Physical Review Letters

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.

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.

Liquid-liquid phase separation (LLPS) widely organizes the cellular interior, yet how third-party macromolecules modulate LLPS remains a puzzle. While one would expect that macromolecules can either promote or suppress phase separation, empirical observations show that a small dosage of macromolecules virtually always promotes phase separation. To resolve this paradox, we study the linear response of phase separation to macromolecule addition. We prove that for macromolecules significantly larger than the solvent molecule, their addition essentially always promotes phase separation, regardless of how they interact with the scaffold protein. Crucially, in the biologically relevant scenario of dilute condensates, the linear responses, including the saturation volume fraction, scale proportionally to [1-v2(1+{chi}12)2], where v2 is the macromolecule size and {chi}12 is the scaffold-macromolecule interaction parameter. Importantly, this universal behavior extends to multicomponent solutions in which the effective interaction parameter is composition-dependent. Our work shifts macromolecular modulation of LLPS from empirical observation to predictable design.

The relatively long flagella of spermatozoa from insects, birds, and octopuses display double waves, characterized by two superimposed helical waves. The prevalance of these highly organized waveforms across diverse taxa and distinct flagellar architectures hints at shared underlying physics, motivating a model of the flagellum as an elastic filament immersed in a viscous fluid, actively driven by a single set of internal bending moment waves. Simulations of a clamped filament show that it can buckle under its own activity into whirling and flapping states. A multiple-scales analysis of the elastohydrodynamic equations reveals how nonlinear interactions between fast undulations generate an effective compression driving buckling, and connects wave-driven buckling to classical follower-force instabilities. Extending the model to a swimming spermatozoon, the same instability produces double waves. Parameter estimates across species show that most observed double waves lie within the regime where buckling is permitted, supporting self-buckling as a generic physical mechanism for double waves.

Cells use ATP-driven chaperones to extract clients from biomolecular condensates selectively, yet no closed-form criterion links molecular parameters to condensate quality control. We derive a minimal non-equilibrium sorting reactor model that reduces the reaction-diffusion dynamics to one algebraic equation. In the idealized low-load limit, a concentration-dependent partition coefficient produces a saddle-node bifurcation between functional clearance and pathological storage. The critical Damk\"ohler number is \(\mathrm{Da}_{0c}=e^{-2}\) and is independent of the feedback strength. Corrections shift the value but preserve the topology. The model predicts a Kramers-type functional lifetime and recovery costs that scale as \(R^3\). Critical slowing down near the bifurcation provides early-warning signatures for FCS and FRAP.

We investigate the dynamics of the spread of the infection due to a phage- during the range expansion of an E coli colony. We find a rich panoply of spatio-temporal dynamics at large colony-level length scales, arising due to the interplay of mechanical forces, growth and viral infection dynamics at smaller cellular length scales. Strikingly, the phages "surf" the front of the growing bacterial colony by hitchhiking on E coli that are advected due to the growth of bacteria in the colony, resulting in an anisotropic spread of the phages. We identify microscopic processes - of the phage release during lysis (occurring on short millisecond timescales at length scales close to that of a single bacterium) and local nematic alignment of the rod-like E coli bacteria (occurring on timescales comparable to the bacterial growth rate and the length scales of a few bacterial cells) - that enhance the advective effects driving the hitchhiking behavior. Combining our experiments with a mathematical model, we explain the multiple spatio-temporal dynamical regimes - from the coexistence of uninfected bacteria, resistant (lysogenic) cells and phages, to fixed points where the entire population turns resistant or remains uninfected. Our work broaches a new frontier in the investigation of eco-evolutionary processes arising from the mechanical and ecological forces due to the interactions between viruses and their hosts.

Inside living cells, many types of biomolecular condensates coexist and interact. Recent experiments have shown that new phases often form at the surface of preexisting condensates. However, the mechanisms for this interface-mediated phase transition remain elusive despite its importance to numerous biological processes. Here, we show that interface-mediated secondary phase separation is a universal pathway for forming a new phase in multicomponent solutions. Using Cahn-Hilliard simulations, we successfully generate puncta of client protein on the surface of scaffold condensates. Based on a quasistatic protocol, we theoretically demonstrate that an interfacial instability triggers new-phase formation and predict the amount of client protein needed for the instability to occur. Remarkably, our quasistatic theory successfully predicts the onset of secondary phase separation even if the client is rapidly added or both the client and scaffold are rapidly added. In the latter case, coarsening of the primary condensates drives secondary phase separation. Our work reveals that cells can exploit existing condensates to lower nucleation barriers of new phases, with important implications for protein aggregation.

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.

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.

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.

