Physical Review Research

Foraging is a central decision-making behavior performed by all animals, essential to garnishing enough energy for an organism to survive. Similarly, mating is crucial for evolutionary continuity and offspring production. Mate choice is one of the central tenets of sexual selection, driving major evolutionary processes, and can be regarded as a decision-making process between potential mating partners. Often researchers have used coarse-grained models to describe macroscopic phenomenology pertaining to mate choice without detailed quantitative mechanisms of how animals use individual and environmental signals to guide their mating decisions. In this letter, we show that mate choice can be cast as a foraging problem, and we present an analytically tractable optimal foraging-inspired mechanistic theory of decision-making underlying mate choice. We begin from the premise that deciding upon which partner with which to mate is at its core a stochastic decision-making process. Agents adopt a variety of decision strategies, tuned by decision thresholds for leaving or committing to a mate. We find that sensitive leaving thresholds are favored independently of signal availability in the population. By contrast, optimal thresholds for committing to a mate depend upon signal availability in the population, with signal-rich populations generally favoring less eager strategies compared to signal-poor populations.

A key component of intraneuronal communication is the modulation of postsynaptic firing frequencies by stochastic transmitter release from presynaptic neurons. The time interval between successive postsynaptic firings is called the inter-spike interval (ISI), and understanding its statistics is integral to neural information processing. We start with a model of an excitatory chemical synapse with postsynaptic neuron firing governed as per a classical integrate-and-fire model. Using a first-passage time framework, we derive exact analytical results for the ISI statistical moments, revealing parameter regimes driving precision in postsynaptic action potential timing. Next, we extended this analysis to include both an excitatory and an inhibitory presynaptic connection onto the same postsynaptic neuron. We consider both a fixed postsynaptic-firing threshold and a threshold that adapts based on the postsynaptic membrane potential history. Our analysis shows that the latter adaptive threshold can result in scenarios where increasing the inhibitory input frequency increases the postsynaptic firing frequency. Moreover, we characterize parameter regimes where ISI noise is hypo-exponential or hyperexponential based on its coefficient of variation being less than or higher than one, respectively.

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.

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.

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.

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.

The interactions of droplets and filaments can lead to mutual deformations and complex combined behavior. Such interactions also occur within the cell, where biomolecular condensates, distinct liquid phases often composed of proteins, have been observed to structure and affect the organization of the cytoskeleton. In particular, biomolecular condensates have been shown to undergo characteristic deformations when cytoskeletal filaments are fully embedded within them. However, a full understanding of the underlying physical mechanisms is still missing. Here, we combine experiments with coarse-grained molecular dynamics simulations and analytical models to uncover the physical mechanisms that define emerging shapes of droplets containing filaments. We find that the surface tension of the liquid phase and the bending energy of the filament(s) suffice to accurately capture emerging shapes if the length of the filament is small compared to the liquid volume. As the volume fraction of filament(s) increases, wetting effects become increasingly important, setting physical constraints within which surface and bending energies compete to define the droplet shapes. We find that mutual deformations of condensate and filament extend accessible shapes beyond classical stability considerations, leading to structuring and entrapment of contained filaments. Shape deformations may further affect ripening dynamics that favor certain geometries. Our findings provide a physical framework for a better understanding of the possible roles of biomolecular condensates in cytoskeletal organization.

Cytokine-mediated communication is a central mechanism by which immune cells coordinate activation, differentiation and proliferation. While mechanistic reaction-diffusion models provide detailed descriptions of cytokine secretion and uptake at the cellular scale, their computational cost limits their applicability to large and densely packed cell populations. Previously employed approximations of cytokine diffusion fields rely on assumptions that neglect the influence of cellular geometry and volume exclusion. In this work, we study a macroscopic description of cytokine diffusion and reaction dynamics based on homogenization techniques, rigorously linking microscopic reaction-diffusion formulations to effective continuum models. The resulting homogenized equations replace discrete responder cells with a continuous density, while retaining essential features of cellular uptake and excluded-volume effects. Further, we show that in regimes with approximate radial symmetry, classical Yukawa-type solutions emerge as limiting cases of the homogenized model, provided appropriate correction factors are included. Overall, our approach allows efficient multiscale modeling of cytokine signaling in complex immune-cell environments.

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.

