Protein-ligand scoring is a central component of structure-based drug design, underpinning molecular docking, virtual screening, and pose optimization. Conventional physics-based energy functions are often computationally expensive, limiting their utility in large-scale screening. In contrast, deep learning-based scoring models offer improved computational efficiency but frequently suffer from limited cross-target generalization and poor interpretability, which restrict their practical applicability. Here we present BioLM-Score, a simple yet generalizable protein-ligand scoring model that couples geometric modeling with representation learning. Specifically, it employs modality-specific and structure-aware encoders for proteins and ligands, each augmented with biomolecular language models to enrich structural and chemical representations. Subsequently, these representations are integrated through a mixture density network to predict multimodal interatomic distance distributions, from which statistically grounded likelihood-based scores are derived. Evaluations on the CASF-2016 benchmark demonstrate that BioLM-Score achieves significant improvements across docking, scoring, ranking, and screening tasks. Moreover, the proposed scoring function serves as an effective optimization objective for guiding docking protocols and conformational search. In summary, BioLM-Score provides a principled and practical alternative to existing scoring functions, combining efficiency, generalization, and interpretability for structure-based drug discovery.

The deployment of wearable-based health prediction systems has accelerated rapidly, yet these systems face a fundamental challenge: they generate alerts under substantial uncertainty without principled mechanisms for user-specific validation. While large language models (LLMs) have been increasingly applied to healthcare tasks, existing work focuses predominantly on diagnosis generation and risk prediction rather than post-prediction validation of detected signals. We introduce Project Hermes, a model-agnostic validation layer that treats signal confirmation as a sequential decision problem. Hermes operates downstream of arbitrary upstream predictors, using LLM-generated contextual queries to elicit targeted user feedback and performing Bayesian confidence updates to distinguish true positives from false alarms. In a 60-day longitudinal case study of migraine prediction, Hermes achieved a 34% reduction in false positive rate (from 61.7% to 12.5%) while maintaining 89% sensitivity, with mean lead time of 4.2 hours before symptom onset. Critically, Hermes does not perform diagnosis or make novel predictions; it validates whether signals detected by upstream models are clinically meaningful for specific individuals at specific times. This work establishes validation as a first-class computational problem distinct from prediction, with implications for trustworthy deployment of consumer health AI systems.

How does the brain predict physical outcomes while acting in the world? Machine learning world models compress visual input into latent spaces, discarding the spatial structure that characterizes sensory cortex. We propose isomorphic world models: architectures preserving sensory topology so that physics prediction becomes geometric propagation rather than abstract state transition. We implement this using neural fields with motor-gated channels, where activity evolves through local lateral connectivity and motor commands multiplicatively modulate specific populations. Three experiments support this approach: (1) local connectivity is sufficient to learn ballistic physics, with predictions traversing intermediate locations rather than "teleporting"; (2) policies trained entirely in imagination transfer to real physics at nearly twice the rate of latent-space alternatives; and (3) motor-gated channels spontaneously develop body-selective encoding through visuomotor prediction alone. These findings suggest intuitive physics and body schema may share a common origin in spatially structured neural dynamics.

The white matter of the brain is organised into axonal bundles that support long-range neural communication. Although diffusion MRI (dMRI) enables detailed mapping of these pathways through tractography, how white matter pathways directly facilitate large-scale neural synchronisation remains poorly understood. We developed a data-driven framework that integrates dMRI and functional MRI (fMRI) to model the dynamic coupling supported by white matter tracks. Specifically, we employed track dynamic functional connectivity (Track-DFC) to characterise functional coupling of remote grey matter connected by individual white matter tracks. Using independent component analysis followed by k-medoids clustering, we derived functionally-coherent clusters of white matter tracks from the Human Connectome Project young adult cohort. When applied to the HCP ageing cohort, these clusters exhibited widespread age-related declines in both functional coupling strength and temporal variability. Importantly, specific clusters encompassing pathways linking control, default mode, attention, and visual systems significantly mediated the relationship between age and cognitive performance. Together, these findings depict the functional organisation of white matter tracks and provide a powerful tool to study brain ageing and cognitive decline.

Coordinating multi-articulated bodies to generate purposeful movement is a formidable computational challenge. Yet the human motor system performs this task robustly in dynamic, uncertain environments, despite noisy and delayed feedback, slow actuators, and strict energetic constraints. A central question is what organizational principles underlie this efficiency. One widely recognized principle of neural organization is modularity, which enables complex problems to be decomposed into simpler subproblems that specialized modules are optimized to solve. In this review, we argue that modularity is a fundamental organizing principle of the motor system. We first summarize evidence for brain modularity, ranging from classical lesion studies to contemporary graph-theoretical analyses. We next discuss the main factors underlying the emergence and evolutionary selection of modular architectures, highlighting the computational advantages they provide. We then review the major neuroanatomical modules that structure current descriptions of the motor system and compare three prominent computational frameworks of motor control$-$optimal feedback control theory, muscle synergy theory, and dynamical systems approaches$-$showing that all implicitly or explicitly rely on specialized computational modules. We conclude by contrasting the key strengths and limitations of existing frameworks and by proposing promising directions toward more comprehensive theories.

