer terms reduce analytically to exact ratios of submatrix determinants (covariance minors), eliminating the need for fitting parameters or molecular dynamics trajectories. Applied to KRAS (PDB: 6GOD), this framework constructs an integrated directional entropy-transfer asymmetry map. Order-1 minors (h(i) = Kii) establish a single-node fluctuation potential gradient, while order-2 minors (Rij) define pairwise channel bandwidths. Higher-order minors show multi-body spatial coupling: order-4 minors identify rigid core residues such as Phe156 as strategic interlobe relay hubs linking Lobe 1 and Lobe 2, and an order-3 triad cooperation index demonstrates that signal transmission from Switch II (Gln61) to Gly60 and Phe156 converges on a single, mechanically integrated allosteric sector. By deriving directional information flow directly from experimental atomic displacement parameters, this approach establishes a rigorous, computationally efficient framework for mapping allosteric networks across structural ensembles.

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

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.

Cell monolayers are active, orientationally ordered materials whose mechanics can depart from near-equilibrium behavior. Existing continuum theories often inherit assumptions from equilibrium liquid-crystal physics, motivating explicit nonequilibrium formulations. Here, we develop a minimal continuum model of two-dimensional monolayers based on odd mechanics, accounting for broken symmetries and nonequilibrium dynamics. We show that nematic order can support an odd viscous modulus generated by broken time-reversal symmetry and spatial anisotropy, without chirality. The model reproduces half-integer defect motion and stress profiles in Madin-Darby canine kidney (MDCK) monolayers, as well as defect-associated cell accumulation and depletion in neural progenitor and ovarian mesothelium systems. Finally, we estimate the viscous-moduli tensor from measured stress, velocity, and orientation fields in MDCK monolayers and identify a nonzero odd modulus. Our results show that odd mechanics provides a minimal framework for nonequilibrium cell monolayers, complementing conventional active-nematic theories.

A central question in neuroscience is how the brains structural connectivity gives rise to its emergent, correlated dynamics. These large-scale dynamical correlations underlie functional networks that support cognitive functions. Here, we identify coupling correlation--the similarity between the input connectivity profiles of brain regions--as a key structural determinant of macroscopic neural dynamical correlation. Using dynamical mean-field theory (DMFT) and numerical simulations of random neural network models, we demonstrate that coupling correlation quantitatively governs dynamical correlation. The functional form of this structure-function mapping is dictated by the eigenvalue spectrum of the coupling correlation matrix: networks with bulk eigenspectra exhibit an exact linear relationship, whereas biologically plausible long-tailed spectra yield an approximately linear mapping except when the magnitude of coupling correlation approaches unity. Particularly, a long-tailed spectrum is necessary to reproduce the appropriate magnitude and size-invariance of coupling correlations observed in empirical data, thereby sustaining non-vanishing dynamical correlations that may support brain function in large systems. The theoretical prediction of approximate linearity is consistently validated using empirical datasets that include both structural coupling and neural dynamics in humans, mice, and Drosophila. Together, these results provide a mechanistic and quantitative framework linking macroscopic brain network structure to emergent neural dynamics--an essential step toward a theory of structure-function relationship in the brain. Significance StatementHow the brains wiring gives rise to its coordinated activity is a fundamental unsolved problem in neuroscience. Prior work has identified correlations between structural and functional connectivity, but these relationships lacked a mechanistic, first-principles explanation. Here, we derive an analytical framework using Dynamical Mean-Field Theory and random neural network models to show that a single structural statistic--coupling correlation, the similarity between the input connectivity profiles of brain regions--linearly and causally determines the magnitude of correlated neural dynamics. We further show that a long-tailed eigenvalue spectrum in biological structural connectivity is necessary to sustain the strong, size-invariant functional correlations observed across species. Validated in humans, mice, and Drosophila using multiple imaging and connectome modalities, this principle may provide a quantitative bridge between structural connectomics and emergent brain dynamics, with implications extending to a broad class of complex networked systems.

Microbes exhibit complex dynamic behavior as the result of a large number of biochemical processes, spatial and temporal interactions, environmental variations, and evolutionary pressure. Although significant progress has been achieved in understanding microbial ecological dynamics, multiple open questions remain, including the microscopic mechanisms of growth and the roles of nutrients and stochasticity. In this work, we present a minimal theoretical approach to clarify the link between consumption of resources by microbes and their growth. A stochastic model that accounts for a single microbial species consuming a single type of resource while growing via cell division is studied analytically and via Monte Carlo computer simulations. We identify three distinct dynamical regimes of microbial growth determined by the relative magnitudes of resource uptake and division rates and initial conditions. We also show that stochasticity influences the dynamic behavior when the amounts of microbes or resources are low. The model recovers Monod growth kinetics and provides a mechanistic interpretation of the Monod constant and maximal growth rate. The theoretical framework presented captures a wide spectrum of dynamic behaviors in microbial systems, providing a clearer microscopic picture to explain their underlying complex mechanisms.

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 [≤] N [≤] 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.

