Physical Review Research

We investigate the dynamics of the spread of the infection due to a phage- during the range expansion of an E coli colony. We find a rich panoply of spatio-temporal dynamics at large colony-level length scales, arising due to the interplay of mechanical forces, growth and viral infection dynamics at smaller cellular length scales. Strikingly, the phages "surf" the front of the growing bacterial colony by hitchhiking on E coli that are advected due to the growth of bacteria in the colony, resulting in an anisotropic spread of the phages. We identify microscopic processes - of the phage release during lysis (occurring on short millisecond timescales at length scales close to that of a single bacterium) and local nematic alignment of the rod-like E coli bacteria (occurring on timescales comparable to the bacterial growth rate and the length scales of a few bacterial cells) - that enhance the advective effects driving the hitchhiking behavior. Combining our experiments with a mathematical model, we explain the multiple spatio-temporal dynamical regimes - from the coexistence of uninfected bacteria, resistant (lysogenic) cells and phages, to fixed points where the entire population turns resistant or remains uninfected. Our work broaches a new frontier in the investigation of eco-evolutionary processes arising from the mechanical and ecological forces due to the interactions between viruses and their hosts.

Non-exponential residence times give rise to history-dependent or memory effects in epidemic dynamics, yet their mathematical formulations remain fragmented. Here we develop a unified framework for a history-dependent SEIR model with general latent- and infectious-period distributions. We first establish the equivalence between the stage-age and renewal formulations and show that both admit a unified transition-flow representation. We then introduce the concept of a transition-flow multiplier, which provides a direct link between residence-time distributions and transition flows. When the multiplier is a weighted sum of shifted power functions, the model admits an exact representation in terms of Riemann-Liouville or tempered Riemann-Liouville fractional operators, providing a first-principles foundation for fractional epidemic models. Finally, using Euler-Lotka equations and stochastic-order arguments, we characterize how the latent- and infectious-period distributions shape epidemic growth and decay. A longer latent period slows both early growth and late decay, while, at fixed means, greater variability in the latent period accelerates early growth but slows late decay, whereas greater variability in the infectious period slows both.

Collective migration is often attributed to complex cell-cell communication, yet coordinated multicellular dynamics can also emerge in organisms lacking social interactions. Continuum descriptions successfully capture such behaviors but generally rely on phenomenological transport coefficients whose microscopic origin remains elusive. Here we show that these coefficients emerge from cell-cell collisions and can be independently determined from experiments. We investigate the aerotactic dispersal of confined colonies of the solitary amoeba Acanthamoeba castellanii, in which oxygen consumption continuously reshapes the local environment to generate self-organized guidance cues. Combining quantitative videomicroscopy, oxygen mapping with phosphorescent sensing films, and oxygen-controlled microfluidics, we directly measure both the oxygen landscape and the aerotactic response governing colony expansion. We then develop a Patlak-Keller-Segel (PKS) -type drift-diffusion model whose transport coefficients are entirely determined from independent experiments and microscopic-to-macroscopic modeling approach, without adjustable parameters. The model quantitatively reproduces the observed dynamics, including the coexistence of a fast ballistic front and a trailing transient accumulation band. We show that both diffusion and aerotactic transport are modulated by the same collision-controlled mechanism through density-dependent changes in cell persistence. More generally, our results establish transport coefficients as measurable emergent properties bridging microscopic cell dynamics and macroscopic collective behavior, providing a predictive framework for oxygen-guided migration in living active matter.

Motivated by correlations between SARS-COV-2 infections and transthyretin (TTR) amyloidosis we use molecular dynamics simulations to study whether three protein fragments from the SARS-CoV-2 virus can initiate dissociation of the transthyretin (TTR) homotetramer as the first step on the pathway to TTR amyloidosis. We find that the peptides reduce the frequency of transient hydrogen bonds at the monomer-monomer interfaces, decreasing in this way the stability of the TTR tetramer.

