Physical Review Research

Radiation-induced DNA double-strand breaks (DSBs) drive cellular mortality, mutagenesis, and severe evolutionary bottlenecks. While classical phenomenological models, such as the Linear-Quadratic (LQ) framework, reliably predict macroscopic population survival, they obscure the intrinsic single-cell stochasticity that governs critical rare events like tumor recurrence or the emergence of radioresistant persisters. To bridge this divide, we develop a mathematically exact stochastic differential equation (SDE) framework that models continuous DSB induction and repair as a Feller square-root process. By deriving exact closed-form expressions for the foci moments, we establish a highly efficient Maximum Likelihood Estimation (MLE) pipeline that circumvents computationally exhaustive Monte Carlo simulations, allowing the direct extraction of deterministic repair velocities and intrinsic molecular noise from empirical single-cell $\gamma$-H2AX data. Integrating this kinetic model with a cumulative damage hazard via the Feynman-Kac formalism, our framework seamlessly recovers the classic macroscopic LQ survival topology from microscopic first principles. Furthermore, systematic sensitivity analysis uncovers a fundamental evolutionary duality: while initial physical damage operates additively, ultimate cellular fate is driven by a nonlinear survival response governed by the trade-off between the damage hazard rate and intrinsic molecular noise strength. Crucially, we demonstrate that this molecular noise inherently enhances population survival. Governed by Jensen's inequality, stochastic variance acts as a non-genetic bet-hedging mechanism that buffers the population by favoring cells with transiently low damage loads. Ultimately, this exact stochastic framework bridges microscopic biophysics and macroscopic demographics, offering deep mechanistic insights into the evolutionary roots of radioresistance.

The collective spatial phenomenon of complement protein opsonization on nanoparticle surfaces is a key component of the immune response to viruses, engineered nanoparticles, and diseased cells. Recent work showed this opsonization follows a sharp, percolation-like transition versus the spacing d between surface-bound attachment sites, leaving two open questions: 1) whether the transition exhibits hallmarks of true criticality, such as diverging susceptibility, and 2) whether it can be distinguished from an alternative first-order cooperative (Hill-type) process producing an equally sharp threshold without true criticality. Here, we resolve both questions using a hierarchical statistical-mechanics treatment spanning stochastic, mean-field, and spatial reaction-diffusion models. The variance of two order parameters, peak complement activity and activation lifetime, diverges near threshold and sharpens systematically with system size, the defining signature of a critical point rather than a smooth cooperative response. Extending the analysis across site spacing and intrinsic kinetic rate constants traces a two-dimensional locus of critical points with consistent critical exponents throughout, establishing a single, robust universality class. The mean-field dynamic exponent for activation lifetime agrees quantitatively with the exact value predicted for the general epidemic process. Finally, a reaction-diffusion model of the nanoparticle surface shows the critical locus is set by a diffusion-limited length scale, establishing complement percolation as a fundamentally transport-limited surface reaction. These results place complement activation within the percolation universality class and identify the physical parameters, diffusion, catalysis, and decay, that govern its critical threshold, with direct implications for rational design of complement-evading nanomaterials, immunology, and evolutionary biology.

Classical neurogeometric models describe the primary visual cortex as a fibered structure in which retinal position and local orientation are coupled through the geometry of the roto-translation group. We extend this approach to the visuomotor cortex by modeling it as an assemblage of visual and motor cortical geometries. The model combines orientation-selective representations, analogous to those of the primary visual cortex, with movement-direction-selective representations, analogous to those of the primary motor cortex, in order to describe the mixed visual and motor selectivity observed in the visuomotor cortex. We introduce a coupled visuomotor structure in which visual orientation and motor direction coexist over a common spatial plane and interact through a relative-orientation constraint. Neural responses are modeled by orientation- and direction-dependent profile functions, and preference maps are obtained from vectorized population responses. Numerical simulations generate visual, motor, and mixed visuomotor response maps. A competition rule between visual and motor responses produces incidence ratios close to experimental observations in macaque visuomotor cortex. This framework provides a first neurogeometric approximation of visuomotor functional architecture and a mathematical setting for studying visually guided action.

