Networks of interconnected neurons display diverse patterns of collective activity. Relating this collective activity to the network's connectivity structure is a key goal of computational neuroscience. We approach this question for clustered networks, which can form via biologically realistic learning rules and allow for the reactivation of learned patterns. Previous studies of clustered networks have focused on metastabilty between fixed points, leaving open the question of whether clustered spiking networks can display richer dynamics—and if so, whether these can be predicted from their connectivity. Here we show that in the limits of large population size and fast inhibition, the combinatorial threshold linear network (CTLN) model is a mean-field theory for inhibition-stabilized nonlinear Hawkes networks with clustered connectivity. The CTLN has a large body of “graph rules” relating network structure to dynamics. By applying these, we can predict the dynamic attractors of our clustered spiking networks from the structure of between-cluster connectivity. This allows us to construct networks displaying a diverse array of nonlinear cluster dynamics, including metastable periodic orbits and chaotic attractors. Relaxing the assumption that inhibition is fast, we see that the CTLN model is still able to predict the activity of clustered spiking networks with reasonable inhibitory timescales. For slow enough inhibition, we observe bifurcations between CTLN-like dynamics and global excitatory/inhibitory oscillations.

The “critical brain hypothesis” posits that neural circuitry may be tuned close to a “critical point” or “phase transition”—a boundary between different operating regimes of the circuit. The renormalization group method was developed to explain the emergence of scale invariance in the statistics of systems tuned to a critical point. In the brain this scale invariance has been hypothesized to have several computational benefits, including increased collective sensitivity to changes in input and robust propagation of information across a circuit. However, our theoretical understanding of critical phenomena in neural circuitry is limited because standard renormalization group methods apply to systems with either highly organized or completely random connections. Connections between neurons lie between these extremes and may be either excitatory (positive) or inhibitory (negative) but not both. In this work we present a scaling theory for the population statistics of critical neural activity on networks with some realistic biological constraints on the connectivity. This scaling theory derives from a renormalization group method we develop for models of spiking neural populations—the spike response model with escape noise, also known as the nonlinear Hawkes process. We show that the scaling theories differ for models of in vitro versus in vivo circuits—they belong to different “universality classes”—and that both may exhibit “anomalous” scaling at a critical balance of inhibition and excitation. We verify our theoretical results on simulations of neural activity data and discuss how our scaling theory can be further extended and applied to real neural data, as well as other biophysical phenomena.

There is a long history of using experimental and computational approaches to study noise in single-cell levels of mRNA and proteins. The noise originates from myriad factors: intrinsic processes of gene expression, partitioning errors during division, and extrinsic effects, such as random cell-cycle times. Although theoretical methods are well developed to analytically understand the statistics of copy numbers for fixed or Erlang distributed cell cycle times, the general problem of random division times is still open. For any random (but uncorrelated) division time distribution, we present a method to address this challenging problem and obtain exact series representations of the copy number distributions in the cyclo-stationary state. We provide explicit cell age-specific and age-averaged results, and analyze the relative contribution to noise from intrinsic and extrinsic sources. Our analytical approach will aid the analysis of single-cell expression data and help in disentangling the impact of variability in division times.

Antigenic escape constitutes the main mechanism allowing rapidly evolving viruses to achieve endemicity. Beyond granting immune escape, empirical evidence also suggests that mutations of viruses might increase their interhost infectiousness. While both mechanisms are well-studied individually, their combined effects on viral endemicity remain to be explored. Here we propose a minimal eco-evolutionary framework to simulate epidemic outbreaks generated by pathogens evolving both their infectiousness and immune escape. Our results reveal that the main driver of viral evolution shifts over time: from intrinsic selection for infectiousness at early stages of the outbreak to antigenic diversification in the transition to the endemic phase. We find that the evolution in both traits during the first epidemic wave plays a critical role in determining long-term viral persistence. Evolution in infectiousness enhances the endemicity of viruses, especially in viruses with lower baseline infectiousness due to the longer duration of their first epidemic wave. Likewise, control policies flattening epidemic curves might increase viral endemicity as a result of the greater antigenic diversity generated in the prolonged epidemic waves. Our results thus prove that the long-term behavior of epidemic trajectories hinges on the complex interplay between both evolutionary pathways and the underlying contagion dynamics.