We develop a general geometrical framework for growth processes in which the growth rate depends exponentially on the number of active growth-supporting components. The framework separates the fraction of active components from the size of the accessible component space, allowing qualitatively different growth laws to arise from the same underlying construction. Bacterial population growth provides an example of a fixed-size component space controlled primarily by activation and deactivation, whereas examples such as human population growth or speciation provide an expanding component space in which interactions between individuals promote further growth. This motivates a Replicative geometrical law, dX/dt= X exp({beta} X^{gamma}), whose exponent characterizes the scaling of the effective growth-supporting component space and is tested against historical human-population regimes and eukaryotic lineage-through-time data. For innovation indicators such as patents and arXiv manuscript submissions, where an existing item need not itself reproduce, the same construction motivates a Direct Geometrical production law without the prefactor X. The framework therefore provides a common description of fixed and expanding component spaces while distinguishing Replicative from Direct Geometrical growth.

Biological processes, from molecules diffusing to their regulatory destinations to whales pursuing food or mates, are widely exploratory. Such behaviors are effective when some verifiable functional state or outcome can be reached regardless of initial conditions. In these cases, systems repeatedly undergo distinct and abortive trajectories; the process only ends when the system finds 'right' outcomes. This dominance of the terminal condition (and indifference to the initial state) provokes a very different perspective than the conventional 'dynamical systems' framework that has been a centerpiece of the quantitative sciences for centuries. We hypothesize that many of these problems defy the initial-condition driven or gradients on landscapes so useful in problems ranging from mechanics to electrodynamics to chemical kinetics to mass and heat transport. We examine several mathematical frameworks that capture and unify key aspects of exploratory dynamics. One powerful way of thinking of such processes is the geometric distribution, where repeated failures are punctuated by a successful trajectory. We develop intuitions for how random walks with resets accelerate search processes. We highlight fresh and surprising behaviors of search under drift, cues, and checkpoints. Last, appreciating the probability of trajectories conditioned on satisfying macroscopic final outcomes reveals a language for the potency of variation sculpted by selection in their broadest forms. This can give the fictitious appearance of the future making itself known in the present, but we view this as conceptually similar to the way 'fictitious forces' arise in non-inertial reference frames. These approaches stress unity, open questions, and applications across a range of biological phenomena.

In the two-process model of sleep-wake regulation, circadian-modulated thresholds time every sleep onset and awakening, yet they remain free parameters rather than quantities derived from neuronal dynamics. This limitation leaves the framework unable to predict how sleep patterns change when neuromodulatory drive is altered, as in aging and narcolepsy. Here we close that gap by deriving closed-form, circadian-modulated threshold expressions from the Phillips-Robinson model with explicit orexinergic excitation of the wake-promoting population. Within this single threshold geometry, aging and narcolepsy appear as opposite deformations along the orexinergic axis: age-related hyperexcitability of orexin neurons elevates the sleep-onset boundary and creates a fragility regime in which minor nocturnal disturbances trigger premature awakenings, whereas orexin loss depresses the same boundary toward the wake-onset threshold and produces the rapid state fragmentation of narcolepsy. Concurrently, reduced circadian amplitude compresses the inter-threshold corridor, advancing sleep onset and shortening sleep duration. These results convert the classical two-process thresholds from descriptive conveniences into mechanistic organizers of sleep-wake dynamics across healthy aging and orexin deficiency. Author summaryThe classical two-process model of sleep relies on a pair of switching thresholds that have been imposed by hand rather than derived from the neurons that actually stabilize sleep and wakefulness. Here we remove this limitation: starting from a biophysical mean-field model of the sleep- and wake-promoting populations, and adding the orexin system that stabilizes arousal, we derive the sleep-onset and awakening thresholds analytically from the bifurcation geometry of the underlying dynamical system. These closed-form thresholds depend explicitly on circadian phase, homeostatic state, and orexinergic tone, revealing that aging and narcolepsy are opposite deformations of a single threshold corridor along one orexinergic axis. In aging, orexin hyperexcitability raises the sleep-onset barrier past a sharp "arousal fragility boundary," beyond which a minor disturbance triggers irreversible awakening; in narcolepsy, orexin loss collapses the same barrier and fragments sleep while paradoxically preserving total sleep time. We further find, contrary to common assumption, that orexin sustains wakefulness chiefly by raising the barrier to falling asleep rather than by resisting awakening. This work turns phenomenological sleep thresholds into physics-derived organizers of behavior, providing a mechanistic bridge from neuronal circuitry to whole-organism sleep dynamics.

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.