Gene regulatory networks (GRNs) define the regulatory relationships among molecules such as transcription factors, chromatin remodelers, and target genes. GRNs play a critical role in diverse biological processes, including development, disease manifestation, and evolution. However, fully characterizing these networks across multiple cell types and states remains a significant challenge. Recent advances in single-cell omics have dramatically enhanced our ability to measure biological systems at unprecedented resolution. These technologies have opened new avenues for computational methods to infer GRNs, offering deeper insights into cell type-specific mechanisms, causality, and dynamic regulatory processes. This review summarizes the current state of GRN inference from single cell omic datasets, with a particular focus on dynamics and perturbations, and outlines key open challenges that must be addressed to advance the field.

Adeno-associated viruses (AAVs) are promising vectors for gene therapy, but their native serotypes face limitations in tissue tropism, immune evasion, and production efficiency. Engineering capsids to overcome these hurdles is challenging due to the vast sequence space and the difficulty of simultaneously optimizing multiple functional properties. The complexity also adds when it comes to the kidney, which presents unique anatomical barriers and cellular targets that require precise and efficient vector engineering. Here, we present AAVGen, a generative artificial intelligence framework for de novo design of AAV capsids with enhanced multi-trait profiles. AAVGen integrates a protein language model (PLM) with supervised fine-tuning (SFT) and a reinforcement learning technique termed Group Sequence Policy Optimization (GSPO). The model is guided by a composite reward signal derived from three ESM-2-based regression predictors, each trained to predict a key property: production fitness, kidney tropism, and thermostability. Our results demonstrate that AAVGen produces a diverse library of novel VP1 protein sequences. In silico validations revealed that the majority of the generated variants have superior performance across all three employed indices, indicating successful multi-objective optimization. Furthermore, structural analysis via AlphaFold3 confirms that the generated sequences preserve the canonical capsid folding despite sequence diversification. AAVGen establishes a foundation for data-driven viral vector engineering, accelerating the development of next-generation AAV vectors with tailored functional characteristics.

We obtain bounds on the Kullback--Leibler divergence to equilibrium for mass-action chemical reaction networks (CRNs) with equilibrium. The associated decay rates are characterized in terms of the singular values of the stoichiometric matrix, convexity parameters, and time-integrated activities via deformed-exponential-type functions. We further extend these bounds within a generalized gradient flow framework. We highlight the biological relevance of this framework: the resulting bounds apply to quasi-steady-state regimes, where long transients and plateau-like behavior are common and functionally important. We illustrate the framework using a catalytic CRN exhibiting plateaus, where the bounds capture slow relaxation induced by local convexity and provide a bound-based approach to quantifying relaxation in CRNs.

Theoretical ecology has traditionally equated persistence with the stability of a fixed equilibrium point. Here we argue that the primary threat to ecosystem persistence need not be the loss of stability, but instead the escape of the stable equilibrium to a negative orthant. In a realistic setting, fluctuations in interactions do not merely disturb abundances about an equilibrium but can displace the equilibrium point itself. We theoretically and empirically analyze such displacements of the equilibrium point in a complex community. Theoretically, we find that light-tailed fluctuations in species interactions, no matter how small, lead to a heavy-tailed power law $P(y)=1/y^\alpha$ for the equilibrium abundance $y$ of a species. Remarkably, the exponent $\alpha=2$ is a universal value independent of interaction structure, community size, and species. Empirically, our analysis of 34 species reveals a power law signal for most, with a median exponent $\alpha \sim2.56$. Next, we derive a formula for the critical noise, $\sigma_c$, beyond which the community experiences feasibility loss ``with near certainty''. We find that $\sigma_c(N)\sim N^{-1}$, implying that larger communities are significantly more fragile to noise induced feasibility loss. Lastly, we define and calculate biologically measurable analytical metrics for both global and species-specific feasibility escape rates, and implement these metrics in dynamic simulations of 98 real world mutualistic and food web networks, to successfully predict their fragility.

EEG-based neural decoding models often fail to generalize across acquisition sites due to structured, site-dependent biases implicitly exploited during training. We reformulate cross-site clinical EEG learning as a bias-factorized generalization problem, in which domain shifts arise from multiple interacting sources. We identify three fundamental bias factors and propose a general training framework that mitigates their influence through data standardization and representation-level constraints. We construct a standardized multi-site EEG benchmark for Major Depressive Disorder and introduce CRCC, a two-stage training paradigm combining encoder-decoder pretraining with joint fine-tuning via cross-subject/site contrastive learning and site-adversarial optimization. CRCC consistently outperforms state-of-the-art baselines and achieves a 10.7 percentage-point improvement in balanced accuracy under strict zero-shot site transfer, demonstrating robust generalization to unseen environments.

Despite significant analysis of bird flight, generative physics models for flight dynamics do not currently exist. Yet the underlying mechanisms responsible for various flight manoeuvres are important for understanding how agile flight can be accomplished. Even in a simple flight, multiple objectives are at play, complicating analysis of the overall flight mechanism. Using the data-driven method of dynamic mode decomposition (DMD) on motion capture recordings of hawks, we show that multiple behavioral states such as flapping, turning, landing, and gliding, can be modeled by simple and interpretable modal structures (i.e. the underlying wing-tail shape) which can be linearly combined to reproduce the experimental flight observations. Moreover, the DMD model can be used to extrapolate naturalistic flapping. Flight is highly individual, with differences in style across the hawks, but we find they share a common set of dynamic modes. The DMD model is a direct fit to data, unlike traditional models constructed from physics principles which can rarely be tested on real data and whose assumptions are typically invalid in real flight. The DMD approach gives a highly accurate reconstruction of the flight dynamics with only three parameters needed to characterize flapping, and a fourth to integrate turning manoeuvres. The DMD analysis further shows that the underlying mechanism of flight, much like simplest walking models, displays a parametric coupling between dominant modes suggesting efficiency for locomotion.

