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.

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.

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.

Arterial thrombosis is initiated when mechanical forces in flowing blood exceed the activation thresholds of platelets and von Willebrand factor (vWF). Despite extensive experimental characterization of shear-induced platelet aggregation, a unified theoretical framework that maps hemodynamic forcing onto clot nucleation is lacking. Here we present Force-Gated Thrombosis (FGT), a non-equilibrium mechanical theory that treats thrombus formation as a continuous phase transition driven by an effective mechanical forcing {Sigma} ={sigma} + |{nabla}{sigma}| + {beta}{varepsilon}, which combines local wall shear stress{sigma} , shear gradient |{nabla}{sigma}|, and extensional strain rate{varepsilon} . We introduce a dimensionless Thrombosis Number {Theta} = ({Sigma}/{Sigma}c)(P/P0)m(C/C0)n, which incorporates platelet concentration P and coagulation factor concentration C, and governs the transition between stable flow ({Theta} < 1) and active clot growth ({Theta} > 1). The thrombus density is represented by a scalar order parameter{varphi} whose dynamics follow a Ginzburg- Landau free energy functional. For a simplified stenosed artery we derive an analytic closed-form thrombosis onset criterion and a critical flow rate [Formula], where{delta} is stenosis severity. Linear stability analysis shows that perturbations grow at rate{omega} (k) = {Lambda}({Theta}) - D{varphi}k2, becoming unstable when {Theta} > 1. Near threshold the clot volume fraction scales as{varphi} [~] ({Theta} - 1)1/2, a mean-field critical exponent consistent with Ginzburg- Landau theory. Systematic comparison with fifteen published experimental and computational datasets spanning shear rates from 100 to 15,000 s-1 confirms that FGT correctly predicts the existence, location, and approximate severity of pathological thrombus formation across diverse vascular geometries. The theory provides a quantitative bridge between single-molecule mechanobiology and macroscale clinical thrombosis, and yields experimentally testable predictions distinguishing FGT from purely biochemical models.

Cell migration is fundamental to various biological processes, including morphogenesis, wound healing, and cancer metastasis. Durotaxis--directed migration of cells in response to spatial variations in stiffness--has been extensively studied using engineered substrates with prescribed stiffness. However, recent work has increasingly shifted toward understanding cell migration in fibrous matrices that can be actively remodeled by the actomyosin contractility, as commonly observed in tumor and epithelial cells. Despite these advances, a theoretical framework explaining how cells structurally remodel their surrounding matrix to promote their own durotaxis, and which cellular forces govern this behavior, remains elusive. To address this gap, we developed a biomechanical model in which polarized cells contract and migrate over a fibrous matrix. Using this model, we first confirmed that cells on an externally strained matrix preferentially migrate along the direction of applied strain. Then, we investigated how cells autonomously remodel the matrix to create stiffness patterns favorable for durotaxis. In the presence of intercellular adhesion, cells acted collectively to stiffen the matrix, after which a small subset of cells escaped the main population and migrated outward. This behavior is reminiscent of intravasation during cancer metastasis, where cohesive cell clusters generate local matrix remodeling that facilitates the departure of more motile subpopulations. These results illustrate how matrix stiffening driven by cell cohesion and contractility regulates durotactic behavior and provide mechanistic insight into collective invasion processes relevant to cancer metastasis.

During vertebrate development, the flat surface of the gut epithelium undergoes a dramatic transformation into densely packed arrays of finger-like projections called intestinal villi. Recent studies show that the villus formation relies on a tissue dewetting process, in which mesenchymal tissues buckle the overlying epithelial layer into periodic folds. However, the mechanisms driving subsequent elongation of these folds into finger-like villi remain largely unexplored. Here, we propose a simple mechanism for villus elongation that couples tissue dewetting to cell differentiation, which emerged as a repeated outcome of multiple independent simulations of an evolutionary-developmental Cellular Potts Model. In this mechanism, a liquid-like mesenchymal tissue continuously differentiates into a solid-like mesenchymal tissue at the interface between them. This differentiation drives the liquid-like tissue to continuously retract from the solid-like tissue in the opposite direction of the interface through dewetting, ultimately creating a finger-like projection. A merit of our proposed mechanism is that it only requires two tissues with different viscosities, high surface tension, and cell differentiation. We develop a simplified phase-field model to determine exactly how villus morphology depends on these three requirements. Since these requirements are satisfied not only in intestinal villi but also in many other developing tissues, we propose that the same mechanism could also drive the elongation of other tissues.