Starting from one totipotent cell, complex multicellular organisms form through a series of differentiation and morphogenetic events, culminating in a multitude of cell types arranged in a functional and intricate spatial pattern. To do so, cells coordinate with each other, resulting in dynamics which follow a precise developmental trajectory, constraining the space of possible embryo-to-embryo variation. Using recent single-cell sequencing data of early ascidian embryos, we leverage natural variation together with modeling and inference techniques to investigate development at the level of a complete interconnected embryo—an embryonic transcriptome. After developing a robust and biophysically motivated approach to identifying distinct transcriptomic states or cell types, a statistical analysis reveals correlations within embryos and across cell types demonstrating the presence of collective variation. From these intraembryo correlations, we infer minimal networks of cell-cell interactions, which reveal the collective modes of gene expression. Our work demonstrates how the existence and nature of spatial interactions along with the collective modes of expression that they give rise to can be inferred from single-cell gene expression measurements, opening up a wider range of biological questions that can be addressed using sequencing-based modalities.

Controlling the stochastic dynamics of biological populations is a challenge that arises across various biological contexts. However, these dynamics are inherently nonlinear and involve a discrete state space, i.e., the number of molecules, cells, or organisms. Additionally, the possibility of extinction has a significant impact on both dynamics and control strategies, particularly when the population size is small. These factors hamper the direct application of conventional control theories to biological systems. To address these challenges, we formulate the optimal control problem for stochastic population dynamics by utilizing control cost functions based on the $f$-divergence, which naturally accounts for population-specific factors. If Kullback-Leibler divergence is adopted for the cost function, the complex nonlinear Hamilton-Jacobi-Bellman equation is simplified into a linear form, facilitating efficient computation of optimal solutions. We demonstrate the effectiveness of our approach by applying it to the control of interacting random walkers, Moran processes, and SIR models, and observe the mode-switching phenomena in the control strategies. Our approach provides new opportunities for applying control theory to a wide range of biological problems.

The critical brain hypothesis posits that neural systems operate near a phase transition, optimizing the processing of information. While scale invariance and non-Gaussian dynamics—hallmarks of criticality—have been observed in brain activity, a direct link between criticality and behavioral performance remains unexplored. Here, we use a phenomenological renormalization group approach to examine neuronal activity in the primary visual cortex of mice performing a visual recognition task. We show that nontrivial scaling in neuronal activity is associated with enhanced task performance, with pronounced scaling observed during successful task completion. When rewards were removed or non-natural stimuli presented, scaling signatures diminished. These results suggest that critical dynamics in the brain is crucial for optimizing behavioral outcomes, offering new insights into the functional role of criticality in cortical processing.

Simulation-based inference provides a powerful framework for cryoelectron microscopy, employing neural networks in methods like CryoSBI to infer biomolecular conformations via learned latent representations. This latent space represents a rich opportunity, encoding valuable information about the physical system and the inference process. Harnessing this potential hinges on understanding the underlying geometric structure of these representations. We investigate this structure by applying manifold learning techniques to CryoSBI representations of a simulated benchmark dataset and both simulated and experimental images of hemagglutinin. We reveal that these high-dimensional data inherently populate low-dimensional, smooth manifolds, with simulated data effectively covering the experimental counterpart. By characterizing the manifold's geometry using Diffusion Maps and identifying its principal axes of variation via coordinate interpretation methods, we establish a direct link between the latent structure and key physical parameters. Discovering this intrinsic low-dimensionality and interpretable geometric organization not only validates the CryoSBI approach but also enables us to learn more from the data structure and provides opportunities for improving future inference strategies by exploiting this revealed manifold geometry.

Protein-small molecule interactions, or receptor-ligand interactions, are essential for understanding biological processes and advancing drug design. Despite advancements, existing prediction models of these interactions still lack the capabilities and accuracy needed to replace traditional screening. In this paper, we introduce DockFormer, a method that leverages multimodal learning to predict both the binding affinity and structure of these interactions. DockFormer employs fully flexible docking, where no part of the receptor remains rigid, by adapting the AlphaFold2 architecture. Instead of relying on protein sequences and multiple sequence alignments, DockFormer uses predicted receptor structures as input. This modification enables the model to concentrate on ligand docking prediction, rather than protein folding, while preserving full receptor flexibility. The streamlined design also reduces the model size to just eight layers, compared to AlphaFold2's 48 layers, greatly accelerating the inference process and making it more efficient for large-scale screening. When evaluated on affinity benchmarks such as CASF-2016, PLINDER, and the recently released CASP16 ligand screening benchmark, DockFormer performs comparably to or better than state-of-the-art methods, which typically rely on templates or bound structures as input. On structural benchmarks such as PoseBusters and PLINDER, DockFormer demonstrated success rates of 20% and 15%, respectively.

