Daily Papers

We report DynaCLR, a self-supervised method for embedding cell and organelle Dynamics via Contrastive Learning of Representations of time-lapse images. DynaCLR integrates single-cell tracking and time-aware contrastive sampling to learn robust, temporally regularized representations of cell dynamics. DynaCLR embeddings generalize effectively to in-distribution and out-of-distribution datasets, and can be used for several downstream tasks with sparse human annotations. We demonstrate efficient annotations of cell states with a human-in-the-loop using fluorescence and label-free imaging channels. DynaCLR method enables diverse downstream biological analyses: classification of cell division and infection, clustering heterogeneous cell migration patterns, cross-modal distillation of cell states from fluorescence to label-free channel, alignment of asynchronous cellular responses and broken cell tracks, and discovering organelle response due to infection. DynaCLR is a flexible method for comparative analyses of dynamic cellular responses to pharmacological, microbial, and genetic perturbations. We provide PyTorch-based implementations of the model training and inference pipeline (https://github.com/mehta-lab/viscy) and a GUI (https://github.com/czbiohub-sf/napari-iohub) for the visualization and annotation of trajectories of cells in the real space and the embedding space.

The advent of single-cell technology has significantly improved our understanding of cellular states and subpopulations in various tissues under normal and diseased conditions by employing data-driven approaches such as clustering and trajectory inference. However, these methods consider cells as independent data points of population distributions. With spatial transcriptomics, we can represent cellular organization, along with dynamic cell-cell interactions that lead to changes in cell state. Still, key computational advances are necessary to enable the data-driven learning of such complex interactive cellular dynamics. While agent-based modeling (ABM) provides a powerful framework, traditional approaches rely on handcrafted rules derived from domain knowledge rather than data-driven approaches. To address this, we introduce Spatio Temporal Agent-Based Graph Evolution Dynamics(STAGED) integrating ABM with deep learning to model intercellular communication, and its effect on the intracellular gene regulatory network. Using graph ODE networks (GDEs) with shared weights per cell type, our approach represents genes as vertices and interactions as directed edges, dynamically learning their strengths through a designed attention mechanism. Trained to match continuous trajectories of simulated as well as inferred trajectories from spatial transcriptomics data, the model captures both intercellular and intracellular interactions, enabling a more adaptive and accurate representation of cellular dynamics.

Recent advances in video generation have opened new avenues for macroscopic simulation of complex dynamic systems, but their application to microscopic phenomena remains largely unexplored. Microscale simulation holds great promise for biomedical applications such as drug discovery, organ-on-chip systems, and disease mechanism studies, while also showing potential in education and interactive visualization. In this work, we introduce MicroWorldBench, a multi-level rubric-based benchmark for microscale simulation tasks. MicroWorldBench enables systematic, rubric-based evaluation through 459 unique expert-annotated criteria spanning multiple microscale simulation task (e.g., organ-level processes, cellular dynamics, and subcellular molecular interactions) and evaluation dimensions (e.g., scientific fidelity, visual quality, instruction following). MicroWorldBench reveals that current SOTA video generation models fail in microscale simulation, showing violations of physical laws, temporal inconsistency, and misalignment with expert criteria. To address these limitations, we construct MicroSim-10K, a high-quality, expert-verified simulation dataset. Leveraging this dataset, we train MicroVerse, a video generation model tailored for microscale simulation. MicroVerse can accurately reproduce complex microscale mechanism. Our work first introduce the concept of Micro-World Simulation and present a proof of concept, paving the way for applications in biology, education, and scientific visualization. Our work demonstrates the potential of educational microscale simulations of biological mechanisms. Our data and code are publicly available at https://github.com/FreedomIntelligence/MicroVerse

Matching objectives underpin the success of modern generative models and rely on constructing conditional paths that transform a source distribution into a target distribution. Despite being a fundamental building block, conditional paths have been designed principally under the assumption of Euclidean geometry, resulting in straight interpolations. However, this can be particularly restrictive for tasks such as trajectory inference, where straight paths might lie outside the data manifold, thus failing to capture the underlying dynamics giving rise to the observed marginals. In this paper, we propose Metric Flow Matching (MFM), a novel simulation-free framework for conditional flow matching where interpolants are approximate geodesics learned by minimizing the kinetic energy of a data-induced Riemannian metric. This way, the generative model matches vector fields on the data manifold, which corresponds to lower uncertainty and more meaningful interpolations. We prescribe general metrics to instantiate MFM, independent of the task, and test it on a suite of challenging problems including LiDAR navigation, unpaired image translation, and modeling cellular dynamics. We observe that MFM outperforms the Euclidean baselines, particularly achieving SOTA on single-cell trajectory prediction.

