Physical Review Research

We propose a novel three-compartment heuristic model that recasts gastric cancer metastasis into a framework of non-equilibrium thermodynamics and nonlinear dynamics. The system, encompassing primary, hepatic, and peritoneal tumor populations, exhibits a well-defined route to chaos: as immune surveillance weakens, the dynamics undergo a supercritical Andronov-Hopf bifurcation, giving rise to a limit cycle, followed by a Shilnikov-type saddle-foci bifurcation cascade leading to chaotic attractors. Our central finding is the introduction of a dissipation function, {Psi}, constructed via a sensitivity-weighted, two-factor ansatz that integrates metabolic flux and dynamical influence. This spatially coarse-grained measure captures the systems thermodynamic robustness. The analysis reveals a dynamical phase transition: while tumor aggressiveness peaks in the pre-metastatic limit-cycle regime, {Psi} emerges as the definitive marker of the chaotic, treatment-resistant metastatic state, quantifying a sharp increase in systemic robustness that correlates decisively with advanced clinical stages (TNM III-IV). Consequently, this work provides a predictive framework grounded in the physics of metastasis, demonstrating that {Psi} not only diagnoses but also defines the primary therapeutic target: the underlying thermodynamic robustness of the metastatic system. Thus, effective intervention must shift from merely reducing tumor mass to strategically destabilizing this robust dissipative structure, thereby preventing recurrence. PACS: 05.45.-a; 87.18.-h; 87.19.xj; 05.70.Ln HighlightsO_LIA novel three-compartment heuristic model reveals phase transitions and chaotic dynamics in gastric cancer metastasis. C_LIO_LIThe dissipation function {Psi} emerges as a quantitative thermodynamic metric of systemic robustness in the metastatic regime. C_LIO_LIDecreasing immune surveillance triggers biological phase transitions towards metastatic disease. C_LIO_LIThe framework integrates nonlinear dynamics with TNM staging, identifying the dissipation function {Psi} as a therapeutic target to overcome metastatic recurrence. C_LI Graphical Abstract O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=102 SRC="FIGDIR/small/702339v1_ufig1.gif" ALT="Figure 1"> View larger version (24K): org.highwire.dtl.DTLVardef@1a605c7org.highwire.dtl.DTLVardef@c56e83org.highwire.dtl.DTLVardef@1da7fc8org.highwire.dtl.DTLVardef@1fb30ba_HPS_FORMAT_FIGEXP M_FIG C_FIG

Dynamical processes on complex networks have a long history of study with increasing applications across many fields. While epidemics in heterogeneous networks have received much attention in terms of how connectivity patterns drive epidemic outbreaks, affect critical thresholds, timescales, final outbreak size and immunization efforts, less attention has been devoted to endemic multi-strain scenarios and questions of selection and coexistence dynamics. Here, we provide an SIS framework for multiple co-circulating strains and co-infection, which can be reduced to a replicator dynamics on a host contact network. Using the analytical tractability of the replicator formalism, we study how network heterogeneity affects multi-strain dynamics, and compare its effects relative to the homogeneous contact distribution, identifying key relevant metrics for comparison. In particular, the pairwise invasion fitness matrix comparison reveals that higher network heterogeneity acts to increase the speed of multi-strain dynamics and typically tends to have stabilizing effects that reduce the number of coexisting strains. While many aspects of the replicator dynamics remain complex to study, especially for high number of strains, the advantage of this model representation lies in the dimensional reduction of a huge system, enabling general, more direct and efficient numerical computations. Furthermore the explicit bottom-up constitution of crucial parameters yields biological and epidemiological insight for critical system transitions across macroscopic gradients and can be used to guide interventions.

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.

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.

In the context of multistability-driven diseases, like cancer, spatio-temporal plasticity plays a significant role to achieve a spectrum of phenotypic variations. The interplay between gene regulatory networks and environmental factors, such as resource competition and spatial diffusion, plays a crucial role in determining cellular behaviour and phenotypic heterogeneity. Though reaction-diffusion frameworks have been widely applied in developmental biology, less attention has been paid to the simultaneous effects of resource competition and growth feedback on spatial organization. In this paper, we observed that a bistable genetic circuit under high resource competition due to growth feedback gives rise to multiple emergent phenotypes, as observed in cancer systems. Furthermore, we observed how spatial diffusion coupled with intrinsic nonlinearity can drive the emergence of distinct spatial dynamics over time. The observed spatiotemporal plasticity can also be driven by the comparative stability of the fixed points, diffusivity, and asymmetry of diffusion. Our findings highlight that growth-induced resource competition combined with diffusion can provide deeper insights into metastasis and cancer progression.