A fundamental biological process of transcription occurs in the cell nucleus, which is a complex medium that also contains multiple heterogeneous structures known as biomolecular condensates. Interestingly, some of these condensates contain mRNA molecules in addition to proteins, suggesting an important cellular role in transcription that is not yet well understood. In this work, we develop a minimal theoretical framework for quantitative investigation of the role of reversible mRNA condensation in transcription. Our discrete-state stochastic approach accounts for the most relevant processes, allowing us to explicitly evaluate the properties of the system and clarify the effects of condensation. Analytical calculations supported by computer simulations suggest that reversible mRNA condensation influences the transcription processes by maintaining a constant level of free mRNA in the nucleoplasm while lowering the degree of stochastic noise and increasing the robustness against external perturbations. Physicochemical arguments are presented to explain these observations. The proposed theoretical framework elucidates important microscopic aspects of transcription, providing a convenient quantitative tool for investigating complex biological phenomena.

Mechanical properties of biological tissues, driven by passive and active forces, play a vital role in several processes ranging from development to cancer metastasis. However, the dynamical responses of cells in tissues, subject to mechanical deformations such as shear and the associated rheological properties, are not well characterized. Here, we use three-dimensional agent-based models for normal and cancer tissues to investigate their responses to simple shear as a function of cell stiffness and stochastic active forces. In the normal epithelium, with uniform strength of active force, the yield stress as a function of shear rate follows the Herschel-Bulkley form over a range of cell volume fraction. Strikingly, the shear rate dependence and the elasticity-dependent changes in the yield stress fall on master curves upon suitable scaling. To model cancer-like behavior, a certain fraction (Np) of cells was chosen to have enhanced activity and decreased stiffness. As Np increases, the extent of collective cell movement decreases, transitioning from affine (collective) to non-affine (individualistic) movement, a finding that is in accord with imaging experiments. Simulations of a model of a stiff solid tumor, with radius Rs embedded in normal tissue, show that as Rs increases, the yield stress increases. Interestingly, the cells migrate collectively as Rs increases. A Gaussian Mixture Model (GMM) and a mean field theory quantitatively account for the simulation as well as experimental results on cancerous, non-cancerous, and a mixture of these two types. The combined theoretical and experimental study establishes that heterogeneity in stiffness and activity determines non-affine movements in normal and cancer tissues.

The study of tissue dynamics has been stimulated during the last decades thanks to the use of quantitative descriptions, with the development of several theoretical and computational frameworks, many of them revolving around the notion of reaction-diffusion systems, eventually with additional structure variables beyond time and space. The use of structure variables can accommodate phenotypic traits. In this work, we study a family of competition models, where a given population depends on a resource (e.g. oxygen) and several populations are competing for it. Our quantitative description incorporates phenotypic traits and heterogeneity at the level of cell cycle variations, which influence replication rates via oxygen consumption. This enables us to replicate the fitness of specific subpopulations to environmental conditions (e.g. oxygen shortage or external influences). Using numerical simulations, we show that such models display dynamical pattern formation in the form of coupled travelling wave profiles that expand or retreat at the same wave speed. The full theoretical analysis of such dynamics is quite involved; to circumvent this difficulty, we introduce a quasi-stationary approximation for the resource dynamics. We find that this approximation can reproduce the overall behaviour very accurately, with the additional benefit of allowing theoretical treatment of the reduced model. In this way, we provide estimates on the wave speed which are numerically shown to be robust across a wide range of macroscopic parameters of the full model. The wave speeds are thus found to depend strongly on the proliferation rate of the fittest population, resembling a winner-takes-all dynamics.

