The emergence of a body axis is a fundamental step in the development of multicellular organisms. In simple systems such as Hydra, growing evidence suggests that mechanical forces generated by collective cellular activity play a central role in this process. Here, we explore a physical mechanism for axis formation based on the coupling between active stresses and tissue elasticity. We develop an active spherical shell model in which the activity of muscle fibers is described by active nematodynamics, while the elastic response of the tissue is captured by linear elasticity. We analyze the elastic deformations induced by activity-generated stresses and show that, owing to the spherical topology of the tissue, forces globally condense toward configurations in which both elastic strain and nematic defects localize at opposite poles. These mechanically selected states define either an apolar or a polar head-foot body axis. To characterize the condensed regime, we introduce a compact parametrization of the active force and flux distributions, enabling analytical predictions and direct comparison with experiments. Using this framework, we calculate experimentally relevant observables, including areal strain, lateral pressure, and normal displacements during muscular contraction, as well as the detailed structure of topological defect complexes in the head and foot regions. Together, our results identify a mechanical route by which active tissues can spontaneously break symmetry at the organismal scale, suggesting a general physical principle underlying body-axis specification during morphogenesis.

Bacteria regulate their motility through a variety of mechanisms, including quorum sensing and other density-dependent responses mediated by diffusible signals. While nonlinear density-dependent motility is well known in active-matter theory to generate nonequilibrium spatial patterns, its consequences for the coexistence of growing, interacting species remain less explored. Here we develop a minimal spatially structured model for two strongly competing species in which local demographic interactions are coupled to an escape response: Each species increases its motility nonlinearly (sigmoidal) with the local abundance of its competitor. We show that this sigmoidal motility regulation promotes optimal spatial self-organization and can sustain long term coexistence via segregation, even in parameter regimes that yield competitive exclusion in well-mixed Lotka-Volterra dynamics. On two-dimensional lattices, the interplay between demographic competition and density-dependent motility generates a range of emergent patterns, including regimes in which the weaker competitor counterintuitively has higher total abundance. Overall, our results identify nonlinear, competitor-induced motility as a fundamental mechanism capable of sustaining coexistence in competing microbial populations.

This work introduces a self-consistent training framework for learning residue–residue interaction parameters in matrix-based coarse-grained protein models. By combining direct coupling analysis with a physics-based design model, we construct a feedback loop in which the interaction matrix is iteratively updated from sequences generated by the model itself. We provide a mathematical foundation for this behavior by showing that, for a given iterative map satisfying explicit contact-locality and spectral assumptions, the training process is a contraction, guaranteeing convergence to a unique fixed point independent of the initial interaction matrix. This fixed-point property is general for coarse-grained models in which the residue-residue energy is represented by a distance-dependent term modulated by a type-dependent coupling matrix, while the learned interaction parameters remain specific to the underlying model physics. We then examine the empirical consequence of this framework in Caterpillar, a coarse-grained potential for folding and design. Independent training trajectories, defined by different target structures and stochastic sampling, converge to statistically equivalent interaction matrices. Each trajectory recovers the full interaction solution without requiring ensemble averaging, and the averaged trajectory reaches the same result. The resulting framework provides a link between sequence statistics and physically modeled interaction energies. Applied to protein design, it yields interaction matrices associated with improved structural fidelity and accurate contact prediction, while clarifying how learned sequence patterns relate to the interactions that stabilize protein structure.

Biological active matter like the cytoskeleton or tissues is characterized by its ability to transform chemical energy into mechanical stress. In addition, it often exhibits orientational order, which is essential for many cellular and morphogenetic processes. Experimental evidence suggests that defects in the orientational order field play an important role in organizing active stress. However, defects tend to annihilate unless the material is in a chaotic state or hydrodynamic interactions are suppressed. Using a hydrodynamic description of compressible active polar fluids, we show that renewal readily leads to a stabilization of defects. Depending on the renewal rate, topological defects arrange in a multitude of different phases, including lattices, active foams, and vortex glasses. Our work suggests that renewal plays a crucial role for organizing biological active matter.