Machine learning models of cellular interaction dynamics hold promise for understanding cell behavior. Natural killer (NK) cell cytotoxicity is a prominent example of such interaction dynamics and is commonly studied using time-resolved multi-channel fluorescence microscopy. Although tumor cell death events can be annotated at single frames, NK cytotoxic outcome emerges over time from cellular interactions and cannot be reliably inferred from frame-wise classification alone. We introduce BLINK, a trajectory-based recurrent state-space model that serves as a cell world model for NK-tumor interactions. BLINK learns latent interaction dynamics from partially observed NK-tumor interaction sequences and predicts apoptosis increments that accumulate into cytotoxic outcomes. Experiments on long-term time-lapse NK-tumor recordings show improved cytotoxic outcome detection and enable forecasting of future outcomes, together with an interpretable latent representation that organizes NK trajectories into coherent behavioral modes and temporally structured interaction phases. BLINK provides a unified framework for quantitative evaluation and structured modeling of NK cytotoxic behavior at the single-cell level.

Biological tissues exhibit complex behaviors with their dynamics often resembling inert soft matter such as liquids, polymers, colloids, and liquid crystals. These analogies enable physics-based approaches for investigations of emergent behaviors in biological processes. A well-studied case is the spreading of cellular aggregates on solid surfaces, where they display dynamics similar to viscous droplets. In vivo, however, cells and tissues are in a confined environment with varying geometries and mechanical properties to which they need to adapt. In this work, we compressed cellular aggregates between two solid surfaces and studied their dynamics using microscopy, and computer simulations. The confined cellular aggregates transitioned from compressed spheres into dynamic living capillary bridges exhibiting bridge thinning and a convex-to-concave meniscus curvature transition. We found that the stability of the bridge is determined by the interplay between cell growth and cell spreading on the confining surfaces. This interaction leads to bridge rupture at a critical length scale determined by the distance between the plates. The force distributions, formation and stability regimes of the living capillary bridges were characterized with full 3D computer simulations that included cell division, migration and growth dynamics, directly showing how mechanical principles govern the behavior of the living bridges; cellular aggregates display jamming and stiffening analogously to granular matter, and cell division along the long axis enhances thinning. Based on our results, we propose a new class of active soft matter behavior, where cellular aggregates exhibit liquid-like adaptation to confinement, but with self-organized rupturing driven by biological activity.

Many cellular processes involve information processing and decision making. We can probe these processes at increasing molecular detail. The analysis of heterogeneous data remains a challenge that requires new ways of thinking about cells in quantitative, predictive, and mechanistic ways. We discuss the role of mathematical models in the context of cell-fate decision making systems across the tree of life. Complex multi-cellular organisms have been a particular focus, but single celled organisms also have to sense and respond to their environment. We center our discussion around the idea of design principles which we can learn from observations and modeling, and exploit in order to (re)-design or guide cellular behavior.

We analyze a class of cell-bulk coupled PDE-ODE models, motivated by quorum and diffusion sensing phenomena in microbial systems, that characterize communication between localized spatially segregated dynamically active signaling compartments that have a permeable boundary. Each cell secretes a signaling chemical into the bulk region at a constant rate and receives a feedback of the bulk chemical from the entire collection of cells. This global feedback, which activates signaling pathways within the cells, modifies the intracellular dynamics according to the external environment. The cell secretion and global feedback are regulated by permeability parameters across the cell membrane. For arbitrary reaction-kinetics within each cell, the method of matched asymptotic expansions is used in the limit of small cell radius to construct steady-state solutions of the PDE-ODE model, and to derive a globally coupled nonlinear matrix eigenvalue problem (GCEP) that characterizes the linear stability properties of the steady-states. In the limit of large bulk diffusivity an asymptotic analysis of the PDE-ODE model leads to a limiting ODE system for the spatial average of the concentration in the bulk region that is coupled to the intracellular dynamics within the cells. Results from the linear stability theory and ODE dynamics are illustrated for Sel'kov reaction-kinetics, where the kinetic parameters are chosen so that each cell is quiescent when uncoupled from the bulk medium. For various specific spatial configurations of cells, the linear stability theory is used to construct phase diagrams in parameter space characterizing where a switch-like emergence of intracellular oscillations can occur through a Hopf bifurcation.