Protein sequences are constrained not only by the need to fold into stable structures, but also by specific functional requirements imposed by natural selection. Yet predictions of how amino-acid changes affect proteins typically collapse these constraints into a single scalar score. Quantitatively separating these effects at scale remains an open challenge, with direct relevance spanning protein design to understanding the molecular mechanisms of disease. Inverse-folding (IF) models have emerged as fast, unsupervised predictors of folding energy changes ({Delta}{Delta}G), but because they learn statistical correspondences between structure and sequence, they can conflate conservation driven by function with conservation driven by stability. Here, we show that blending IF models with a physics-based coarse-grained potential improves global correlation with experimental {Delta}{Delta}G and, crucially, reduces IF model bias at functional sites. Applying the best-performing blend together with an evolutionary language model, we decompose each variants evolutionary cost into folding energy and dark energy, the latter capturing functional constraints beyond folding stability. With this decomposition, and without the need for supervision, we find that disease gain-of-function variants show a distinct functional signature from loss-of-function variants. In particular, we identify oncogenic drivers as largely preserving stability while exhibiting high dark energy, as opposed to tumor suppressors which are predominantly destabilized, paving the way to a mechanistic understanding of driver mutations in cancer. Together, these results provide a scalable framework for accurate {Delta}{Delta}G prediction and mechanistic disentanglement of variant effects.

Bacteria assemble a precise number of flagella to navigate their environment, yet the molecular mechanisms underlying this robust counting remain poorly understood. We propose that robust flagellar number control does not require a strictly conserved transcriptional gene hierarchy, but instead emerges from a conserved network motif in which transcriptional feedback is coupled to the assembly progress of the flagellar C-ring. Specifically, upon C-ring growth, the ATPase FlhG is released from a non-inhibitory FlhG-FliM complex, dimerizes, and inactivates the master regulator FlrA, shutting down early flagellar gene expression. We analyze this assembly-coupled feedback mechanism using stochastic simulations and analytical calculations, revealing a trade-off between robustness to intrinsic fluctuations and to cell-to-cell variability in regulator abundance. Only at the crossover between fast and slow inactivation regimes can robustness to both noise sources be achieved simultaneously. These results provide quantitative, organism-independent insight into flagellar number control and connect to the broader problem of stochastic regulation of absorbing-state statistics.

Electrical signaling in biological systems is generally understood through the lens of single-channel biophysics, yet whether ensembles of ion channels can undergo cooperative opening and closing remains unclear. Here, we show that ensembles of voltage-gated ion channels can undergo bioelectrical order-disorder phase transitions driven by feedback between channel currents and local membrane voltage. When channels open, they carry ion-selective current that redistributes ions near the membrane and perturbs the transmembrane potential, thereby biasing the gating of nearby channels. This emergent nonequilibrium coupling generates a bona fide phase transition in ion channel ensembles. Finite-size analyses of the open-channel fraction, its fluctuations, and the distribution of collective channel states yield a voltage-temperature phase diagram with a first-order line separating collectively open and closed states and terminating at a critical point. The critical temperature is governed by a dimensionless conductance ratio set by ion transport, channel density, and confinement geometry. Applying this framework to measurements from the squid giant axon, the axon initial segment, and the nodes of Ranvier suggests that collective activation may be favored by high sodium-channel densities in large-diameter nerves, whereas the lower densities typical of potassium channels place them in an independent-gating regime.

Intrinsically disordered proteins and regions are found across all kingdoms of life, yet the computational characterisation of their conformational ensembles has remained almost entirely confined to the human proteome. Whether the physics-based force fields developed on eukaryotic sequences remain reliable for taxonomically distant organisms, and whether the sequence ensemble relationships they reveal reflect conserved physical laws or the peculiarities of a single evolutionary window, are questions fundamental to the field. Here we introduce BENDER, a dataset of 11,533 IDP sequences spanning 13 taxonomic groups, each simulated under CALVADOS 2 molecular dynamics and annotated with ensemble-level geometric and novel contact-network properties, together with per-sequence pi pi and cation pi contact frequencies linked to phase-separation propensity. We show that CALVADOS 2 ensembles agree strongly with an orthogonal structural reference across the full dataset, with both held-out taxa performing above the dataset median, and that direct comparison against a second independently parameterised force field reveals no systematic scaling-exponent bias. We find that cross-taxon training data improves out-of-distribution ensemble prediction in two independent architectures, and that ensemble contact-network global efficiency is accurately predictable from sequence alone on held-out viral sequences. Positive degree assortativity is conserved across all taxonomic groups, suggesting that hub topology in disordered protein contact networks is a conserved physical feature of sequence-encoded disorder rather than an evolutionary contingency.

Developmental patterns can scale with size during growth, a phenomenon commonly attributed to morphogen scaling. Although patterning is orchestrated by gene regulatory networks (GRNs) activated by morphogens, how GRN dynamics interact with growth is not understood. We present a theoretical framework that integrates morphogen signalling, GRN dynamics, and tissue growth. We show that pattern scaling emerges from the interplay of GRN dynamics and growth, even in the absence of morphogen scaling. This relies on memory effects encoded in the GRNs, providing a cell-autonomous route to global scaling, and offering a general mechanism for size-invariant patterning beyond morphogen-based models.

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.