Biomolecular condensates formed by liquid-liquid phase separation organize many cellular processes, yet it remains unclear how condensate localization is coupled to protein synthesis. In particular, proteins are often translated on polysomes, where multiple ribosomes on a single mRNA generate a bottlebrush-like assembly of nascent chains, raising the possibility that translation itself could be spatially coupled to condensates. Here we develop a theoretical framework for CoTranslational Condensation (CTC), in which nascent chains on a polysome for condensate proteins interact with their condensate and thus localize translation there. Using coarse-grained simulations, we show that protein domain architecture dictates the thermodynamics of CTC, consistent with a Langmuir adsorption model. Proteins with high-affinity regions exposed early on nascent chains display much stronger condensate association than architectures in which these regions appear only late in translation. A bioinformatic analysis of 7667 condensate-associated proteins further shows that sequence architectures compatible with strong CTC are common. At the dynamical level, combining simulations with reaction-diffusion modeling reveals that CTC is kinetically feasible within typical polysome lifetimes, either through densely packed polysomes nucleating new condensates or via diffusion to preexisting condensates. As an illustrative consequence, we show that CTC can reduce the accumulation of unmodified protein intermediates by localizing their synthesis with condensates, where modification can occur promptly. Together, our results establish physical principles for how translation can couple to phase separation and identify protein architectures and cellular regimes that favor CTC.

Collective motion in animal groups emerges from local interactions, yet how individuals select and integrate social information remains poorly understood. In schooling fish, inferring which neighbors drive an individual's behavior at any given moment is extremely challenging because the analysis of trajectories alone does not unambiguously reveal the underlying causal interactions that generate the observed motion. Here, we used a closed-loop virtual-reality system in which a single real rummy-nose tetra Hemigrammus rhodostomus interacted in real time with four model-driven virtual conspecifics whose interaction rules could be precisely controlled. By systematically varying the number of influential neighbors of the virtual fish and combining experiments with simulations, we quantified how social information filtering shapes individual and collective dynamics. Collective coordination increased with stronger social coupling, but analyses of kinematics, spatial organization, correlations, and turning dynamics consistently showed that the real fish behaved as if it were responding primarily to the single most influential neighbor, whose identity could change over time. These results demonstrate that selective interaction with the most influential neighbor is sufficient to sustain coordinated group motion and highlight the power of biohybrid closed-loop experiments to reveal causal mechanisms of collective behavior.

The cytoskeleton organizes the cellular interior using cytoskeletal filaments that rely on bundling, usually executed by stable and ordered cross-linking proteins. Bundling often requires protein complexes with at least two defined microtubule binding regions, as present in many molecular motors. Here, we establish a mechanism of microtubule bundling based on capillary forces, analogous to how wet hair sticks together. We show using in vitro experiments and theory that condensates can bundle microtubules through capillary forces, wherein liquidlike capillary bridges form between microtubules and adhere them together through interfacial and wetting forces. We quantify the structure and dynamics of these capillary bundles using total internal reflection fluorescence microscopy, and directly measure the interfacial tensions of condensates on microtubules using atomic force microscopy. Lastly, we show that these capillary bridges provide viscous resistance to motor-driven microtubule sliding that is insensitive to the bulk protein concentration. Taken together, we provide a novel mechanism for how cytoskeletal filaments bundle: through condensate-mediated capillary forces.