Understanding how biological shape and movement interact with surrounding fluids represents a fundamental challenge at the intersection of biology, physics, and engineering. Fish locomotion exemplifies this challenge: body morphology and swimming kinematics together determine the hydrodynamic forces and flow structures that enable efficient propulsion and maneuverability. Whereas biologists have long sought to connect morphological variation to swimming performance, traditional morphometric approaches provide limited insight into the fluid mechanical consequences of shape differences. Similarly, although computational fluid dynamics can reveal detailed flow physics, simulating hydrodynamics across diverse and dynamic morphologies remains prohibitively expensive for systematic investigation. To bridge this gap, we introduce a data-driven framework that connects fish body shape dynamics to hydro-dynamic performance through compact morphospace parameterization and reduced-order modeling. Using CFD simulations of 15 fish species from the Digital Life Project database (www.digitallife3d.org/3d-model), we generate hydrodynamic datasets capturing the shape-flow relationship. Principal Component Analysis (PCA) extracts four dominant shape parameters from dorsal body profiles, which are then integrated into an Inverse-Design with Dynamic Mode Decomposition (ID-DMD) framework to model the resulting fluid dynamics. The resulting modal analysis suggests that locomotion strategies emerge from specific shape-flow interactions. We further demonstrate the frameworks utility through single- and multi-objective shape optimization, showing how it enables efficient exploration of the morphology-hydrodynamics relationship. This approach offers a novel analysis and design tool for understanding how biological form and motion interact with fluid mechanics, with applications ranging from bio-inspired vehicle development to evolutionary biomechanics.

1Although resources are typically distributed continuously in space, species distributions often organize into discrete clusters. In his seminal paper [36], Turing demonstrated that such clusters can spontaneously arise in population densities, even when populations evolve in environments with continuously varying conditions. This phenomenon is known as Turing instability. In this work, we focus on two models grounded in population dynamics: a one-dimensional model based on the nonlocal Fisher-KPP equation, and a two-dimensional model involving an environmental gradient. We show that phenotypic clusters (sometimes referred to as "species") emerge in these models. We prove that they do not emerge because of Turing instability, but because of stochasticity, and that they disappear when stochasticity is reduced. First, for both models, we start our simulations with initial populations uniformly distributed in the state space. We show that phenotypic clusters quickly emerge and that the distances between them depend on the population size, that is, on the degree of stochasticity. Next, we start from already clearly defined phenotypic clusters. We identify three regimes in the connection between population size, the initial distances between clusters, and the distances between clusters at equilibrium. Last, on the two-dimensional model, we relax the hypothesis of complete clonality by varying the effective recombination rate, explore its effect on phenotypic clustering, and show that phenotypic clustering decays drastically with slight recombination.

The awake brain is known to display asynchronous (AS) states during periods of attention and arousal, but the responsiveness properties of such states remain unclear. Here, we investigate this question using computational models of spiking networks of excitatory and inhibitory neurons, mimicking recurrently-connected networks in layer 2/3 of the cerebral cortex. The networks can generate a continuum of AS states, but with different responsiveness characteristics. By using a mean-field model to infer the dynamic properties of the system, we find that there are two families of AS states, which we call "underdamped" (UD) and "overdamped" (OD). Responsiveness is maximised at the transition between OD and UD states, which identifies a "working point" that may present advantageous computational properties.

Neural oscillations are thought to play a central role in encoding and transmitting cognitive information across large-scale brain networks, yet the relative contributions of phase synchrony and amplitude co-modulations to distributed coding remain unclear. A key obstacle is the absence of tools that can simultaneously quantify task-relevant information in the frequency domain and disentangle its phase and amplitude components across pairwise and higher-order interactions. Here, we introduce a spectral partial information decomposition framework (named NeOPID) for quantifying information about cognitive variables in power and phase contributions, and to quantify redundant and synergistic information in brain relations, from pairwise to higher-order interactions. We validated the approach on Kuramoto and Stuart-Landau oscillator networks, including a whole-brain model constrained by macaque anatomical connectivity. NeOPID accurately recovers ground-truth encoding schemes and reveals that phase relations and amplitude co-modulations act as complementary coding channels with both redundant and synergistic components. NeOPID further extends this decomposition to higher-order functional interactions enabling the characterization of how cognitive information is collectively distributed across multiple oscillatory edges via redundant and synergistic encoding. To illustrate biological applicability, we applied NeOPID to local field potentials (LFPs) recorded from the macaque fronto-parietal network during a working memory task. In this dataset, NeOPID identified beta-band amplitude co-modulations as the primary carrier of stimulus information, and revealed that higher-order phase interactions exhibit both redundant and synergistic structure during the memory delay. These results establish NeOPID as a principled tool for dissecting the informational architecture about cognitive processes of oscillatory brain networks.

