Physical Review Research

Mechanical properties of epithelial tissues play essential roles in morphogenesis and physiological function. In this study, we analytically derived the in-plane bulk modulus, shear modulus, and Poissons ratio of a three-dimensional cell vertex model of epithelial monolayers. We showed that the model can robustly reproduce a near-zero in-plane Poissons ratio, a mechanical feature reported in cultured epithelial tissues. Numerical simulations further confirmed that the theoretically predicted Poissons ratio accurately describes the response of the model under finite, biologically relevant strains. In addition, the model exhibits not only morphological bistability between squamous-like and columnar-like states, but also mechanical bistability characterized by distinct elastic responses. Together, these results provide a minimal three-dimensional framework that links cell-scale mechanical interactions and epithelial morphology to tissue-scale elastic properties.

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.

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.

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.

Take-off is a fast and energy-efficient strategy for bipedal animals, such as birds, to achieve rapid movement; however, how muscle physiology scales to govern this universal behavior remains unresolved. Research in other species physiologies is not readily applicable. As a result, important questions, whether theropod dinosaurs such as Tyrannosaurus rex were capable of jumping, remain unanswered. In this article, we coupled Lagrangian dynamics with Hills muscle equations and developed new experimental methods to quantify joint rotational stiffness and damping, thereby enabling a systematic description of lower-limb mechanics. The approach establishes a novel kinetic framework that links muscle contractile properties to lower-limb performance without invoking control optimization. Animal observations and tabletop mechanisms validate the framework. The mechanics model reveals that the take-off time of about 0.1 s across body masses of 0.003 to 90 kg is achievable, as heavier birds generate proportionally higher reaction forces. Additionally, Tyrannosaurus rex should be capable of jumping, based on the available physiology data. Beyond evolutionary insights, our framework provides a new methodology for analyzing the mechanical properties of biological joints and informing the design of scalable bio-inspired robots.

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.

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.

Cellular monolayers often exhibit orientational order, with nematic alignment of cell shape and cytoskeletal structures governing tissue-scale collective dynamics. Despite extensive studies, a unified analysis framework for characterizing active nematics in living systems remains partial, and key discrepancies with theory persist. Here, we present a systematic and comparative analysis of nematic order and tissue flow dynamics across twelve distinct cell types. We quantify the impact of analysis parameters and provide data-driven guidelines to improve reproducibility and cross-study comparability. Across all nematic systems, we uncover remarkably consistent static properties, supporting the universality of nematic behavior in living tissues. By combining orientation-field analysis with velocity-field measurements and numerical simulations, we show that all examined systems display contractile active nematic signatures, with characteristic flow structures around topological defects. However, direct tracking of individual defects reveals subdiffusive dynamics, in stark contrast with the superdiffusive, self-propelled motion predicted by the hydrodynamic theory of active nematics. Our results establish a standardized framework for nematic analysis in biological systems and highlight fundamental limitations of current active nematic models in describing defect dynamics in living tissues.

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.

A major challenge in neuroscience is to predict how currents in nanodomains affect voltage and ionic concentrations. Cable and Rall theory provide analytic current-voltage relations by neglecting concentration gradients, and the impact of concentration gradients is usually studied numerically with the Poisson-Nernst-Planck (PNP) model. A precise quantitative understanding of the combined dynamics remains limited because analytic current-voltage-concentration relations are missing. In this work we derive such relations using a novel approach based on cross-diffusion equations. For narrow cylindrical domains, we derive time-dependent and steady-state expressions that explicitly show how currents affect voltage and ionic concentrations. We find that the influx of only one ion can significantly change the concentrations of all the other ions even if no channels for these ions are present. After a current injection we compute a biphasic voltage transient where the small-time asymptotic corresponds to the steady-state solution of the cable equation. We show that the accuracy of cable theory prediction for the voltage depends on how the current is distributed among the various ions. Finally, we develop an iterative method to accurately compute steady-state profiles for voltage and concentrations using first-order results by subdividing a cylinder into small segments.

AO_SCPLOWBSTRACTC_SCPLOWTransitions between stable states are a defining feature of nonlinear dynamical systems, yet the factors controlling their probabilities and timescales remain poorly understood in non-conservative settings. In many theoretical frameworks, such control is commonly interpreted in terms of potential depth, a concept that becomes ambiguous outside equilibrium. By analyzing a gene regulatory network associated with breast cancer subtypes, we uncover a geometric framework in which the phase-space distance between stationary states, together with the bifurcation structure organizing multistability, provides a robust and well-defined determinant of transition probabilities, times, and variability. Our results show that the coexistence of stable states is only a necessary condition for transitions, while their accessibility is constrained by geometric features of the underlying state space. Within this framework, we find that the HER2+ regime exhibits dynamical robustness to intrinsic parameter variations, whereas the TNBC regime displays strong sensitivity and amplified variability. These differences emerge naturally from the geometric organization of the bistable region and offer a dynamical explanation for the pronounced heterogeneity observed in TNBC. Together, our results establish a general geometric perspective on transitions in non-conservative regulatory networks, with implications for understanding phenotypic plasticity in complex biological systems.

The primary morphological transition in Hydra regeneration, from an initially quasi-spherical tissue fragment to an elongated body, the hallmark of a mature Hydra, is preceded by a prolonged period of modest shape changes. Here, we ask whether this early stage already contains signatures of morphogenetic organization consistent with canalization toward the main morphological transition. We analyzed shape fluctuations during this period in tissue fragments with different initial and physiological conditions. Using principal component analysis, we quantified the effective dimension of the dynamical morphological fluctuation modes. We find that this effective dimension decreases progressively during the preparatory stage, well before the onset of significant elongation, indicating a progressive restriction of the accessible fluctuation manifold. This decrease is not explained by a single global measure of shape and persists when early and late states are compared at approximately matched shapes. We further show that calcium activity is associated with both the visible morphological changes and this hidden dynamical state. Tissues retaining positional cues from the parent Hydra exhibit lower effective dimensions, whereas tissues lacking such cues or subjected to mechanochemical perturbation maintain higher effective dimensions. These results identify an early, hidden dynamical phase of canalization in Hydra regeneration.