Contact inhibition of proliferation (CIP) enables epithelial tissues to self-regulate growth and maintain tissue homeostasis. However, how cell-level mechanical contact, tissue-scale structural order, and proliferation kinetics interplay remains a fundamental open question in living matter physics. Here, we present a particle-based model of a confluent epithelial monolayer governed by overdamped dynamics, where individual cells interact via a two-dimensional hard core- soft shoulder potential. By comparing structural evolution during quasistatic densification with previously reported experimental division kinetics, we find that the dynamics of proliferation arrest mimics the onset of direct steric contacts between the hard cores of the shell. Identifying hard core contacts as the physical driver of CIP, we couple our mechanical model with a stochastic Monte Carlo division scheme in which the instantaneous division rate decreases to zero from an intrinsic value as the number of hard core contact increases to six from zero. We demonstrate that for high intrinsic division rates, the cellular densification outpaces mechanical relaxation. This kinetic mismatch drives premature hard-core contact formation, shifts the onset of jamming and contact inhibition to lower packing fractions, and induces increasingly disordered transient configurations before the tissue universally converges to a hexagonal close-packed limit. Our model's predicted division kinetics and structural order evolution are consistent with epithelial monolayer experiments, both reported and our own. This minimal physical framework links single-cell steric contact mechanics directly to tissue-scale growth regulation and structural evolution.

Fingertip friction plays a central role in tactile exploration and object manipulation. During sliding, tangential force depends jointly on the real contact area and the interfacial shear stress, both of which can be influenced by sliding conditions. However, changes in fingertip friction are often interpreted primarily through changes in real contact area, whereas the accompanying changes in interfacial shear stress remain less well characterized. This gap is especially relevant for electrostatic surface haptic displays, which modulate fingertip friction by applying a voltage between the finger and the touch surface. Here, we experimentally quantify the mean interfacial shear stress of a sliding fingertip on an electrostatically actuated touchscreen using simultaneous measurements of tangential force and optically resolved real contact area. Ten participants performed sliding trials across three speeds and three normal forces with and without electrostatic actuation. Interfacial shear stress increased with speed and decreased with normal force; in both cases, these trends arose because real contact area varied more strongly than tangential force. Electrostatic actuation further reduced interfacial shear stress, as increasing voltage produced a larger increase in real contact area than in tangential force. These findings show that interfacial shear stress varies systematically with sliding conditions and electrostatic actuation, clarifying how changes in real contact area and interfacial shear stress combine to shape fingertip-surface friction.

Electrostatic actuation is an emerging technology for generating tactile sensations on capacitive touchscreens through voltage-induced attractive forces between a fingertip and the surface. However, accurate control of electrostatic attraction during natural touchscreen interactions remains challenging because the applied normal force and sliding speed continuously vary, and their effects on the fingertip-screen contact and resulting actuation strength are not fully characterized. Here, we show how normal force and sliding speed systematically alter fingertip- screen contact area and electrical impedance, and use these measured changes to estimate electrostatic attraction during sliding. Contact area, interaction forces, and electrical impedance were measured simultaneously as participants slid their fingertips across an electrostatic surface under systematically varied normal forces and sliding speeds. These measurements revealed condition-dependent changes in fingertip contact, electrical interaction impedance, effective capacitance, derived effective gap thickness, and electrostatic attraction. We then incorporated these measured contact quantities into a physics-informed, data-driven model based on parallel-plate capacitor theory, in which effective capacitance, apparent contact area, and effective voltage determine the estimated electrostatic attraction. The resulting model links force- and speed-dependent changes in these quantities to electrostatic attraction while accounting for inter-participant variability through a participant-specific scaling factor. These findings provide experimentally grounded guidance for designing electrostatic surface-haptic feedback and future adaptive control strategies under realistic touch conditions.