The Poisson-Nernst-Planck (PNP) system is an accurate model of electrodiffusion of ionic species. It is commonly used in situations where nanoscale resolution is required, for instance close to ion channels in the membranes of biological cells. The inherent stiffness of the equations has made them challenging to solve and has limited the applicability of the system. In particular, the time step required for stable solutions has typically needed to be very short (nanoseconds), which makes simulations on the time scale of an action potential (milliseconds) difficult. Recently, it has been observed that avoiding operator splitting and instead solving the concentration equations and the electrostatic equation in a coupled manner relaxes the time-step limitation considerably. However, no theoretical explanation of this observation has been provided. Here, we aim to explain why the coupled scheme allows much larger time steps. We illustrate the mechanism by considering special cases that define necessary, but not sufficient, conditions for stability. We also show that these conditions remain relevant for the fully coupled PNP model in 3D.

Embryonically, the vertebrate brain begins as an approximately uniform, fluid-filled epithelial tube that undergoes rapid volumetric expansion and regionalization to form the morphologically distinct primary brain vesicles. Hydrostatic pressure from fluid secretion into the inner lumen generates tension in the neural tube that has been implicated as a potential driver of cell proliferation during these early stages of brain development. However, a quantitatively rigorous view of 3D morphology and cellular proliferation has remained elusive. Here, we provide a standardized mapping for the mechanical and biological landscape of the developing neuroepithelium along anatomical axes. Using this 3D morphometric framework in chicken embryos, we show that localized curvature characterizes compartmental boundaries. While rapid inflation would typically be expected to stretch and thin the epithelium, we find the opposite: global expansion is coupled with significant tissue thickening, identifying the early brain as an active shell. Moreover, spatial patterns of thickness remain invariant to local curvature. Our results demonstrate a decoupling of geometry and growth, showing that spatially stable distributions of tissue thickness and mitotic activity are maintained throughout massive volumetric expansion, independent of the dramatic geometric reorganization driven by luminal pressure. We conclude that, while tension in the neuroepithelium may contribute to proliferative growth at some level, biological pre-pattern likely plays a driving role in the regionalized expansion of the early embryonic brain. Why it mattersThe embryonic brain begins as a simple fluid-filled tube that undergoes rapid and heterogeneous expansion to set up the basic organizational plan of the adult brain. Errors in this process are linked to severe neurological and congenital disorders. This work investigates the biophysical basis of expansion and regionalization of the early brain, a complex three-dimensional process driven by inflation from internal fluid pressure together with active cell behaviors that ultimately produce regionally distinct growth and curvature profiles amid a complex mechanical landscape. Graphical Abstract O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=200 SRC="FIGDIR/small/726048v1_ufig1.gif" ALT="Figure 1"> View larger version (49K): org.highwire.dtl.DTLVardef@17c442forg.highwire.dtl.DTLVardef@1609374org.highwire.dtl.DTLVardef@170c00corg.highwire.dtl.DTLVardef@15080ad_HPS_FORMAT_FIGEXP M_FIG C_FIG

Cells communicate via extracellular ligands, such as hormones, which bind to plasma membrane receptors and trigger intracellular signaling cascades. G Protein-Coupled Receptors (GPCRs) exemplify this mechanism by initiating signaling both at the cell surface and, from intracellular compartments such as endosomes. The kinetics and spatial localization of these signals are critical determinants of cellular responses, yet receptor trafficking-including internalization, endosomal sorting, and recycling-remains a pivotal but often overlooked component of theoretical GPCR models. In this study, we present a mathematical framework that integrates receptor trafficking and signaling compartmentalization into generic GPCR dynamic models. Using a compartmentalized approach based on systems of ordinary differential equations (Chemical Reaction Networks), we analyze how receptor internalization and recycling modulate ligand-induced responses. Our results show that the balance between plasma membrane and endosomal signaling can significantly enhance or diminish ligand efficacy. Calibrated with high-throughput kinetic data, our model offers a refined tool for ligand pharmacological characterization and advances the understanding of GPCR signaling spatial organization.