How genetically identical cells spontaneously break symmetry to assume divergent fates is a fundamental problem in developmental biology. While modern genomics has mapped the vast molecular repertoire involved in gene regulation, understanding the mechanism of cell state transitions that drive differentiation remains a formidable challenge. To address this, we use a reaction-kinetic framework to analyze recurring motifs of two and three competing master regulators. While typically such circuits are studied numerically, we show that assuming symmetry in nodes and interactions provides exact analytical description of the bifurcations governing cell fate transitions. We find that the possible cell fates across all considered topologies are dictated by a single dimensionless quantity, {beta}--the ratio of protein degradation to production rates. In the binary Toggle Switch (TS), decreasing {beta} destabilizes the symmetric (stem cell) state, giving rise to two asymmetric (differentiated) fates via a supercritical pitchfork bifurcation. In the three-component Toggle Triad (TT), low values of {beta} yield three asymmetric fates through subcritical pitchfork bifurcation, creating an intermediate range of {beta} where both symmetric and asymmetric fates are simultaneously stable. For the Self-Activating Toggle Switch (SATS), we identify a new parameter for the self-activation threshold ({theta}) and show that decreasing{theta} progressively stabilizes the uncommitted state, leading to a regime of tristability. Building on these temporal bifurcations, we next address the feasibility of spatial structure formation: can these multistable fates stably coexist within a spatial domain? Through a minimal model of cell-cell communication via free diffusion, we extend these motifs into reaction-diffusion systems, which reveals a direct role of network topology on spatial organization. We prove that any heterogeneous pattern in two-node circuits is inherently transient and unstable. In contrast, the three-node repressive network supports the stable spatial coexistence of differentiated phenotypes through pure diffusion, a phenomenon we analyze by studying heteroclinic interface solutions as building blocks. By reducing complex regulatory dynamics to tractable models with physically meaningful parameters, we establish a minimal framework which relates topology to cell fate. Finally, the effects of temporal multistability on pattern formation provide an excellent studying ground for morphogenesis, synthetic biology, and the overarching problem of spatiotemporal self-organization.

Cerebrospinal fluid (CSF) is a Newtonian fluid that bathes the brain and spinal cord and oscillates in response to the physiological periodic changes in brain volume, of which the cardiac cycle is a major driver. Understanding this motion is essential for clarifying its contribution to solute transport, waste clearance, and drug delivery. In this work, we study oscillatory and steady streaming flow in the cranial subarachnoid space using a lubrication-based theoretical framework. The model represents the cranial CSF compartment as a thin fluid layer bounded internally by the brain surface and externally by the dura, driven by time-dependent brain surface displacements. We first derive simplified governing equations for flow over an arbitrary smooth sphere-like brain surface and obtain analytical solutions for an idealised spherical geometry with uniform displacements. We then incorporate realistic displacement fields reconstructed from MRI measurements in healthy subjects and solve the reduced equations numerically. The results show that oscillatory forcing produces a steady streaming component that may enhance solute transport compared with diffusion alone. This work provides a mechanistic description of the flow generated by physiological brain motion and highlights the potential presence of steady streaming in cranial subarachnoid fluid dynamics.

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.

Understanding how cells migrate through confined environments is crucial for elucidating fundamental biological processes, including cancer invasion, immune surveillance, and tissue morphogenesis. The nucleus, as the largest and stiffest cellular organelle, often limits cellular deformability, making it a key factor in migration through narrow pores or highly constrained spaces. In this work, we introduce a geometric surface partial differential equation (GS-PDE) model in which the cell plasma membrane and nuclear envelope are described as evolving energetic closed surfaces governed by force-balance equations. We replicate the results of a biophysical experiment, where a microfluidic device is used to impose compressive stresses on cells by driving them through narrow microchannels under a controlled pressure gradient. The model is validated by reproducing cell entry into the microchannels. A parametric sensitivity analysis highlights the dominant influence of specific parameters, whose accurate estimation is essential for faithfully capturing the experimental setup. We found that surface tension and confinement geometry emerge as key determinants of translocation efficiency. Although tailored to this specific setup for validation purposes, the framework is sufficiently general to be applied to a broad range of cell mechanics scenarios, providing a robust and flexible tool for investigating the interplay between cell mechanics and confinement. It also offers a solid foundation for future extensions integrating more complex biochemical processes such as active confined migration.

Genetic surveillance is increasingly used to track malaria transmission, yet genomic metrics can respond nonlinearly to changes in transmission intensity and depend on the diversity already present in the parasite population. Here, we present a stochastic agent-based model of hu-man-mosquito transmission that integrates SEIS-like epidemiological dynamics with within-host Plasmodium falciparum haplotype dynamics. By varying the maximum mosquito biting rate and the initial parasite diversity, we examine how transmission intensity and standing diversity jointly shape mixed infections, recombination, and long-term population structure across a continuous transmission gradient. Our study revealed a sequential pattern in which increasing biting intensity first increases infection prevalence and multiplicity of infection, then expands opportunities for outcrossing, and only thereafter increases effective recombination and recombinant haplotype generation. These responses are strongest in low- to intermediate transmission and tend to plateau at higher transmission levels. Initial population diversity constrains the amount of diversity that can be maintained and the magnitude of recombination output, while temporal trajectories show that haplotype evenness can pass through transient non-equilibrium phases before stabilizing. Together, these results show that the structure of the parasite population is shaped not by trans-mission intensity alone but by its interaction with standing genetic diversity. Furthermore, this study works to clarify when and how genomic metrics reliably reflect transmission conditions across heterogeneous malaria settings.

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.

