Entropy

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.

We develop a theoretical proposal linking vacuum stability and brain dynamics through superconductivity-inspired coherence, symmetry reduction, and the thermodynamic stabilization of low-entropy regimes. We take an unbroken SU(3) structure as a candidate stable residue of the low-temperature vacuum. At the neural level, we formulate a coarse-grained analog in which a two-fluid model with dissipative and coherence-supporting components describes brain dynamics. Specifically, the coherence-supporting component is proposed as a possible basis for the efficient binding and integration required to sustain a stable, unified conscious state. The proposal offers a common geometric language for relating physics and neuroscience with falsifiable signatures in coherence and state-dependent transitions. The main technical contribution is a computational algebraic model of conscious-state dynamics, where neural data are mapped to reconstructed state trajectories. Effective generators are inferred from those trajectories, and the two-fluid split is tested as a Cartan-root decomposition of su(3), with a rank-two commuting sector for coherence-preserving balance and six root directions for state transitions. This structure can be tested on neural data and contrasted with alternative dynamical models.

Despite extensive study of cellular mechanisms underlying long-term potentiation, no single specific protein or gene has been identified which encodes an individual unit of information, or memory bit. Indeed, the brain engram remains a knowledge gap. The theory of exclusion led us to cancel one-by-one several unrealistic biological options, suggesting that the explanation resides somewhere else. Superposition of up to concentric 300 myelin layers, spiraled, and highly compacted wrapping a single axon and each wrap could host hundreds to thousands of niches, as memory cells, collectively consisting of a massive array of cells. The disjointed 3D spatial superposition allows storage of charges, nodes not facing from a layer to next. The thickness of a single myelin layer ranges from 7.0 to 20 nm. The dimension scale is approximately the exact dimensions of the charge trap, the tunnel and dielectric also equipping current AI microchips. Stored charges are positive ions, with similar effect whether charges are negative or positive charges creating an electromagnetic field. To write data, following an action potential, this voltage applies to the control gates of the myelin layers producing an ionic charge injection. This causes charges to gain energy and tunnel through the myelin layer across Ranvier nodes, via quantum tunneling, and deep into the concentric myelin multilayers. This is creating an insulated trapping of K+ ions isolated from the system. In a long white matter tract bundle, the near-perfect isolation of millions of axons within compressed myelin wrap-ion channel K+/Na+ systems provides quantum coherence and precision of asynchronous firing property. The injected ionic charges (K+) become physically stuck in traps within the myelin layers. The K+ ions may not move freely, completely trapped after AP ceases. Mirroring a single-bit, single-level-cell, a trapped ionic charge (ions K+) may represent a 1, while an empty cell (absence of K+) represents a 0. The trial-and-error process, with a Bayesian inference which may have also been the core evolution of the learning human brain. Based on selected mathematical equations, we analyzed the general scheme on how deep learning may be embedded in the brain

Systems-level immune profiling data arising from longitudinal studies of vaccination or infection has an inherent multi-index array structure. While tensor decomposition of such datasets has gained popularity, choosing a rank and trial for a decomposition is not straightforward. We show that taking into account the experimental data model can inspire the development of new metrics to assess the quality of a Non-negative CANDECOMP/PARAFAC (NCPD) decomposition, and can thus be used to choose a rank and trial for the decomposition. Moreover, we show how framing the results via a dictionary learning framework can better enable interpretation of the components of the decomposition.

Mechanistic ordinary differential equation models are widely used in systems biology to represent biochemical networks, population dynamics, cell-state transitions, and other biological processes; however, their predictive value depends critically on accurate parameter estimation from noisy and often sparse experimental data. In this tutorial, we present the Weak-form Estimation of Nonlinear Dynamics (WENDy) method as a forward-solver-free approach that reformulates parameter estimation as a covariance-corrected weak-form regression problem by integrating the model equations against compactly supported test functions. We present the background on the methodology through the lens of the familiar logistic equation, and we demonstrate applications of the method on real experimental data through two systems biology examples: a glycolytic oscillator with relatively dense time-course data and a sparse epithelial-mesenchymal cellstate transition model with multiple experimental replicates. Ultimately, using WENDy, we estimate interpretable biological parameters with uncertainty for systems with noisy and sometimes sparse available experimental data.

