Ecosystems frequently display the coexistence of diverse species under resource competition, typically resulting in skewed distributions of rarity and abundance. A potential driver of such coexistence is environmental fluctuations that favor different species over time. How to include and treat such temporal variability in existing consumer-resource models is still an open problem. In this work, we study correlated temporal fluctuations in species' resource uptake rates—i.e., metabolic strategies—within a stochastic consumer-resource framework. In a biologically relevant regime, we are able to find analytically the species abundance distributions through the path integral formalism. Our results reveal that stochastic dynamic metabolic strategies induce community structures that align more closely with empirical ecological observations. Within this framework, ecological communities show a higher diversity than expected under static competitive scenarios. We find that all species become extinct when the ratio of the number of species to the number of resources exceeds a critical threshold. Conversely, diversity peaks at intermediate values of the same ratio. Furthermore, when metabolic strategies of different species are different on average, maximal biodiversity is achieved for intermediate values of the amplitude of fluctuations. This work establishes a robust theoretical framework for exploring how temporal dynamics and stochasticity drive biodiversity and community structure.

The migration behavior of colliding cells is critically determined by transient contact interactions. During these interactions, the motility machinery, including the front-rear polarization of the cell, dynamically responds to surface protein-mediated transmission of forces and biochemical signals between cells. While biomolecular details of such contact interactions are increasingly well understood, it remains unclear what biophysical interaction mechanisms govern the cell-level dynamics of colliding cells and how these mechanisms vary across cell types. Here we develop a phenomenological theory based on 14 candidate contact-interaction mechanisms coupling cell position, protrusion, and polarity. Using high-throughput micropattern experiments, we detect which of these phenomenological contact interactions captures the interaction behaviors of cells. We find that various cell types—ranging from mesenchymal to epithelial cells—are accurately captured by a single model with only two interaction mechanisms: polarity-protrusion coupling and polarity-polarity coupling. Remarkably, the qualitatively different interaction behaviors of distinct cells, as well as cells subject to molecular perturbations of surface protein-mediated signaling, can all be quantitatively captured by varying the strength and sign of the polarity-polarity coupling mechanism. Altogether, our data-driven phenomenological theory of cell-cell interactions reveals polarity-polarity coupling as a versatile and general contact-interaction mechanism, which may underlie diverse collective migration behaviors of motile cells.

Protein language models trained on the masked language modeling objective learn to predict the identity of hidden amino acid residues within a sequence using the remaining observable sequence as context. They do so by embedding the residues into a high dimensional space that encapsulates the relevant contextual cues. These embedding vectors serve as an informative context-sensitive representation that not only aids with the defined training objective, but can also be used for other tasks by downstream models. We propose a scheme to use the embeddings of an unmasked sequence to estimate the corresponding masked probability vectors for all the positions in a single forward pass through the language model. This one fell swoop (OFS) approach allows us to efficiently estimate the pseudo-perplexity of the sequence, a measure of the model's uncertainty in its predictions, that can also serve as a fitness estimate. We find that ESM2 OFS pseudo-perplexity performs nearly as well as the true pseudo-perplexity at fitness estimation, and more notably it defines a new state of the art on the ProteinGym Indels benchmark. The strong performance of the fitness measure prompted us to investigate if it could be used to detect the elevated stability reported in reconstructed ancestral sequences. We find that this measure ranks ancestral reconstructions as more fit than extant sequences. Finally, we show that the computational efficiency of the technique allows for the use of Monte Carlo methods that can rapidly explore functional sequence space.

Protein language models are significantly advancing the modeling of sequence-function relationships. However, most of them are not directly informed of homology and evolutionary relationships between protein sequences. Here, we propose a method to make them homology aware. We introduce RAG-ESM, a retrieval-augmented-generation (RAG) framework that allows us to condition pretrained ESM2 protein language models on homologous sequences, using a minimal number of additional cross-attention parameters and minimal computational cost. We show that RAG-ESM models outperform larger ESM2 models for masked amino acid prediction. We find that sequence alignment capabilities spontaneously emerge in specific cross-attention heads of RAG-ESM. By using a discrete diffusion objective for training, and by conditioning on homologs during inference, RAG-ESM reaches state-of-the-art performance for conditional protein sequence generation and motif scaffolding, among sequence-based models. Our method thus possesses strong potential for scalable, efficient and controlled protein engineering.

