Physical Review X

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.

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.

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.

Unveiling directional causality in complex, high-dimensional dynamical systems remains a fundamental challenge. Conventional nonparametric approaches, such as Convergent Cross Mapping, require computationally intensive surrogate tests and frequently yield false-positive detections under strong coupling due to generalized synchronization. Here, we present F-CODEC (Forest-weighted Conditional Dependence Coefficient), a forward-looking causal discovery framework integrating generalized random forests with adaptive rank conditioning. Nonparametrically conditioning on the target variable's intrinsic delay coordinates systematically neutralizes shared manifold representations, suppressing false positives without surrogate data. Furthermore, an analytical time-series threshold allows instant, rigorous hypothesis testing directly from raw observations. We demonstrate F-CODEC's resilience against generalized synchronization and high-dimensional noise across canonical chaotic benchmarks and multi-species network motifs. Applying F-CODEC to historical lynx-hare cycles resolves delayed trophic forcing, while in-situ IoT honeybee monitoring captures real-time microclimate-acoustic causal surges preceding colony-level behavioral events. F-CODEC establishes a practical, scalable, and surrogate-free tool for causal discovery in nonlinear dynamical systems.

Behavioral variability reflects differences in internal and external parameters and provides a substrate for natural selection. However, uncovering its structure is challenging because behavior evolves nonlinearly across multiple timescales. Our goal is to reconstruct phenotypic variation from finite behavioral observations without prescribing the scales at which individuals should be compared. To achieve this, we introduce a multiscale dissimilarity that compares dynamics across all statistically resolvable resolutions by constructing reduced transfer operators at progressively finer scales and weighting their differences by finite-sampling uncertainty. This dissimilarity defines a geometry of dynamical phenotypes, which we reconstruct using diffusion maps. We show that the resulting phenotypic coordinates locally follow the parameter directions to which dynamics are most sensitive. We validate our approach in a stochastic model and apply it to bacterial and larval zebrafish behavior. In bacteria, we identify run speed as a major component of inter-individual variability, associated with the chemotaxis protein CheB. In zebrafish, we find that prior prey experience reshapes behavioral dynamics and phenotypic variability, with paramecia experience concentrating fish in a prey-capture-associated region of phenotypic space. Together, these results provide a framework for identifying internal and environmental variables that structure dynamical phenotypes across scales.

Mixed-timescale signals are ubiquitous in natural stimuli and real-world applications, yet they remain challenging to process with recurrent neural networks. Reservoir computing offers an efficient framework for temporal processing, but extending its temporal range typically requires tuning neuronal timescales, which can compromise the representation of faster dynamics. Here, we propose an alternative approach in which synaptic plasticity provides an additional, slower timescale for computation. We introduce Hebbian plasticity into recurrent networks and show that its dynamics enable the reservoir to simultaneously process fast and slow components of mixed-timescale inputs: neuronal dynamics encode fast fluctuations, while synaptic dynamics support slower components. Remarkably, the resulting computational benefit extends over more than an order of magnitude beyond the intrinsic timescale of the plasticity. We show that this extended processing range arises from the dependence of the plasticity rule on postsynaptic activity, which effectively injects a filtered memory of past states into the network current. These results identify synaptic plasticity as a mechanism for extending the temporal processing capabilities of recurrent networks without altering neuronal timescales, and also suggest a potential computational role for plastic synapses in the processing of slowly varying stimuli in biological neuronal networks.

Circadian clocks are found in myriad species across the tree of life. They are commonly assumed to provide a selective advantage by enabling organisms to anticipate daily environmental changes. It has proven remarkably difficult, however, to move beyond this general idea to explain precisely what advantage anticipation confers and to quantify how large this benefit is. Here, we address these challenges by developing a mathematical model of diurnally varying growth and metabolism in the cyanobacterium Synechococcus elongatus, which fixes carbon through photosynthesis during the day and stores a portion of it as glycogen for use during the night. Specifically, we extend the framework introduced by Hwa and coworkers (Scott et al., Science 330, 1099 (2010)), which quantifies the relationship between growth and proteome composition, to a circadian context. We find that the fastest growth is achieved when glycogen production during the day is minimized to the amount required to sustain essential nighttime processes; growth then occurs exclusively during the day, in agreement with experimental observations. However, the slow relaxation of the proteome, arising from the intrinsically slow growth rate of S. elongatus, severely constrains the implementation of this optimal strategy: In the absence of anticipation, the cell must grow at night in order to produce proteins essential for nighttime metabolism. In contrast, with anticipation enabled by a circadian clock, the bacterium can instead adjust its proteome late in the day, allowing it to avoid less efficient nighttime growth altogether, thereby significantly enhancing its growth rate.

