Physical Review Letters

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.

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.

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.

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.

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.

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.

Dense, well-ordered material states of proteins form the amyloid fibers that are a hallmark of neurodegenerative disease in the brain. Beyond forming amyloid fibers, some of these proteins can also adopt other material states termed condensates which are initially liquid-like but evolve to a soft, glassy phase. Fiber growth requires a large supply of monomers and, thus, it is often speculated that fibers emerge from within a dense condensate as it ages and its microscopic dynamics slow into a glassy state. Here, we use the well-established model system Fused in Sarcoma (FUS) to directly observe, quantify and theoretically describe fiber growth and its interplay with condensates. We report the discovery that fibers grow overwhelmingly in the dilute phase surrounding the condensates while the condensates concurrently evolve to a glassy arrested solid. The resulting protein fibers and glassy condensates are both distinct solid-like phases that coexist but do not directly interconvert. Taken together, these findings reveal that there are two competitive aging pathways in FUS condensation that are linked through phase separation kinetics.

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.

Adherent cells must continuously adapt to rapid environmental fluctuations to preserve mechanical integrity. However, conventional theoretical frameworks predominantly rely on quasi-static assumptions, thereby limiting their ability to capture the transient dynamics of cellular responses to high-rate perturbations, such as acute osmotic shocks. To address this limitation, we developed a biophysical model incorporating a Hill-type law that couples active cytoskeletal mechanics to cell-edge velocity, explaining the counterintuitive experimental observation that traction forces transiently decrease during rapid hypotonic swelling despite an increase in cell size. We further construct a kinematic-geometric phase diagram that connects classical quasi-static theories with our dynamic model. Moreover, we show that traction-force dynamics are sensitive to the loading rate and amplitude of osmotic shock. In addition, stiffness-associated simulations and supporting perturbation evidence suggest a cellular stiffness-associated recovery trend in which stiffer cells exhibit faster volume recovery driven by stronger recoil of hydrostatic pressure.

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.

Tumor progression is shaped by a continuous competition between malignant expansion and immune access within the surrounding microenvironment. Although spatial assays can reveal where T cells accumulate, most current approaches remain descriptive, treating immune organization as a static pattern and failing to infer the latent resistance structure that governs progression. Here we show that changes in peri-tumoral T-cell distribution can support noninvasive tomography of tumor progression. Using spatially resolved human breast tumor sections and controlled numerical experiments, we formulate immune-tumor interaction within a mean-field game framework in which T cells act as agents responding to a heterogeneous microenvironment while the tumor shapes an equivalent barrier field that restricts infiltration. This framework converts boundary enrichment, layered blocking and core penetration patterns into a constrained inference problem whose solution yields quantitative maps of immune exclusion, barrier strength and progression-associated internal states. Forward simulations show that barrier geometry reshapes immune-density equilibria, and inference experiments show that closely related barrier fields can be recovered from immune-density observations under controlled and tissue-shaped proxy settings. By linking observable T-cell redistribution to latent microenvironmental resistance, this approach establishes a route toward noninvasive, repeatable assessment of tumor progression without direct biopsy of the underlying barrier structure.

The epidermal growth factor receptor (EGFR) is a tyrosine kinase receptor that plays a fundamental role in regulating cellular proliferation, survival, and differentiation. EGFR's kinase domain catalyses the autophosphorylation that drives downstream signalling and is a known hotspot for cancer-associated mutations. Such substitutions often enhance receptor activation, driving oncogenesis and therapeutic resistance, with major implications for prognosis and treatment choice; consequently, a detailed understanding of this domain's functional dynamics, and how mutations reshape them, is essential. Here, we apply dynamical-nonequilibrium molecular dynamics (D-NEMD) simulations to probe how changes at the ATP-binding site are transmitted throughout the kinase domain, ultimately shaping the behaviour of distal regions in the wild-type protein and in two of the most clinically observed non-small cell lung cancer variants, L858R and L858R+T790M. D-NEMD reveals previously uncharacterised communication networks linking the ATP pocket to key functional motifs, including the P-loop, C-helix, hinge region, activation loop, and F-helix, showing the intricate allosteric connectivity within this domain. Notably, numerous cancer-related mutation sites, despite being distant from the ATP site, map onto or lie close to these communication pathways, indicating that D-NEMD simulations can identify functionally relevant allosteric positions and potential mutation sites in EGFR. Our simulations further reveal that the two variants rewire EGFR's internal signal propagation network in distinct ways: L858R diminishes the transmission of structural changes to distal regions of the C-lobe, whereas introducing T790M in addition to L858R partially restores wild-type-like behaviour through compensatory rerouting of early-stage dynamical pathways.