Recurrent cortical circuits are hypothesized to perform Bayesian posterior sampling through their stochastic dynamics. Yet identifying which sampling algorithm a circuit intrinsically implements, as opposed to mapping manually designing algorithms onto circuits, requires rigorous theoretical analysis of the biological circuit dynamics, and remains a fundamental open challenge because of the analytical intractability of nonlinear recurrent dynamics. Here, we tackle this challenge through comprehensive theoretical analysis of analytically tractable nonlinear recurrent circuit dynamics used in neuroscience research-- the continuous attractor network (CAN). Surprisingly, we find that the circuit, without any non-Gaussian components in its connectivity or internal variability, intrinsically emerges heavy-tailed subspaces dynamics described as scale-mixture Langevin posterior sampling. The mechanism emerges from the circuits own nonlinear dynamics: divisive normalization renders the overall population activation Gamma-distributed which multiplicatively modulates the time constant of the Langevin sampling in the stimulus feature subspace. Eventually, this scale-mixture structure produces a heavy-tailed (Student-t) sampling step size distribution, significantly accelerating the sampling speed. Moreover, the scale-mixture Langevin sampling approaches a Levy-like regime in the weak input limit. Our results analytically identify an intrinsic circuit algorithm embedded in subspaces of nonlinear recurrent dynamics, and establish a minimal circuit mechanism for endogenous heavy-tail statistics without any explicit non-Gaussian components.

We develop a general geometrical framework for growth processes in which the growth rate depends exponentially on the number of active growth-supporting components. The framework separates the fraction of active components from the size of the accessible component space, allowing qualitatively different growth laws to arise from the same underlying construction. Bacterial population growth provides an example of a fixed-size component space controlled primarily by activation and deactivation, whereas examples such as human population growth or speciation provide an expanding component space in which interactions between individuals promote further growth. This motivates a Replicative geometrical law, dX/dt= X exp({beta} X^{gamma}), whose exponent characterizes the scaling of the effective growth-supporting component space and is tested against historical human-population regimes and eukaryotic lineage-through-time data. For innovation indicators such as patents and arXiv manuscript submissions, where an existing item need not itself reproduce, the same construction motivates a Direct Geometrical production law without the prefactor X. The framework therefore provides a common description of fixed and expanding component spaces while distinguishing Replicative from Direct Geometrical growth.

Cells use ATP-driven chaperones to extract clients from biomolecular condensates selectively, yet no closed-form criterion links molecular parameters to condensate quality control. We derive a minimal non-equilibrium sorting reactor model that reduces the reaction-diffusion dynamics to one algebraic equation. In the idealized low-load limit, a concentration-dependent partition coefficient produces a saddle-node bifurcation between functional clearance and pathological storage. The critical Damk\"ohler number is \(\mathrm{Da}_{0c}=e^{-2}\) and is independent of the feedback strength. Corrections shift the value but preserve the topology. The model predicts a Kramers-type functional lifetime and recovery costs that scale as \(R^3\). Critical slowing down near the bifurcation provides early-warning signatures for FCS and FRAP.

The emergence of treatment resistant mutants is one of the primary contributors to therapy failure in cancer. Evolution-based adaptive therapies aim to exploit the competition between sensitive and resistant cells to prolong therapeutic control. However, in the densely packed tissues of solid tumors, competition is not only determined by cell-intrinsic factors but also a result of local physical interactions between neighboring cells. The successful development of physics-informed adaptive therapies therefore hinges upon the bottom-up integration of tissue mechanics and experimentally grounded models of tumor evolution. Here, we show how population-level treatment response emerges from mechanical interactions between individual cells. Combining genetically tailored therapy-mimicry experiments in spatially structured 2D melanoma colonies with mechanistic, particle-based tissue simulations as digital twins in a real-to-sim-to-real framework, we reveal how treatment-induced changes in mechanical crowding shape a cascade of resistance expansion, spatial competitive escape, and consequent therapy failure. We then link these underlying physical mechanisms to population-level observables in an abstracted mathematical model for reinforcement-learning-based therapy optimization and a distilled treatment-decision-heuristic, which we test experimentally. Together, our results identify mechanical crowding and escape as governing principles of resistance-mediated therapy failure in solid tumours and provide a basis for mechanistically informed, evolution-based treatment strategies.