Extracting stable individual traits from behavior observed across diverse contexts is a central challenge in behavioral modeling. We propose a framework for inferring domain-invariant individual latent representations by jointly encoding behaviors across multiple domains. Using large-scale telemetry data from professional Counter-Strike 2 gameplay, we demonstrate that these representations are stable across distinct environments and roles, improving behavior prediction in novel domains. Our analysis reveals that complex idiosyncratic movement policies can be effectively compressed into low-dimensional embeddings, with as few as two dimensions capturing the majority of individual strategic variation. Crucially, the learned latent space forms a structured metric space where Euclidean distances predict the degradation of transfer performance. Furthermore, we show that the latent axes align with interpretable behavioral phenotypes, such as risk-taking and social cohesion. These findings suggest that multi-domain integration is a robust method for uncovering the functional structure of latent individuality in complex decision-making tasks, bridging the gap between high-dimensional telemetry data and meaningful psychological constructs.

Biological rhythms are governed by intricate interactions among oscillatory subsystems, yet how they balance functional demands and energy efficiency remains unclear. We present a bimodal coupling optimization strategy where physiological systems dynamically alternate between synchronized (energy-saving) and desynchronized (function-priority) coupling modes. By employing the water-filling principle developed in communications engineering, we prove synchronized heart rate(HR)-respiration oscillations maximize energy efficiency (oxygen uptake per cardiac work). Then, system modeling confirms task/stress-induced oxygen demands enhance oxygen uptake at the cost of desynchronization and reduced efficiency. Experiments reveal a 70.36% decrease in HR-respiration synchronization during arithmetic versus relaxation, enabling 4.43% higher oxygen uptake but with 11.38% lower energy efficiency. This bimodal coupling optimization strategy is also evident in pancreatic islets, with their insulin/glucagon oscillator alternating between in-phase (energy-saving) and anti-phase (rapid glucose reduction) coupling. This framework, integrating engineering and life sciences, reveals a universal regulatory principle for biological oscillatory systems.

Understanding the structural dynamics of biomolecules is crucial for uncovering biological functions. As molecular dynamics (MD) simulation data becomes more available, deep generative models have been developed to synthesize realistic MD trajectories. However, existing methods produce fixed-length trajectories by jointly denoising high-dimensional spatiotemporal representations, which conflicts with MDs frame-by-frame integration process and fails to capture time-dependent conformational diversity. Inspired by MDs sequential nature, we introduce a new probabilistic autoregressive (ProAR) framework for trajectory generation. ProAR uses a dual-network system that models each frame as a multivariate Gaussian distribution and employs an anti-drifting sampling strategy to reduce cumulative errors. This approach captures conformational uncertainty and time-coupled structural changes while allowing flexible generation of trajectories of arbitrary length. Experiments on ATLAS, a large-scale protein MD dataset, demonstrate that for long trajectory generation, our model achieves a 7.5% reduction in reconstruction RMSE and an average 25.8% improvement in conformation change accuracy compared to previous state-of-the-art methods. For conformation sampling task, it performs comparably to specialized time-independent models, providing a flexible and dependable alternative to standard MD simulations.

Many respiratory pathogens co-circulate within human populations. Yet, how pathogen community structure shapes the dynamics of infectious diseases remains poorly understood. At the population level, investigating polymicrobial dynamics, with potential underlying competitive or cooperative interactions, is challenging, because of confounding factors such as differing seasonality. This is particularly true for endemic pathogens which typically exhibit stable periodic dynamics. Their disruption due to the implementation of non-pharmaceutical interventions during the COVID-19 pandemic thus represents a unique large-scale natural experiment that can be leveraged to provide valuable insights into the complex interplay between respiratory pathogens. Here, we focus on the population dynamics of human rhinovirus (common cold) and on the potential viral interference of influenza A virus (flu A), which is hypothesized to account for their asynchronous circulation. Using a Bayesian framework, we first show based on simulations that exogenous perturbations can be a powerful tool to disentangle the contribution of pathogen interaction from other epidemiological factors. We then apply our framework to long surveillance time series from the US and Canada spanning the COVID-19 pandemic. We estimate key parameters of rhinovirus but find no conclusive support for an influence of influenza A virus at the population level.

Natural populations exhibit complex class structures that profoundly shape evolutionary trajectories. While evolutionary demography provides a formal framework to predict adaptation using invasion fitness, the high mathematical dimensionality of these models often precludes analytical solutions, obscuring biological interpretation and hindering the analysis of long-term evolutionary outcomes. Because current reduction techniques remain fragmented, a unifying theoretical foundation is critically needed. Here, we introduce "structural evolutionary invasion analysis," a systematic framework that integrates two complementary tools to simplify complex life cycles. First, we formulate the "invasion determinant," an algebraic method that yields a direct scalar condition for mutant invasion. Second, we develop the Projected Next-Generation Matrix (PNGM), which structurally compresses life-cycle graphs by eliminating secondary classes. We demonstrate that this reduction is mathematically equivalent to separating dynamical timescales, explicitly preserving Fishers reproductive values for the retained focal classes. Crucially, under the standard assumption of weak selection, our synthesized framework guarantees that all properties of evolutionary singularities--including their location, convergence stability, and evolutionary stability--are strictly identical to those derived from the full, unreduced model. Illustrated with diverse ecological examples, this framework provides modellers with a rigorous and tractable toolkit for decoding state-dependent selection in high-dimensional populations.