Physical Review X

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.

Sequestration of gene products through diverse mechanisms forms a fundamental layer of regulation in intracellular biochemical processes, including post-translational modification, promiscuous binding to genomic decoy sites, and partitioning into membraneless compartments formed through phase separation. Here, we develop a unified stochastic framework to quantify how such sequestration-type processes, when coupled to noisy gene expression, modulate cell-to-cell variation in protein levels. In this model, protein molecules reversibly switch between active (free) and inactive (sequestered) states, whose switching rates are arbitrary functions of the molecular counts. Using exact analytical calculations and the linear noise approximation, we derive expressions for the Fano factor of the active-protein level and identify fluctuation attenuation regimes in terms of the logarithmic sensitivities of the switching rates to protein abundances. We show that inactive-protein-dependent switching, of which genomic decoy binding is a natural example, can preserve Poisson-level fluctuations in the active-protein level under appropriate conditions. Enzymatic inactivation, a type of post-translational modification, emerges as a special case of active-protein-dependent sequestration, where greater responsiveness of the inactivation propensity attenuates active-protein fluctuations. In both decoy binding and enzymatic inactivation, protecting the inactive protein from decay lowers active-protein fluctuations. Finally, a noise-buffering regime associated with intracellular phase separation is recovered when the inactive-to-active switching rate depends inversely on the inactive-protein level. Together, the examples of genomic decoy binding, enzymatic inactivation, and intracellular phase separation suggest that noise buffering observed across diverse intracellular processes is rooted in a broader class of reversible sequestration mechanisms that attenuate protein-level fluctuations.

Public-health surveillance systems rely on downstream indicators to infer latent infection incidence, but delays and observation noise provide only an indirect and temporally distorted view of the underlying epidemic process. Reconstructing upstream epidemic trajectories from these observations is therefore an ill-posed inverse problem, in which different reconstruction assumptions may produce different trajectories that remain consistent with the observed data. Here, we develop a general spectral framework that quantifies the statistical distinguishability of candidate upstream trajectories under delayed and noisy observations. We show that epidemiological delay distributions impose a frequency-dependent temporal resolution limit on epidemic surveillance, fundamentally constraining the distinguishability of rapid upstream variation. This limitation propagates to epidemiological inference, making some quantities substantially more sensitive to reconstruction assumptions than others and rendering distinct event-impact profiles difficult to distinguish from downstream observations.

Spatial proofreading is a mechanism that can enhance molecular discrimination by exploiting nonequilibrium diffusive transport between spatially separated source and readout regions. Here, we introduce a thermodynamically consistent reaction-diffusion model in which a gradient of active substrates is generated self-consistently by a reversible kinase-phosphatase switch coupled to nucleotide chemostats. The resulting chemical-potential gradient explicitly controls the nonequilibrium driving and allows the discrimination potential to be related to microscopic chemical rates and diffusive transport. A simple one-dimensional analysis shows that the ability of an enzyme to discriminate between wrong and right substrates is governed by a subtle balance between substrate-gradient confinement, controlled by phosphatase activity, the diffusive crossing time across the source-readout domain, and selective complex dissociation. We then extend the model to two-dimensional domains, showing that source, i.e. kinase, localization modulates spatial specificity by shaping the effective diffusive paths to the readout boundary. Finally, stochastic simulations reveal that molecular fluctuations generate intermittent wrong-readout events, which can be characterized through an event-weighted measure of specificity. Interestingly, we find that fluctuations promote frequent transitions to long-residence states in which discrimination is better than predicted by the deterministic estimate. Overall, our work highlights the importance of thermodynamically consistent descriptions of spatial proofreading and clarifies how energy input, transport, and spatial organization jointly shape biochemical discrimination.

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.

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.

Non-exponential residence times give rise to history-dependent or memory effects in epidemic dynamics, yet their mathematical formulations remain fragmented. Here we develop a unified framework for a history-dependent SEIR model with general latent- and infectious-period distributions. We first establish the equivalence between the stage-age and renewal formulations and show that both admit a unified transition-flow representation. We then introduce the concept of a transition-flow multiplier, which provides a direct link between residence-time distributions and transition flows. When the multiplier is a weighted sum of shifted power functions, the model admits an exact representation in terms of Riemann-Liouville or tempered Riemann-Liouville fractional operators, providing a first-principles foundation for fractional epidemic models. Finally, using Euler-Lotka equations and stochastic-order arguments, we characterize how the latent- and infectious-period distributions shape epidemic growth and decay. A longer latent period slows both early growth and late decay, while, at fixed means, greater variability in the latent period accelerates early growth but slows late decay, whereas greater variability in the infectious period slows both.