Known for their rapid water surface locomotion, whirligig beetles (Gyrinidae) are also fast divers. They can transition from the surface to underwater swimming in under 100 ms. Diving requires them to generate sufficient hydrodynamic torque to break the water surface and reorient the body. However, the mechanism by which whirligigs create the necessary pitch-down torque is unknown. Here, we show that their diving is achieved by bending the abdomen. The inertial hydrodynamic pressure on the flexed abdomen generates the torque necessary for surface breaking and body rotation. The torque is maximized at an abdominal angle of 45{degrees}, whereas for effective diving, whirligigs display a preferential abdominal angle of around 28{degrees}, closely aligning with the angle that maximizes the torque-to-drag ratio. This abdominal angle is optimized by balancing torque generation with the drag penalty. Our findings inspire a mechanism for surface-to-underwater transition, offering design principles for multimodal robots capable of locomotion across the air-water interface.

We show that the p53-Mdm2 gene interaction can be understood as a form of antithetic feedback, but with mixed feedback loops. In particular, we show that this viewpoint sheds light on the emergence and robustness properties of p53's oscillatory behaviour, as observed experimentally.

Interception of moving objects is a universal pattern of animal behavior with many industrial applications. Inspired by the behavior of the characid fish Brycon guatemalensis, which catches fruits falling onto the surface of a river, we study one-shot (i.e., open-loop) interceptions using both stochastic optimal control theory and reinforcement learning. In the first instance, an agent actuates a control (wait time before launch and heading angle) to meet its target, given a noisy estimate of the target initial state. In a minimal setting, where launch velocity and actuated control are constants, we show that the optimal wait time is attenuated by noise in both the target measurement and control actuation, as well as agent energy conservation. We then derive an upper bound for the heading angle variance which scales as the ratio of the non-vanishing optimal interception error to the initial planar separation. Complementing our control framework, our deep reinforcement learning approach shows that the neural network representing the fish first learns the value function for the interception, then learns how to aim, and finally learns the optimal wait time. Beyond the specific problem at hand, our results may also have applications to problems with little time for feedback or corrections such as perching, landing, and docking.

Behavioral variability reflects differences in internal and external parameters and provides a substrate for natural selection. However, uncovering its structure is challenging because behavior evolves nonlinearly across multiple timescales. Our goal is to reconstruct phenotypic variation from finite behavioral observations without prescribing the scales at which individuals should be compared. To achieve this, we introduce a multiscale dissimilarity that compares dynamics across all statistically resolvable resolutions by constructing reduced transfer operators at progressively finer scales and weighting their differences by finite-sampling uncertainty. This dissimilarity defines a geometry of dynamical phenotypes, which we reconstruct using diffusion maps. We show that the resulting phenotypic coordinates locally follow the parameter directions to which dynamics are most sensitive. We validate our approach in a stochastic model and apply it to bacterial and larval zebrafish behavior. In bacteria, we identify run speed as a major component of inter-individual variability, associated with the chemotaxis protein CheB. In zebrafish, we find that prior prey experience reshapes behavioral dynamics and phenotypic variability, with paramecia experience concentrating fish in a prey-capture-associated region of phenotypic space. Together, these results provide a framework for identifying internal and environmental variables that structure dynamical phenotypes across scales.

Phase separating biopolymers are often described by the sticker-spacer model, which accounts for non-attractive linkers that connect discrete attractive moieties. "Associative polymer" theories describe these systems as two coexisting fluids of stickers and spacers, respectively. In such theories the stickers and spacers are decoupled in the sense that sticker binding does not affect spacer conformations or vice versa. Informed by coarse-grained simulations, we develop a phenomenological mean-field theory to determine the microscopic coupling between the sticker and spacer degrees of freedom. Accounting for linkers connecting adjacent spacers introduces free energy contributions due to conformational entropy of the spacer and the binding combinatorics of the stickers. These contributions have opposite dependencies on spacer length because longer spacers allow a greater volume to search for binding partners but incur a greater entropy cost upon bond formation. The length dependent terms from these contributions cancel leaving a length-independent elastic term arising from the fact that a small amount of spacer stretching lowers the free energy by increasing the number of possible binding partners. The cancellation of spacer length from the theory justifies the decoupling approximation and supports mean-field treatments of heterogeneous spacers.