Building Virtual Cells that can accurately simulate cellular responses to perturbations is a long-standing goal in systems biology. A fundamental challenge is that high-throughput single-cell sequencing is destructive: the same cell cannot be observed both before and after a perturbation. Thus, perturbation prediction requires mapping unpaired control and perturbed populations. Existing models address this by learning maps between distributions, but typically assume a single fixed response distribution when conditioned on observed cellular context (e.g., cell type) and the perturbation type. In reality, responses vary systematically due to unobservable latent factors such as microenvironmental fluctuations and complex batch effects, forming a manifold of possible distributions for the same observed conditions. To account for this variability, we introduce PerturbDiff, which shifts modeling from individual cells to entire distributions. By embedding distributions as points in a Hilbert space, we define a diffusion-based generative process operating directly over probability distributions. This allows PerturbDiff to capture population-level response shifts across hidden factors. Benchmarks on established datasets show that PerturbDiff achieves state-of-the-art performance in single-cell response prediction and generalizes substantially better to unseen perturbations. See our project page (https://katarinayuan.github.io/PerturbDiff-ProjectPage/), where code and data will be made publicly available (https://github.com/DeepGraphLearning/PerturbDiff).

Numerous biological and physical processes can be modeled as systems of interacting entities evolving continuously over time, e.g. the dynamics of communicating cells or physical particles. Learning the dynamics of such systems is essential for predicting the temporal evolution of populations across novel samples and unseen environments. Flow-based models allow for learning these dynamics at the population level - they model the evolution of the entire distribution of samples. However, current flow-based models are limited to a single initial population and a set of predefined conditions which describe different dynamics. We argue that multiple processes in natural sciences have to be represented as vector fields on the Wasserstein manifold of probability densities. That is, the change of the population at any moment in time depends on the population itself due to the interactions between samples. In particular, this is crucial for personalized medicine where the development of diseases and their respective treatment response depends on the microenvironment of cells specific to each patient. We propose Meta Flow Matching (MFM), a practical approach to integrating along these vector fields on the Wasserstein manifold by amortizing the flow model over the initial populations. Namely, we embed the population of samples using a Graph Neural Network (GNN) and use these embeddings to train a Flow Matching model. This gives MFM the ability to generalize over the initial distributions unlike previously proposed methods. We demonstrate the ability of MFM to improve prediction of individual treatment responses on a large scale multi-patient single-cell drug screen dataset.

Building a virtual cell capable of accurately simulating cellular behaviors in silico has long been a dream in computational biology. We introduce CellFlux, an image-generative model that simulates cellular morphology changes induced by chemical and genetic perturbations using flow matching. Unlike prior methods, CellFlux models distribution-wise transformations from unperturbed to perturbed cell states, effectively distinguishing actual perturbation effects from experimental artifacts such as batch effects -- a major challenge in biological data. Evaluated on chemical (BBBC021), genetic (RxRx1), and combined perturbation (JUMP) datasets, CellFlux generates biologically meaningful cell images that faithfully capture perturbation-specific morphological changes, achieving a 35% improvement in FID scores and a 12% increase in mode-of-action prediction accuracy over existing methods. Additionally, CellFlux enables continuous interpolation between cellular states, providing a potential tool for studying perturbation dynamics. These capabilities mark a significant step toward realizing virtual cell modeling for biomedical research. Project page: https://yuhui-zh15.github.io/CellFlux/.

We present a general computational theory of cancer and its developmental dynamics. The theory is based on a theory of the architecture and function of developmental control networks which guide the formation of multicellular organisms. Cancer networks are special cases of developmental control networks. Cancer results from transformations of normal developmental networks. Our theory generates a natural classification of all possible cancers based on their network architecture. Each cancer network has a unique topology and semantics and developmental dynamics that result in distinct clinical tumor phenotypes. We apply this new theory with a series of proof of concept cases for all the basic cancer types. These cases have been computationally modeled, their behavior simulated and mathematically described using a multicellular systems biology approach. There are fascinating correspondences between the dynamic developmental phenotype of computationally modeled {\em in silico} cancers and natural {\em in vivo} cancers. The theory lays the foundation for a new research paradigm for understanding and investigating cancer. The theory of cancer networks implies that new diagnostic methods and new treatments to cure cancer will become possible.

This paper reports on patterns exhibiting self-replication with spontaneous, inheritable mutations and exponential genetic drift in Neural Cellular Automata. Despite the models not being explicitly trained for mutation or inheritability, the descendant patterns exponentially drift away from ancestral patterns, even when the automaton is deterministic. While this is far from being the first instance of evolutionary dynamics in a cellular automaton, it is the first to do so by exploiting the power and convenience of Neural Cellular Automata, arguably increasing the space of variations and the opportunity for Open Ended Evolution.

