Physical Review X

Metabolic rate scales with body size, however its universality remains debated and unresolved. We show that such universal scaling may arise from information neutrality in stochastic cell dynamics. Using a stochastic ontogenetic growth model of cellular dynamics, we identify an optimal microscopic noise structure where organism level metabolic fluctuations are least sensitive to the underlying microscopic cellular noise and have maximal dependence on organism size. At this point, the macroscopic scaling exponent collapses to a universal value across species size close to Kleibers law. These results reveal a noncritical RG-like behavior, suggesting that universality emerges here from an information-theoretic optimum of stochastic metabolic fluctuations.

Understanding why specific metabolic states become stable in cancer has remained a fundamental challenge, as current pathway-centric frameworks lack a unifying physical principle governing global metabolic organization. We introduce the Metabolic Spin-Glass (MSG) model, which recasts cellular metabolism as a frustrated many-body system governed by a Hamiltonian that integrates reaction free energies, cofactor-mediated thermodynamic couplings, and patient-specific transcriptomic fields. The Hamiltonian is formulated as a binary optimization problem and solved using hybrid quantum annealing. Embedding gastric cancer transcriptomes (n=497) reveals that malignant phenotypes correspond to thermodynamically distinct ground states rather than isolated pathway perturbations. The Warburg effect emerges intrinsically as a thermodynamic phase transition, and stem-like tumors occupy the deepest attractor basin reflecting high energetic stability. A thermodynamic order parameter stratifies patients into prognostically distinct subtypes independently of transcriptomic classification, suggesting clinically applicable non-redundant biomarkers. This work establishes a spin-glass energy landscape framework for physically principled, patient-specific cancer metabolic stratification.

Quantifying task difficulty remains an open theoretical problem in neuroscience and artificial intelligence. While difficulty is often treated as a scalar property of stimuli or optimization landscapes, neural computation unfolds as a transient reconfiguration of high-dimensional dynamical systems. Here we propose a dynamical manifold theory of difficulty based on heterogeneous, modular FitzHugh-Nagumo networks subjected to structured task demand. Task difficulty is modeled as a conflict-driven control parameter that perturbs competing neural submodules. We define four dynamical metrics: (i) transition action (energetic cost), (ii) peak dispersion entropy, (iii) coherence recovery deficit, and (iv) mean-field trajectory curvature. Across systematic sweeps of task demand, we demonstrate that difficulty does not collapse to a single axis but instead emerges as a multidimensional manifold. Energetic cost and dispersion entropy form a dominant axis, while geometric curvature and integration recovery exhibit partial independence and nontrivial correlations. These results suggest that cognitive difficulty corresponds to structured reorganization in neural state space rather than mere increases in activation amplitude. The proposed framework provides a biophysically interpretable foundation for linking neural dynamics, cognitive effort, and difficulty estimation in artificial systems.

Computational protein design is a foundational challenge in biotechnology, advantageous for engineering novel enzymes and therapeutics, yet its combinatorial complexity remains a bottleneck for classical optimization. We formulate fixed-backbone computational protein design as a quadratic Hamiltonian over rotamer variables to naturally map onto a hybrid photonic entropy computing platform, Dirac-3. To assess solution quality and runtime performance, we benchmark the photonic solver against an exact classical cost function network (CFN) solver, which provides provably optimal baselines. For protein instances ranging from 493 to 943 variables, Dirac-3 attains solutions within 0.16-2.47 % of optimal energies. Empirical scaling analysis reveals a comparatively gentle effective runtime growth for the photonic solver over the measured regime, consistent with near-linear polynomial scaling, in contrast to the sharp super-polynomial growth observed for the classical baseline beyond approximately 1000 variables. These results suggest a near-term crossover regime in which hardware-aligned continuous-variable optimization may offer a practical promise for large computational protein design instances where exact classical methods become time-prohibitive.

Molecular dynamics (MD) simulations yield atomic-level insights into molecular motion but struggle to reach the long timescales needed for rare events due to prohibitive computational costs. Generative machine-learning models (e.g., diffusion models and normalizing flows) offer a promising route to accelerate sampling, yet they generate independent equilibrium snapshots without temporal correlation or kinetic information. Autoregressive sequence models can learn time evolution by producing one frame at a time, but this stepwise generation often accumulates errors and drifts from true dynamics. Here, we propose a complementary approach inspired by advances in image and video generation: we treat finite MD trajectory segments as high-dimensional objects and learn their joint distribution using Generative Adversarial Networks (GANs). Using a Wasserstein GAN with gradient penalty, we directly generate entire time-series trajectories in one shot, that remain physically coherent over time without explicitly integrating the equations of motion. We demonstrate the generality of this method on molecular systems of increasing complexity: a 2D triple-well potential energy landscape, a protein-ligand binding process (cytochrome P450), the dynamics of an intrinsically disordered protein (-synuclein) in a latent coordinate space, and even the conditional generation of folding trajectories for the Trp-cage mini-protein. In all cases, the GAN-generated trajectories closely reproduce the true free-energy landscapes and kinetic signatures of the systems, while enabling efficient sampling of rare events that would ordinarily require months of conventional MD simulation.