Helicobacter pylori infections present a persistent global health challenge due to increasing antibiotic resistance and the bacteriums ability to survive in the acidic gastric environment. Existing within-host models of H. pylori infection neglect the gastric pH fluctuation, despite its role in modulating bacterial growth and antibiotic efficacy. To address this gap, we extend a published in-host model by explicitly incorporating gastric pH as a dynamic state variable, influenced by three key physiological processes (i) bacteria urease which neutralizes gastric acid to create a protective niche; (ii) host acid secretion response, which attempts to restore baseline acidity; and (iii) dietary perturbations, which induce temporary pH changes. Equilibrium and stability analysis reveal pH-dependent reproductive thresholds [R]s(H) and [R]r(H) that determine the conditions for bacterial persistence and treatment outcome. Successful eradication requires driving both thresholds below unity. Numerical simulations validate distinct clinical scenarios including complete bacterial clearance, resistant strain dominance, stable bacterial coexistence, and oscillatory persistence. These outcomes emerge from the coupled interplay between antibiotic pressure, immune response, and pH regulation. Our model provides a comprehensive theoretical framework for understanding H. pylori treatment failures and highlights how adjuvant pH-modulation strategies could enhance antibiotic efficacy against resistant infections.

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.

The early stages of viral infection constitute a race between viral proliferation and interferon (IFN)-mediated defenses. Recent experiments on single-cell viral kinetics have demonstrated a high degree of stochasticity in the timing of viral release, but how this shapes the competition between virus and host remains unclear. We formulate a stochastic spatial model to address the question of how variability in the release of viral progeny and IFN affect the early infection dynamics. The model distinguishes between two types of timing noise: stochasticity in the initiation of release, and variability in the secretion time of individual virions. Our key result is an asymmetry in how noise affects outcomes: For the virus, stochastic initiation accelerates expansion, while for the host, effective containment via IFN benefits from precisely timed responses. For the secreting states, we find that a broader secretion profile (higher variability in particle release times) is always advantageous. In all cases, we find that stochasticity in signal timing plays a huge/central role in the early infections states.

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.

One of the most critical steps in human reproduction is the selection of the dominant follicle when a single follicle is chosen from a large group of follicles to ovulate. Although this process involves complex hormonal regulation, the complete microscopic picture of unique selectivity remains unclear. We propose a novel stochastic mechanism for dominant follicle selection that incorporates the actions of the most relevant hormones, follicle-stimulating hormone (FSH) and estradiol. Our theoretical picture suggests the following sequence of events. As soon as the FSH concentration reaches the critical threshold, one of the available follicles is randomly selected, which immediately stimulates the production of estradiol, which, via a negative feedback mechanism, suppresses further FSH production, lowering its concentration below the critical threshold. This suppression limits the time window for the possible second follicle selection event, allowing only a single follicle to be selected. Based on this picture, a minimal quantitative theoretical model of dominant follicle selection is developed and analyzed using analytical calculations and computer simulations. Theoretical analysis shows how the interplay between different parameters that govern follicle selection leads to high selectivity. Our theoretical approach can explain some key known observations, providing a quantitative tool for analyzing biological reproduction phenomena.

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.

Cerebrospinal fluid (CSF) circulates around and through the brain, supporting neural homeostasis by regulating the extracellular chemical environment. Yet the physical mechanisms governing CSF-driven solute transport remain poorly understood, limiting the design of diagnostic and therapeutic strategies targeting brain clearance and drug delivery. Pulsatile CSF flow in the cranial subarachnoid space (cSAS), is driven by cardiac, respiratory, and sleep-related vasomotion. Over longer timescales weaker steady flows, such as inertial steady streaming, Stokes drift, and production-drainage flow, may contribute to solute transport, but their role and relative importance remain unclear. Here, we develop a simplified two-dimensional model of CSF flow and solute transport in the cSAS using lubrication theory. Through multiple-timescale and asymptotic analyses, we derive a reduced long-time transport equation in which advection is governed by the Lagrangian mean velocity, incorporating steady streaming, production-drainage flow, and Stokes drift. Analysing three physiologically relevant case studies, we show that steady flows can substantially reshape concentration profiles, enhance dispersion, and alter clearance efficiency. Our results clarify the mechanisms underlying CSF-mediated transport, predict distinct regimes in humans and mice, and highlight the importance of subject-specific physiological parameters when interpreting contrast-agent and intrathecal drug-delivery studies.

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.

