PRX Life

Biomolecular condensates are dynamic assemblies whose functions depend on continuous exchange of molecular components with the surrounding environment. While scaffold molecules drive phase separation and condensate architecture, many functional components are clients that are recruited through interactions with the scaffold-rich environment. Despite their prevalence, how client-scaffold interactions shape client exchange dynamics remains poorly understood. Here, we develop a reaction-diffusion model for client exchange in scaffold-driven condensates, in which clients switch between a scaffold-bound state and an unbound state. Bound clients exchange through scaffold-mediated transport, whereas unbound clients diffuse through the pore space of the condensate. Using the fluorescence recovery of fully photobleached condensates as a measure of client exchange, we compare transport through these two pathways with bound-unbound conversion and identify three limiting regimes. In the slow-conversion regime, bound and unbound clients recover through distinct scaffold- and pore-mediated pathways. In the intermediate-conversion regime, recovery of bound clients becomes limited by client unbinding. In the fast-conversion regime, local equilibrium between bound and unbound clients produces an effective single-state recovery. We further propose a unifying description that connects these regimes and quantitatively captures the apparent recovery timescales extracted from numerical simulations across condensate sizes. Our results provide a framework for interpreting component-specific exchange dynamics, and highlight client size, client-scaffold binding, and condensate porosity as key regulators of client turnover in multicomponent condensates.

Phages must locate and bind to bacterial surface receptors to initiate infection. Their tail fiber configuration critically influences this process. We develop a stochastic model describing surface search as a renewal process, incorporating attachment, detachment, and target-finding steps. Using both numerical simulations and analytical calculations, we quantify how tail fiber number, attachment-detachment rates, and geometric constraints impact the mean and the distribution of time to successful adsorption. Notably, the search efficiency shows a nonmonotonic dependence on tail fibers number, governed by a trade-off between binding stability and diffusion-mediated mobility. This optimum shifts depending on the effective bacterial density, target radius, and fiber reach. Short fiber reach imposes severe geometric constraints, reducing mobility at high tail fiber counts and leading to performance degradation. Our findings suggest that phage adsorption strategies are shaped by a balance between anchoring and exploration, with evolutionary implications for tail fiber design and infection efficiency.

The rapid emergence of spatial transcriptomics offers unprecedented opportunities to study cell-cell communication (CCC) by capturing gene expression alongside spatial context. However, existing CCC inference methods often rely on static, heuristic models that overlook the inherently spatiotemporal dynamics and mechanistic complexity of intercellular signaling, limiting both accuracy and biological interpretability. Here, we present SpaGRD, a first-principles-based method that explicitly models ligand-receptor interactions through partial differential equations derived from Fick law of diffusion and the mass action law. Leveraging graph signal processing techniques, SpaGRD solves these equations on spatial graphs, providing a principled and generalizable approach to CCC inference. Through extensive simulations, SpaGRD demonstrates superior accuracy and robustness compared to existing methods. Applications to multiple datasets across diverse tissues and platforms reveal dynamic CCC patterns with spatially resolved signaling heterogeneity, providing biologically meaningful insights into cellular coordination and developmental processes. By bridging physical modeling with spatial transcriptomics, SpaGRD provides an accurate, interpretable, and mechanistically grounded framework for advancing quantitative studies of spatiotemporal cell-cell communication.

We perform a large-scale computational characterization of the map of protein primary to secondary structure using an AVR3a class protein effector domain from the plant pathogen P. palmivora as a case study. We formulate a modified site-scanning approach for exploring the neutral component of secondary structure phenotypes based on predictions from the machine-learning algorithm Porter 5 and apply it to the AVR3a phenotype. We predict a set of sensitive sites within the effector domain that are generally located at or near the boundaries of structured regions, with restrictions on the possible amino acid residues at these sites dictated by the secondary structure type that they participate in within the WT. We characterize a set of mutated phenotypes derived through the exploration of the neutral component of the WT effector domain, selecting them so that they span a range including both very rarely and very commonly seen secondary structures, and that they include both secondary structures nearly identical to the WT and ones far removed from it. We find that all these diverse phenotypes have an estimated robustness of the same order as that of the WT, and that the robustness scales logarithmically phenotype frequency, as seen in other genotype-to-phenotype maps. Furthermore, we observe that the dependence of the estimated phenotype frequency on the Kolmogorov complexity indicates simplicity bias in the protein secondary structure map.