Collective foraging in animal groups often relies on behavioral diversity, with individuals adopting different, sometimes complementary roles during shared tasks. However, most theoretical models predict that individuals responding to similar information cues in a shared environment should converge on a single optimal behavioral strategy. Using a spatially explicit multi-agent deep reinforcement learning model embedded in a three-species food chain, we show that stable behavioral diversity can emerge spontaneously among initially naive agents. Rather than converging on a single optimum, agents differentiate along a low-dimensional manifold of sensorimotor control, reflecting tradeoffs in speed regulation, spatial exploration, and deterministic turning rules. While multiple strategies yield comparable individual energetic returns, they are not interchangeable; group performance depends on how specific strategies combine to produce spatial resource partitioning and distributed directional influence. Replacing co-learned individuals with similarly competent agents trained in other groups disrupts these interaction structures and strongly reduces total energy acquisition. These results demonstrate that coordinated collective behavior and diverse, compatible strategies can arise endogenously from shared learning histories, but that this form of collective performance is path dependent and may be fragile to changes in group composition.

Complex systems with nonreciprocal interactions are often stratified into layers. Ecosystems are a prime example, where species at one trophic level grow by consuming those at another. Yet the dynamical consequences of such stratified nonreciprocity--where the correlation between growth and consumption differs across trophic levels--remain unexplored. Here, using an ecological model with three trophic levels, we reveal an emergent asymmetry: nonreciprocal interactions between consumers and predators (top and middle level) destabilize ecosystems far more readily than non-reciprocity between consumers and resources (middle and bottom level). We analytically derive the phase diagram for the model and show that its stability boundary is controlled by energy flow across trophic levels. Because energy flows upward--from resources to predators--diversity is progressively lower at higher trophic levels, which we show explains the asymmetry. Lowering energy flow efficiency flips the asymmetry toward resources and remarkably expands the stable region of the phase diagram, suggesting that the famous "10% energy transfer" seen in natural ecosystems might promote stability. More broadly, our findings show that the location of nonreciprocity within a complex network, not merely its magnitude, determines stability.

A fundamental paradox in ecology is the relationship between species diversity and ecosystem stability: Mays stability condition predicts that species diversity destabilises communities, yet many diverse ecosystems in nature are stable. Here, we show that this paradox can be resolved by explicitly considering resources, which May neglects. Specifically, Mays framework and the competitive exclusion principle jointly predict that resource diversity, which promotes species diversity, should destabilise communities. However, from computer simulations and analytical calculations using the finite-size cavity method, we find the opposite: resource diversity consistently generates stable, species-rich communities. Importantly, this stabilising effect disappears when resource dynamics is neglected (set to steady state). We also show that, contrary to the prevailing belief that interaction heterogeneity is always destabilising, different biological sources of heterogeneity have opposing effects on stability. Our work provides a solution to Mays paradox and demonstrates that resource dynamics are not just negligible background but are central drivers of ecosystem stability.

We investigate the target search process by proteins locating specific target sites along DNA - a phenomenon fundamental to biological functions such as gene regulation, transcription, replication, recombination, and gene-editing technologies. This process proceeds through a repetitive sequence of stochastic motions: consisting of one-dimensional (1D) sliding along the DNA contour interspersed with detachment and three-dimensional (3D) excursions in the bulk, and then reattachment to a random location on DNA. Recognizing this sequence of random events as analogous to the resetting processes widely studied in statistical physics, we employ a first-passage-renewal framework and derive general expressions for both the mean and fluctuations of the total search time. Our results are completely generic and do not depend on the detailed microscopic dynamics of either the 1D or 3D phases. Quite interestingly, we find that intermittent detachment can not only accelerate the mean search but can also regulate fluctuations around it. Our analysis reveals a universal fluctuation inequality that links the variability and mean of the sliding time to the mean excursion time, thereby identifying the fundamental conditions under which target search process becomes efficient. Notably, we find that broad distributions of sliding times emerge as a universal characteristic for optimal search efficiency--a feature emanating from the slow dynamics along the DNA. Using the facilitated diffusion mechanism as a representative example, we validate the generality of our results. These findings provide a unified theoretical framework connecting stochastic search, resetting dynamics, and biological efficiency, while also highlighting the crucial role of DNA structure such as its contour length in modulating search performance.

