Physical Review Letters

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.

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.

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 develop a theoretical proposal linking vacuum stability and brain dynamics through superconductivity-inspired coherence, symmetry reduction, and the thermodynamic stabilization of low-entropy regimes. We take an unbroken SU(3) structure as a candidate stable residue of the low-temperature vacuum. At the neural level, we formulate a coarse-grained analog in which a two-fluid model with dissipative and coherence-supporting components describes brain dynamics. Specifically, the coherence-supporting component is proposed as a possible basis for the efficient binding and integration required to sustain a stable, unified conscious state. The proposal offers a common geometric language for relating physics and neuroscience with falsifiable signatures in coherence and state-dependent transitions. The main technical contribution is a computational algebraic model of conscious-state dynamics, where neural data are mapped to reconstructed state trajectories. Effective generators are inferred from those trajectories, and the two-fluid split is tested as a Cartan-root decomposition of su(3), with a rank-two commuting sector for coherence-preserving balance and six root directions for state transitions. This structure can be tested on neural data and contrasted with alternative dynamical models.

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.

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.

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.

Structural Maintenance of Chromosomes (SMC) complexes are large protein assemblies that play a central role in chromosomal organization across all domains of life by acting as molecular motors that extrude DNA loops. Although the molecular architecture of SMCs has been characterized in considerable detail, their mechanistic mode of action remains actively debated. One proposed mechanism is the segment-capture model, in which SMC complexes undergo an asymmetric conformational change upon ATP binding and hydrolysis, effectively pumping short DNA segments through the SMC ring and thereby enlarging loops. While this model accounts for several experimentally observed features of loop extrusion, it has been questioned in light of experiments showing that SMC complexes can traverse large nanoparticle-sized obstacles on DNA. Moreover, recent experimental advances have provided new insights that extend beyond the original formulation of the model. Here we show that, contrary to previous criticisms, the segment-capture model can naturally account for key features of recent experiments, including the bypass of large obstacles when the SMC hinge acts as a bypass gate. Furthermore, we outline a set of targeted experiments designed to critically test the model predictions, providing a clear path toward resolving outstanding questions about the mechanistic basis of loop extrusion.

Efficient operation of neural networks has been linked to criticality in their underlying non-equilibrium excitation dynamics. However, obtaining experimental evidence of this conjecture remains challenging due to limited control and undersampling in biological systems. Here, we experimentally explore neural network criticality using an ultracold Rydberg gas as a highly controllable simulator. We highlight the similarity of the excitation spreading via Rydberg facilitation and the synaptic connection of spiking activity of neurons, giving rise to distinct absorbing and active phases. We systematically explore and resolve criticality criteria, including power-law scaling of excitation avalanches and the emergence of universal avalanche shape collapse. Crucially, we implement a controlled gain mechanism to compensate for atom loss, mimicking metabolic resource replenishment and stabilizing the system in a controlled non-equilibrium steady state. We find peak temporal correlations at the critical point and stochastic oscillations with dragon king avalanches in the active phase, consistent with predictions for systems orbiting criticality. Our work establishes facilitated Rydberg gases as a platform for investigating criticality, resource dynamics, and emergent oscillations in neural networks.

Mucus transport is essential for lung health, as ciliated cells constantly propel mucus outward to clear bacteria, viruses, and particles. This defense relies on a material that must be elastic enough to maintain ciliary traction, but capable of reorganizing under sustained directional loading. How the mucin network reconciles these demands, and whether it retains a memory of the stresses it experiences, remains poorly understood. Here we show that lung mucus develops a persistent, direction-dependent mechanical asymmetry under physiologically relevant stress--a mechanical memory encoded in the slow scaffold of the network. Using bulk rheology, we find that directional pre-stress produces a residual anisotropy that grows with stress magnitude and persists long after the load is removed. A transient network model attributes this memory to a separation of timescales between transient bonds and a long-lived crosslink scaffold, and particle-tracking microrheology confirms that the memory reorganizes the network geometry at the scale of biological particles, biasing tracer diffusion along the axis of applied stress. The stresses required to induce memory are within the range generated by ciliary beating and remain below the mucus yield threshold, suggesting that mucociliary clearance operates in a regime where directional alignment accumulates without compromising the coherence of the mucus layer. This proximity to yield may not be coincidental, it allows mucus to accumulate mechanical memory under physiological forcing while remaining poised to flow during clearance events such as coughing.

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.

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.