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.

Recurrent cortical circuits are hypothesized to perform Bayesian posterior sampling through their stochastic dynamics. Yet identifying which sampling algorithm a circuit intrinsically implements, as opposed to mapping manually designing algorithms onto circuits, requires rigorous theoretical analysis of the biological circuit dynamics, and remains a fundamental open challenge because of the analytical intractability of nonlinear recurrent dynamics. Here, we tackle this challenge through comprehensive theoretical analysis of analytically tractable nonlinear recurrent circuit dynamics used in neuroscience research-- the continuous attractor network (CAN). Surprisingly, we find that the circuit, without any non-Gaussian components in its connectivity or internal variability, intrinsically emerges heavy-tailed subspaces dynamics described as scale-mixture Langevin posterior sampling. The mechanism emerges from the circuits own nonlinear dynamics: divisive normalization renders the overall population activation Gamma-distributed which multiplicatively modulates the time constant of the Langevin sampling in the stimulus feature subspace. Eventually, this scale-mixture structure produces a heavy-tailed (Student-t) sampling step size distribution, significantly accelerating the sampling speed. Moreover, the scale-mixture Langevin sampling approaches a Levy-like regime in the weak input limit. Our results analytically identify an intrinsic circuit algorithm embedded in subspaces of nonlinear recurrent dynamics, and establish a minimal circuit mechanism for endogenous heavy-tail statistics without any explicit non-Gaussian components.

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 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.

Catalysis and allostery are complementary principles of biological function: catalysis accelerates bio-chemical reactions, whereas allosteric regulation dynamically controls molecular interactions. The emergence and persistence of early autocatalytic ribozyme systems likely depended not only on template-directed self-replication but also on ATP production, utilization, and recycling through prebiotically plausible energy-conversion processes. We previously proposed that resistance to molecular parasitism in autocatalytic RNA networks can emerge through hyperparasitic regulation, whereby hyperparasitic ribozymes compete with parasitic ribozymes for binding to the host replicase while additionally binding parasitic ribozymes, thereby redirecting competitive interactions away from host exploitation. Here, we develop a minimal mathematical model of an autocatalytic RNA-world system in which replication, ATP/ADP-based energy conversion, and ATP-dependent allosteric regulation become dynamically coupled. Building on a general reaction framework describing ribozyme replication, catalytic interactions, and ATP/ADP cycling, we identify the minimal regulatory architecture required for stable RNA replication in the presence of parasitic mutants. Our simulations reveal a sequential evolutionary transition in which control precedes optimization. ATP-dependent allosteric regulation first evolves to tame molecular parasitism through hyperparasitic binding, whereby ATP-loaded parasitic ribozymes compete with ATP-free parasites for binding to the host replicase while also binding directly to parasitic ribozymes. This stabilizes RNA replication but simultaneously imposes an energetic cost by sequestering ATP and thereby reducing ATP-ADP turnover. The resulting regulatory burden creates selective pressure for the evolution of ATP synthase/ATPase ribozymes that accelerate ATP-ADP cycling and restore the metabolic flux required for sustained RNA replication. We further identify two plausible evolutionary routes to parasite control: parasitic ribozymes either become intrinsically allostery-prone or are converted into allostery-prone forms by an evolved allosterase ribozyme. Once ATP turnover is sufficiently rapid, both mechanisms confer long-term resistance to recurrent parasitic invasion. These results suggest that stable RNA-based evolution required the progressive integration of information replication, molecular regulation, and increasingly efficient metabolic energy conversion. More generally, the model identifies ATP-dependent allosteric regulation as a plausible evolutionary bridge linking autocatalytic RNA replication to the emergence of regulated proto-metabolism, transforming a parasite-limited replicating system into a self-regulating proto-biological organization capable of sustained evolutionary dynamics. HighlightsO_LIA minimal autocatalytic RNA network achieves stable self-replication despite recurrent parasitic invasion C_LIO_LIATP-dependent allostery tames molecular parasitism through hyperparasitic binding C_LIO_LIControl of molecular parasitism precedes optimization of metabolic energy conversion C_LIO_LIATP sequestration creates an energetic burden that drives increased ATP-ADP turnover C_LIO_LIStable parasite control evolves through either intrinsic allostery or allosterase-mediated regulation C_LIO_LIStable RNA autocatalysis emerges through the sequential integration of replication, molecular regulation, and energy conversion C_LI

The ability of enzymes to sense signals and respond by changing their structure and activity underlies cellular processes from signaling to metabolic control. While there have been recent advances in the de novo design of enzymes and conformationally switching proteins, combining these to achieve allosteric regulation of enzymatic activity in a fully designed system remains an outstanding challenge. Here, we show that denoising diffusion models enable the design of compact de novo enzymes whose activity can be allosterically activated or repressed by designed protein effectors. Our results establish a general route to allosteric control over a wide range of catalytic and other protein functions.