Micro-calorimetry offers significant potential as a quantitative method for studying the structure and function of biological systems, for instance, by probing the excess heat released by cellular or sub-cellular structures, isothermal or not, when external parameters change. We present the conceptual framework of nonequilibrium calorimetry, and as illustrations, we compute the heat capacity of biophysical models with few degrees of freedom related to ciliar motion (rowing model) and molecular motor motion (flashing ratchets). Our quantitative predictions reveal intriguing dependencies of the (nonequilibrium) heat capacity as a function of relevant biophysical parameters, which can even take negative values as a result of biological activity.

A central goal of ecology is understanding how the architecture of food webs, which represent the structural backbone of ecosystems, affects their stability. The analysis of stability in the classical sense of population dynamics (i.e. return to equilibrium) can be successful for a single instance of an empirical food web but ignores the multiplicity of alternative states in which the system could be found as a result of intrinsic variability and fluctuations. Here we propose and test a new methodology to reconstruct, from single empirical observations of a food web, the viable ensemble of alternative realizations respecting the observed resource-consumer linkages and empirical ener-getics. The reconstruction can be handled analytically within a maximum-entropy framework which predicts how empirical food webs access a multitude of alternative states with comparable stability and reactivity. The (measurable) entropy of the reconstructed ensemble directly quantifies this multiplicity and serves as a novel proxy of system resilience, that is the rate of return to equilibrium in response to an external perturbation. We show that the associated ensemble fluctuations provide explicit predictions for the expected response of food webs to external perturbations, such as anthropogenic or climate-induced stresses. We do that by validating the proposed fluctuation-response relation on empirical soil food webs subjected to experimentally controlled perturbations, confirming that intrinsic fluctuations in the unperturbed state predict responses to subsequent stresses. The perturbed states are associated with higher entropy, indicating less likely spontaneous recovery.

Planarian fragments can regenerate with normal gross anatomy after a transient bioelectric perturbation yet display altered outcomes upon re-cutting, implying that regeneration can store a persistent hidden state. Here we formulate an open-path version of Tangential Action Spaces (TAS) for this setting. Regeneration after a given cut is represented as a prescribed coarse anatomical trajectory together with multiple physiological lifts in a higher-dimensional state space. A metric on physiological state space defines a baseline lift, an effective excess-cost functional, and a baseline-relative endpoint displacement that serves as written hidden regenerative state. Re-cutting converts this open-path construction into a challenge readout. Locally, the theory yields a cut-dependent memory co-metric that identifies latent directions that are easy, difficult, or inaccessible to rewrite. We show that this geometry is consistent with published observations of cryptic phenotypes, stable re-challenge ratios, and near-absorbing double-headed outcomes. A reduced rank-one latent-threshold realization fitted to published 8-OH immediate and re-challenge counts identifies a challenge-sensitive cryptic interval below the immediate double-headed threshold and predicts out-of-sample re-challenge penetrances near 15% for nigericin- and monensin-treated immediate single-headed survivors using only their immediate phenotype penetrances. As a mechanistic bridge, a local electrodiffusive in-silico example instantiates a local version of the physiological-state effort metric G. This metric defines the baseline lift and excess rewriting cost, in relative biophysical units, and yields explicit example local write geometry. An illustrative semimechanistic readout based on integrated wound-edge gap-junction contrast and Na/K-ATPase load reproduces the treated-family ordering and similar transfer predictions when the untreated baseline is softly anchored near zero. These quantitative layers are intended as proof-of-concept calibratability and mechanistic-grounding checks rather than full validation of the complete open-path model. The framework therefore turns cryptic regenerative memory into a geometric, costed, and experimentally testable object, yielding predictions about temporal-profile dependence, compensatory cancellation, sign-reversing controls, cut dependence, anisotropic rewriting, and multi-round accumulation of hidden regenerative state.