A hallmark of development is the generation of spatial patterns driven by morphogen gradients and gene regulatory networks (GRNs). Although the mechanistic basis by which GRNs orchestrate cellular responses and tissue patterning during development is well understood, their evolutionary dynamics remain less clear. Still, mutations in regulatory elements that govern GRN-driven patterning are a key mechanism for patterning evolution. In this study, we use the de novo evolution of a stripe phenotype as a model framework to investigate the evolutionary dynamics associated with the emergence of new spatial gene expression boundaries and the adjustment of existing boundaries. To probe general principles of GRN-driven pattern evolution we introduce a new high-throughput theoretical framework that rapidly produces a comprehensive dataset of evolutionary trajectories. We leverage this large dataset to investigate the types of mutations that drive different phenotypic shifts in spatial patterning. Our findings suggest that the order in which mutations in gene-gene interactions appear and the specific combination of gene-gene interactions that mutate together determine the evolvability of novel spatial gene expression patterns. We interpret our results in the context of epistatic effects that naturally arise in networks of interconnected genes and show how contingencies and constraints emerge in our system. Our results elucidate the interplay between mutation and gene network organization, revealing how historical contingencies arise and impact the evolvability of GRNs and the predictability of their evolutionary outcomes.

The qualitative study of dynamical systems using bifurcation theory is key to understanding systems from biological clocks and neurons to physical phase transitions. Data generated from such systems can feature complex transients, an unknown number of attractors, and stochasticity. Characterization of these often-complicated behaviors remains challenging. Making an analogy to bifurcation analysis, which specifies that useful dynamical features are often invariant to coordinate transformations, we leverage contrastive learning to devise a generic tool to discover dynamical classes from stochastic trajectory data. By providing a model-free trajectory analysis tool, this method automatically recovers the dynamical phase diagram of known models and provides a “map” of dynamical behaviors for a large ensemble of dynamical systems. The method thus provides a way to characterize and compare dynamical trajectories without governing equations or prior knowledge of target behavior. We additionally show that the same strategy can be used to characterize the stochastic motion of bacteria, establishing that this approach can be used as a stand-alone analysis tool or as a component of a broader data-driven analysis framework for dynamical data.

The connectome describes the complete set of synaptic contacts through which neurons communicate. While the architecture of the Caenorhabditis elegans connectome has been extensively characterized, much less is known about the organization of causal signaling networks arising from functional interactions between neurons. Understanding how effective communication pathways relate to or diverge from the underlying structure is a central question in neuroscience. Here we analyze the modular architecture of the C. elegans signal propagation network, measured via calcium imaging and optogenetics, and compare it to the underlying anatomical wiring measured by electron microscopy. Compared to the connectome, we find that signaling modules are not aligned with the modular boundaries of the anatomical network, highlighting an instance where function deviates from structure. However, we find that some of the most striking features of the anatomical network are preserved, as exemplified by the pharynx, which is delineated into a separate community in both anatomy and signaling. We analyze the cellular compositions of the signaling architecture and find that its modules are enriched for specific cell types and functions, suggesting that the network modules are neurobiologically relevant. Lastly, we identify a “rich club” of hub neurons in the signaling network. The membership of the signaling rich club differs from the rich club detected in the anatomical network, challenging the view that structural hubs occupy positions of influence in functional (signaling) networks. The only overlap between the two rich clubs is given by neurons AVEL/R, which have some of the highest degrees in the anatomical network, again illustrating the preservation of the most pronounced features of the network. Our results provide new insight into the interplay between brain structure, in the form of a complete synaptic-level connectome, and brain function, in the form of a system-wide causal signal propagation atlas.

Diffusion and anomalous diffusion are widely observed and used to study movement across organisms, resulting in extensive use of the mean and mean-squared displacement,. However, these measures, corresponding to specific displacement moments, do not capture the full complexity of movement behavior. Using high-resolution data from more than 70 million localizations of young and adult free-ranging barn owls (Tyto alba), we reveal strong anomalous diffusion as nonlinear growth of displacement moments. The moment spectrum function ${\lambda }_t\left(q\right)$, defined by ${\langle \left|\mathit{x}\left(t\right)\right|}^q\rangle \sim t^{{\lambda }_t\left(q\right)}$, displays piecewise linearity in $q$, with a critical moment marking the crossover between scaling regimes. This highlights the need of a broad spectrum of displacement moments to characterize movement, which we link to age-specific ecological drivers. Furthermore, a characteristic timescale of 5 minutes marks an unexpected transition from a convex to a concave ${\lambda }_t\left(q\right)$. Using two stochastic models, a bounded Lévy walk and a multimode behavioral model, we account for the observed phenomena, showing good agreement with data, relating age-specific behavioral states to environmentally confined movement, and demonstrating how Lévy-walklike patterns can arise from the underlying behavioral structure. Finally, we discuss the ecological significance of our results, arguing that strong anomalous diffusion may be widespread in animal movement.