Background: KRAS mutations are the largest oncogenic subset in NSCLC. While KRAS G12C is now targetable, no approved therapies exist for G12D. We examined time-to-next-treatment (TTNT) and overall survival (OS) differences between G12C and G12D, allowing for time-varying hazard effects. Methods: De-identified data from AACR Project GENIE BPC NSCLC v2.0-public were analyzed. TTNT served as a real-world surrogate for progression-free survival. Co-mutations (TP53, STK11, KEAP1, SMARCA4, MET), TMB, and PD-L1 were harmonized. Kaplan-Meier, multivariable Cox, and a pre-specified piecewise Cox model (split at median TTNT = 23 months) were applied. Schoenfeld residuals assessed proportional hazards; bootstrap resampling (B=1000) evaluated stability. Results: Among 162 TTNT-evaluable patients (G12C n=130; G12D n=32), median TTNT was 28.6 versus 32.0 months (log-rank p=0.79). Adjusted Cox regression showed no overall hazard difference (HR=0.85; 95% CI 0.53-1.37; p=0.50), but Schoenfeld testing indicated borderline non-proportionality (p=0.053). Piecewise Cox modeling revealed time-varying effects: early TTNT hazard favored G12D (HR=0.41; 95% CI 0.17-0.97; p=0.043) with significant KRAS x period interaction (HR=3.33; p=0.021) and late-period attenuation (HR=1.38; 95% CI 0.77-2.47; p=0.285). Bootstrap resampling confirmed this pattern (median HRearly=0.39; HRlate=1.41). Among 278 OS-evaluable patients (133 deaths), G12D showed improved OS (adjusted HR=0.63; 95% CI 0.39-0.99; p=0.048). G12C tumors exhibited higher TMB (9.79 vs 7.83 mut/Mb; p=0.002) and greater STK11/KEAP1 enrichment. Conclusions: KRAS G12D demonstrated early TTNT advantage and improved OS. Late-period TTNT differences were non-significant (post-hoc power: 12.3%). These exploratory findings require validation in larger cohorts but support allele-specific therapeutic development for G12D.

Atherosclerotic plaques are fatty, cellular lesions that form in artery walls. The early plaque contains monocyte-derived macrophages, which are recruited to consume locally bound lipid deposits. Plaque progression is characterised by an imbalance in the rates of cell entry and exit from the plaque, which can occur if macrophages die in situ rather than leave by emigration. The mechanisms that regulate macrophage emigration are not well understood, but there is evidence that a chemotactic response can guide macrophages out of the plaque towards the artery wall lymphatics. In this paper, we develop a novel spatial model of the early plaque to study the implications of macrophage chemotactic emigration. Using mathematical analysis and numerical simulations, we investigate how the properties of the chemotactic response contribute to the spatial characteristics and lipid burden of the model plaque. Calculations of macrophage transit times are found to provide a reliable indicator of long-term plaque lipid burden, and also highlight the potential rate-limiting effect of the internal elastic lamina (IEL) on chemotactic emigration. When macrophage emigration is rate-limited by the IEL, we observe non-monotonic cell and lipid profiles that are associated with macrophage accumulation deep in the plaque. The model further predicts that when the chemoattractant penetrates only a short distance into the plaque, the proportion of emigrating macrophages may increase relative to that for a longer-range signal. The theoretical observations in this study can potentially be used to identify evidence of macrophage emigration in data from real atherosclerotic plaques.

Exact stochastic simulation of continuous-time Markov chains (CTMCs) is essential when discreteness and noise drive system behavior, but the hard categorical event selection in Gillespie-type algorithms blocks gradient-based learning. We eliminate this constraint by decoupling forward simulation from backward differentiation, with hard categorical sampling generating exact trajectories and gradients propagating through a continuous massively-parallel Gumbel-Softmax straight-through surrogate. Our approach enables accurate optimization at parameter scales over four orders of magnitude beyond existing simulators. We validate for accuracy, scalability, and reliability on a reversible dimerization model (0.09% error), a genetic oscillator (1.2% error), a 203,796-parameter gene regulatory network achieving 98.4% MNIST accuracy (a prototypical deep-learning multilayer perceptron benchmark), and experimental patch-clamp recordings of ion channel gating (R^2 = 0.987) in the single-channel regime. Our GPU implementation delivers 1.9 billion steps per second, matching the scale of non-differentiable simulators. By making exact stochastic simulation massively parallel and autodiff-compatible, our results enable high-dimensional parameter inference and inverse design across systems biology, chemical kinetics, physics, and related CTMC-governed domains.

Physiologically Based Pharmacokinetic (PBPK) modeling is a cornerstone of model-informed drug development (MIDD), providing a mechanistic framework to predict drug absorption, distribution, metabolism, and excretion (ADME). Despite its utility, adoption is hindered by high computational costs for large-scale simulations, difficulty in parameter identification for complex biological systems, and uncertainty in interspecies extrapolation. In this work, we propose a unified Scientific Machine Learning (SciML) framework that bridges mechanistic rigor and data-driven flexibility. We introduce three contributions: (1) Foundation PBPK Transformers, which treat pharmacokinetic forecasting as a sequence modeling task; (2) Physiologically Constrained Diffusion Models (PCDM), a generative approach that uses a physics-informed loss to synthesize biologically compliant virtual patient populations; and (3) Neural Allometry, a hybrid architecture combining Graph Neural Networks (GNNs) with Neural ODEs to learn continuous cross-species scaling laws. Experiments on synthetic datasets show that the framework reduces physiological violation rates from 2.00% to 0.50% under constraints while offering a path to faster simulation.