Neural correlations play a critical role in sensory information coding. They are of two kinds: signal correlations, when neurons have overlapping sensitivities, and noise correlations from network effects and shared noise. In experiments from early sensory systems and cortexes, many pairs of neurons typically show both types of correlations to be positive and large, especially between nearby neurons with similar stimulus sensitivity. However, theoretical arguments have suggested that the stimulus and noise correlations should have opposite signs to improve coding, at odds with experimental observations. We analyze retinal recording in response to a large variety of stimuli and show that, contrary to common belief, large noise correlations are beneficial for coding, even if aligned with signal correlations. To understand this result, we develop a theory of visual information coding by correlated neurons, which resolves that paradox. We show that noise correlations are always beneficial if they are strong enough, unless neurons are perfectly correlated by the stimulus. Finally, using neuronal recordings and modeling, we show that for high-dimensional stimuli noise correlation benefits the encoding of fine-grained details of visual stimuli, at the expense of large-scale features, which are already well encoded.

Coclustering of subsequent enzymes in a pathway can accelerate the processing of metabolic intermediates, with benefits including increased pathway fluxes, reduced toxicity, and sensitive branch-point regulation. While the optimal organization of such clusters has been explored theoretically, little is known about how to achieve such organization inside cells. Here we propose that phase-separating enzymes can self-organize into nearly optimally sized and spaced clusters, provided that their “stickiness” is regulated by local substrate availability. In a nutshell, enzyme clusters only form when and where they are needed to process substrate. We study a mathematical model that implements this scheme for simple metabolic pathways, including all thermodynamic constraints. We find that pathway fluxes can be increased by 50- to 1000-fold and toxic metabolites can be decreased by 10- to 100-fold at realistic enzyme densities. Finally, we discuss how enzyme “stickiness” could be allosterically regulated. This study presents a self-organization strategy that goes beyond current paradigms for natural and engineered enzyme clusters and thus represents a motivating challenge to the fields of synthetic biology and metabolic engineering.

The condensation of charged polymers is an important driver for the formation of biomolecular condensates. Recent experiments suggest that this mechanism also controls the clustering of eukaryotic chromosomes during the late stages of cell division. In this process, interchromosome attraction is driven by the condensation of cytoplasmic RNA and Ki-67, a charged intrinsically disordered protein that coats the chromosomes as a brush. Attraction between chromosomes has been shown to be specifically promoted by a localized charged patch on Ki-67, although the physical mechanism remains unclear. To elucidate this process, we combine coarse-grained simulations and analytical theory to study the RNA-mediated interaction between charged polymer brushes on the chromosome surfaces. We show that the charged patch on Ki-67 leads to interchromosome attraction via RNA bridging between the two brushes, whereby the RNA preferentially interacts with the charged patches, leading to stable, long-range forces. By contrast, if the brush is uniformly charged, bridging is basically absent due to complete adsorption of RNA onto the brush. Moreover, the RNA dynamics becomes caged in presence of the charged patch while remaining diffusive with uniform charge. Our work sheds light on the physical origin of chromosome clustering, while also suggesting a general mechanism for cells to tune work production by biomolecular condensates via different charge distributions.

As with many creative human activities, physics resists definition. Physics, as the saying goes, is what physicists do. But we can recognize major themes. One theme is the reductionist search for the building blocks of matter. In another direction is the exploration of the origins and history of the universe writ large. At intermediate scales, we explore the emergence of macroscopic behaviors that are more than the sum of their parts. An important lesson of the late 20th century is that these seemingly distinct themes are intertwined, so that theoretical physics today is more unified while at the same time reaching ambitiously across an even broader range of topics. The 2024 Nobel Prize in Physics, awarded jointly to John Hopfield and Geoffrey Hinton, celebrates the discovery of new classes of emergent phenomena, inspired by the function of brains and minds.