Cancer progression often requires the accumulation of multiple driver mutations, yet the same set of drivers may be acquired in different orders. How these alternative mutation-order pathways jointly shape tumor clonal structure remains unclear. We develop a multitype branching-process model in which malignant transformation requires two driver mutations and distinguish malignant cells both by their mutation order and by the independent transformation event that founded their clone. Under a successive exponential approximation, we establish point-process limits for the pathway-specific clone-size processes and derive a closed-form expression for the limiting expected Simpson's index of the combined malignant population. When the two mutation orders produce malignant cells with the same net growth rate, the limiting index separates into effective pathway weights, determined by mutation rates and birth-death dynamics at preceding stages, and within-pathway concentration terms, determined by intermediate-to-malignant growth-rate ratios. This decomposition shows that a driver's effect on heterogeneity depends critically on when it is acquired. A strong driver acquired early expands the intermediate lineage and increases the supply of independent malignant founders, whereas the same driver acquired at the final transition strengthens the growth and age advantage of early-founded malignant clones. Under additive fitness effects, these counteracting mechanisms can produce a non-monotone relationship between selective advantage and clonal concentration. We further show that threshold-like non-additive fitness effects can generate highly concentrated malignant populations, while order-dependent terminal fitness leads the faster-growing pathway to dominate asymptotically. Together, these results reveal how mutation order, mutational accessibility, selection, and epistasis jointly determine lineage-level intratumor heterogeneity.

Large shear deformation in cartilage can lead to tissue failure and injury, which are often precursors to diseases such as post-traumatic osteoarthritis. Under shear, cartilage strain-stiffens prior to failure, which makes stiffening an important indicator of changes to the loading of the extracellular matrix that gives rise to this tissue's properties. While a variety of stiffening mechanisms ranging from uncrimping to fiber-alignment have been explored, whether such mechanisms apply to the depth dependent shear strain stiffening in articular cartilage remains poorly understood. Here, we present experiments and theory that support the idea that the strain-stiffening behavior is caused by a mechanical phase transition from a random isotropic network whose mechanics arise primarily from bending-dominated modes to one where the mechanics arise from stretching-dominated modes. Indeed, consistent with network model predictions, we find that stress-strain data for all depths can be collapsed onto a single universal curve that diverges at a depth-dependent critical strain. These results show that increasing the local concentration of collagen, which constitutes the primary load-bearing network in cartilage, decreases the critical strain at which the strain-stiffening transition occurs, while increasing the low-strain elastic modulus. Furthermore, we demonstrate that bulk compression leads to a higher critical strain and decreased low-strain elastic modulus. Network simulations capture this rich behavior, and indicate that under compression the network collapses, which allows for larger strains before the transition from bending-dominated to stretching-dominated mechanics occurs. Collectively, these findings shed light on the roles that tissue composition and axial strain play in the mechanisms that organize how articular cartilage stiffens during the lead-up to injury.

Nanopore sensors have transformed single-molecule analysis, enabling real-time detection of biomolecules with unprecedented resolution. Understanding and modelling noise in nanopore sensing is essential to unlocking their full analytical potential. Although mechanistic models of nanopore noise exist, a rigorous statistical framework that characterises noise structure across diverse experimental conditions is still lacking. Here, we present a comprehensive empirical analysis of nanopore noise using twelve diverse experimental conditions acquired with different nanopores, analytes, and electronic recording systems. By employing multiple, mutually reinforcing statistical methods, we establish that nanopore noise is well described by a composite fractional model comprising multiple fractional Gaussian noise and fractional Brownian motion components. This finding is supported by confirmation of Gaussianity, rigorous interpretation of second-order exponents, multifractal analysis, and evidence that transient deviations are attributable to deterministic or experimental artefacts rather than alternative stochastic mechanisms. We further resolve quasi-deterministic structures, such as baseline trends and structural breaks, and demonstrate their separability from the underlying stochastic profile. Collectively, these results provide the first formal statistical validation of a composite fractional model for nanopore noise and establish a principled basis for noise reconstruction, realistic simulation, and statistically grounded algorithm design for nanopore sensing applications. This study provides the foundation for the creation of high-fidelity performance evaluation datasets for signal processing, and the controlled generation and augmentation of data for machine learning while maintaining statistical fidelity to experimental conditions.