Within the studies of stochastic gene expression, apart from the variability of copy number of gene products, the problems of threshold crossing of those products are biologically important as they often lead to terminal cellular events. Here, we study the threshold crossing problem of the messenger ribonucleic acid (mRNA) and present an exact probability distribution of first passage times in Laplace space. The function furnishes moments of any order and also predicts the characteristic time of the exponential tail of the distribution, which we match against Gillespie simulations. We find that all the measures of relative fluctuations of the threshold crossing times show U-shapes within this simple model of mRNA, as was found earlier in more mathematically involved models of threshold crossing time statistics of proteins. Furthermore, we extend the exact formula to include the phenomenon of DNA duplication and the corresponding doubling of transcription rate. As expected, the distribution varies considerably depending on the onset of the duplication stage within the cell cycle.

Structural network representations of metastatic dissemination typically focus on static topology without resolving transport dynamics, relaxation timescales, or steady-state behaviour. Here, we formulate a discrete Markovian transport model on a directed higher-order network with transition rates derived from qualitative clinical affinity classes. By constructing a non-Hermitian row-stochastic transfer operator, we characterise the relaxation dynamics through its spectral decomposition. The system exhibits a fast-mixing regime characterised by a spectral gap of {gamma} {approx} 0.67, corresponding to a characteristic relaxation timescale of {tau} {approx} 1.49 discrete steps, with the influence of the primary tumour origin progressively attenuated during dissemination. Convergence towards a non-equilibrium steady state (NESS) is accompanied by a reduction in Shannon entropy, concentrating probability mass within specific topological sinks. This spectral relaxation delineates two distinct dynamical regimes: early transient dissemination (n < {tau}), dominated by local organ-specific transition probabilities (organotropism), and the asymptotic regime (n > {tau}), determined increasingly by the global transport architecture of the network. Comparison with independent clinical and autopsy observations across 21 primary tumours and 23 target organs indicates that the predicted stationary distribution is consistent with the observed hierarchy of metastatic organ involvement.

With 302 neurons and a rigorously characterized connectome, the nematode Caenorhabditis elegans represents a powerful model organism to study the fundamental roles of neuronal circuits in behavior. However, despite the breadth of research, many questions remain unanswered regarding how these organisms are able to successfully navigate their environment. Here, we present a biologically grounded dynamical circuit model for the investigation of sensory-guided behavior during C. elegans chemotaxis. Our mathematical model consists of the chemosensory neuron AWA, interneurons RIM and RIA, motor neurons, including SMDs and RMDs, and body wall muscles that provide proprioceptive feedback through stretch receptors. After optimization with an evolutionary algorithm, the model locomotes effectively toward a chemical attractant, realistically capturing nematode chemotactic behavior. Chemotaxis is ensured by sharp turns, which resemble the omega turns of living nematodes, as a key emergent property of the model. The sharp turning behavior is triggered by decreases in the concentration of the attractant. These result in reduced AWA activity, which in turn triggers disinhibition of RIM and subsequent changes in RIA oscillations. The ensuing coordinated changes in downstream motor neurons activity patterns produce sharp turns, which correct the nematodes path, so that the model worm heads toward the attractant, and remains at its proximity, after it reaches the gradient peak. The proposed framework, along with its emergent dynamics, provides new insights into the minimum requirements for C. elegans circuitry to display major features of its chemotactic behavior, including omega turns. In parallel, it generates experimentally testable hypotheses with respect to the participating neuronal elements.

Focal adhesions maintain force-bearing attachment between cells and the extracellular matrix but can also undergo dynamic remodeling. Their assembly and actomyosin tension are coupled through mechanochemical feedback. The processes underlying this feedback are not instantaneous and therefore involve a time delay. However, how this delayed feedback gives rise to stable adhesion maintenance or dynamic remodeling remains unclear. Here, paired time-lapse measurements of vinculin fluorescence and traction stress revealed distinct local adhesion-force dynamics, including low-fluctuation and recurrent fluctuation patterns. To examine how these patterns could arise, we formulated a minimal mechanochemical model coupling focal adhesion assembly and actomyosin force through delayed reciprocal feedback. The model exhibited stable and oscillatory modes depending on feedback strength, the balance of opposing feedback effects, and the effective feedback delay. Bistability and hysteretic switching also occurred in a subset of parameter space, and the oscillation period followed a power-law relation with the delay. These results suggest that stable adhesion maintenance and dynamic remodeling can emerge from a common mechanochemical feedback architecture.