Plants employ diverse mating strategies, including self- and cross-fertilization or their combination. Despite the ubiquity of mixed mating—the use of both self- and cross-fertilization within the same population—its evolutionary origins and dynamic stability remain elusive. Here, we study self-incompatibility, in which self-fertilization is disabled by molecular recognition and enabled when mutations disrupt this recognition. Using population-level stochastic simulations, we model the effects of two main parameters on the prevailing mating mode: promiscuity of molecular recognition and inbreeding depression, which penalizes self-compatibility. We reveal a phase diagram with three phases: complete self-incompatibility, complete self-compatibility, and a mixture combining both. The mixed phase exhibits newly described vigorous, nondecaying fluctuations in the proportions of individuals occupying either mating mode. Pollen limitation extends the parameter range over which complete self-incompatibility is favored, contrary to the commonly held view. This study offers new insight into the evolutionary dynamics of plant reproductive systems.

Characterizing the long-term behavior of dynamical systems given limited measurements is a common challenge throughout the physical and biological sciences. This is a challenging task due to the sparsity and noise inherent to empirical observations, as well as the variability of possible long-term dynamics. We address this by introducing smooth prototype equivalences (SPE), a framework for matching sparse observations to prototypical behaviors using invertible neural networks that model smooth phase-space deformations. SPE can localize the invariant sets describing long-term behavior of the observed dynamics through the learned mapping from prototype space to data space. Furthermore, SPE can classify dynamical regimes by comparing the data residual of the deformed measurements to prototype dynamics. Our method outperforms existing techniques in the classification of oscillatory systems and can efficiently identify invariant structures like limit cycles and fixed points in an equation-free manner, even when only a small, noisy subset of the phase space is observed. SPE further reveals driving genes in synthetic oscillators such as the repressilator regulatory circuit, and traces cyclic biological processes like the cell cycle trajectory directly from experimental high-dimensional single-cell gene expression data. Finally, the flexibility of the prototype-matching approach of SPE makes it possible to interrogate a diverse set of biologically relevant behaviors, enabling the localization of a bifurcation between epiblast and primitive endoderm fates in the early mouse embryo, and identification of differentiation endpoints, along with candidate marker genes, from hematopoietic lineage-tracing data.

The bacterial flagellar motor (BFM) converts transmembrane ion flux into directed mechanical rotation, driving bacterial motility. Despite extensive study, the frictional forces and energetics governing its torque generation remain poorly understood. Here we combine single-molecule rotation measurements with stochastic thermodynamics to quantitatively estimate its effective torque, viscous drag, and activation energy barriers. We present three complementary methods based on solutions to the Smoluchowski equation for overdamped diffusion in a tilted periodic potential, which use as input the steady-state angular velocity and rotational diffusion data from individual Escherichia coli motors spanning different dynamical regimes. Crucially, these three methods require neither active external torque control, nor prior knowledge of the system's viscous drag or the motor's torque output. The first method assumes as input a model-dependent sinusoidal effective potential (single Fourier mode), albeit with unknown periodicity, yielding closed-form results in the low- and high-tilt limits, whereas the last two methods use a full Fourier-based reconstruction to output the now model-independent effective potential landscape. These approaches yield consistent estimates of the potential periodicity ($\approx$26-fold symmetry), energy barrier height ($\approx$2–4 $k_{\mathrm{B}}T$), and internal friction coefficient ($\approx 0.1 \mathrm{pN}\mathrm{nm}\mathrm{s}/{\mathrm{rad}}^2$). These findings suggest that the reconstructed effective energy landscape is dominated by interactions associated with the LP-ring bearing. Our results reveal that the BFM's torque-velocity relationship deviates significantly from the linear approximation near the critical tilt, where angular diffusion is maximized. More broadly, our framework provides a coherent strategy for reconstructing nanoscale energy landscapes from single-molecule data and is generalizable to other stepping molecular motors operating in cyclic conditions.