SynGAP and PSD-95 undergo liquid-liquid phase separation in vitro, motivating models of the postsynaptic density (PSD) as a biomolecular condensate. However, how their association kinetics and intermolecular interactions shape activity-dependent partitioning remains unclear. We develop a multicomponent framework that couples equilibrium Flory-Huggins calculations in conserved total-composition space to four-species Cahn-Hilliard-reaction dynamics for free SynGAP, free PSD-95, the SynGAP-PSD-95 complex, and solvent. Complex formation and dissociation are represented by explicit forward and reverse activity-based mass-action rates. These calculations show that the equilibrium association constant and self- and cross-interaction energies jointly control the extent and composition of the two-phase region. For an illustrative LTP-like parameter switch, decreasing the equilibrium association constant and altering selected interaction energies redistributes SynGAP from the PSD-95-rich phase to the PSD-95-poor phase without eliminating the PSD-95-rich phase. A separate equilibrium comparison represents haploinsufficiency as a 50% reduction in total SynGAP. For the illustrative parameter sets, the reduced-SynGAP composition remains within the two-phase region but has different tie-line endpoints and phase compositions than the control composition.

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 epidermal growth factor receptor (EGFR) is a tyrosine kinase receptor that plays a fundamental role in regulating cellular proliferation, survival, and differentiation. EGFR's kinase domain catalyses the autophosphorylation that drives downstream signalling and is a known hotspot for cancer-associated mutations. Such substitutions often enhance receptor activation, driving oncogenesis and therapeutic resistance, with major implications for prognosis and treatment choice; consequently, a detailed understanding of this domain's functional dynamics, and how mutations reshape them, is essential. Here, we apply dynamical-nonequilibrium molecular dynamics (D-NEMD) simulations to probe how changes at the ATP-binding site are transmitted throughout the kinase domain, ultimately shaping the behaviour of distal regions in the wild-type protein and in two of the most clinically observed non-small cell lung cancer variants, L858R and L858R+T790M. D-NEMD reveals previously uncharacterised communication networks linking the ATP pocket to key functional motifs, including the P-loop, C-helix, hinge region, activation loop, and F-helix, showing the intricate allosteric connectivity within this domain. Notably, numerous cancer-related mutation sites, despite being distant from the ATP site, map onto or lie close to these communication pathways, indicating that D-NEMD simulations can identify functionally relevant allosteric positions and potential mutation sites in EGFR. Our simulations further reveal that the two variants rewire EGFR's internal signal propagation network in distinct ways: L858R diminishes the transmission of structural changes to distal regions of the C-lobe, whereas introducing T790M in addition to L858R partially restores wild-type-like behaviour through compensatory rerouting of early-stage dynamical pathways.

The emergence of treatment resistant mutants is one of the primary contributors to therapy failure in cancer. Evolution-based adaptive therapies aim to exploit the competition between sensitive and resistant cells to prolong therapeutic control. However, in the densely packed tissues of solid tumors, competition is not only determined by cell-intrinsic factors but also a result of local physical interactions between neighboring cells. The successful development of physics-informed adaptive therapies therefore hinges upon the bottom-up integration of tissue mechanics and experimentally grounded models of tumor evolution. Here, we show how population-level treatment response emerges from mechanical interactions between individual cells. Combining genetically tailored therapy-mimicry experiments in spatially structured 2D melanoma colonies with mechanistic, particle-based tissue simulations as digital twins in a real-to-sim-to-real framework, we reveal how treatment-induced changes in mechanical crowding shape a cascade of resistance expansion, spatial competitive escape, and consequent therapy failure. We then link these underlying physical mechanisms to population-level observables in an abstracted mathematical model for reinforcement-learning-based therapy optimization and a distilled treatment-decision-heuristic, which we test experimentally. Together, our results identify mechanical crowding and escape as governing principles of resistance-mediated therapy failure in solid tumours and provide a basis for mechanistically informed, evolution-based treatment strategies.

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.