Protein folding is the process by which a polypeptide chain organizes into its three-dimensional structure through a balance of stabilizing and destabilizing interactions encoded by the sequence. A central question in protein biophysics is how thermodynamic factors guide a polypeptide toward its native folded state despite the rugged energy landscape and the competing influence of nonnative interactions. In many biomolecular processes, cooperativity provides a mechanism by which multiple weak interactions act collectively to generate a robust response. In the context of protein folding, such cooperative effects may arise when the formation of one native contact enhances the stability or likelihood of nearby native contacts, thereby promoting collective organization toward the folded state. At the same time, folding is opposed by the much larger number of non-native interactions, whose heterogeneity can introduce frustration and destabilize folding even when the average native bias favors the folded phase. The interplay of these competing effects in determining foldability remains unclear in statistical-mechanical models. Here, we address this problem using a one-dimensional spin-glass model of protein folding with explicit shared-residue cooperative interactions encoded through wedge-based motifs. We show that modest cooperative bias can stabilize folding even where the noncooperative system remains unfolded, whereas non-native energetic fluctuation suppresses folding and shifts the transition to higher cooperative strengths. We further find that partial cooperative coverage is sufficient to lower the folding threshold. Therefore, the model provides a mean-field framework for incorporating cooperative interaction strength into the native one-dimensional model of protein folding and for describing how local cooperativity reshapes the folding transition.

Cells communicate with their environment by integrating signals, often chemical in nature, triggered by specific molecules bind to specific membrane-bound receptors, resulting in a downstream signaling cascade. Arguably, G-protein-coupled receptors (GPCRs) constitute the most pharmacologically important family of such receptors, binding small molecules, peptides, lipids, and hormones with high specificity. However, despite a highly conserved fold and sequence similarity, GPCRs are still mostly studied on a case-by-case basis. Here, we infer a general, evolutionarily conserved mechanism of class A GPCR activation. By leveraging coevolution and machine learning methods applied to all class A GPCRs structures, we derive a mathematical description (a so-called collective variable - CV) of the receptor's activation state which is independent of its sequence. Then, we bias molecular dynamics simulations along this CV to obtain transitions between activation states of a diverse set of class A GPCR family members. To demonstrate that our model generalizes beyond GPCRs in our training set, we obtain conformational transitions of an orphan receptor, GPR183. Finally, we show that we can model ligand effect on the receptors by converging Free Energy Surfaces of activation of the {beta}2-adrenergic receptor within this common mechanism framework. These results, to our knowledge, prove for the first time the existence of a mechanism uniting all class A GPCRs. Our approach thus facilitates direct comparisons between receptors and opens up the possibility of structural and dynamical studies of many orphan and understudied GPCRs. It also serves as a blueprint for inferring family-wide protein mechanisms.

Animals navigating complex vertical environments must secure stable footholds, a challenge for species without feet. While arboreal climbing has evolved repeatedly in snakes, the physical mechanisms they use to scale broad, nearly flat surfaces remain poorly understood. By measuring three-dimensional body kinematics and per-contact forces on a smooth vertical wall with protruding posts, we show that cornsnakes climb by dynamically balancing forces across a highly redundant network of 5 to 16 simultaneous contacts--far exceeding the three contacts minimally required for physical stability. Using a computational model and a robotic climber, we demonstrate that while simple body undulations and passive friction are mechanically sufficient to climb this terrain, snakes systematically deviate from this passive baseline. While downward climbing relies primarily on friction, ascending snakes actively generate positive mechanical work at their contacts to propel themselves. Furthermore, we found that whenever a snake engages a new contact, it triggers a stereotyped, system-wide redistribution of force that seamlessly integrates the new foothold without disrupting whole-body balance. These results reveal how a continuous, flexible body can transform sparse environmental features into a robust, fault-tolerant network. This mechanism provides a biomechanical framework for understanding the repeated evolution of limbless climbing and offers physical principles for designing agile robots for unstructured terrain.

Electrical signaling in biological systems is generally understood through the lens of single-channel biophysics, yet whether ensembles of ion channels can undergo cooperative opening and closing remains unclear. Here, we show that ensembles of voltage-gated ion channels can undergo bioelectrical order-disorder phase transitions driven by feedback between channel currents and local membrane voltage. When channels open, they carry ion-selective current that redistributes ions near the membrane and perturbs the transmembrane potential, thereby biasing the gating of nearby channels. This emergent nonequilibrium coupling generates a bona fide phase transition in ion channel ensembles. Finite-size analyses of the open-channel fraction, its fluctuations, and the distribution of collective channel states yield a voltage-temperature phase diagram with a first-order line separating collectively open and closed states and terminating at a critical point. The critical temperature is governed by a dimensionless conductance ratio set by ion transport, channel density, and confinement geometry. Applying this framework to measurements from the squid giant axon, the axon initial segment, and the nodes of Ranvier suggests that collective activation may be favored by high sodium-channel densities in large-diameter nerves, whereas the lower densities typical of potassium channels place them in an independent-gating regime.

