Physical Review X

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.

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.

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.

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.

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.

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.

Evolutionary therapies regulate heterogeneous populations by altering selective pressures through treatment sequences in cancer and infections. This letter develops an invariant-set framework for treatment-induced containment based on positive triangular invariant sets. For periodically switched systems, sufficient conditions are derived for the existence of such invariant regions. Robustness with respect to mutation is established by showing that the invariant simplex persists under small perturbations of the subsystem matrices. In the two-phenotype case, the analysis yields an explicit mutation threshold that separates regimes in which therapy cycling maintains containment from regimes in which mutation can enable evolutionary escape. Simulations illustrate the geometry of the invariant sets and the role of mutation and dwell time in containment robustness.

Cross-scale integration remains a persistent challenge in ecology. Mechanistic network models have advanced this integration by linking individual behavior to community dynamics. Their complexity, however, often limits exploration to numerical simulations, which tend to be insufficient for fully unveiling the fundamental rules governing system behavior. Extracting these rules requires moving beyond numerical observation to establish exact, analytical constraints. Here, a complete mathematical analysis of a mechanistically detailed plant-pollinator model is presented. This cross-scale analysis decouples transient and equilibrium dynamics, proving that pollination strictly gates plant persistence while recruitment competition caps equilibrium abundance. The precise behavioral mechanisms scaling up to determine network stability are determined: nestedness stabilizes communities by generating floral reward gradients that guide adaptive foraging, whereas connectance destabilizes by eroding these rescue pathways. Additionally, native community persistence and biological invasions are conceptually unified; a single, multi-scale reward threshold (R*) is shown to govern both native survival and alien establishment. These analytical derivations are distilled into conceptual frameworks and visual summaries accessible for empiricists interested in theory and conceptual unification. By translating numerical observations into rigorous, trait-grounded proofs, this analysis demonstrates that complex, cross-scale networks are tractable, revealing the precise conditions under which communities assemble, persist, and collapse.

DNA is the largest biopolymer in nature, and chromatin contact maps are widely interpreted as quantitative readouts of its three-dimensional organization. However, the validity of such interpretations critically depends on how these maps are processed. Here, we identify a previously overlooked but fundamental source of bias in chromatin contact data analysis. We demonstrate that a widely adopted preprocessing convention, namely whole-matrix percentile clipping, systematically distorts sparse contact maps by collapsing their dynamic range. This effect is strongest in near-diagonal interactions, precisely the regime encoding chromatin domains and looping structures, thereby compromising quantitative interpretation while preserving superficial structural features. We show that this distortion represents a sparsity-dependent failure mode of current preprocessing standards and affects the comparability of datasets and computational methods across technologies and sequencing depths. To address this, we introduce a statistically consistent preprocessing framework based on nonzero-percentile clipping and log-space normalization, which preserves the intrinsic dynamic range of observed contacts. Building on this foundation, we present CCUT, a modular deep learning framework for chromatin contact map reconstruction. Under corrected preprocessing, reconstructed maps recover domain organization, contact decay, and scaling behavior consistent with polymer physics. Importantly, we demonstrate quantitative agreement between reconstructed maps and simulated contact patterns derived from a kinetic Monte Carlo loop extrusion model, enabling direct comparison between experimental data and physical models. Together, our results establish preprocessing as a decisive determinant of the physical interpretability of chromatin contact maps and provide a principled framework for robust and comparable analysis across chromatin conformation capture technologies.

We present a new formulation of the low-field effect (LFE) in spin-correlated radical pairs based on a zero-field singlet-triplet basis for the isotropic spin Hamiltonian. The aim is to provide a description that is both formally rigorous and mechanistically transparent, especially in the regime of weak magnetic fields such as the geomagnetic field. For the standard model radical pair containing a single spin [Formula] nucleus, we show that the conventional singlet-triplet basis obscures the distinct dynamical roles of the hyperfine and Zeeman interactions. In the zero-field S-T basis, by contrast, the mechanism separates cleanly: isotropic hyperfine coupling mixes singlet-doublet and triplet-doublet states, whereas the weak-field Zeeman interaction mixes triplet-quartet and triplet-doublet states without directly introducing an additional singlet-triplet coupling. The LFE is therefore revealed as a sequential process in which a weak field unlocks access from a triplet-only manifold to a singlet-accessible triplet manifold, from which hyperfine-driven singlet-triplet interconversion can occur. We then generalize this picture to radical pairs with arbitrary isotropic hyperfine structures by identifying maximal, interior, and, when present, minimal triplet-only manifolds in the zero-field spectrum. Finally, we introduce a practical blockwise dark-state recruitment measure for the triplet-only zero-field state space made singlet-accessible by a weak field, and show how this quantity depends on hyperfine symmetry, including the effects of equivalent nuclei. The resulting framework provides both a simple physical picture of the LFE and a general route to estimating its structural upper bound for arbitrary radical pairs.