Hippocampal adult neurogenesis (HANG) is a highly regulated process where neural stem cells progress through distinct stages--from Type 1 radial glia-like cells to mature neurons--via a complex series of proliferative and differentiative divisions. While recent in vivo imaging has provided valuable insights to cellular processes, the exact relationship between individual cell-fate decisions and long-term population stability remains difficult to quantify empirically. In this study, we utilized an agent-based (AB) model to simulate the stochastic dynamics of the hippocampal neurogenic niche. Our results demonstrate that while individual progenitor lineages exhibit high variability and probabilistic division symmetries (proliferative symmetric, asymmetric, and differentiative symmetric), the system achieves deterministic stability as the initial progenitor density increases. We found that the T1 progenitor pool follows a negative exponential decay profile, with its longevity primarily dictated by the differentiation rate (d,0). Critically, the terminal output of immature neurons (CIN,t) was non-linearly coupled to the proliferative capacity of transit-amplifying cells (pp,0); even marginal increases in symmetric proliferative divisions resulted in an exponential expansion of the neuronal pool. These findings suggest that the homeostatic maintenance of the hippocampal niche is governed by a kinetic tuning of division probabilities, providing a theoretical bridge between single-cell stochasticity and robust tissue-level output.

Cell migration plays a central role in numerous physiological and pathological processes and emerges from the coordinated interplay between intracellular force generation, adhesion dynamics, and mechanical interactions with the environment. A minimal, mechanistically grounded understanding of these processes is required to disentangle the respective contributions of cell-intrinsic and environmental cues. Here, a two-dimensional in silico cell motility model is introduced to describe mesenchymal migration driven by intracellular traction forces generated within actin-rich protrusions anchored to a substrate. The model explicitly accounts for adhesion nucleation, maturation, force buildup and rupture, and relies on a small set of physically interpretable parameters. A systematic mechanical analysis identifies parameter regimes that permit effective cell translocation and delineates conditions leading to stalled or mobile cells. Within motile regimes, the model reproduces a broad spectrum of cell morphologies and migratory behaviours. In particular, cell trajectories exhibit the statistical features of a persistent random walk, with a crossover from ballistic to diffusive motion that arises solely from adhesion dynamics and force balance, without imposing polarization or directional bias. Cell morphology is shown to strongly regulate migration speed, persistence, and pausing behaviour. Altogether, this model provides a minimal reference framework for cell migration on non-deformable substrates and establishes a baseline for future studies of mechanically driven guidance. By construction, it is well suited for extension to deformable fibrous substrates, where cell-induced matrix remodeling and stiffness feedback are expected to bias migration and regulate cell encounters relevant to tissue morphogenesis and anastomosis.

Neuronal computation depends on the balance between excitation and inhibition, yet how this balance is implemented across the dendritic tree remains unclear. Classical views predict that inhibition should be most effective near the soma or along the path from excitation to output, but many interneuron subtypes preferentially target remote dendritic compartments. This apparent paradox is sharpened by active dendrites, where local NMDA spikes, calcium plateaus and backpropagating action potentials can make distal branches powerful contributors to somatic firing. Here we develop an analytical framework that extracts general principles of inhibition from biophysically detailed multi-compartment simulations. By reformulating the implicit voltage update of detailed neuron models as a matrix recursion, we derive exact voltage sensitivities to inhibitory synaptic perturbations. This leads to a unified {Phi}-a law: the somatic impact of inhibition factorizes into a global dendritic susceptibility term and a local synaptic perturbation term. Using this law to map inhibitory leverage and identify optimal inhibitory interventions, we show that active dendritic excitation can shift inhibitory hot zones from perisomatic regions toward distal or intermediate compartments. Across neocortical, hippocampal and striatal neuron models, the same response law explains convergent inhibitory strategies despite distinct cellular mechanisms. Our framework turns detailed numerical simulation into analytical theory, providing a general principle for how diverse dendritic inhibition controls active neurons.

Multivalent ligand-receptor interactions underlie most forms of cell-cell communication, yet a general quantitative framework for "avidity" has remained elusive for over a century. Here, we derive closed-form expressions for signaling potency (EC50) in multivalent systems directly from first principles, extending exact analytical models of ternary complex equilibria to account for receptor confinement at cell surfaces. These equations unify antibody-antigen and cytokine-receptor interactions under a common mathematical framework in which potency emerges as a function of binding constants and receptor density. In contrast to monovalent models, EC50 is no longer equal to the dissociation constant (Kd), but instead reflects receptor-dependent avidity effects that vary across cellular contexts. We validate these predictions across biophysical measurements, in vitro binding and signaling assays, in vivo murine cytokine perturbation data, and human spatial transcriptomic datasets. The framework explains longstanding empirical observations, including enhanced antibody potency through avidity and asymmetric control of cytokine signaling by receptor subunits. By embedding these equations within a regression-compatible formulation, we enable inference of signaling drivers from single-cell and spatial transcriptomic data. This work establishes a mechanistic bridge between molecular binding, receptor context, and tissue-level signaling, providing a quantitative foundation for interpreting and modeling intercellular communication in health and disease.