Collagen IV is one of the main components of the basement membrane, a layer of material that lines the majority of tissues in multicellular organisms. Collagen IV molecules assemble into networks, providing stiffness and elasticity to tissues and informing cell and organ shape, especially during development. In this work, we develop two coarse-grained models for collagen IV molecules that retain biochemical bond specificity and coarse grain at different length scales. Through molecular-dynamics simulations, we test the assembly and mechanics of the resulting networks and measure their response to strain in terms of stress, microscopic alignment, and bond dynamics. Within the basement membrane, collagen IV networks rearrange by molecule turnover, which affects tissue organization and can be linked with enzyme activity. Here we explore network rearrangements via bond remodeling, the process of breaking and remaking of bonds between network molecules. We then investigate the effects of active (enzymatic) bond remodeling. We find that this nonequilibrium remodeling allows a network to keep its integrity under strain, while relaxing fully over a variety of timescales, a dynamic response that is unavailable to networks undergoing equilibrium remodeling.

How animal groups dynamically adjust their collective behavior in response to environmental changes remains an open and challenging question. Here we investigate the mechanisms that allow fish schools to tune their collective state under stress, testing the hypothesis that these systems operate near criticality, a state that maximizes sensitivity, responsiveness, and adaptability. We combine experiments and data-driven computational modeling to study how group size and stress influence the collective behavior of rummy-nose tetras (Hemigrammus rhodostomus). We quantify the collective state of fish schools using polarization, milling, and cohesion metrics and use a burst-and-coast model to infer the social interaction parameters that drive these behaviors. Our results indicate that group size modulates stress levels, with smaller groups experiencing higher baseline stress, likely due to a reduced social buffering effect. Under stress, fish adjust the strength of their social interactions in a way that leads the group into a critical state, thus enhancing its sensitivity to perturbations and facilitating rapid adaptation. However, while large groups require an external stressor to enter the critical regime, small groups are already near this state. Our findings suggest that adjusting interaction strength is a simple yet effective mechanism that drives collective state transitions while minimizing individual cognitive load. By revealing how stress and group size drive self-organization toward criticality, our study provides fundamental insights into the adaptability of collective biological systems and the emergent properties in animal groups.

This paper explores the idea that information is an essential and distinctive feature of living systems. Unlike nonliving systems, living systems actively acquire, process, and use information about their environments to respond to changing conditions, sustain themselves, and achieve other intrinsic goals. We discuss relevant theoretical frameworks such as semantic information and fitness value of information. We also highlight the broader implications of our perspective for fields such as origin-of-life research and astrobiology. In particular, we touch on the transition to information-driven systems as a key step in abiogenesis, informational constraints as determinants of planetary habitability, and informational biosignatures for detecting life beyond Earth. We briefly discuss experimental platforms which offer opportunities to investigate these theoretical concepts in controlled environments. By integrating theoretical and experimental approaches, this perspective advances our understanding of life's informational dynamics and its universal principles across diverse scientific domains.

Central carbon metabolism in model cyanobacteria involves multiple pathways to adapt to energy-light limitations across diel cycles. However, the success in mechanistic modeling for phenotypic prediction of the protein regulators in the metabolic state depends on capturing the vast possibilities emerging from multiple regulatory pathways in complex biological processes. Here, we developed a physics-informed machine learning approach based on energy-landscape concepts to predict regulatory proteins responding to cyclic circadian and unforeseen light perturbations in cyanobacterial metabolic networks. Our approach provides interpretable de novo models for inferring gene expression dynamics from Synechococcus elongatus over diel cycles and using redox proteome analysis to distinguish immediate light-responsive elements from circadian-regulated processes in carbon metabolism pathways. We identified distinct temporal signatures with the analysis of the redox proteome: there was an immediate shift in cysteine redox states accompanied by a limited change in protein abundance under constant illumination and after 2 hours of darkness. This discovery indicates that the generation of reductants coordinates photoinduced electron transport with redox metabolic pathways in two discernable molecular mechanisms: fast redox-based protein modifications occur immediately after the light disturbance, followed by slow transcriptional regulations across networks. This temporal regulation reveals how metabolic networks integrate rapid light responses with programmed circadian rhythms to maintain cellular homeostasis under the light-energy limitations over the diel cycle.

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.