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.

Ecological coarse-graining of individuals or species into aggregate variables, such as total biomass or regional abundance, is common practice, yet differences among species can still influence aggregate dynamics. We propose a metric for quantifying this irreducible dynamical heterogeneity. For small fluctuations near a stable equilibrium, we compare the aggregate fluctuation spectrum of the full dynamical system with that of the best Ornstein-Uhlenbeck model having the same dimension as the aggregate. The remaining spectral mismatch quantifies the dynamical effects of hidden differences that the fitted aggregate model cannot capture. For weakly interacting random community models at fixed collective interaction strength, we show that increasing species richness can either reduce or increase this heterogeneity, depending on how species interact. Our framework helps understand when ecological and evolutionary differences average out versus when their dynamical effects persist.

Interception of moving objects is a universal pattern of animal behavior with many industrial applications. Inspired by the behavior of the characid fish Brycon guatemalensis, which catches fruits falling onto the surface of a river, we study one-shot (i.e., open-loop) interceptions using both stochastic optimal control theory and reinforcement learning. In the first instance, an agent actuates a control (wait time before launch and heading angle) to meet its target, given a noisy estimate of the target initial state. In a minimal setting, where launch velocity and actuated control are constants, we show that the optimal wait time is attenuated by noise in both the target measurement and control actuation, as well as agent energy conservation. We then derive an upper bound for the heading angle variance which scales as the ratio of the non-vanishing optimal interception error to the initial planar separation. Complementing our control framework, our deep reinforcement learning approach shows that the neural network representing the fish first learns the value function for the interception, then learns how to aim, and finally learns the optimal wait time. Beyond the specific problem at hand, our results may also have applications to problems with little time for feedback or corrections such as perching, landing, and docking.

Phase separating biopolymers are often described by the sticker-spacer model, which accounts for non-attractive linkers that connect discrete attractive moieties. "Associative polymer" theories describe these systems as two coexisting fluids of stickers and spacers, respectively. In such theories the stickers and spacers are decoupled in the sense that sticker binding does not affect spacer conformations or vice versa. Informed by coarse-grained simulations, we develop a phenomenological mean-field theory to determine the microscopic coupling between the sticker and spacer degrees of freedom. Accounting for linkers connecting adjacent spacers introduces free energy contributions due to conformational entropy of the spacer and the binding combinatorics of the stickers. These contributions have opposite dependencies on spacer length because longer spacers allow a greater volume to search for binding partners but incur a greater entropy cost upon bond formation. The length dependent terms from these contributions cancel leaving a length-independent elastic term arising from the fact that a small amount of spacer stretching lowers the free energy by increasing the number of possible binding partners. The cancellation of spacer length from the theory justifies the decoupling approximation and supports mean-field treatments of heterogeneous spacers.

Dense, well-ordered material states of proteins form the amyloid fibers that are a hallmark of neurodegenerative disease in the brain. Beyond forming amyloid fibers, some of these proteins can also adopt other material states termed condensates which are initially liquid-like but evolve to a soft, glassy phase. Fiber growth requires a large supply of monomers and, thus, it is often speculated that fibers emerge from within a dense condensate as it ages and its microscopic dynamics slow into a glassy state. Here, we use the well-established model system Fused in Sarcoma (FUS) to directly observe, quantify and theoretically describe fiber growth and its interplay with condensates. We report the discovery that fibers grow overwhelmingly in the dilute phase surrounding the condensates while the condensates concurrently evolve to a glassy arrested solid. The resulting protein fibers and glassy condensates are both distinct solid-like phases that coexist but do not directly interconvert. Taken together, these findings reveal that there are two competitive aging pathways in FUS condensation that are linked through phase separation kinetics.

Cell density is a fundamental biophysical property of living cells, yet the dynamical architecture underlying density homeostasis remains unknown. Here, we reconstruct the geometry, dynamics, and control structure governing cellular density regulation from single-cell mass-volume measurements acquired during recovery from osmotic perturbation. We identify a persistent anisotropic attractor in mass-volume state space that permits coordinated density-preserving fluctuations while strongly suppressing density-changing deviations. Optimal transport analysis reveals directed recovery trajectories confined to this attractor, enabling inference of an effective density-restoring control law. Density deviations are associated with coordinated changes in biomass accumulation and volume expansion that together generate an effective density-restoring control law. Moreover, density error contains significant predictive information regarding future corrective behavior, revealing an information-rich component of cellular regulation. Together, these findings establish cellular density homeostasis as an emergent dynamical control process and demonstrate how attractor reconstruction, optimal transport, and information theory can be combined to uncover the organizing principles of biological homeostasis.