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.

A foundational tenet of modern biophysics dictates that protein-solvent interactions and charge-transport dynamics operate strictly within microscopic, sub-nanometer boundaries where long-range coordination is natively suppressed by rapid room-temperature thermal dephasing. Here, we report an unexpected phenomenon that fundamentally challenges this paradigm: the long-distance, quantum-coherent communication between isolated protein samples in aqueous solution across macroscopic spatial separations. By mapping the distance-dependence of a weak, protein-emitted electromagnetic field on the response dynamics of an adjacent complex, we demonstrate that this inter-protein communication establishes a stable, intermolecular vibronic coupling operating across millimeter-scale distances up to at least 40 mm. This field interference induces a robust quantum coherence that lowers the local potential energy surface, transforming the coupled protein-solvent network into an un-attenuated, low-barrier energy transfer conduit. This stabilized pathway launches a topologically protected, non-dispersive soliton that exhibits exceptional phase stability against room-temperature thermal dephasing. These findings provide definitive empirical evidence of a sophisticated, field-driven quantum infrastructure embedded within a biological macromolecule. More explicitly, they reveal that a protein can possess an inherent capacity to preserve coherent wave propagation over macroscopic scales previously deemed impossible in room-temperature aqueous environments.

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.

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.

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.

Allergic conjunctivitis is an inflammation of the conjunctiva caused by allergen; it is common disorder affecting up to 40% of the population. In this work, we study seasonal allergic conjunctivitis (SAC), also called "hay fever eyes", which is caused by exposure to airborne pollens. We develop a mathematical model quantifying the ocular immune system response to the allergens. First, we present a simplified qualitative description of the immunopathogenesis of SAC. Then, we express each chosen immunopathological mechanism mathematically to construct a system of thirty-one ordinary differential equations. We compare summary statistics of the predicted observable immune signals to experimental measurements and find our model captures key qualitative features of SAC progression. We then compare our predicted time series of histamine concentration to symptom scores and find a strong correlation suggesting the model predicts relevant clinically trends. Next, we calibrate the model through multi-step process. We find the most influential parameters are the production and depletion rates of IL-4, and the production rates of IL-5 and IL-8. These cytokines are targeted in treatments for asthma, atopic dermatitis, and severe eosinophilic associated disorder and suggest potential therapeutic targets for SAC. Our calibrated model mimics most of the summary statistics of the experimentally observable immune signals with discrepancies for IL-5 and IL-13 indicating that additional immunopathological mechanisms could be important.

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.

Biomolecular condensates are condensed assemblies of biomolecules that form through the process of liquid phase separation. Condensates in biology typically function as membraneless organelles, providing compartmentalization in the absence of a dividing lipid membrane. The molecular make-up of different condensates includes diverse multivalent proteins and nucleic acids as the primary drivers, many of them including significant fractions of intrinsically disordered regions (IDRs). To date, the sequence to phase separation relationship of IDRs has focused largely on one protein at a time, studying single-component condensate formation, or single-component partitioning into condensates. The co-phase separation and mixing of two or more IDRs is considerably more complex as both sequences can vary widely in their self- and cross-interactions, as well as their relative abundance in solution. It is unclear that a rule which predicts how a single sequence behaves will also predict what happens when two sequences are mixed. In this study, we disentangle the influence of sequence from that of composition using a set of 18 LAF-1 RGG variants that keep the same length and amino-acid composition and change only the order of the residues. This lets us vary charge patterning and, to a lesser extent, hydropathy patterning while keeping protein composition fixed. By themselves, the sequences phase separation and single-chain compaction are controlled by their degree of charge and hydropathy patterning. Within single-component condensed phases, each sequence adopts a more extended conformational ensemble, due to a more favorable, selfsolvated environment. We find that mixing two IDRs together into a condensate causes this universal scaling behavior to break, impacted by the relative interactions of the two components and overall composition of the slab. We find two different qualitative behaviors, one characterized by cooperative co-condensation when both sequences are subcritical, and the other by scaffold-client behavior when one sequence is supercritical. The scaffold-client systems generally show a high degree of demixing, while the co-condensing systems are generally quite well-mixed in the dense phase. This is surprising because even in cases where both partners have significantly different patterning parameters, they still mix. Thus, the descriptor that predicts a sequence's behavior alone can help indicate whether it will mix with or separate from a second component, but it does not fully determine the outcome on its own.