Cell-cell adhesion is a key regulator of cancer invasion. In this work, we extend a pre-existing individual based cancer invasion model by introducing a stochastic representation of N-cadherin-mediated adhesion, where the lifetime of a cell-cell bond depends on the pulling force acting on the bond. Using experimental data, we derive expressions for the mean and standard deviation of N-cadherin bond lifetimes and fit them to Gamma distributions, enabling their treatment as force-dependent random variables. These distributions are then used to modify the diffusion coefficient of mesenchymal cancer cells. The model predicts reduced random motility with increasing adhesion and incorporates a dynamic transition between catch- and slip-bond behaviour. Along with this model for cell motility, we propose a preliminary physical framework, that can be used to model pattern formation as a result of the new adhesion mechanic.

Melanoma is a cancer of the melanocyte, known to have an ability to readily switch between different transcriptional cell states that convey different phenotypic properties (e.g. hyper-differentiated, neural crest-like). This ability is believed to underpin intratumour heterogeneity and plastic adaptation, which contributes to resistance to therapy and immune evasion of the tumour. Therefore, understanding the mechanisms underlying acquisition of transcriptional cell states and cell-state switching is crucial for the development of therapies. We model a minimal gene regulatory network comprising three key transcription factors, whose varying gene expression encodes different melanoma cell states, and use deterministic spatiotemporal differential-equation models to study gene-expression dynamics. We exploit an approximation, based on cooperative binding of transcription factors, in which the models are piecewise-linear. We classify stable states of the local model in a biologically relevant manner and, using a naive model of intercellular communication, we explore how a population of cells can take on a shared characteristic through travelling waves of gene expression. We derive a condition determining which characteristic will become dominant, under sufficiently strong cell-cell signalling, which creates a partition of parameter space.

Colorectal cancer (CRC) is the second most common cause of cancer-related mortality. At the molecular level, CRC is associated with genetic mutations and epigenetic modifications that dysregulate various signaling networks. From the biophysical viewpoint, invasive and metastatic cell migration need to be empowered by mechanical forces. In this study, we analyze the dynamic deformation of patient-derived CRC organoids in Fourier space and demonstrate how organoids with protooncogene BRAF mutation exhibit deformation phenotypes at an early stage. The organoids with BRAFmut have significantly lower elasticity and higher viscosity than those with BRAFWT, which mathematically indicated as the weakening of cell-cell adhesion. Immunohistochemical images, qRT-PCR, and TCGA data analysis confirm the downregulation of E-cadherin (CDH1) in BRAFmut organoids as well as in BRAFmut CRC, suggesting that the decrease in cell-cell adhesion in BRAFmut CRC facilitates invasive and metastatic migration. Notably, the recovery of CDH1 expression by pharmacological inhibition of DNA methylation can quantitatively be detected as the change in mechanical properties, suggesting that the complementary combination of dynamic phenotyping, mathematical modelling, and molecular-level analyses has a potential to unravel the mechanistic causality of the critical gene mutation and CRCs prognosis and the response to therapeutic interventions.

The blood vasculature has a high capacity for structural regeneration, driven by the blood endothelial cells (BECs) that comprise it. This regenerative process, which involves BEC migration and proliferation to form these complex tissues, is linked to low frequency (< 0.1 Hz) calcium spiking that precedes these activities. However, we need new approaches to stimulating angiogenic responses in tissue engineering applications. By conducting experiments that manipulate local ionic concentrations and developing a simple, yet powerful, computational analysis, we demonstrate that sodium-calcium cross-talk is a crucial component that regulates the calcium signaling and downstream angiogenic responses. Activation and deactivation of the inositol triphosphate 3 receptors (IP3Rs) on the endoplasmic reticulum (ER) and the switch between forward and reverse modes of the sodium-calcium exchanger (NCX) are proposed to be the key mechanisms underlying calcium oscillations when cells are exposed to temporary cationic depletion. The spiking is suggested to be a release of intracellular calcium mediated by IP3R activity, and transport in or out of the cell is driven by NCX for the calcium oscillatory signaling pattern. The NCX and IP3R both contribute to manage intracellular calcium and ionic concentration as initially there is a long ER deactivation period while intracellular sodium slowly increases until a sudden onset of calcium is released by the ER. Other calcium and sodium ion channels can change this resonant coupling of ER and NCX to alter the inter-spike duration. Synchronization of the spiking intervals between cells is triggered by stimulating with vascular endothelial growth factor (VEGF), which induces a propagating wave of intracellular calcium across the 2D tissue culture, prior to coordinated cell migration and proliferation towards the VEGF source. This wave, which can be artificially induced and studied using electrical stimulation, suggests that the underlying sodium-calcium crosstalk mechanism introduces intracellular calcium polarization, whose orientation is transferred across cells through spike synchronization. Thus, control of calcium signaling dynamics through regulation of ionic depletion can serve as useful method for generating angiogenic responses in engineered tissue constructs.

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.