Recent viral coinfection experiments show that recombinant genomes are generated readily and depend strongly on infection timing and order, yet only a small fraction give rise to persistent lineages. We develop a hybrid deterministic-stochastic framework that resolves this discrepancy by coupling density-dependent recombinant generation with stochastic establishment of rare lineages. The resulting hazard of successful lineage formation is generically non-monotonic, increasing with parental abundance through enhanced generation while decreasing under competitive suppression, and exhibits a unique interior maximum in parental-density space. As parental populations evolve, their trajectory across this hazard landscape defines a sharply localized temporal window of evolutionary opportunity. These results reveal a general principle: evolutionary success is determined not only by intrinsic fitness, but by when variants arise within a dynamically changing ecological context.

Receptor-mediated ligand endocytosis is traditionally viewed as a negative feedback mechanism for signal attenuation. Here we show that ligand removal can paradoxically enhance directional information in autonomous cell-cell attraction. Many cell systems migrate toward one another in the absence of externally imposed gradients, implying that secretion, diffusion, and uptake must themselves generate usable directional cues. We develop a surface-resolved theory of a finite-sized detector exposed to a nearby source and derive analytical expressions for the steady-state ligand field. The resulting concentration profiles are governed by a single dimensionless Damkohler number that compares receptor-mediated endocytosis to diffusive ligand transport. Increasing ligand removal lowers extracellular ligand concentrations and reduces absolute concentration differences across the detector surface, but preferentially enhances relative surface anisotropy. Thus, destroying the signal can increase the usable information encoded in relative gradients. Incorporating nonlinear downstream processing reveals a tradeoff between contrast enhancement and signal depletion that yields a well-defined optimal endocytosis rate, in a regime consistent with experimentally measured receptor internalization kinetics. These results recast receptor-mediated endocytosis as an extracellular information-processing mechanism that reshapes self-generated gradients to enhance directional information.

While the regulation of bacterial cell size is widely studied across generations, the stochastic nature of cell volume growth remains elusive within a cell cycle. Here, we investigate the fluctuations of cell volume growth and report a deviation from standard white-noise models: the random growth rate exhibits subdiffusive dynamics. Specifically, the mean square displacement of the growth-rate noise scales as {Delta}t with an anomalous exponent {approx} 0.27. This low exponent implies strong negative temporal correlations in growth rate noise on timescales of minutes, which are significantly faster than those of gene expression dynamics. We attribute this phenomenon to the physical mechanics of the cell wall. By modeling the peptidoglycan network as a complex viscoelastic material with power-law-distributed relaxation times, we successfully recapitulate the observed subdiffusive behavior. Our results suggest that the heterogeneous mechanical constraints of the peptidoglycan network, rather than biological regulatory programs,govern the short-timescale fluctuations of bacterial growth.

SignificanceThis work establishes a probabilistic magnetometry framework for detecting weak stochastic magnetic fluctuations at the nanoscale, which provides the first quantitative access to intrinsic magnetic activity in living cells. Weak stochastic magnetic fluctuations at nanoscale are difficult to quantify. In living cells, ionic transport and molecular currents generate electromagnetic activity whose magnetic component is likewise nanoscale, weak, stochastic, and rapidly varying and has therefore remained experimentally inaccessible. Here we introduce Bio-Spin Probabilistic Inference (BISPIN), a digital statistical framework that can quantify weak, stochastic magnetic fluctuations at the nanoscale. Using threshold-resolved signals from enhanced nitrogen-vacancy quantum sensors, BISPIN converts unstable analog magnetic readouts into statistically convergent digital observables and infers fluctuation strength through probabilistic modeling, enabling robust quantification under random sensor orientations and biological heterogeneity within the experimental bandwidth. Applied to living cells, this approach distinguishes live from fixed cells, resolves agonist-induced activation, and maps subcellular variations in magnetic fluctuation strength. By providing the first quantitative access to intrinsic stochastic magnetic fluctuations in living cells, this work establishes a probabilistic magnetometry framework for cellular electrodynamics and opens a new magnetic dimension of cellular phenotyping for bio-spin omics.

Theory predicts that pathogenic organisms benefit from aligning to host circadian rhythms, but observable data provide an incomplete picture of infection rhythms. Models are needed to reconstruct unobservable dynamics and uncover fitness impacts, challenges typified in malaria infections. Malaria parasites often synchronize their development to multiples of 24 hours and reschedule their developmental rhythms following perturbation. Yet it remains uncertain how parasites reschedule--including any cost to parasite multiplication rates-- due to the difficulty of detecting parasites in all phases of their development. As parasites mature, the red blood cells they occupy adhere to blood vessel walls (sequestration, an immune evasion tactic) where they cannot be readily sampled. Existing methods cannot determine sequestration timing in vivo nor how that timing varies in perturbed within-host environments. To address these challenges, we fit a mathematical model tracking parasite development and sequestration to high-resolution time series from the rodent malaria parasite Plasmodium chabaudi. We show that parasites hasten late development--but not sequestration--to realign with host rhythms following perturbation. That rescheduling reduces multiplication rates, a result only apparent from model-reconstructed dynamics. Our novel approach recovers the timing of development and sequestration, providing insight into the consequences of circadian rhythms for parasite fitness.