Capturing naturalistic behavioral dynamics is essential for understanding social interaction in ecologically valid settings. Existing investigations of naturalistic social interaction rely on time-aggregated analysis methods better suited for task-based experiments, which lose the complex, moment-to-moment dynamics exhibited in naturalistic settings. The emerging field of topological data analysis (TDA) provides new tools to characterize fine-grained dynamics in time-series data that cannot be captured by time-averaged methods. The present work utilizes Temporal Mapper, a recently developed TDA specifically tailored to analyzing dynamical systems. Temporal Mapper characterizes complex temporal dynamics as transition networks, where nodes are stable states and edges are transitions between states. Originally designed for human neural time series analysis, here we demonstrate the utility of Temporal Mapper to capture rich animal postural dynamics during naturalistic social interaction. We utilized an existing dataset with 12 video recording sessions of two domestic ferrets (Mustela putorius furo) during naturalistic interaction and tracked the postures of animals during social interaction. Ferrets were chosen due to their strong social-cognitive skills and rich postural dynamics for investigating social behavior via posture estimation. Temporal Mapper was then used to represent the postural dynamics as transition networks for each recording session. Here, we found that posture states are significantly smaller and more widespread during active social interaction compared to non-social activities. Additionally, the number of sequential postural states before transitioning to new behaviors is more consistent during active social interaction than non-social activities. Together, our findings suggest that social activity has a broad range of unstable postural states arranged in consistent sequences. Our method, Temporal Mapper, allows for network structure analysis of complex naturalistic data, applicable for characterizing rich dynamics in different species, scales, and paradigms.

AO_SCPLOWBSTRACTC_SCPLOWCell fate decisions are driven by gene regulatory networks (GRNs). While the mutually inhibitory toggle switch effectively models binary fate decisions, fully connected inhibitory networks with more than two nodes fail to capture multi-fate decisions due to the low prevalence of "single high states", where only a single master regulator is highly expressed. The goal of this study is to find network structures that support all single high states. We find that the only network that attains the highest possible prevalence of all single high states within the set of monotone Boolean (MB) models is completely disconnected. Since biological networks typically require connectivity, we investigate network structures that support equipotency, where all single high states have equal prevalence within MB models. Finally, we characterize the networks that support multistability between all single high states, finding that it is possible only in networks in which each node either has self-activations or is inhibited by every other network node. Our findings provide a theoretical framework for understanding the network design principles that can support simultaneous differentiation into multiple distinct cell types.

Predicting gene essentiality across cellular contexts is a central challenge in computational biology, with implications for identifying cancer vulnerabilities. Graph neural networks (GNNs) integrate molecular interaction networks with gene-level features, but it remains unclear whether their performance gains arise from biologically meaningful connectivity or generic graph structure. Here, we systematically evaluate the role of network information in gene essentiality prediction using 2,741 genes across three tissues. We compare GNNs to feature-only baselines, including multilayer perceptron (MLP) and random forest (RF) methods, under a strict gene-level 5-fold cross-validation scheme to prevent information leakage. To isolate the role of network information, we assess models on the STRING protein-protein interaction network, a degree-preserving shuffled network, and a fully randomized network, with and without network-derived features. GNNs outperform feature-only models, reducing mean squared error and improving Matthews correlation coefficient across all tissues. However, these gains depend critically on biologically structured connectivity: performance degrades substantially under randomized topology and is not preserved by degree-constrained rewiring. Network features are largely redundant when using biologically meaningful graphs, as their information is recovered through message passing, but become important when topology is uninformative. Per-gene analyses reveal uniformly low correlations across models, highlighting intrinsic limits imposed by data variability. Graph Transformer models incorporating global attention do not outperform standard GNNs, indicating that predictive signals are predominantly local. Together, these results show that predictive gains arise from biologically structured connectivity rather than generic graph topology.

A priori assessment of target proteins' druggability remains an unsolved problem in the field of drug development. The empirical approaches widely used to solve this problem demonstrate low efficiency. In this work, we investigated the factor of hydration of a representative set of 65 evolutionarily and structurally unrelated human enzymes in a water environment. This factor depends only on the structure of the proteins, and not on the physical and chemical properties of any potential ligands. The results show that, unlike the widely used approaches based on calculations of the accessible surface area (ASA), the content of low-entropy water molecules (LEW) in the active sites of human enzymes is systematically higher than that in other areas of their surface, including inactive cavities. Optimal criteria and a step-by-step procedure for identifying protein ligand binding sites are proposed. The proposed approach, based on the calculation of the LEW content in the first hydration layer of potentially interesting target proteins, makes it possible to evaluate their medicinal suitability even before the development of any ligands. The article also presents the results of a comparative analysis of experimental Raman spectroscopy data and the results of molecular dynamics simulations of water hydrogen bonds using three widely used water models (TIP3P, OPC3, and TIP5P) and standard algorithms for calculating hydrogen bond networks.