Amino acids (AAs) are a key target in the search for life beyond Earth due to their extensive role in the machinery of all known life, persistence over geologic timescales, and analytical detectability. However, AAs can also arise from abiotic processes on planets and in space. For example, material from asteroid Bennu contained 33 AAs, including 15 of the 20 proteinogenic AAs that are fundamental to life's functions. Distinguishing life from non-life based on AAs in a sample remains an unsolved problem, particularly when their isotopic and structural signatures (e.g., chirality) could be altered via physicochemical processes. Here we introduce LUMOS (Life Unveiled via Molecular Orbital Signatures), a statistical framework that distinguishes life from non-life by analyzing the distribution of abundance-weighted HOMO-LUMO gap (HLG) values of AAs within a sample. Compilation of AAs datasets from diverse environments and provenances revealed that abiotic samples display highly uniform distributions of AAs HLGs. In contrast, biotic samples show greater variance and preference towards AAs with lower HLG, likely reflecting the need for life to control when, where, and how chemical reactions occur. LUMOS achieves >95% accuracy in distinguishing biotic versus abiotic provenance across diverse environmental and extraterrestrial conditions. These results suggest that varied molecular reactivity within biochemical systems may be a universal feature of life, representing an agnostic biosignature unlinked to the specific set of AAs used by life as we know it. LUMOS is compatible with existing analytical instrumentation, applicable to returned samples or in situ analyses. Broader characterization of abiotic and biotic environments will further refine the chemical boundaries separating biotic from abiotic chemical systems.

Neural networks have long strived to emulate the learning capabilities of the human brain. While deep neural networks (DNNs) draw inspiration from the brain in neuron design, their training methods diverge from biological foundations. Backpropagation, the primary training method for DNNs, requires substantial computational resources and fully labeled datasets, presenting major bottlenecks in development and application. This work demonstrates that by returning to biomimicry, specifically mimicking how the brain learns through pruning, we can solve various classical machine learning problems while utilizing orders of magnitude fewer computational resources and no labels. Our experiments successfully personalized multiple speech recognition and image classification models, including ResNet50 on ImageNet, resulting in increased sparsity of approximately 70\% while simultaneously improving model accuracy to around 90\%, all without the limitations of backpropagation. This biologically inspired approach offers a promising avenue for efficient, personalized machine learning models in resource-constrained environments.

This paper provides experimental and numerical evidence supporting the occurrence of liposome congregation at the floors of meteor craters on Early Earth. This work builds on our earlier research, which demonstrated that liposomes submerged in a shallow Archean pond are protected from harmful UV radiation. This protection allows them to survive long enough for autocatalytic replication of amphiphiles and for mutation and selection of assemblies that maximize membrane stability. For liposomes to fuse, grow, exchange contents and membranes, and divide, they need to establish a population, which means forming a dense conglomerate that enables close physical contact. The study demonstrates that such a congregation is feasible in bowl-shaped meteor craters on Early Earth, especially under periodic seismic disturbances.

$\textit{Objective.}$ Accurate neural decoding of locomotion holds promise for advancing rehabilitation, prosthetic control, and understanding neural correlates of action. Recent studies have demonstrated decoding of locomotion kinematics across species on motorized treadmills. However, efforts to decode locomotion speed in more natural contexts$-$where pace is self-selected rather than externally imposed$-$are scarce, generally achieve only modest accuracy, and require intracranial implants. Here, we aim to decode self-paced locomotion speed non-invasively and continuously using cortex-wide EEG recordings from rats. $\textit{Approach.}$ We introduce an asynchronous brain$-$computer interface (BCI) that processes a stream of 32-electrode skull-surface EEG (0.01$-$45 Hz) to decode instantaneous speed from a non-motorized treadmill during self-paced locomotion in head-fixed rats. Using recurrent neural networks and a dataset of over 133 h of recordings, we trained decoders to map ongoing EEG activity to treadmill speed. $\textit{Main results.}$ Our decoding achieves a correlation of 0.88 ($R^2$ = 0.78) for speed, primarily driven by visual cortex electrodes and low-frequency ($< 8$ Hz) oscillations. Moreover, pre-training on a single session permitted decoding on other sessions from the same rat, suggesting uniform neural signatures that generalize across sessions but fail to transfer across animals. Finally, we found that cortical states not only carry information about current speed, but also about future and past dynamics, extending up to 1000 ms. $\textit{Significance.}$ These findings demonstrate that self-paced locomotion speed can be decoded accurately and continuously from non-invasive, cortex-wide EEG. Our approach provides a framework for developing high-performing, non-invasive BCI systems and contributes to understanding distributed neural representations of action dynamics.