The cytoskeleton is an active and complex composite network of actin, microtubules, and intermediate filaments (IFs). Networks of these distinct biopolymers work in partnership to fulfill fundamental cellular processes, such as cell polarization, intracellular transport, and cell migration. While there is evidence that the different cytoskeletal filaments interact through biochemical signaling and physical interactions, many basic questions remain regarding how this crosstalk impacts the dynamics and organization of the cytoskeletal filaments. Here, we combine Fourier image analysis methods with live cell experiments to characterize the impacts of cytoskeletal crosstalk on the structure and dynamics of microtubules in mouse embryonic fibroblasts. Specifically, we investigate the impacts of depleting vimentin IFs ($\mathrm{vim}-/-$) as well as inhibiting actomyosin activity or inducing actin depolymerization. Using spatial image autocorrelation analysis, we identify that depleting vimentin decreases the effective mesh size of the microtubule network regardless of the state of the actin, while inhibiting myosin activity or depolymerizing actin increases the microtubule mesh size in cells with and without vimentin. Moreover, using differential dynamic microscopy, we reveal that microtubules exhibit superdiffusive motion over a wide range of length- and timescales, with rates that are enhanced in all cells lacking vimentin and suppressed in all cells where actin is disrupted. Our results reveal competing and seemingly independent roles that vimentin and actin play in mediating the dynamics and structure of the network of microtubules in cells across decades of spatiotemporal scales. We argue that these effects arise from the scaffolding ability of the vimentin and active dynamics of the actin, which independently sculpt microtubule network dynamics and structure in cells.

Feedbacks between evolution and ecology are ubiquitous, with ecological interactions determining which mutants are successful, and these mutants in turn modifying community structure. We study the evolutionary dynamics of several ecological models with overlapping niches, including consumer resource and Lotka-Volterra models. Evolution is assumed slow, with ecological dynamics producing a stable community (with some strains going permanently extinct) between successive introductions of an invader or mutant. When new strains are slowly added to the community, either from an external pool or by large-effect mutations of exant strains, an initial evolutionary transient gives way to a diverse eco-evolutionary steady state. In this “Red Queen” phase of continual evolution, the biodiversity continues to turn over without the invasion probability of new variants getting smaller. For resource-mediated interactions, the Red Queen phase obtains for any amount of asymmetry in the interactions between strains, and is robust to “general fitness” differences in the intrinsic growth rates of strains. Via a dynamical mean-field theory framework valid for high-dimensional phenotype space, we analytically characterize the Red Queen eco-evolutionary steady state in a particular limit of model parameters. Scaling arguments enable a more general understanding of the steady state and evolutionary transients toward it. This work therefore establishes simple models of continual evolution in an ecological context without host-pathogen arms races and points to the generality of Red Queen evolution. However, we also find other eco-evolutionary phases in simple models: For generalized Lotka-Volterra models with near-symmetric interactions an “oligarch” phase emerges in which the evolutionary dynamics continually slow down and a substantial fraction of the community's abundance condenses into a handful of slowly turning-over strains.

This review explores the critical role of the physics of the body and the environment in shaping behaviors within the emerging field of the physics of social interactions. We revisit the intriguing case study where a dead fish, lacking neural control, appeared to swim upstream, propelled by its body resonating with vortices. This example expanded the conventional view of behavior as solely a product of biological processes, underscoring the significant influence of physical forces on living and nonliving entities alike. We build upon this foundational understanding and review how the physical characteristics of individual organisms interact with other individuals and with their environments to produce complex group dynamics, focusing on key examples: hydrodynamic interactions in fish schools where individual movements are influenced by water flow and collective swimming patterns; thermoregulation in penguin huddles, where individuals closely pack to minimize heat loss and optimize energy use in harsh climates; and raft formation in ants as a survival strategy during floods, leveraging their collective buoyancy and waterproofing properties. Our discussion emphasizes the importance of considering both the physics of the bodies and the environmental factors in understanding these intricate dynamics. By combining findings from a range of taxa to showcase the interplay between physical and biological aspects of collective social behaviors, we hope to encourage further research that explores their many facets and implications.