Transitive inference (TI) is the ability to reason about transitive relationships in an ordered set of items (e.g., if A>B and B>C, then A>C). TI is widely held to depend on a linear representation of the serial (rank) order of those items. By what computational mechanism is such an ordering constructed during learning, and how is it used to make choices that obey transitivity? Here we take a minimalist approach, applying least-squares estimation (LSE) to a serial learning task commonly used to test TI in humans and animals. In this formulation, LSE computes a linear classifier that maps task conditions onto behavioral outcomes. This algorithm makes no explicit assumptions about transitivity or serial order, yet it reproduces key empirical features of TI; namely, the ability to generalize beyond the training set, and a symbolic distance effect (SDE) in performance accuracy. Applying the classifier to individual items produces an internally ordered representation of rank from which both generalization and the SDE naturally emerge. The approach also yields a decision mechanism, in the form of a differencing operation, for selecting the correct item from any pair. These findings reframe TI as a linear classification problem, challenging conventional assumptions about the cognitive mechanisms required for transitive reasoning.

In many brain regions, the stimulus tuning of neurons is stable on a timescale of hours but not on a timescale of weeks, a phenomenon often called representational drift. This would seem to imply that these brain regions cannot be used for stable recognition of sensory stimuli or the retrieval of associative memories learned several weeks prior. However, decoding approaches have demonstrated that in some cases, stable decoding of drifting representations is possible. In principle, adaptive decoding provides a plausible resolution to the paradox of how the brain operates with drifting representations, but we lack a deep understanding of what the requirements are for stable decoding to be possible. Here, we offer a general mathematical framework that explains when and why stable decoding from a drifting representation can be achieved. First, we demonstrate that both feedforward and recurrent networks preserve the geometry of their inputs when the network is sufficiently large, meaning that representational drift must also preserve geometry in these networks. Second, we demonstrate that drifting representations that have stable geometry are decodable with adaptive decoders. Therefore, not only the existence of preserved geometry in the presence of representational drift but also the ability to decode from drifting representations simply requires the population of neurons exhibiting representational drift to be large. This theoretical framework not only suggests that preserved geometry should be a general feature of drifting representations, it also explains the conditions under which empirical efforts to measure stable geometry will be successful.

The Protein Data Bank (PDB) is an ever-growing, open-access repository of structural data of biological molecules. This international database has been instrumental in the development of artificial intelligence and deep learning models for protein structure prediction and design. The PDB growth is a crucially important factor influencing further development of these models. Therefore, after analyzing the growth trend in PDB depositions since the archive's launch, we found that it is well fitted by the Gompertz function, a growth curve used across various disciplines. Furthermore, we observed that the function captures the "discovery of novel folds", i.e., the cumulative number of distinct folds among protein domains that constitute most of the PDB. Consequently, based on the fitting results, we estimated the likely numbers of PDB entries and protein folds. These findings provide insights into deceleration of growth in recent years and enable us to assess anticipated trends.

Many neural recordings have revealed low-dimensional sets of behaviorally relevant variables encoded within large-scale neural activity patterns. However, dimensionality reduction analyses alone cannot yield causal explanations for how networks stably implement computations that are resilient to the substantial variability of single neuron dynamics. Further, existing methods for dimensionality reduction often rely on simplifying assumptions about network structure that limit their applicability and explanatory power. To provide a theoretical framework describing the dynamics of low-dimensional computation in high-dimensional neural networks, here we introduce the concept of latent processing units (LPUs), which are architecture-agnostic computational elements operating within biological neural circuitry. Six theorems governing coding and computation by LPUs collectively provide explanations for a range of common biological findings: low-dimensional sets of coding variables can generate high-dimensional neural dynamics; many neurons have activity patterns that represent behaviorally relevant variables but exert little influence on downstream circuits; linear readouts of neural population activity commonly permit near-optimal decoding; the drift of neural representations is often substantial even while network computations remain intact. Overall, our treatment of LPUs, as enacted in network dynamics, unifies the geometric and dynamical views of neural computation under a joint framework and provides systems neuroscience with a causal account of how the brain executes reliable computations.

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.

What drove nucleic acids (NA) to associate with proteins (PR) at the Origins of Life? We reason from polymer physics and the Central Dogma (CD) that the fitness value of cooperating through a division of labor - NA for replication fidelity and PR for functional fitness - is much higher than for either polymer alone. Our model shows a Pareto Front, where NA and PR can bootstrap each other to achieve autocatalytic cooperativity towards biology.