MINFLUX (Minimal Photon Flux) is a single-molecule imaging technique capable of resolving fluorophores at a precision of <5 nm. Interpretation of the point patterns generated by this technique presents challenges due to variable emitter density, incomplete bio-labelling of target molecules and their detection, error prone measurement processes, and the presence of spurious (non-structure associated) fluorescent detections. Together, these challenges ensure structural inferences from single-molecule imaging datasets are non-trivial in the absence of strong a priori information, for all but the smallest of point patterns. In addition, current methods often require subjective parameter tuning and presuppose known structural templates, limiting reference-free discovery. We present a statistically grounded, end-to-end analysis framework. Focusing on MINFLUX derived datasets and leveraging Bayesian and spatial statistical methods, a pipeline is presented that demonstrates 1) uncertainty aware clustering of measurements into emitter groups that performs better than current gold standards, 2) rapid identification of molecular structure supergroups, and 3) reconstruction of repeating structures within the dataset without substantial prior knowledge. This pipeline is demonstrated using simulated and real MINFLUX datasets, where emitter clustering and centre detection maintain high performance (emitter subset assignment accuracy > 0.75) across all conditions evaluated, while structural inference achieves reliable discrimination (F1 approx. 0.9) at high labelling efficiency. Template-free reconstruction of Nup96 and DNA-Origami 3x3 grids are achieved.

Cells often divide under mechanical confinement, where surrounding structures restrict shape changes during cytokinesis. Although forces generated during confined division have been measured experimentally, it remains unclear how confinement geometry and mechanics determine the transmitted force. Here we develop a minimal mechanical theory of cell division under confinement. Modeling the cell as an incompressible volume bounded by an interface with effective isotropic tension, we show that confinement restricts the set of mechanically admissible furrow shapes. As the furrow radius decreases, it reaches it reaches a confinement-induced minimum. Beyond this point, further ingression does not alter the interface shape, and both pressure and axial force saturate. We analyze force and pressure in rigid, soft, and strong three-dimensional confinement and demonstrate that a single geometric mechanism underlies these distinct cases. After rescaling force and length by the appropriate geometric scale, cells of different size and surface tension collapse onto a single universal curve. The relevant length scale is the cell size for rigid and soft confinement, and the confinement size in fully enclosing three-dimensional confinement. In soft confinement, environmental stiffness and spindle-generated axial forces determine the operating force and pressure, while the geometric constraint fixes the maximal attainable levels. In summary, our results show that mitotic force transmission and mitotic pressure during cytokinesis are bounded by confinement geometry, with material properties and active forces selecting the operating point within these geometry-imposed limits.

The remarkable performance of modern AI systems has been driven by unprecedented scales of data, computation, and energy -- far exceeding the resources required by human intelligence. This disparity highlights the need for new guiding principles and motivates drawing inspiration from the fundamental organizational principles of brain computation. Among these principles, modularity has been shown to be critical for supporting the efficient learning and strong generalization abilities consistently exhibited by humans. Furthermore, modularity aligns well with the No Free Lunch Theorem, which highlights the need for problem-specific inductive biases and motivates architectures composed of specialized components that solve subproblems. However, despite its fundamental role in natural intelligence and its demonstrated benefits across a range of seemingly disparate AI subfields, modularity remains relatively underappreciated in mainstream AI research. In this work, we review several research threads in artificial intelligence and neuroscience through a conceptual framework that highlights the central role of modularity in supporting both artificial and natural intelligence. In particular, we examine what computational advantages modularity provides, how it has emerged as a solution across several AI research areas, which modularity principles the brain exploits, and how modularity can help bridge the gap between natural and artificial intelligence.

Common deep learning approaches for antibody engineering focus on modeling the marginal distribution of sequences. By treating sequences as independent samples, however, these methods overlook affinity maturation as a rich and largely untapped source of information about the evolutionary process by which antibodies explore the underlying fitness landscape. In contrast, classical phylogenetic models explicitly represent evolutionary dynamics but lack the expressivity to capture complex epistatic interactions. We bridge this gap with CoSiNE, a continuous-time Markov chain parameterized by a deep neural network. Mathematically, we prove that CoSiNE provides a first-order approximation to the intractable sequential point mutation process, capturing epistatic effects with an error bound that is quadratic in branch length. Empirically, CoSiNE outperforms state-of-the-art language models in zero-shot variant effect prediction by explicitly disentangling selection from context-dependent somatic hypermutation. Finally, we introduce Guided Gillespie, a classifier-guided sampling scheme that steers CoSiNE at inference time, enabling efficient optimization of antibody binding affinity toward specific antigens.

We formulate a phenomenological effective field theory in which biological intelligence emerges as a macroscopic order parameter sustained by continuous metabolic flux. By modeling cognition as a coarse-grained neural activity field governed by a variational free energy, we derive closed-form expressions for information capacity and structural susceptibility using a Gaussian maximum entropy approximation. The theory predicts a universal algebraic divergence of the susceptibility, $\chi \sim K^{-3/2}$, as the structural stiffness $K$ approaches the instability threshold. The exponent $\gamma = 3/2$ is consistent with the mean-field branching process universality class, thereby providing a theoretical rationale for the observed avalanche size exponent $\tau \approx 3/2$ in cortical dynamics without invoking microscopic equivalence. We identify adult cognition as a metabolically pinned non-equilibrium steady state maintained near the critical regime $\Gamma \equiv K/\alpha \approx 1$ by continuous metabolic regulation, while pathological decline corresponds to a delocalization transition triggered by the violation of structural stability conditions. The framework generates concrete, falsifiable predictions for attention scaling, altered states of consciousness, and transcranial magnetic stimulation responses, each of which can be tested against existing neuroimaging and electrophysiological datasets.