Cetaceans reduce the net cost of sustained swimming through intermittent locomotion, alternating active fluking with unpowered gliding. The energy balance of this strategy is central to understanding survival rates, population sustainability, and the effects of anthropogenic and environmental pressures. While active-phase energetics have been characterized extensively, the glide phase remains largely unexplored. Here we derive the optimal glide duration (Topt) and the maximum glide duration beyond which energy savings vanish (Tzero) for three odontocetes spanning a 20-fold range in body mass, using high-fidelity CAD models and wall-modeled large eddy simulations. We show analytically that speed retention at Topt and mass-specific peak energy savings are both fully determined by the active-to-passive drag ratio, propulsive efficiency, and swimming speed, independently of body morphometry and drag coefficient, and are therefore invariant across species at any given speed. These passive-phase optima extend the known size-independent active-phase invariants to the glide phase, towards a scale-independent energetic framework for burst-and-glide locomotion in small cetaceans.

Protein-RNA binding and biomolecular condensation are two key processes underlying the assembly and function of ribonucleoprotein (RNP) condensates. However, the understanding of the physical consequences of their interplay is still incomplete. To investigate this coupling, here we develop a minimal coarse-grained molecular model that combines specific, saturable protein-RNA binding with multivalent protein-protein interactions. Our results show that RNA acts as a molecular scaffold whose ability to promote condensation depends on the distribution of bound proteins across RNA molecules. This provides a simple microscopic explanation for both RNA-length-dependent condensation and re-entrant phase behavior, showing that condensate dissolution at high RNA concentration can emerge from entropic effects without requiring explicit electrostatic interactions. Conversely, condensate assembly markedly enhances effective protein-RNA binding, demonstrating that substantial changes in binding behavior can emerge without changes in intrinsic affinity. This provides a general physical mechanism through which condensates can reshape molecular competition between RNA-binding proteins. Together, these findings establish a framework linking RNA binding and biomolecular condensation, illustrating how their interplay governs condensate assembly.

Biomolecular condensates are widespread cellular self-assembled structures with essential functions. There are suggestions of condensates formed by different proteins being near criticality. However, systematic investigation of the criticality of condensates is absent, and critical exponents defining their universality class have not been found. Here, using long-time simulations, we show that condensates exhibit typical critical phenomena, including scale-free spatiotemporal correlations, critical slowing down, divergence of correlation length and dynamic scaling. From these scaling behaviors, a set of critical exponents is determined. Based on dynamic critical exponent, diverse condensates can be divided into two distinct universality classes, arising from differences in their molecular components and interaction types.

Chromatin is an actively remodeled polymeric system whose organization emerges from the interplay of equilibrium interactions and ATP-dependent processes. Recent in vitro experiments show that nucleosome spacing and ATP-dependent remodeler activity significantly influence chromatin condensate properties. Here, guided by these observations, we develop a hierarchy of coarse-grained models that systematically dissect the roles of nucleosome spacing, remodeler-mediated binding-unbinding kinetics, and active force generation in governing condensate dynamics. We demonstrate that nucleosome spacing heterogeneity is a key determinant of condensate material properties. Condensates formed from regularly spaced fibers exhibit enhanced internal mixing, whereas those assembled from disordered spacing develop pronounced structural correlations, increased entanglement, and suppressed internal dynamics. Incorporating remodeler-like binding-unbinding nonequilibrium kinetics drives local structural reorganization, leading to condensate swelling and a substantial acceleration of internal relaxation. In condensates of heterogeneous fibers, contrasts in spacing and activity robustly drive spatial segregation, giving rise to stable core-shell architectures. Strikingly, when dipolar forces are coupled to hydrodynamic interactions, serving as a minimal representation of active nucleosome translocation, condensates exhibit enhanced center-of-mass motion. Together, our results establish a predictive coarse-grained framework that quantitatively links structural heterogeneity and active processes to emergent chromatin-like condensate organization, mechanics, and transport.