Nonlinear neural networks develop structured internal representations, yet how their geometry is determined by the tasks being learned remains poorly understood. Here, we develop an analytical framework for piecewise-linear feedforward and recurrent networks that links learning, activation-region structure, and neural selectivity. We show that, at any stationary point of gradient-aligned learning, a nonlinear network decomposes into local linear regressions over its activation regions. Deviations from the corresponding least-squares solutions are jointly constrained by network weights shared across regions and vanish in the low-error regime, yielding an approximate piecewise least-squares decomposition of the task. This structure admits a decision-tree interpretation, which we recover numerically by fitting trees to predict network activation patterns from the input. We further derive how the regions in which neurons are active determine the task statistics they capture, thereby organizing neural selectivity into distinct subpopulations. The resulting predictions closely match the selectivity geometry observed in simulated networks and two empirical neural datasets. Finally, we show that neural baseline regulates activation pattern diversity, placing networks along a continuum between coarse, generalizing representations and fine-grained, expressive representations. Together, these results establish activation regions as a unifying framework for describing how nonlinear networks decompose task structure into local computations and how those computations can be revealed through neural activity.

Clathrin-mediated endocytosis (CME) is the primary pathway for internalization of extracellular and membrane cargo in eukaryotic cells. It is characterized by a patch of the plasma membrane invaginating and pinching off to generate a cytoplasmic vesicle. Recently, experimental evidence has begun to accumulate in support of proteins assembling into liquid-like condensates at nascent CME sites, but potential functional consequences are not understood. Given that condensate capillary forces can influence membrane bending, we constructed complementary analytical and numerical model systems to probe the mechanical influence of a protein droplet on endocytosis. Model evaluations and analysis reveal that a droplet can regulate the progression of endocytosis by stalling invagination until the droplet grows past a threshold size. After the droplet-mediated brake is released, the droplet provides a force that can drive the membrane bud toward scission. Thus, we propose a ``mechanical timer'' mechanism as a function for protein phase separation in cellular membrane trafficking.

Precise neural circuit formation requires growth cones to integrate multiple, sometimes competing, guidance signals into persistent yet adaptable movement. Here, we propose a theoretical framework that recasts axon guidance as a thermodynamically regulated computation. An artificial neural network, trained on in vivo genetic data and associated outgrowth patterns, maps the microstates of a localized guidance signaling network to macroscopic outgrowth behaviors. Using the trained model, we simulated axon pathfinding through extracellular gradients of molecular cues and created dynamic entropic landscapes. These results reveal that growth cones navigate high-entropy ridges that preserve plasticity. Navigation along these ridges supports persistent extension, whereas turning and branching occur near boundaries between competing entropic macrostates, consistent with transitions in the cytoskeletal machinery that controls growth-cone movement. More broadly, the framework proposes that robust biological patterning can emerge from microscopic variability when signaling networks operate near boundaries between competing behavioral states.

Centrosome positioning is governed by mechanical interactions between the actin and microtubule cytoskeletons, yet the contribution of different actin architectures and their attachment to the cell membrane remains unclear. We use numerical simulations to study a centrosomal array of microtubules interacting with cortical, bulk, and centrosome-associated actin networks, including passive cross-linkers, motor proteins, and ERM-mediated coupling of actin to the cell membrane. We find that bulk and centrosome-associated actin alone are insufficient for robust centrosome centering, whereas sufficiently dense cortical actin promotes centering through steric interactions with growing microtubules. ERM-mediated attachment of cortical actin to the cell membrane enhances this effect, allowing stable centering at lower actin densities. In a two-centrosome system, microtubule interactions generate a spindle-like structure, while the organization of actin and its membrane attachment through ERM regulate centrosome separation. Antagonistic microtubule motors further limit centrosome separation and establish a finite spindle length. These results demonstrate that ERM-mediated coupling of actin to the cell membrane provides an important mechanical link between the actin cortex and microtubule-driven centrosome positioning, influencing both centrosome centering and spindle geometry.