Tumor cell migration within the microenvironment is a crucial aspect for cancer progression and, in this context, hypoxia has a significant role. An inadequate oxygen supply acts as an environmental stressor inducing migratory bias and phenotypic changes. In this paper, we propose a novel multi-scale mathematical model to analyze the pivotal role of Snail protein expression in the cellular responses to hypoxia. Starting from the description of single-cell dynamics driven by the Snail protein, we construct the corresponding kinetic transport equation that describes the evolution of the cell distribution. Subsequently, we employ proper scaling arguments to formally derive the equations for the statistical moments of the cell distribution, which govern the macroscopic tumor dynamics. Numerical simulations of the model are performed in various scenarios with biological relevance to provide insights into the role of the multiple tactic terms, the impact of Snail expression on cell proliferation, and the emergence of hypoxia-induced migration patterns. Moreover, quantitative comparison with experimental data shows the model's reliability in measuring the impact of Snail transcription on cell migratory potential. Through our findings, we shed light on the potential of our mathematical framework in advancing the understanding of the biological mechanisms driving tumor progression.

We propose a mathematical kinetic framework to investigate interactions between tumor cells and the immune system, focusing on the spatial dynamics of tumor progression and immune responses. We develop two kinetic models: one describes a conservative scenario where immune cells switch between active and passive states without proliferation, while the other incorporates immune cell proliferation and apoptosis. By considering specific assumptions about the microscopic processes, we derive macroscopic systems featuring linear diffusion, nonlinear cross-diffusion, and nonlinear self-diffusion. Our analysis provides insights into equilibrium configurations and stability, revealing clear correspondences among the macroscopic models derived from the same kinetic framework. Using dynamical systems theory, we examine the stability of equilibrium states and conduct numerical simulations to validate our findings. These results highlight the significance of spatial interactions in tumor-immune dynamics, paving the way for a structured exploration of therapeutic strategies and further investigations into immune responses in various pathological contexts.

Go-or-grow approaches represent a specific class of mathematical models used to describe populations where individuals either migrate or reproduce, but not both simultaneously. These models have a wide range of applications in biology and medicine, chiefly among those the modeling of brain cancer spread. The analysis of go-or-grow models has inspired new mathematics, and it is the purpose of this review to highlight interesting and challenging mathematical properties of reaction--diffusion models of the go-or-grow type. We provide a detailed review of biological and medical applications before focusing on key results concerning solution existence and uniqueness, pattern formation, critical domain size problems, and traveling waves. We present new general results related to the critical domain size and traveling wave problems, and we connect these findings to the existing literature. Moreover, we demonstrate the high level of instability inherent in go-or-grow models. We argue that there is currently no accurate numerical solver for these models, and emphasize that special care must be taken when dealing with the "monster on a leash".

We developed a theory showing that under appropriate normalizations and rescalings, temperature response curves show a remarkably regular behavior and follow a general, universal law. The impressive universality of temperature response curves remained hidden due to various curve-fitting models not well-grounded in first principles. In addition, this framework has the potential to explain the origin of different scaling relationships in thermal performance in biology, from molecules to ecosystems. Here, we summarize the background, principles and assumptions, predictions, implications, and possible extensions of this theory.

Amortized Bayesian inference (ABI) with neural networks has emerged as a powerful simulation-based approach for estimating complex mechanistic models. However, extending ABI to hierarchical models, a cornerstone of modern Bayesian analysis, has been a major hurdle due to the need to simulate and process massive datasets. Our study tackles these challenges by extending compositional score matching (CSM), a divide-and-conquer strategy for Bayesian updating using diffusion models. We develop a new error-damping estimator to address previous stability issues of CSM when aggregating large numbers of data points. We first verified the numerical stability with up to 100,000 data points on a controlled benchmark. We then evaluated our method on a hierarchical AR model, achieving competitive performance to direct ABI baselines on smaller problem sizes while using less than one full model simulation for larger problem sizes. Finally, we address a large-scale inverse problem in advanced microscopy with over 750,000 parameters, demonstrating its relevance to real scientific applications.

We explore a functionalist approach to emotion by employing an ansatz -- an initial set of assumptions -- that a hypothetical concept generation model incorporates unproven but biologically plausible traits. From these traits, we mathematically construct a theoretical reinforcement learning framework grounded in functionalist principles and examine how the resulting utility function aligns with emotional valence in biological systems. Our focus is on structuring the functionalist perspective through a conceptual network, particularly emphasizing the construction of the utility function, not to provide an exhaustive explanation of emotions. The primary emphasis is not of planning or action execution, but such factors are addressed when pertinent. Finally, we apply the framework to psychological phenomena such as humor, psychopathy, and advertising, demonstrating its breadth of explanatory power.

Population size is a key metric for management and conservation. This is especially true for large carnivore populations for which management decisions are often based on population size estimates. In France, gray wolves (Canis lupus) have been monitored for more than two decades using non-invasive genetic sampling and capture-recapture models. Population size estimates directly inform the annual number of wolves that can be killed legally. It is therefore key to use appropriate methods to obtain robust population size estimates. To track the recent numerical and geographical expansion of the population, a substantial increase in sample collection was performed during the winter 2023/24 within the entire wolf distribution range in France. A total of 1964 samples were genotyped and assigned to 576 different individuals using microsatellites genetic markers. During the winter 2023/24, spatial capture-recapture models estimated the wolf population size in France to be likely between 920 and 1125 individuals (95% credible interval). Detection probability varied spatially and was positively influenced by snow cover and accessibility. Wolf density was strongly associated with the recent presence of the species, reflecting the ongoing recolonization process from the Alps. This work illustrates the usefulness of non-invasive genetic data and spatial capture-recapture for large-scale population assessment. It also lays the ground for future improvements in monitoring to fully exploit the potential of spatial capture-recapture models.