Nanobodies (Nbs) that depolymerize bacterial surface-layers (S-layers) offer a route to antivirulence therapeutics, but their mechanisms have been difficult to infer from binding structures alone. In B. anthracis, several Nbs bind to Sap, the S-layer protein that assembles into a paracrystalline lattice surrounding the cell. Despite similar binding poses and sequences, only a subset of these (inhibitory) Nbs induce disassembly of the protein lattice, ultimately abrogating pathogenicity. In this study, we leveraged multiscale simulations to test whether representative Nb-induced fluctuations local to the binding site are sufficient to reproduce and explain lattice-scale depolymerization. Using a divide-and-conquer strategy, we first developed a bottom-up coarse-grained (CG) model of the multidomain Sap monomer. We then compared machine learning (ML) and information theoretic approaches to identify Nb-induced collective fluctuations that are predictive and potentially causative for depolymerization. We found that motions encoding Nb rigidification and partial clamping of the binding site instigate early-stage Sap depolymerization when propagated into lattice-scale computational depolymerization assays. Furthermore, the model informed by correlation-grouped ML analysis correctly reproduced both inhibitory and non-inhibitory phenotypes for 10 out of 12 (Nb)-Sap systems. Combined time-resolved defect and strain analyses revealed that inhibitory Nbs cooperatively apply a critical amount of tensile stress that destabilizes Sap-Sap interfaces parallel to the direction of strain and proximal to the Nb binding site, thereby supporting a mechanism in which local, Nb-imposed fluctuations propagate into lattice-scale mechanical instability. More broadly, this work demonstrates how multiscale simulations combined with ML analysis can test whether molecular-scale conformational signatures are sufficient to drive emergent phenotypes in large protein assemblies. In the future, this general approach can be adapted for mechanistic study and subsequent rational design of therapeutics that rely on dynamical interventions of protein virulence factors, such as through rigidification or assembly-disrupting modes of action.

Biomolecular condensates are dynamic, membrane-free compartments that continuously exchange molecules with their surroundings. The dwell time, defined as the time a molecule remains inside a condensate between entry and exit, determines how extensively the molecule can explore the dense phase and encounter potential binding partners or reaction sites, thereby modulating condensate function. Motivated by our single-molecule measurements of RNA dwell times, we developed an analytical theory to understand dwell-time distributions in biomolecular condensates. Our theory predicts that the dwell-time distributions generally exhibit an early-time power-law regime followed by a late-time exponential tail. The form of the distribution encodes the rate-limiting mechanism of molecular escape: dense-phase diffusion-limited transport feature a -1.5 power law with an exponential tail set by a diffusion timescale, whereas interfacial barrier-crossing-limited transport feature a -0.5 power law with a decay governed by a barrier-crossing timescale. These distinct signatures provide a direct readout of the physical processes that control molecular retention in condensates, with implications for both natural and synthetic condensates.

Directed migration along chemical gradients controls immune surveillance, development, and cancer invasion. However, the same chemical cue can produce different responses depending on its concentration and whether cells move alone or in groups. For example, in steep gradients, isolated malignant lymphocyte cells migrate away from the chemoattractant source, whereas clusters of the same cells continue to migrate toward it. Here, combining computational modeling and experimental observations, we show that this reversal is governed by coupled mechanisms acting across molecular, cellular, and collective scales. At the single-cell level, our model predicts that receptor endocytosis generates a feedback that produces a nonmonotonic surface receptor density with increasing chemoattractant concentration. Above a critical concentration that depends on the cell's volume-to-sensing-area ratio, receptor depletion reverses cell polarity and drives chemorepulsion. However, in clusters, cell-cell contacts reduce the membrane area exposed to ligand, increasing the volume-to-sensing-area ratio, thus increasing the critical concentration and preserving chemotaxis. An agent-based model incorporating these mechanisms quantitatively reproduces the sign reversal of the migration index across gradient steepness and cluster size. We show that collective rearrangements further stabilize chemoattraction with exchanges between the cluster rim and core helping remove chemorepulsive cells from the leading edge, keeping their fraction below the threshold required to reverse cluster migration. The model further predicts, and experiments confirm, that increasing ambient ligand concentration while keeping the gradient fixed reduces cluster chemoattraction. Our results identify receptor trafficking, cell geometry, and cluster fluidity as physical determinants of collective directional decision-making, with implications for immune cell homing, tissue morphogenesis, and cancer dissemination.

Defining a body axis is a central aspect of animal morphogenesis. During regeneration from excised Hydra tissue pieces, the newly formed body axis typically preserves the orientation of the parent body axis and aligns with the inherited nematic organization of the supracellular actomyosin fibers. Here we show that this inherited orientation can be overridden by geometric confinement. Tissue spheroids confined in narrow cylindrical channels in a frustrating configuration, with the inherited axis initially perpendicular to the channel, regenerate with their body axis aligned along the channel. Using high-resolution live imaging we show that this reorientation is accompanied by remodeling of the nematic fiber organization. New fibers form parallel to the channel axis in the initially disordered closure regions, creating sharp domain boundaries with the inherited transverse fibers. These domain boundaries subsequently propagate, with perpendicular fibers dissolving and new fibers forming along the channel axis. The confined tissue behaves as a solid-like active nematic material, storing anisotropic strain over long timescales while allowing nematic reorganization relative to the material frame. Our results suggest that coupling between tissue strain and nematic alignment contributes to fiber reorientation and body-axis patterning, highlighting how external mechanical constraints can redirect the body axis during morphogenesis.