We introduce a mechanistic, nonlocal tumour-growth model designed specifically to capture explosive dynamics that are not adequately explained by standard logistic reaction-diffusion descriptions. The motivation is empirical: the universal scaling law reported in [1] provides compelling cross-sectional evidence of superlinear tumour activity versus tumour burden, but as a phenomenological relationship it does not by itself supply a dynamical mechanism, nor does it rigorously describe how explosive growth emerges, how fast it develops, or how spatial interactions and tissue boundaries influence it. Our model addresses this gap by incorporating nonlocal proliferative feedback--cells respond to a spatially aggregated neighbourhood signal--and a singular, Kawarada-type acceleration that produces "quenching": tumour density stays bounded while the proliferative drive becomes unbounded as the aggregated signal approaches a critical threshold. This offers a concrete mechanistic route to explosive escalation consistent with physical boundedness. We analyse the model under no-flux (Neumann) boundary conditions, appropriate for reflecting tissue interfaces. In the spatially homogeneous setting we prove finite-time onset of the explosive regime and obtain explicit rates for how rapidly it is approached. For spatially heterogeneous perturbations we derive a transparent spectral stability theory showing how the interaction kernel selects spatial scales and how the singular acceleration tightens stability margins as the explosive threshold is approached. These results provide interpretable links between nonlocal interaction structure, boundary effects, and the emergence of rapid growth. Finally, to connect mechanism to data in the spirit of [1], we embed the model in a Bayesian inference framework that treats the interaction kernel and the acceleration strength as unknown and learned from tumour-growth observations. This enables uncertainty-aware estimation of explosive onset times, escalation rates, and stability margins, while positioning the scaling law of [1] as an observable signature that our mechanistic model can explain and quantify rather than merely fit.

How and why do species interactions produce unstable dynamics? In the simplest models, the answers are straightforward. In the Rosenzweig-MacArthur predator-prey model, resource self-facilitation due to predation mortality triggers oscillations; in Lotka-Volterra competition, positive feedback from stronger interspecific competition underlies alternative states. However, when unstable dynamics arise with three or more species, how and why answers become more opaque. We propose that dissection of feedback loops, chains of direct species interactions, can answer these questions in meso-scale models. To demonstrate, we disentangle instabilities in epidemics using three variations of a general yet mechanistic resource-host-parasite model. Resources introduce destabilizing self-facilitation but also positive interspecific direct effects on propagule production and transmission rate. Those direct effects then produce instabilities through feedback loops. First, we trace how resource self-facilitation catalyzes oscillations by weakening faster, shorter, lower levels of feedback relative to longer, slower feedback of the whole system. Then, we show how resource-dependent propagule yield introduces positive cascade fueling feedback, creating an Allee threshold inhibiting invasion of parasites. In a third variant, we traced how both resource-dependent components produced those unstable dynamics and more complex behaviors, including a period-doubling route to chaos to which we apply a form of loop tracing. Hence, we show how and why direct, positive effects of resources modulate feedbacks underlying oscillations, Allee effects, and more during epidemics. We propose that loop tracing, a generally applicable method, could empower ecologists to glean much deeper insight into dynamics of species interactions.

Robust development depends on maintaining correct proportions as overall size varies. What controls and limits this ability to scale remains poorly understood in part due to the complex interplay between mechanical and biochemical factors within developing embryos. Using confinement of dissociated embryonic presomitic mesoderm cells, combined with imaging and chemical perturbations, we identified aggregation as the initial event in de novo anterior-posterior axis patterning. Using a continuum model solely based on cell-cell attraction, we quantitatively map out how the time available for aggregation-driven patterning limits the system size over which scaling can be maintained: Small systems allow for rapid and robust pattern scaling whereas coarsening dynamics substantially de-lay the appearance of a scaled pattern in large systems. Our experiments quantitatively confirm these predicted scaling regimes. Together, our results suggest a developmental time-size tradeoff on the scaling of aggregation-driven patterns.

We introduce a spectral existence criterion for the evolution of cooperation in the form of the inequality{lambda} maxb > c, where{lambda} max is the leading eigenvalue of an interaction operator encoding population structure, and b and c represent benefit and cost tradeoffs, respectively. Nowaks five rules for the evolution of cooperation correspond to cases in which the cooperation condition reduces to a scalar assortment coefficient. These results follow from the Price equation, which sheds light on a long-standing debate on the role of inclusive fitness and evolutionary dynamics in explaining the evolution of cooperation.