At the nucleosome scale, chromatin is an actively remodeled polymeric system whose organization is continuously reshaped by ATP-dependent remodelers that slide, evict, and reassemble nucleosomes along DNA. However, how the local structural rearrangements generated by such remodeling events influence condensate-scale organization and dynamics remains poorly understood. Here, we introduce a coarse-grained model of chromatin condensates composed of short polymers that explicitly incorporates enzyme-assisted nucleosome sliding together with nucleosome eviction and reassembly, coupled to Langevin relaxation dynamics. By explicitly accounting for the DNA length sequestered within individual nucleosomes, the model captures the steric constraints and local conformational relaxation that accompany nucleosome sliding, eviction, and reassembly. We find that nucleosome activity drives condensate swelling, enhances condensate-size fluctuations, and promotes internal mixing. In condensates containing both active and passive polymers, differences in nucleosome activity further induce radial segregation, with active polymers enriched near the periphery and passive polymers concentrated in the interior. These results identify active nucleosome remodeling as a physical mechanism for regulating chromatin condensate structure, fluidity, and spatial organization.

Division of labor is commonly associated with cooperative behavior, yet one of its most extreme forms occurs during bacterial warfare, where a subset of cells undergoes suicidal lysis to release toxins. Why bacteria divide labor among a few cells rather than producing toxin uniformly remains unknown. Here, we combine timelapse microscopy and simulations, to understand the division of labor during bacterial warfare using bacteriocin (colicin) production by the gut bacterium Escherichia coli as a model system. At the single-cell level, we find that lytic toxin production is a tightly regulated event: only cells that commit to lysis produce significant toxin and then lysis only occurs once a large amount of toxin has been made. This high threshold ensures each sacrifice delivers a large dose, which is released in a rapid burst from a lysing cell. While such burst-like release appears to provide no advantage over uniform labor in well-mixed conditions, we show it becomes extremely effective in spatially structured populations where the rapid release of toxin by one cell can generate lethal concentrations locally and eliminate competitors. Finally, we explain why the lysing fraction remains so small. While an increase in the producing cells increases toxin levels, it also increases the probability of local patch extinctions. The division of labor during bacterial warfare, therefore, enables powerful localized killing while safeguarding the population from self-destruction.

Enzymes are central to biological function, catalyzing the chemical transformations that sustain metabolism, signalling, molecular transport, and cellular regulation. Understanding their catalytic activity requires connecting molecular structure and conformational dynamics to measurable reaction kinetics. Classical Michaelis--Menten kinetics describes turnover through a dominant catalytic pathway approaching a single saturation limit, whereas conformational-selection, induced-fit, allosteric, and dynamic-disorder models account for additional complexity arising from conformational exchange and heterogeneous catalytic states. Experimental studies further reveal concentration-dependent changes in pathway usage, cooperative or sigmoidal responses, transitions between distinct turnover regimes, and intermittent single-molecule activity. These behaviours are typically treated within separate kinetic descriptions, leaving their mechanistic relationship within a common physical picture incompletely resolved. Here, we formulate a minimal conformational free-energy landscape with interconverting enzyme states and competing catalytic routes to examine whether these apparently distinct kinetic signatures can arise from a shared physical mechanism. In this framework, substrate availability and conformational barriers redistribute catalytic flux between slower and faster pathways, thereby altering both pathway occupancy and turnover times. Stochastic Gillespie simulations together with deterministic mean-first-passage-time analysis show that different parameter regimes generate low- and high-turnover states, concentration-dependent kinetic crossovers, burst--halt intermittency consistent with single-molecule observations, and effectively Michaelis--Menten-like or sigmoidal allosteric-like responses. The same underlying landscape can therefore produce qualitatively different kinetic behaviours depending on how conformational exchange and substrate capture partition catalytic flux. It also explains how finite substrate windows can mask underlying bimodal behaviour. These results provide a physically interpretable framework linking conformational dynamics, pathway selection, and experimentally observed enzyme kinetics.