The actin cortex is a dynamic biopolymer network that, despite constant architectural changes through the assembly and disassembly of filaments and crosslinkers, sustains a rigid homeostatic state, i.e., a steady state of positive elastic moduli, and exhibits an elastic memory that far outlasts the structural turnover timescale. We still lack simple models that maintain collective rigidity and elastic memory at long times compared to the turnover time. To address this, we develop two complementary elastic network models in which rigidity homeostasis and long-lived elastic memory with complete turnover emerge as a result of mechanosensitive dynamics of filaments (edges) and crosslinkers (nodes), respectively. Both models require the following minimal ingredients: (1) preferential disassembly of edges or nodes under small tension or force, (2) a small but nonzero rate of random disassembly, and (3) energy injection upon assembly. Our models are robust to variations in random disassembly rates, can recover from drastic structural disruption, and exhibit diffusion of nodes and edges in steady state, displaying representational drift similar to that found in neuronal activities and physical learning circuits. We propose that the cortex is an example of “tunable matter,” i.e., its mechanosensitive remodeling dynamics tune properties of its edges and nodes so that the cortex as a whole can maintain robust but flexible rigidity in fluctuating mechanical environments.

Living cells exhibit a complex organization comprising numerous compartments, among which are RNA- and protein-rich membraneless, liquidlike organelles known as biomolecular condensates. Energy-consuming processes regulate their formation and dissolution, with (de)phosphorylation by specific enzymes being among the most commonly involved reactions. By employing a model system consisting of a phosphorylatable peptide and homopolymeric RNA, and thanks to time-resolved ultra-small-angle x-ray scattering enabling us to probe a wide range of length and time scales, we elucidate how enzymatic activity remodels the growth kinetics and the internal structure of biomolecular condensates. Under a passive condition, we reveal a nucleation-driven coalescence mechanism maintained over four decades in time, similar to the coarsening of simple binary fluid mixtures. Coarse-grained molecular-dynamics simulations show that peptide-decorated RNA chains assembled immediately after mixing constitute the basic subunits. In contrast, actively formed condensates initially display a networklike internal structure, which gradually matures upon dephosphorylation prior to coalescence. Both pathways lead to a steady state, but fluorescence recovery after photobleaching indicates a peptide diffusivity that is twice as high in actively formed condensates consistent with their loosely packed internal structure. This study contributes to linking effectively cellular active processes such as post-translational modifications to the formation and dissolution pathways of membraneless organelles, impacting other fields including synthetic biology.

Affinity maturation is a stochastic evolutionary process allowing the adaptive immune system to produce B cells capable of recognizing antigenic molecules. One of the main factors influencing the quality of the maturation outcome, quantified by the affinity of the produced antibodies to the antigen, is the time course of antigen availability. In this paper, we develop a stochastic model for affinity maturation, calibrated against in vivo lineage dynamics and deep mutational scanning data, and address the following question: What is the best antigen-concentration protocol maximizing the probability of reaching a target affinity value at the end of the process? We introduce a path-integral formalism to identify the maturation trajectories of the rare clones ending at the desired target affinity, estimate their probabilities, and maximize them over the antigen-concentration temporal profile. The theoretical optimal concentration protocol is approximated by a discrete three-injection schedule; we show that such temporal modulation of selection pressure outperforms constant-dosage regimes.

The statistical physics view of microbial ecosystems often invokes random unstructured interactions, consistent with bacterial coexistence in very high-dimensional niche spaces. While this approach successfully reproduces broad community-level statistics, its central assumption of high-dimensional coexistence remains untested due to a lack of direct empirical estimates. Here we evaluate this assumption by inferring the effective niche dimensionality directly from abundance profile data using a joint species distribution model, a nonlinear low-rank matrix factorization approach. The inferred niche dimensionality, ${\eta }_D$, tracks ecological expectations: It correlates significantly with the dimensionality of the metabolic environment across paired 16S-metabolomics datasets, supporting the abundance-only inference. Applying this framework across nearly 200 human gut microbiome studies, we find that the inferred dimensionality is consistently low (median ${\eta }_D\approx 4$), markedly lower than median ${\eta }_D\approx 13$ predicted by diversity-matched disordered consumer-resource models, directly contradicting the high-dimensional assumption underlying current theoretical models. Low dimensionality was associated with stronger interspecies competition and reduced biodiversity, consistent with the long-standing macroecological predictions. Consumer-resource simulations reproduced these empirical relationships only when extrinsic resource availability trade-offs were imposed, with species-intrinsic metabolic trade-offs contributing an additional reduction in the effective dimensionality. Together, our results challenge the high-dimensional assumption underlying current physics-based descriptions of microbiomes and identify low-dimensional coexistence as an essential feature of host associated microbiomes.