Collective migration is often attributed to complex cell-cell communication, yet coordinated multicellular dynamics can also emerge in organisms lacking social interactions. Continuum descriptions successfully capture such behaviors but generally rely on phenomenological transport coefficients whose microscopic origin remains elusive. Here we show that these coefficients emerge from cell-cell collisions and can be independently determined from experiments. We investigate the aerotactic dispersal of confined colonies of the solitary amoeba Acanthamoeba castellanii, in which oxygen consumption continuously reshapes the local environment to generate self-organized guidance cues. Combining quantitative videomicroscopy, oxygen mapping with phosphorescent sensing films, and oxygen-controlled microfluidics, we directly measure both the oxygen landscape and the aerotactic response governing colony expansion. We then develop a Patlak-Keller-Segel (PKS) -type drift-diffusion model whose transport coefficients are entirely determined from independent experiments and microscopic-to-macroscopic modeling approach, without adjustable parameters. The model quantitatively reproduces the observed dynamics, including the coexistence of a fast ballistic front and a trailing transient accumulation band. We show that both diffusion and aerotactic transport are modulated by the same collision-controlled mechanism through density-dependent changes in cell persistence. More generally, our results establish transport coefficients as measurable emergent properties bridging microscopic cell dynamics and macroscopic collective behavior, providing a predictive framework for oxygen-guided migration in living active matter.

We investigate the mechanical principles underlying fruiting body morphogenesis in Dictyostelium discoideum. Quantitative shape analysis based on the Young--Laplace law, together with AFM indentation measurements, indicate surface tension as the dominant tissue-scale force acting on the culminating fruiting body. Based on this observation, we construct a hydrodynamic phase-field model with tunable surface and interfacial tensions, and analyze its behavior numerically. Our results show that, once a stalk begins to form, the elevation of the cell mass arises naturally through a dewetting process. Through quantitative comparisons with experimental measurements, we identify the mechanical conditions required for detachment from the substrate and for establishment of the characteristic morphology of the culminating fruiting body. Together, our model analysis highlights the importance of stalk-tip elongation and tissue-scale surface and interfacial tensions in the construction of large-scale three-dimensional tissues.

Recent experiments show that protein condensates sitting on opposite surfaces of a flat lipid membrane move together and prefer to overlap, even though they cannot touch each other. This points to an indirect, membrane-mediated interaction. Two mechanisms could be responsible: a curvature-induced interaction, which is energetic in origin, and a fluctuation-induced interaction, which is entropic. Here we study both with coarse-grained molecular dynamics simulations, using Cookes implicit-solvent lipid model together with a generic bead-spring polymer model for the condensate. We compute the potential of mean force between two condensates across the membrane. For condensates of the same size, full overlap is unfavorable, and the pair instead settles into a partially overlapping state that bends the membrane into an S-like shape. When the two condensates differ strongly in size, full overlap becomes favorable. We explain this with a simple geometric picture. The condensate wets the membrane as a thin film and imposes curvature only along its rim, while membrane tension flattens the membrane under its interior. The resulting ring of curvature can trap a smaller condensate on the opposite side. We also compare the bending undulations and the effective bending modulus of a bare membrane, a membrane with one condensate, and a membrane with condensates on both sides. A wetting condensate suppresses the undulation modes and stiffens the membrane, but whether this makes overlap entropically favorable remains inconclusive. Our results indicate that the coupling is driven mainly by curvature, and that it depends on the wetting mechanism and on the membrane tension.

A classical study found no excitation transfer when isolated cardiomyocytes were placed side by side, whereas a recent paper reported action potential transfer in carrdiomyocytes placed end to end. We use nanoscale numerical simulations based on the full Poisson-Nernst-Planck equations to investigate whether these apparently opposing observations can be explained by the different geometrical configurations. The computations show that in the end-to-end configuration, ephaptic coupling occurs when the intercellular cleft is sufficiently narrow and a sufficiently large fraction of the sodium channels is localized at the intercalated disc. Coupling is strengthened when the sodium channels are concentrated in fewer clusters and when ionic diffusion within the cleft is reduced. Under these conditions, excitation transfer occurs on a timescale consistent with rapid cell-to-cell activation. Conduction depends biphasically on cleft width and terminates abruptly beyond a critical width. Localization of potassium channels at the intercalated disc has only a moderate effect, whereas gap junctions substantially improve conduction and reduce the relative contribution of ephaptic coupling. In the side-by-side configuration, excitation transfer does not occur under physiological conditions and requires highly flattened cells, minimal separation, and unrealistically strong sodium-channel clustering. The different outcomes of the side-by-side and end-to-end experiments can therefore be explained by the fundamentally different geometrical conditions for ephaptic coupling.