A longstanding puzzle in cortical research is how the cerebral cortex, having largely uniform interconnected architecture, gives rise to such diverse yet highly structured spatiotemporal activity. Here, we propose that local cortical networks distance from criticality (DTC) provides a unifying principle related to this conundrum. Analyzing resting-state fMRI BOLD signals and leveraging simple network models of randomly connected recurrent units, we show that DTC robustly explains key dynamical features, in particular, local power spectra and functional connectivity, across the full set of 360 cortical areas. Our analysis shows that a rank-order distribution of DTC values is highly conserved across subjects. Moreover, the empirical analysis of cortical slow dynamics and its fitted network simulations demonstrate similar power-laws across hierarchies of the cortical sheet. These results suggest that recurrent neuronal networks, operating close to criticality, can generate a remarkably rich dynamical repertoire which fit the entire range of experimentally observed cortical dynamics. Our findings underscore the importance of DTC as a powerful, fundamental generator underlying the spectrum of diverse cortical dynamics. HighlightsO_LISpontaneous (resting-state) activity in the human cortex is shown to be organized along a conserved spatial gradient of distance from criticality (DTC), with regions exhibiting a stable cross-individual rank order along this axis. C_LIO_LIMulti-subject fMRI data of regional power spectra and functional connectivity can be fitted with a single parameter simulation model based on DTC. C_LIO_LIQuantitative estimation of the DTC across cortical regions can be achieved using a simple sparse recurrent neural network model. C_LIO_LIThe model fits the power spectra of low frequency fluctuations and the distribution of functional connectivity. C_LIO_LIShape collapse analysis of the power spectrum demonstrates a universal profile across the resting cortex depending only on the DTC. C_LI

Cerebellar neural circuit dynamics rely on a rich repertoire of synaptic and excitability mechanisms, which are thought to determine network computation in physiological and pathological conditions. In this work, we develop and validate a biologically-grounded spiking neural network of the cerebellar cortex, embedding key mechanisms of cellular excitability and synaptic transmission, and assess their impact on signal processing. Neuronal input-output functions, short-term synaptic plasticity, receptor-specific kinetics, and NMDA channel voltage-dependent gating were calibrated against detailed multicompartmental models through automatic tuning procedures. Incorporating these realistic biological properties allowed the network model to simulate key features observed in recordings from acute cerebellar slices. The neuronal discharge and local field potentials elicited by mossy fiber stimulation faithfully reproduced the natural patterns with millisecond precision. Then, selective receptor switch-off revealed the contribution of NMDA, GABA, and AMPA receptors to the frequency-dependent input-output function of the granular layer and Purkinje cells, linking previous empirical findings to specific synaptic mechanisms. This model combines high computational performance with biological realism and offers a computationally efficient framework to investigate neurophysiological phenomena and the neural correlates of behavior in large-scale long-lasting simulations, such as those needed to address the neural underpinnings of learning and of cerebellar pathologies.

The routing of information across the brains structural network is central to its wide range of functional capabilities. However, the mechanisms underlying information routing in complex brain networks, particularly between regions that do not share a direct anatomical connection, remain poorly understood. Neural mass models (NMMs), a computational modelling framework capable of capturing complex neural dynamics across scales, can potentially be used to study the dynamical and network bases of these vital polysynaptic routing processes. In this study, we investigate polysynaptic signalling in three widely used NMMs, obeying Ornstein-Uhlenbeck, Stuart-Landau, and Jansen-Rit dynamics, by tracking the propagation of a discrete, focal, high-amplitude perturbation across the underlying network. We find that polysynaptic propagation emerges in all tested NMMs when configured within dynamical regimes that effectively enhance the persistence of perturbations. We also find distinct parameter domains that maximise signal propagation to directly connected regions and to those separated from the source by at least two hops. Finally, we benchmark in silico stimulus propagation in the brain network against an empirical dataset of direct electrical stimulation trials, to explore the relative capabilities of the NMMs in capturing signal propagation to connected versus unconnected regions. This analysis highlights the significance of dynamical repertoire in capturing stimulus propagation outcomes. Overall, this study provides insights into how dynamical and network features shape signal propagation over complex brain networks.