It often is emphasized that gene expression is noisy. A seemingly contradictory view is that control mechanisms have been optimized to squeeze as much information as possible out of a limited number of molecules. Here we revisit these issues in a simple model where a single transcription factor (TF) controls a large number of target genes. We include only the physically required noise sources—random arrival of TFs at their targets and counting noise in the synthesis and degradation of messenger RNA (mRNA). If the cell has a limited total number of mRNA molecules, then the capacity to transmit information about TF concentration is maximized when these resources are distributed across the largest possible number of target genes. To realize this capacity the distribution of TF concentrations must be biased toward smaller values. Thus, in some limits, information transmission is optimized when individual expression levels are noisy. In addition, the dependence of information transmission on the parameters of this multigene system has a “sloppy” spectrum, so that optimal performance can coexist with substantial variability.

Cellular metabolism is globally regulated by various currency metabolites such as ATP, GTP, and NAD(P)H. These metabolites cycle between charged (high-energy) and uncharged (low-energy) states to mediate energy transfer. While distinct currency metabolites are associated with different metabolic functions, their charged and uncharged forms are generally interconverted through biochemical reactions such as $\mathrm{ATP}+\mathrm{GDP}\rightleftharpoons \mathrm{ADP}+\mathrm{GTP}$ and ${\mathrm{NADP}}^{+}+\mathrm{NADH}\rightleftharpoons \mathrm{NADPH}+{\mathrm{NAD}}^{+}$. Thus, their energetic states are generally coupled and influence each other, which would hinder the independent regulation of different currency metabolites. Despite extensive knowledge of the molecular biology of individual currency metabolites, it remains poorly understood how the coordination of various coupled currency metabolites shapes metabolic regulation, efficiency, and ultimately the evolution of organisms. Here, we present a minimal theoretical model of metabolic currency coupling and reveal a fundamental tradeoff relationship between metabolic controllability and thermodynamic cost: increasing the capacity to independently regulate multiple currency metabolites generally requires comparable abundances of those metabolites, which in turn incurs a higher entropy production rate. The tradeoff suggests that in complex environments, organisms evolutionarily favor comparably sized currency-metabolite pools to enhance metabolic controllability at the expense of a higher thermodynamic cost; conversely, in simple environments, organisms are expected to evolve more imbalanced currency pools to reduce heat dissipation. These considerations also offer a hypothesis regarding evolutionary trends in nucleotide-pool balance and genomic GC content.

How can protein-independent, side-by-side alignment of homologous double-stranded DNA (dsDNA) arise as an early step in genome repair and genetic exchange, and what determines their kinetics under confinement? Although recombination proteins are known to facilitate this process, experiments indicate that an initial side-by-side arrangement of homologs can occur even in their absence. Helical Coherence Theory (HCT) proposes that sequence-dependent distortions of the double helix lead to commensurate charge patterns between interacting dsDNAs, favoring homologous over nonhomologous alignment. However, HCT has largely been developed for straight, rigid dsDNA rods, an approximation limited to roughly one persistence length (${\ell }_B\approx 50$ nm), leaving the question open as to how recognition manifests in longer, fluctuating chains. Moreover, the dynamics and timescales of homolog searching under confinement, and the internal dynamics of the paired state, such as transient formation of local unpaired regions (“bubbles”) and end fraying, remain unexplored. Here we extend HCT to dsDNA chains of multiple persistence lengths under confinement using coarse-grained simulations with a custom HCT-based force field to promote our understanding of how homologous genes pair in vivo. We simulate two homologous chains in spherical cavities spanning 0.3 to 1 times the free-space gyration radius under two limiting ionic conditions, and use the ratio of confinement radius to free-space gyration radius as a control parameter. Pairing occurs on microsecond timescales, with intermediate confinement giving the most favorable balance between rapid encounter and avoidance of kinetically trapped states. This behavior reflects a crossover from diffusion-limited search under weak confinement to trapping-dominated dynamics under strong confinement. To resolve pairing dynamics, we develop and fit a kinetic theory to simulation trajectories, distinguishing rates of independent pairing modes underlying bubble formation and fraying. Together, these results establish a general physical principle: confinement acts as a control parameter that governs a crossover between diffusion-limited and kinetically trapped pairing regimes for homologous DNA chains, contributing to a minimal protein-free mechanism for homologous recognition on biologically relevant timescales.