Enzymatic reactions in biomolecular condensates are often assumed to be regulated through local enrichment of reactants. However, condensates also reshape molecular transport and reaction kinetics, making it unclear how phase separation controls catalysis in living cells. Here, we develop a quantitative theory of biomolecular catalysis in phase-separated systems and find that liquid condensates can act as tunable catalytic switches, transitioning between regimes of enhanced and suppressed enzymatic activity, exhibiting optimal responses at biologically relevant condensate sizes. We show that condensate-mediated catalysis cannot be understood from reactant enrichment alone, but instead emerges from the coupled interplay of molecular partitioning, diffusive transport, and phase-dependent reaction kinetics. The strongest regulatory effects occur under rapid interphase exchange, where the spatially heterogeneous catalytic network admits a system-level Michaelis-Menten description governed by system-averaged concentrations and reaction kinetics. Our framework predicts that micron-sized condensates can either enhance or suppress enzymatic activity by up to two orders of magnitude, and that optimal catalytic regulation can emerge at condensate sizes comparable to many biomolecular condensates. These results provide experimentally testable predictions for condensate-mediated catalysis and establish quantitative principles for understanding and engineering enzyme-catalysed reactions in biomolecular condensates.

A classical study found no excitation transfer when isolated cardiomyocytes were placed side by side, whereas a recent paper reported action potential transfer in carrdiomyocytes placed end to end. We use nanoscale numerical simulations based on the full Poisson-Nernst-Planck equations to investigate whether these apparently opposing observations can be explained by the different geometrical configurations. The computations show that in the end-to-end configuration, ephaptic coupling occurs when the intercellular cleft is sufficiently narrow and a sufficiently large fraction of the sodium channels is localized at the intercalated disc. Coupling is strengthened when the sodium channels are concentrated in fewer clusters and when ionic diffusion within the cleft is reduced. Under these conditions, excitation transfer occurs on a timescale consistent with rapid cell-to-cell activation. Conduction depends biphasically on cleft width and terminates abruptly beyond a critical width. Localization of potassium channels at the intercalated disc has only a moderate effect, whereas gap junctions substantially improve conduction and reduce the relative contribution of ephaptic coupling. In the side-by-side configuration, excitation transfer does not occur under physiological conditions and requires highly flattened cells, minimal separation, and unrealistically strong sodium-channel clustering. The different outcomes of the side-by-side and end-to-end experiments can therefore be explained by the fundamentally different geometrical conditions for ephaptic coupling.

Solitary animals face a tradeoff when detecting threats: faster detection means accepting more false alarms. We show that groups can manage this tradeoff better by treating an undisturbed neighbor as evidence against a threat, becoming both faster and more accurate than lone individuals. Modeling each animal as a noisy evidence-accumulator that flees when its belief crosses a threshold, we find that a neighbor's flight signals danger while its stillness signals safety. A naive responder reacts only to flights and inflates false alarms as the group grows; a Bayesian responder weighs both, approximated by a single social discounting rate that interpolates between these limits. This yields closed-form expressions for group performance, including cascade branching ratios that stay strongly subcritical in safety and turn supercritical under threat, so the rate at which an animal discounts a threat while its neighbors stay still can be inferred from behavior alone, and it sets a ceiling on how many neighbors an animal can attend before discounting alone can no longer hold its false-alarm rate. Wild sulphur molly shoals under bird attack are best described by discounting rates well above what individually Bayesian updating supplies over any neighborhood they could plausibly attend, and the same model, at the inferred value, predicts a false-alarm rate that stays constant as shoals grow.