In multi-cellular eukaryotic organisms, cell type and specific functional identity are defined by the epigenetic patterning of chemical modifications to DNA and chromatin that modulate the expression and silencing of specific genes. When a cell divides, histones containing important epigenetic marks are distributed between the two daughter strands leading to a temporary dilution of epigenetic information and cell identity. In this work we introduce a physics-based model of epigenetic memory that explains how cells restore and maintain H3K9me3 and H3K27me3 histone methylation patterning after cell division. We demonstrate that emergence and maintenance of the epigenetic program is driven by an evolved mechanism that makes use of the biophysics of polymers, phase condensates and enzymatic activity. We validate our model via genome-wide epigenetic time-course simulation and comparison to experimental epigenetic data from multiple donors, multiple cell types, and for multiple epigenetic marks. Finally, we use our model as a conceptual framework to understand cellular reprogramming by hypothesizing that these processes first contend with and later utilize somatic epigenetic maintenance programs.

Molecular dynamics (MD) simulations provide detailed insights into biomolecular motion but are often limited by the prohibitive cost of sampling long-timescale behavior. Here, we present a Transformer-based framework that reconstructs temporally continuous dynamical trajectories from only a small fraction of the initial data, directly targeting time-ordered evolution rather than independent ensemble snapshots. Using three systems spanning distinct dynamical regimes (intrinsically disordered -Synuclein, Cytochrome P450 ligand-binding motion, and a synthetic three-well potential), we show that the model learns both local fluctuations and long-range temporal structure. At inference time, the model generates full trajectories autoregressively from an initial prefix as prompt, capturing metastable transitions, basin-to-basin movements, and system-specific dynamical signatures. Free-energy surfaces computed from generated trajectories closely match ground-truth landscapes and, in several cases, we observe enhanced sampling in generated trajectories relative to the trained trajectories--while preserving kinetically meaningful transition patterns. These results demon-strate that Transformer architectures can serve as efficient, system-agnostic tools for time-continuous molecular trajectory prediction, offering a data-driven complement to long MD simulations and enabling accelerated exploration of conformational space.

Network-based epidemic models have been instrumental in understanding how contact structure shapes infectious disease dynamics, yet widely used frameworks such as Erd[o]s-Renyi, configuration-model, and stochastic block networks do not explicitly capture the combination of fully accessible (saturated) within-group interactions and constrained between-group connectivity characteristic of many real-world settings. Here, we introduce the Multi-Clique (MC) network model, a generative framework in which individuals are organised into fully connected cliques representing stable contact groups (e.g., households, classrooms, or workplaces), with a limited number of external connections governing inter-group transmission. Using stochastic susceptible-infectious-recovered (SIR) simulations on degree-matched networks, we compare epidemic dynamics on MC networks with those on classical random graph models. Despite having an identical mean degree, MC networks exhibit systematically distinct behaviour, including slower epidemic growth, reduced peak prevalence, increased fade-out probability, and delayed time to peak. These effects arise from rapid within but constrained between clique transmission, creating structural bottlenecks that standard models do not capture. The MC framework provides an interpretable, data-driven representation of recurrent contact structure, with parameters that map directly to observable quantities such as household and classroom sizes. By isolating the role of intergroup connectivity, the model offers a basis for evaluating targeted intervention strategies that reduce between-group mixing while preserving within-group interactions. Our results highlight the importance of explicitly representing the real-life clique-based network structure in epidemic models and suggest that classical degree-matched networks may systematically overestimate epidemic speed and intensity in structured populations.

Mechanical adaptation underlies mechanical homeostasis by allowing living systems to restore characteristic mechanical variables under sustained perturbations. Across biological scales, turnover-mediated remodeling enables mechanical adaptation by continuously renewing internal structures under load. Despite extensive progress in this field, it remains to be established what closed-loop mathematical structure of mechanics-turnover coupling is sufficient to guarantee homeostasis and how the characteristic adaptation timescale emerges from this coupling. Here, we identify the minimal mathematical structure of closed-loop mechanics-turnover coupling, providing a unifying description of mechanically adaptive remodeling across scales. We derive an analytical expression for the adaptation timescale as a function of the coupling between internal mechanical parameters and turnover kinetics, enabling direct cross-system comparison. To isolate this structure, we formulate a dynamical model linking mechanics and turnover, and establish conditions under which the closed-loop dynamics exhibit integral action. Specifically, our model describes how deviations in the mechanical state modulate the turnover of an internal structural state, and the renewed structure feeds back onto mechanics in a negative-feedback direction, driving recovery toward a reference state. We define systems satisfying this structure as Feedback Adaptive Turnover-mediated Environment-Dependent (FATED) systems. As an experimental example, we formulate mechanical adaptation in terms of mechanically regulated actin turnover. With the generalization of this architecture, we evaluate cross-system consistency by comparing reported adaptation and turnover timescales across representative remodeling systems.