Foraging is a widespread behavior. Specifically, social foraging can bring several benefits compared to solitary foraging, such as collective pooling of information and reducing environmental uncertainty. Based on an evidence accumulation framework, we developed a model of patch-leaving decisions in a large egalitarian group, going through two intertwined paradigms: in which habitat to forage and, inside habitats, how to balance exploration and exploitation in patches. In this paper, we define patches as small areas that are rapidly depleted, in contrast to habitats, defined as larger areas, almost nondepleted. Across these two environments, we used numerical simulations and analytical tools to quantify the collective foraging dynamics. We showed that three variables—the cohesion of a group, the mean residence times, and the accuracy in finding the best habitat—are relevant metrics to characterize the collective processes. In particular, cohesion, a less studied aspect in classical foraging approaches, characterizes the initial nonstationarity of the dynamics and is ecologically relevant as it provides risk dilution in the presence of threat. These metrics are shaped by different environment statistics, such as reward probabilities, travel time between areas, or the depletion rate. They also enable the quantification of the impact of social information. We found that these metrics are strongly modulated by social interactions and that different types of information sharing mechanisms give rise to a variety of emergent collective patterns. In particular, most interaction types increase accuracy, but have nontrivial and various effects on cohesion and exploration-exploitation tradeoff. The effects of these social interactions were similar in habitats and patches. We expect this flexible and quantitative model to be relevant for analyzing large scale foraging datasets and formulating hypotheses.

In bacteria, fluctuations in transcription factor (TF) concentrations and stochastic binding to promoters drive gene expression fluctuations in their target genes. However, how this “noise propagation” from TFs to their targets determines the expression fluctuations in target genes has so far not been quantitatively characterized. Here, we use fluorescence time-lapse microscopy in combination with microfluidics and automated image analysis to quantitatively track the single-cell expression dynamics of target promoters of the SOS response regulator LexA in Escherichia coli under mild DNA damage using the antibiotic Ciprofloxacin (Cipro). We find that all target promoters exhibit short stochastic expression bursts which become more frequent as the Cipro concentration increases, but whose durations are identical for all promoters, with exponentially distributed heights that vary across promoters, but that are independent of Cipro concentration. We show that these observations are inconsistent with popular “equilibrium” models of bacterial gene regulation that assume that binding and unbinding of TFs to promoters is fast relative to TF concentration fluctuations. Instead, all observations are quantitatively fit by a model in which DNA damage events lead to rapid transient dips in LexA concentration, and an expression burst occurs when LexA unbinds from the target promoter during such a short dip. Crucially, because these LexA concentration fluctuations occur on the same timescale as individual TF unbinding events, the responses of different target promoters to individual DNA damage events are complex stochastic and nonequilibrium functions of the strengths of their LexA binding sites and the durations of the events. Our results show that when induction events cause rapid TF concentration changes, i.e., on the timescale of individual TF binding and unbinding events, different target promoters exhibit distinct stochastic responses that read out different kinetics of the induction events. Since many bacterial TFs are activated through phosphorylation or binding to small signaling molecules, such nonequilibrium gene regulation is likely pervasive in bacteria, and may have been exploited by natural selection to encode distinct responses by different targets of the same TF.