In linear polysomes, excluded-volume interactions among ribosomes can induce dimensional reduction of mRNA. Yet linear architectures allow steric stress to relax at open ends-- limiting how strongly crowding can remodel the mRNA's structure and dynamics. Using coarse-grained molecular-dynamics simulations, we compare circular and linear polysomes over a range of ribosome densities. Circular closure selects a predominantly quasi-planar global conformational ensemble, as indicated by a shape dimensionality dshape {approx} 2 over a range of ribosome densities. Crucially, circular topology and ribosome crowding act cooperatively to suppress structural fluctuations. While closure alone or linear crowding reduces relative global size fluctuations ({Delta}Rg/Rg) only to {approx} 0.16, their combined effect drives this fluctuation down to {approx} 0.07. Within this stabilized architecture, increasing ribosome density drives a distinct in-plane reorganization: the ring becomes more isotropic, global size fluctuations are strongly suppressed, and the scaling exponent increases toward {nu} [~=] 0.74 - 0.77, consistent with two-dimensional self-avoiding walk-like value over the accessible finite-size window, 1000 [&le;] N [&le;] 4969. Closure shortens the radius-of-gyration decorrelation time of circular polysomes by 40-fold relative to matched linear systems, reflecting the topological elimination of free ends. Within this closureselected ensemble, ribosome crowding further reduces the decorrelation time by up to 20% at the highest density. A fluctuation-informed crossover model links the density dependence of the global scaling exponent to inter-ribosomal subchain statistics. These results distinguish the geometric role of circular closure from the density-dependent steric response that it enables, revealing a confined yet dynamically responsive conformational regime for circular polysomes.

Tumor spheroid mechanics arise from both the mechanical properties of individual cells and the adhesive interactions that organize them into tissues. The relative contribution of these two factors to the bulk mechanical behavior, however, remains difficult to disentangle experimentally. Here, we develop a computational model of micropipette aspiration to compare the mechanical response of isolated cells and multicellular spheroids within a common computational framework. By independently varying single-cell stiffness and cell-cell adhesion, we quantify their effects on aspiration dynamics, effective elastic modulus, and viscoelastic relaxation. Our results show that increasing single-cell stiffness substantially alters the mechanics of isolated cells but has limited influence on the effective elastic modulus of multicellular spheroids. In contrast, changes in cell-cell adhesion produce pronounced effects on spheroid effective elastic modulus. Nevertheless, both parameters increase the retardation time governing the transition from the initial elastic response to long-time viscous deformation. These findings suggest that multicellular elasticity is governed primarily by intercellular mechanical coupling, whereas the dynamical response to applied stress depends jointly on cell-scale mechanics and cell-cell adhesion.

Animals use long-range signals, such as hormones and neural signals, to coordinate the actions of distant organs. There is no precise, quantitative framework that explains the problems these control systems must solve and thus predicts their behavior under varied conditions. We consider this problem in the context of blood glucose regulation by the hormone insulin, the failure of which produces diabetes. We show that existing mathematical models of glucose regulation admit equivalent control strategies with no hormones at all, and thus cannot explain the need for hormonal regulation. We therefore introduce a minimal model of inter-organ variations in local glucose, and show that control strategies based on local glucose measurements face severe trade-offs between different control objectives. In contrast, we show that hormonal control signals from the pancreas can overcome these limitations. By exposing the benefits of hormonal control, our work paves the way to a detailed understanding of physiological design principles, with possible implications for the engineering of an artificial pancreas.

Humans often collaborate under asymmetric information, for example when two people carry a table and only one knows the destination. They coordinate without speech using cues from movement kinematics, interaction forces, and object states. Characterizing this sensorimotor communication is difficult because these signals both execute the task and convey information, whose meaning is context-dependent. Here, we investigated a virtual table-carrying task where one partner knew the target while the other inferred it from visuo-haptic feedback. Participants flexibly adapted kinematic and haptic cues across contexts to convey intention. We introduce an explainable machine-learning framework that decodes intent from ongoing multimodal signals and quantifies where individual features are informative. Incorporating the decoded signals into a drift-diffusion model accurately predicted the uninformed partner's target choices and decision times. Together, our framework explains how humans communicate through action and offers principles for collaborative robots to infer and express intent through physical interaction.