Since the earliest microscopic observations, the geometric organisation of cells has captured biologists interest. Recent work by Gorgi et al. showed that bacterial colony organisation, including biofilms, can be explained across diverse species by radial expansion from fixed initial seeding sites and contact-inhibited growth, with little need for species-specific mechanisms. Here, we extend this geometric framework by incorporating seeding time as an additional driver of colony organisation. Using simulations and analytical models for expected colony size, we show that staggered seeding yields order of magnitude increases in the expected size of early seeded founder colonies. At realistic biofilm growth rates, a 2-day lag between founder and subsequent colony seeding produces an approximately 10-fold increase in expected founder size, while a 1-week lag produces a 25-fold increase. These findings provide a simple geometric basis for biological priority effects, illustrating temporal advantage alone can generate substantial spatial dominance, with implications for cardiovascular devices where host and bacterial cells compete in a race for the surface.

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.

We perform a large-scale computational characterization of the map of protein primary to secondary structure using an AVR3a class protein effector domain from the plant pathogen P. palmivora as a case study. We formulate a modified site-scanning approach for exploring the neutral component of secondary structure phenotypes based on predictions from the machine-learning algorithm Porter 5 and apply it to the AVR3a phenotype. We predict a set of sensitive sites within the effector domain that are generally located at or near the boundaries of structured regions, with restrictions on the possible amino acid residues at these sites dictated by the secondary structure type that they participate in within the WT. We characterize a set of mutated phenotypes derived through the exploration of the neutral component of the WT effector domain, selecting them so that they span a range including both very rarely and very commonly seen secondary structures, and that they include both secondary structures nearly identical to the WT and ones far removed from it. We find that all these diverse phenotypes have an estimated robustness of the same order as that of the WT, and that the robustness scales logarithmically phenotype frequency, as seen in other genotype-to-phenotype maps. Furthermore, we observe that the dependence of the estimated phenotype frequency on the Kolmogorov complexity indicates simplicity bias in the protein secondary structure map.

Bacterial metabolic strategies are tied to cell size and shape, yet how geometry constrains the efficiency of biomass production is not well understood. Here we develop a coarse-grained whole-cell model of bacterial physiology that couples proteome allocation, metabolic fluxes, and cell geometry to physical limits on surface area and intracellular diffusion. We define the biosynthetic energy efficiency as the fraction of ATP available from imported carbon that is invested in biomass, and find that it is non-monotonic in nutrient availability, peaking precisely at the onset of overflow metabolism. This identifies the metabolic switch as an optimal trade-off between efficient use of imported carbon and rapid growth. Perturbing cell morphology away from the empirical scaling laws shows that increasing surface area at a fixed volume raises both growth rate and efficiency, so the observed size and shape relations sit close to an efficiency optimum rather than being arbitrary. When the empirical growth laws are relaxed and geometry is treated as a free parameter, the model predicts a hard physical limit: the maximum sustainable cell size falls as the target growth rate rises. This ceiling arises from a conflict within the finite proteome budget between the cost of fast growth and the cost of large size, the latter set by the slowing of intracellular diffusion. A few physical rules thus delimit the metabolic strategies and size range available to bacterial life.

Within the studies of stochastic gene expression, apart from the variability of copy number of gene products, the problems of threshold crossing of those products are biologically important as they often lead to terminal cellular events. Here, we study the threshold crossing problem of the messenger ribonucleic acid (mRNA) and present an exact probability distribution of first passage times in Laplace space. The function furnishes moments of any order and also predicts the characteristic time of the exponential tail of the distribution, which we match against Gillespie simulations. We find that all the measures of relative fluctuations of the threshold crossing times show U-shapes within this simple model of mRNA, as was found earlier in more mathematically involved models of threshold crossing time statistics of proteins. Furthermore, we extend the exact formula to include the phenomenon of DNA duplication and the corresponding doubling of transcription rate. As expected, the distribution varies considerably depending on the onset of the duplication stage within the cell cycle.

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.

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.

AO_SCPLOWBSTRACTC_SCPLOWCellular automata and graph reaction-diffusion systems encode local spatial interactions in different mathematical forms. We develop a cochain-operator calculus for these two settings. Over a finite field Fq, every local rule on a finite neighborhood has a unique reduced polynomial representative. On an oriented line, the coboundary and endpoint maps recover the left and right shifts. Our main theorem shows that these operators, together with linear operations, constant cochains, and the degree-zero cup product, generate every finite-radius polynomial cellular automaton. Explicit formulas for Rules 30, 110, and 22 show how reflection-invariant linear coupling, directed transport, and nonlinear neighbor interactions enter the calculus. On a general graph, d*d is the unweighted combinatorial Laplacian and enters a graph reaction- diffusion recurrence. Over [R], the term - Dd*d with D [≥] 0 admits the usual diffusion interpretation; over Fq, the corresponding expression defines modular coupling without an intrinsic order. In the morphogenetic examples, we therefore distinguish pattern-generating dynamics from finite-state observation and use the Betti numbers of active induced subcomplexes to summarize observed patterns. This yields a common algebraic representation without identifying real-valued diffusion with finite-field dynamics.