Evolutionary analyses of large populations commonly incorporate stochasticity through temporal variation in selection while treating genetic transmission as fixed. Much less attention has been given to stochasticity in transmission itself. We study a selected locus with alleles $A$ and $a$ under constant selection, linked to a neutral modifier locus whose alleles $M_1$ and $M_2$ control the mutation rate from $A$ to $a$. Under constant transmission, the Reduction Principle applies: near a mutation--selection balance where $M_1$ is fixed with mutation rate $u_1$, a rare allele $M_2$ invades if its associated rate $u_2$ is smaller than $u_1$, but cannot invade if $u_2$ is larger than $u_1$. This result holds for both haploid and diploid populations and is independent of recombination, which affects only the rate, not the direction, of evolutionary change. We extend this framework by allowing the mutation rate associated with the invading modifier to fluctuate randomly across generations. In this stochastic setting, invasion is no longer determined by mean mutation rates alone. Instead, it depends on the temporal distribution of mutation rates, the strength of selection at the selected locus, and the recombination rate between modifier and target. Stochastic transmission and recombination therefore do not merely rescale deterministic predictions based on the Reduction Principle; they can alter the direction of selection on modifier alleles.

Discovering the neural mechanisms underpinning cognition is one of the grand challenges of neuroscience. However, previous approaches for building models of RNN dynamics that explain behaviour required iterative refinement of architectures and/or optimisation objectives, resulting in a piecemeal, and mostly heuristic, human-in-the-loop process. Here, we offer an alternative approach that automates the discovery of viable RNN mechanisms by explicitly training RNNs to reproduce behaviour, including the same characteristic errors and suboptimalities, that humans and animals produce in a cognitive task. Achieving this required two main innovations. First, as the amount of behavioural data that can be collected in experiments is often too limited to train RNNs, we use a non-parametric generative model of behavioural responses to produce surrogate data for training RNNs. Second, to capture all relevant statistical aspects of the data, we developed a novel diffusion model-based approach for training RNNs. To showcase the potential of our approach, we chose a visual working memory task as our test-bed, as behaviour in this task is well known to produce response distributions that are patently multimodal (due to swap errors). The resulting network dynamics correctly qualitative features of macaque neural data. Importantly, these results were not possible to obtain with more traditional approaches, i.e., when only a limited set of behavioural signatures (rather than the full richness of behavioural response distributions) were fitted, or when RNNs were trained for task optimality (instead of reproducing behaviour). Our approach also yields novel predictions about the mechanism of swap errors, which can be readily tested in experiments. These results suggest that fitting RNNs to rich patterns of behaviour provides a powerful way to automatically discover mechanisms of important cognitive functions.

Bacterial chemotactic sensing converts noisy chemical signals into running and tumbling. We analyze the static sensing limits of mixed Tar/Tsr chemoreceptor clusters in individual Escherichia coli cells using a heterogeneous Monod-Wyman-Changeux (MWC) model. By sweeping a seven-dimensional parameter space, we compute three sensing performance metrics-channel capacity, dynamic range, and effective Hill coefficient. Across E. coli-like parameter regimes, we consistently observe pronounced global maxima of channel capacity and global maxima of the related dynamic range, whereas the effective Hill coefficient does not exhibit comparable optimization. The capacity-achieving input distribution is bimodal, which implies that individual cells maximize information by sampling both low- and high-concentration regimes. Together, these results suggest that, at the individual-cell level, channel capacity and dynamic range may be selected for in E. coli receptor clusters.

The computational design of antibodies with high specificity and affinity is a cornerstone of modern therapeutic development. While deep generative models have demonstrated potential, they often struggle to balance high-fidelity geometric conditioning with the discrete nature of amino acid sequences. In this work, we present AntibodyDesignBFN, a novel framework for fixed-backbone antibody design based on Discrete Bayesian Flow Networks (BFN). Unlike standard diffusion models, BFNs operate on a continuous probability simplex, enabling a fully differentiable generative process that seamlessly integrates geometric gradients. By combining a lightweight Geometric Transformer with Invariant Point Attention (IPA) and a resource-efficient training strategy, our model establishes a new state-of-the-art. Evaluations on a rigorous 2025 temporal test set (43 complexes) demonstrate that AntibodyDesignBFN achieves an unprecedented Amino Acid Recovery(AAR) of 67.8%, significantly outperforming leading graph-based baselines. Furthermore, the model is highly efficient, enabling millisecond-scale inference on consumer-grade hardware. AntibodyDesignBFN thus offers a powerful, accessible, and mathematically robust framework for next generation antibody engineering. Code and model checkpoints are available at this https URL and this https URL.