The biophysical interactions between the T cell receptor (TCR) and its ligands determine the specificity of the cellular immune response. However, the immense diversity of receptors and ligands has made it challenging to discover generalizable rules across the distinct binding affinity landscapes created by different ligands. Here, we present an optimization framework for discovering biophysical rules that predict whether TCRs share specificity to a ligand. Applying this framework to TCRs associated with a collection of SARS-CoV-2 peptides, we systematically characterize how cospecificity depends on the type and position of amino-acid differences between receptors. We also demonstrate that the inferred rules generalize to ligands highly dissimilar to any seen during training. Our analysis reveals that the matching of steric properties between substituted amino acids is more important for receptor cospecificity than the hydrophobic properties that prominently determine evolutionary substitutability. Our analysis also quantifies the substantial importance of positions not in direct contact with the peptide for specificity. These findings highlight the potential for data-driven approaches to uncover the molecular mechanisms underpinning the specificity of adaptive immune responses.

The onset of neural induction in the anterior ectoderm of ascidian embryos is regulated at the extracellular level by FGF signaling molecules, which control the acquisition of neural fate through the activation of the ERK pathway. Among the anterior ectoderm cells exposed to FGF, only a fraction will acquire neural fate. The selection of neural precursors depends on the quasi-invariant geometry of the embryo, which imposes upon each ectoderm cell a precise area of cell surface contact with underlying FGF-expressing (mesendoderm) cells. Here we investigate information transmission between FGF and activated ERK and how this depends on the geometry of the system. Optimizing information transmission with the constraint that the total FGF-emitting surface area is restricted, as in the embryo, we find that the surface contacts with FGF that maximize information transmission are close to those observed experimentally. This information optimal solution is compatible with the anterior ectoderm cells having different areas of cell surface exposure to FGF, allowing the embryo to use cell surface areas as a regulatory mechanism for differentiating the outcome of cells that sense a constant FGF concentration.

How neurons integrate the myriad synaptic inputs scattered across their dendrites is a fundamental question in neuroscience. Multiple neurophysiological experiments have shown that dendritic nonlinearities can have a strong influence on synaptic input integration. These nonlinearities have motivated mathematical descriptions of single neurons as a two-layer computational units, which have been shown to increase substantially the computational abilities of neurons, compared to linear dendritic integration. However, current analytical studies are restricted to neurons with unconstrained synaptic weights and unplausible dendritic nonlinearities. Here we introduce a two-layer model with sign-constrained synaptic weights and a biologically plausible form of dendritic nonlinearity and investigate its properties using both statistical physics methods and numerical simulations. We find that the dendritic nonlinearity enhances both the number of possible learned input-output associations and the learning velocity. We characterize how capacity and learning speed depend on the implemented nonlinearity and the levels of dendritic and somatic inhibition. We calculate analytically the distribution of synaptic weights in networks close to maximal capacity and find that the dendritic nonlinearity increases the fraction of zero-weight (“silent” or “potential”) synapses, compared with the standard perceptron model, when no or weak robustness constraints are present, while the opposite occurs with strong robustness constraints. We test our model on standard real-world benchmark datasets and observe empirically that the nonlinearity provides an enhancement in generalization performance and that it enables to capture more complex input-output relations, compared to the perceptron model.

To maintain normal functionality, it is necessary for a multicellular organism to generate robust responses to external temporal signals. However, the underlying mechanisms to coordinate the collective dynamics of cells remain poorly understood. Here, we study the calcium activity of biological neuron networks excited by periodic ATP stimuli. We use micropatterning to control the cells' physical connectivity. We find that whereas isolated cells become more synchronized in their calcium activity at long driving periods, connected cells become less synchronized, despite expressing more gap junctions which enable calcium exchange. To understand this result, we use a mathematical model in which a bifurcation analysis has previously shown coupling-induced desynchronization in an oscillatory network. Using parameters close to this bifurcation but in the excitable regime, we find that this desynchronization persists and can explain the experimental observations. The model further predicts that co-culturing with gap-junction-deficient cells should restore synchronization, which experiments confirm. Combining quantitative experiments, the physical and biological manipulation of cells, and mathematical modeling, our results suggest that cell-to-cell connectivity significantly affects how populations encode an external temporal signal as it slows down: Sparse networks synchronize due to longer entrainment, whereas highly connected networks can desynchronize due to dynamic frustration.