Understanding the dynamical mechanisms underlying epidemic wave formation remains a central problem in mathematical epidemiology. Population-level epidemic waves are commonly interpreted as emergent consequences of nonlinear transmission feedback between susceptible and infectious individuals. However, epidemic time series from different regions often display markedly different waveform regimes, ranging from sharply peaked epidemics with rapid post-peak decline to more prolonged plateau-like dynamics. Here we propose the SEVA (Seasonal/Environmental Viral Activity) framework as a parsimonious alternative dynamical interpretation of epidemic wave formation. In this formulation, epidemic waveforms arise from depletion of a finite vulnerable population under a temporally structured viral activity field. The activity function is represented by a monotonic logistic hazard describing the temporal evolution of viral activity. With activation timing and steepness held constant across regions, daily incidence emerges as the product of activity intensity and the remaining vulnerable population. The framework is applied to first-wave COVID-19 hospitalization and mortality data from selected European countries and U.S. states during spring 2020. With fixed activation parameters and region-specific activity intensity, the model provides a simple dynamical explanation for diverse epidemic waveform regimes--including sharply peaked waves and plateau-like dynamics--without modification of the underlying dynamical structure. When epidemic trajectories are expressed in normalized form, curves from regions with very different mortality burdens display closely similar temporal structures. Within the SEVA formulation, this behaviour arises naturally from the interaction between a common temporal activation profile and regionally varying activity intensity. In this perspective, sharply peaked epidemics and plateau-like trajectories represent different dynamical regimes of the same activity-driven depletion process.

Cells sense and respond to the mechanical properties of their environment, yet the minimal physical principles sufficient to reproduce mechanotransduction and durotaxis remain debated. This work introduces FraCeMM, a physics-first mechanochemical simulation framework coupling stochastic ligand-integrin-talin binding to a deformable soft-body cell model on an elastic substrate. Without imposed polarity, directional cues, or migration rules, the model reproduces hallmark mechanobiological behaviors including stiffness-dependent spreading, traction reinforcement, focal adhesion asymmetry, and directed durotaxis. A finite pool of adhesion molecules, mechanically coupled through elastic linkages, drives emergent force asymmetry and polarization via self-consistent feedback between stochastic binding, molecular availability, and substrate stiffness. Despite minimal assumptions and a coarse-grained molecular representation, resulting traction forces, adhesion loads, and migration speeds fall within experimentally reported ranges. These results support the view that local force balance, limited adhesion resources, and mechanically binding are sufficient to generate adaptive mechanosensing and directed migration, establishing a transparent and extensible foundation for computational mechanobiology.

Epidemic growth rates, reproduction numbers and counts of new infections are universally used to guide public health intervention decisions. It is widely and reasonably believed that larger values of these indicators evidence the need for more urgent or stringent control. Here we show that this intuition can fail dramatically. We construct pairs of epidemics with indistinguishable growth rates, reproduction numbers and infection curves but fundamentally divergent responses to identical interventions, with one epidemic subsiding while the other grows exponentially. Conversely, we identify pairs in which one epidemic exhibits larger indicators and causes three times as many infections, yet both become suppressed with equal effectiveness under the same intervention. These paradoxical outcomes arise from structural uncertainties in transmission, which are invisible to standard outbreak indicators but become decisive under feedback control. Because structural uncertainty is unavoidable when representing real outbreaks, epidemic controllability and intervention performance cannot be reliably inferred without explicitly modelling this feedback between transmission and intervention.

Neural population activity typically evolves on low-dimensional manifolds and can be described as trajectories in attractor-like state spaces, including metastable switching among quasi-stable assembly states. Here we develop a unified definition of clustered neural networks with local excitatory-inhibitory balance in which enhanced within-cluster effective coupling can be realized by connection probability (structural clustering), synaptic efficacy (weight clustering), or any mixture of both. We introduce a single mixing parameter{kappa} [isin] [0, 1] that redistributes a defined clustering contrast between connection probabilities and synaptic efficacies while preserving the mean input of a balanced random network. Using mean-field theory and network simulations, we show that metastable dynamics are supported across the full{kappa} continuum. Shifting contrast between structural and weight clustering changes higher-order input structure, reshaping multistable regimes, neuronal correlations, and the balance between single- and multi-cluster episodes. Because real nervous systems jointly organize topology and synaptic strength, our approach provides a biologically realistic assembly definition and a basis for future models combining structural and functional plasticity. In practical terms,{kappa} offers a translation axis for neuromorphic and other constrained substrates, clarifying trade-offs between routing resources and synaptic weight resolution when implementing attractor-based computational primitives such as winner-take-all decisions and working-memory states for artificial agents.