Multiple phenotypic protein expressions arising from one genome represent variations in the protein relative abundance and their stoichiometry. A lack of definite compositional parts challenges the modeling of protein megacomplexes and cellular architectures. Despite the advances in protein structural predictions with AI, the mechanism of protein interactions and the emergence of megacomplexes they assemble remains unclear. Here, we present a statistical physics framework of grand canonical ensemble to explore the protein interactions that drive the emergent assembly of a megacomplex using the observational mass spectrometry datasets including protein relative abundance and the cross linked connections. Using chromatin remodeler megacomplex, INO80, as an example, we discovered a class of divergent protein that plays a critical role in orchestrating the assembly beyond nearest neighbors, dependent on the excluded volumes exerted by others. With the constraints of the excluded volumes by varying crowding contents, these divergent subunits orchestrate and form clusters with selective components growing into configurationally distinct architectures. We propose a machinery view for the INO80 chromatin remodeler complex where each loosely associated subunits can be occasionally recruited for parts as attachment into a core assembly driven by excluded volumes. Our computational framework provides a mechanistic insight into taking the macromolecular crowding as necessary physicochemical variables representing cell states to remodel the configurations of protein megacomplexes with structurally loose modules.

The representation of protein backbone geometry through the discrete nonlinear Schrödinger equation provides a theoretical connection between biological structure and integrable systems. Although the global application of this framework is constrained by chiral degeneracies and non-local interactions, helical peptides can be modeled as piecewise integrable systems where the discrete Hasimoto map remains applicable within specific geometric boundaries. We delineate these boundaries through an analytic mapping $(\phi,\psi) \rightarrow (\kappa,\tau)$ between biochemical dihedral angles and Frenet frame parameters for 50 helical peptide chains. This transformation is globally information-preserving but ill-conditioned within the helical basin (median Jacobian condition number 31), suggesting chiral information loss arises primarily from local coordinate compression rather than topological singularities. Using a local integrability error $E[n]$ derived from the discrete dispersion relation, we show deviations from integrability are driven predominantly by torsion non-uniformity, while curvature remains rigid. This metric identifies integrable islands where the analytic dispersion relation predicts backbone coordinates with sub-angstrom accuracy (median RMSD 0.77\,Å), enabling a segmentation strategy that isolates structural defects and trims non-integrable terminal fraying. Evaluating only these integrable islands, the dispersion relation extracts high-accuracy structural cores for 88\% of the dataset. Inverse backbone design is feasible within a defined integrability zone where the design constraint reduces essentially to controlling torsion uniformity. These findings advance the Hasimoto formalism from a qualitative descriptor toward a precise quantitative framework for analyzing and designing local protein geometry within the limits of piecewise integrability.

Clustering large high-dimensional datasets with diverse variable is essential for extracting high-level latent information from these datasets. Here, we developed an unsupervised clustering algorithm, we call "Village-Net". Village-Net is specifically designed to effectively cluster high-dimension data without priori knowledge on the number of existing clusters. The algorithm operates in two phases: first, utilizing K-Means clustering, it divides the dataset into distinct subsets we refer to as "villages". Next, a weighted network is created, with each node representing a village, capturing their proximity relationships. To achieve optimal clustering, we process this network using a community detection algorithm called Walk-likelihood Community Finder (WLCF), a community detection algorithm developed by one of our team members. A salient feature of Village-Net Clustering is its ability to autonomously determine an optimal number of clusters for further analysis based on inherent characteristics of the data. We present extensive benchmarking on extant real-world datasets with known ground-truth labels to showcase its competitive performance, particularly in terms of the normalized mutual information (NMI) score, when compared to other state-of-the-art methods. The algorithm is computationally efficient, boasting a time complexity of O(N*k*d), where N signifies the number of instances, k represents the number of villages and d represents the dimension of the dataset, which makes it well suited for effectively handling large-scale datasets.

How do humans move? Advances in reinforcement learning (RL) have produced impressive results in capturing human motion using physics-based humanoid control. However, torque-controlled humanoids fail to model key aspects of human motor control such as biomechanical joint constraints \& non-linear and overactuated musculotendon control. We present KINESIS, a model-free motion imitation framework that tackles these challenges. KINESIS is trained on 1.8 hours of locomotion data and achieves strong motion imitation performance on unseen trajectories. Through a negative mining approach, KINESIS learns robust locomotion priors that we leverage to deploy the policy on several downstream tasks such as text-to-control, target point reaching, and football penalty kicks. Importantly, KINESIS learns to generate muscle activity patterns that correlate well with human EMG activity. We show that these results scale seamlessly across biomechanical model complexity, demonstrating control of up to 290 muscles. Overall, the physiological plausibility makes KINESIS a promising model for tackling challenging problems in human motor control. Code, videos and benchmarks are available at this https URL.

In eukaryotic cells, mitochondria form networks that range from highly fused interconnected structures to fragmented populations of individual organelles that undergo transient interactions. These structures can be described as temporal networks of physical units, whose dynamic topology is determined by fusion, fission, and motion of the mitochondria through intracellular space. The heterogeneity of the mitochondrial population is governed by diffusive transport and inter-unit exchange of proteins, lipids, ions, and RNA within these networks. We present a unifying framework for the dispersion of material within temporal networks of spatially embedded units that span across a broad connectivity range. Specifically, we consider filling of the networks with a locally produced but globally consumed material, demonstrating that the steady-state content is determined by the balance of timescales for spatial encounter between clusters, local fusion, fission, and diffusive transport within a cluster. As the connectivity increases, filling behavior transitions from three-dimensional spread through a `social network' limited by cluster interactions to low-dimensional transport through a largely stationary `physical network' limited by material diffusivity. We extract parameters for mitochondrial networks in three human cell lines, demonstrating that different cells can access both the social and the physical network regimes. These results provide a quantitative basis for predicting the homogenization of biomolecules through a mitochondrial population. Our framework unifies a variety of temporal network structures into an overarching theory for transport through populations of interacting and interconnected units.