The ability to tune protein function through the binding of modulatory ligands enables the development of therapeutics that steer a biological system away from dysfunctional states underlying disease. Understanding the dynamic mechanisms by which allosteric ligands alter protein function remains an important open question. Dynamical network models allow us to quantify information flow between protein functional sites. However, existing network models use time-symmetric metrics for computing information from correlated residue motions extracted from molecular dynamics (MD) simulations, failing to fully capture directional information flow between sites. Here, we developed a Python library, TEntroPy, and analysis workflow using transfer entropy to generate a directional protein network from equilibrium MD trajectories. Applying this workflow to proteins with known allosteric ligands, we identified residues in both allosteric and orthosteric (primary) binding sites acting as broadcasters and receivers of information. We then computed optimal paths of directional information flow between binding sites. The presence of temporal asymmetry in residue coupling identified from simulations of the unbound (apo) state suggests that directional information flow is encoded in the intrinsic dynamics of the protein. To test this, we perturbed key binding-site residues and demonstrated that our TE-weighted network captures perturbation-induced changes in dynamics along communication routes between binding sites. Identifying residue pairs with high temporal asymmetry provides an additional tool for understanding the dynamic mechanisms of allosteric communication.

Developmental patterns can scale with size during growth, a phenomenon commonly attributed to morphogen scaling. Although patterning is orchestrated by gene regulatory networks (GRNs) activated by morphogens, how GRN dynamics interact with growth is not understood. We present a theoretical framework that integrates morphogen signalling, GRN dynamics, and tissue growth. We show that pattern scaling emerges from the interplay of GRN dynamics and growth, even in the absence of morphogen scaling. This relies on memory effects encoded in the GRNs, providing a cell-autonomous route to global scaling, and offering a general mechanism for size-invariant patterning beyond morphogen-based models.

Principles of collective motion are now well established, though research has largely focused on homogeneous groups. Heterogeneity is widespread in animal groups, e.g. arising from sex, size or even species, raising a central question: can collective behaviour emerge when individuals have distinct behaviours? Here, we combine experiments and modelling to investigate mixed-species collective motion using two closely related fish species, rosy barbs and tiger barbs. In conspecific groups, both species exhibit collective motion, but they differ strikingly in their intrinsic movement: tiger barbs exhibit slowand fast-swimming, whereas rosy barbs display fast swimming only. Despite this difference, these species readily form mixed-species schools where the slow swimming speed of tiger barbs disappears, and the collective motion is dominated by a single fast-swimming mode. We develop an individual-based model incorporating local interactions involving speed matching. Our model demonstrates that bimodal speed in conspecific schools of tiger barbs is an emergent property that is lost in mixed-species groups. Additionally, despite high cohesion, we observe spatial sorting of the two species within the mixed-species groups, which our model explains through differences in inter- and intra-specific interactions. Our results provide experimental evidence that canonical principles of collective motion extend to heterogeneous mixed-species groups.

Understanding how mutations combine to shape protein fitness remains a central challenge in biology, driven in part by the prevalence of highorder epistasis. Existing analyses of epistasis, however, implicitly define epistatic interactions under a uniform probability measure over sequence space, even though evolution constrains natural proteins to a highly structured, non-uniform distribution of sequences. Here, we show that the apparent complexity of protein epistasis depends fundamentally on the underlying evolutionary distribution of sequences. We develop an evolution-aware spectral framework that incorporates the evolutionary distribution of amino acids at each sequence position, inducing an orthogonal decomposition under the evolutionary measure while preserving efficient spectral algorithms for scalable analysis. Across diverse protein fitness landscapes, this framework consistently produces more compact spectral representations, explaining more phenotypic variation with fewer epistatic interactions while substantially reducing apparent high-order epistasis. It also enables more accurate recovery of fitness landscapes from limited experimental measurements and concentrates the remaining higher-order interactions into localized, structurally interpretable motifs. These results suggest that a substantial fraction of apparent high-order epistasis arises from defining epistatic interactions under a uniform measure over sequence space and can be resolved by aligning spectral analysis with evolutionary constraints.