Circuits in the brain commonly exhibit modular architectures that factorize complex tasks, resulting in the ability to compositionally generalize and reduce catastrophic forgetting. In contrast, artificial neural networks (ANNs) appear to mix all processing, because modular solutions are difficult to find as they are vanishing subspaces in the space of possible solutions. Here we draw inspiration from fault-tolerant computation and the Poisson-like firing of real neurons to show that activity-dependent neural noise, combined with nonlinear neural responses, drives the emergence of solutions that reflect an accurate understanding of modular tasks, corresponding to acquisition of a correct world model. We find that noise-driven modularization can be recapitulated by a deterministic regularizer that multiplicatively combines weights and activations, revealing rich phenomenology not captured in linear networks or by standard regularization methods. We show that modularized ANNs exhibit superior robustness to noise and adversarial attacks. When applied as an architectural constraint, a premodularized ANN acquires the ability to generalize and extrapolate well beyond training data, compared to ANNs without such inductive biases. Together, our work demonstrates a regularizer and architectures that could encourage modularity emergence to yield functional benefits.

Cytoplasm is a heterogeneous mixture containing many types of proteins that self-assemble into a wide variety of complexes. The accuracy and speed of cytoplasmic self-assembly is astonishing because it involves the correct identification of components shared among different structures, despite pervasive thermal fluctuations. Typical toy models of self-assembly are based on the specificity of binding energies among components. However, kinetics plays a key role in biological self-assembly, often catalyzed by a plethora of assembly factors. Building on this observation, we extend a previous heteropolymer growth model to describe the retrieval of two-dimensional structures via quasi-two-dimensional growth. We find that the self-assembly of structures in this model is subject to strong speed and encoding bottlenecks. Moreover, we show that these bottlenecks can be suppressed by increasing the connectivity of a small fraction of components. This mechanism of kinetically controlling a small number of critical binding events provides a simple explanation for the timely assembly of large heteromeric protein complexes and suggests a unifying principle for the role of assembly factors.

Biological cells contain actin structures of different types and sizes, but all of them are continuously turned over. Since they all compete for a shared pool of actin monomers, the question arises how they can coexist in these dynamic steady states. Recently, the coexistence of branched actin networks with different densities growing in a shared and finite pool of purified proteins has been demonstrated in a biomimetic bead assay. However, theoretical work in the context of organelle size regulation has mainly been focused on linear architectures, such as single filaments and bundles, and thus is not able to explain this observation. Here we show theoretically that the local depletion of actin monomers caused by the growth of a branched network naturally gives rise to a negative feedback loop between network density and growth rate and that this competition is captured by one central ordinary differential equation. A comprehensive bifurcation analysis shows that the theory leads to well-defined steady states even in the case of multiple networks sharing the same pool of monomers, without any need for specific molecular processes. Under increasing competition strength, coexistence is replaced by selection. We also show that our theory is in excellent agreement with spatiotemporal simulations, implemented in a finite element framework, and that local depletion even occurs in the presence of a large pool of nonpolymerizable actin. In summary, our work suggests that local monomer depletion is the decisive and universal factor controlling growth of branched actin networks.