Simple vertex models, where the cell shape is defined as a network of edges and vertices, have made useful predictions about the collective behavior of confluent biological tissues, including rigidity transitions. Quite a few different versions of vertex models have appeared in the literature, and they propose substantial differences in how the mechanical energy depends on vertex positions, yet all seem to make correct predictions. To understand how this is possible, we search for universality in the emergent mechanical behavior—including the shear modulus defined in the limit of zero-strain rate and the viscoelastic response at finite strain rates—of six different vertex models. We identify a class of models with a well-defined shear modulus, and demonstrate that these models all exhibit a crossover from a soft or floppy regime to a stiff regime. We find that the observed cell shape index (the ratio of the cell perimeter to the square root of the cell area) is a good observable order parameter for the crossover, even though the input model parameter that controls the crossover is different in each model. We also find that the finite-strain-rate viscoelastic response of all models exhibits a universal scaling with frequency, following the Zener model in the rigid phase and Burgers model in the fluid phase. The observation that a geometric observable like cell shape governs the transition, rather than a topological observable such as coordination number, suggests that second-order rigidity may be a good framework for explaining this universality. It generates an empirical prediction that a broad class of vertex models with second-order rigidity transitions should also exhibit these universal mechanical features, and helps to explain why many different vertex models are able to robustly predict these features in experiments.

The competition for resources is a defining feature of microbial communities. In many contexts, from soils to host-associated communities, highly diverse microbes are organized into metabolic groups or guilds with similar resource preferences. The resource preferences of individual taxa that give rise to these guilds are critical for understanding fluxes of resources through the community and the structure of diversity in the system. However, inferring the metabolic capabilities of individual taxa, as well as their competition with other taxa, within a community is challenging and unresolved. Here we address this gap in knowledge by leveraging dynamic measurements of abundances in communities. We show that simple correlations are often misleading in predicting resource competition. We show that spectral methods such as the cross-power spectral density and coherence that account for time-delayed effects are superior metrics for inferring the structure of resource competition in communities. We demonstrate this fact on synthetic data generated from consumer-resource models with time-dependent resource availability, where taxa are organized into groups or guilds with similar resource preferences. By applying spectral methods to oceanic plankton time-series data, we demonstrate that these methods detect interaction structures among species with similar genomic sequences. Our results indicate that analyzing temporal data across multiple timescales can reveal the underlying structure of resource competition within communities.

Targeted cancer therapies often induce a reversible drug-tolerant state in subpopulations of cells, akin to bacterial persistence. Precise characterization of these “cancer persisters” may inform the design of more effective treatment strategies. A previous investigation into the transition to persistence of colorectal cancer cell lines has revealed a distinct dependence on drug presence and concentration, not typical of bacterial systems. Leveraging these findings, this study uses mathematical modeling to explore intermittent treatment protocols aimed at diminishing the long-term fitness of the treated population, thereby enhancing therapeutic efficacy. We adapt a mathematical model originally designed for bacteria to describe colorectal cancer population dynamics in response to a series of treatment and release cycles. The model predicts the long-term increase or reduction of a treated population, as well as its asymptotic composition, leading us to identify success and failure regions within a clinically accessible parameter space, also in combination with hypothetical drugs that act on persisters. Strikingly, our analysis suggests, perhaps counterintuitively, that optimal treatment outcomes may be achieved in correspondence of nonzero recovery periods and lower than currently administered in the clinics drug concentrations. Furthermore, by incorporating patient drug pharmacokinetics in the model, we demonstrate that intermittent dosing strategies currently explored in clinical trials can be optimized to potentially rival the efficacy of continuous dosing regimens. These findings underscore the potential of mathematical models in guiding the design of optimal treatment protocols by fine-tuning nontrivial decisional trade-offs.