Abnormal states such as erroneous behaviors are generally difficult to represent from neural data. However, such states are also known to have specific spatiotemporal features, indicating a feasibility of developing a method to focus on them. If a method can highlight these spatiotemporal features, it may effectively represent such abnormal states, helping evaluate abnormal brain functions. In the present study, we proposed the hierarchy of supported modules (HSM) to highlight spatiotemporal features that can represent abnormal states. HSM spatiotemporally transforms multidimensional neural time-series based on their spatiotemporal context. We evaluated HSM through decoding and similarity analyses using multiple publicly available datasets. In the HSM results, decoding accuracies were higher for erroneous behaviors than for normal behaviors, and similarities were lower between erroneous behaviors and normal behaviors than between normal behaviors, demonstrating the ability of HSM to capture the spatiotemporal features of erroneous behaviors. Surprisingly, many parts of these results were also present even before HSM learning, showing the virtue of HSM as a simple-to-use method. The proposed HSM method may help elucidate the mechanisms underlying erroneous behaviors.

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.

Approximate Bayesian computation sequential Monte Carlo (ABC-SMC) propagates its particles with a perturbation kernel, and with the standard Normal kernel it degrades sharply as the parameter dimension grows, a failure usually attributed to dimension itself. We show instead that it is governed by the quality of the summary statistics, with dimension entering only through a separate and milder mechanism, and that the two must act together for the Normal kernel to break. The first ingredient is covariance overinflation: the kernel covariance, estimated from the particle cloud, overshoots the true posterior covariance by a factor set by information loss in the summary statistics. We derive this overscaling factor in closed form for a Gaussian model with sufficient statistics and show that it stays modest at any dimension, shrinking toward its baseline value as the tolerance tightens; the extreme values seen in practice (of order 103) are a signature of insufficient summaries, not of dimension. The second ingredient is perturbation overconcentration: the normalised Normal step size concentrates around one as the dimension grows, so every proposal overshoots by the same factor. Either ingredient alone is harmless; only their combination breaks the Normal kernel. A Cauchy kernel (multivariate t with one degree of freedom) removes the concentration, keeping a positive acceptance rate under arbitrary overscaling at a bounded worst-case cost of 1.87x in expected squared jump distance. In a Metropolis-Hastings framework we derive closed-form acceptance rates for both kernels that illustrate the advantage of the Cauchy kernel in this limit. A series of full ABC-SMC computational experiments on five problems at d = 12, including a hierarchical gene-expression model, show the Cauchy reducing the sliced Wasserstein distance to the reference posterior by factors of up to 50 with the same simulation budget. Since the summary statistics are commonly insufficient for the models that require ABC, overinflation is structural and the Cauchy perturbation kernel is the right default for problems in higher dimensions.

Single-molecule (SM) imaging (SMI)-based approaches have the powerful ability to capture receptor interactions, which are necessary for cell signaling, in their native live-cell environment. Yet, due to substoichiometric labeling, SMI generally provides only partial information on these interactions. We developed Deep-FISIK, which utilizes graph neural networks and multi-head attention for message-passing, to predict from SMI data the kinetics of homotypic interactions of the full receptor system. The input to Deep-FISIK are the SM detections in SMI experiments, without the need for explicit tracking. Thus, Deep-FISIK is compatible with labeling a higher fraction of receptors in the SMI experiments, increasing the prediction accuracy of the interaction kinetics parameters. The performance of Deep-FISIK is robust in the presence of a variety of deviations from the training data, indicating the applicability of Deep-FISIK to many receptor systems and SMI experiments.

Every brain must adapt to an unpredictable world, yet individuals differ in how readily they learn. Theoretical work suggests that learning is fastest when a system, whether biological or synthetic, is initialized in a state close to instability - i.e., near criticality - because critical dynamics are imbued with a diverse repertoire of patterns and multi-scale correlations. Here, we empirically estimate distance to criticality in the brain and show that it predicts the rate of adaptability underlying learning, neuronal tuning, and general intelligence. In mouse motor cortex, proximity to criticality forecasts learning rate of two future complex tasks: prey capture hunt and ladder crossing. In contrast, distance to criticality predicted neither an animal's naive ability nor its asymptotic skill - isolating the rate of learning itself. In visual cortex of young ferrets, proximity to criticality predicts how strongly experience reshapes neural tuning. In human frontal cortex, it correlates with general cognitive ability. A minimal recurrent network model reproduced these results and offers a mechanism: proximity to criticality defines the timescale over which a system can learn from its past experiences, directly setting the rate of learning. A single dynamical property can account for the capacity to learn, from artificial networks to the mammalian brain.