Pre-training is crucial for large language models (LLMs), as it is when most representations and capabilities are acquired. However, natural language pre-training has problems: high-quality text is finite, it contains human biases, and it entangles knowledge with reasoning. This raises a fundamental question: is natural language the only path to intelligence? We propose using neural cellular automata (NCA) to generate synthetic, non-linguistic data for pre-pre-training LLMs--training on synthetic-then-natural language. NCA data exhibits rich spatiotemporal structure and statistics resembling natural language while being controllable and cheap to generate at scale. We find that pre-pre-training on only 164M NCA tokens improves downstream language modeling by up to 6% and accelerates convergence by up to 1.6x. Surprisingly, this even outperforms pre-pre-training on 1.6B tokens of natural language from Common Crawl with more compute. These gains also transfer to reasoning benchmarks, including GSM8K, HumanEval, and BigBench-Lite. Investigating what drives transfer, we find that attention layers are the most transferable, and that optimal NCA complexity varies by domain: code benefits from simpler dynamics, while math and web text favor more complex ones. These results enable systematic tuning of the synthetic distribution to target domains. More broadly, our work opens a path toward more efficient models with fully synthetic pre-training.

The Game of Life (Life), a well known algorithm within the broader class of cellular automata (CA), exhibits complex emergent dynamics, with extreme sensitivity to initial conditions. Modeling and predicting such intricate behavior without explicit knowledge of the system's underlying topology presents a significant challenge, motivating the development of algorithms that can generalize across various grid configurations and boundary conditions. We develop a decoder-only generative pretrained transformer model to solve this problem, showing that our model can simulate Life on a toroidal grid with no prior knowledge on the size of the grid, or its periodic boundary conditions (LifeGPT). LifeGPT is topology-agnostic with respect to its training data and our results show that a GPT model is capable of capturing the deterministic rules of a Turing-complete system with near-perfect accuracy, given sufficiently diverse training data. We also introduce the idea of an `autoregressive autoregressor' to recursively implement Life using LifeGPT. Our results pave the path towards true universal computation within a large language model (LLM) framework, synthesizing of mathematical analysis with natural language processing, and probing AI systems for situational awareness about the evolution of such algorithms without ever having to compute them. Similar GPTs could potentially solve inverse problems in multicellular self-assembly by extracting CA-compatible rulesets from real-world biological systems to create new predictive models, which would have significant consequences for the fields of bioinspired materials, tissue engineering, and architected materials design.

Learning the underlying dynamics of single cells from snapshot data has gained increasing attention in scientific and machine learning research. The destructive measurement technique and cell proliferation/death result in unpaired and unbalanced data between snapshots, making the learning of the underlying dynamics challenging. In this paper, we propose joint Velocity-Growth Flow Matching (VGFM), a novel paradigm that jointly learns state transition and mass growth of single-cell populations via flow matching. VGFM builds an ideal single-cell dynamics containing velocity of state and growth of mass, driven by a presented two-period dynamic understanding of the static semi-relaxed optimal transport, a mathematical tool that seeks the coupling between unpaired and unbalanced data. To enable practical usage, we approximate the ideal dynamics using neural networks, forming our joint velocity and growth matching framework. A distribution fitting loss is also employed in VGFM to further improve the fitting performance for snapshot data. Extensive experimental results on both synthetic and real datasets demonstrate that VGFM can capture the underlying biological dynamics accounting for mass and state variations over time, outperforming existing approaches for single-cell dynamics modeling.

Uncovering the rules governing the nonequilibrium dynamics of the membranes that define biological cells is of central importance to understanding the physics of living systems. We theoretically and computationally investigate the behavior of flexible quasispherical vesicles that exchange membrane constituents, internal volume, and heat with an external reservoir. The excess chemical potential and osmotic pressure difference imposed by the reservoir act as generalized thermodynamic driving forces that modulate vesicle morphology. We show that the renormalization of membrane mechanical properties by nonequilibrium driving gives rise to a morphological transition between a weakly driven regime, in which growing vesicles remain quasispherical, and a strongly driven regime, in which vesicles accommodate rapid membrane uptake by developing surface wrinkles. Additionally, we propose a minimal vesicle growth-shape law, derived using insights from stochastic thermodynamics, that robustly describes vesicle growth dynamics even in strongly driven, far-from-equilibrium regimes.

Dynamical systems with complex behaviours, e.g. immune system cells interacting with a pathogen, are commonly modelled by splitting the behaviour into different regimes, or modes, each with simpler dynamics, and then learning the switching behaviour from one mode to another. Switching Dynamical Systems (SDS) are a powerful tool that automatically discovers these modes and mode-switching behaviour from time series data. While effective, these methods focus on independent objects, where the modes of one object are independent of the modes of the other objects. In this paper, we focus on the more general interacting object setting for switching dynamical systems, where the per-object dynamics also depends on an unknown and dynamically changing subset of other objects and their modes. To this end, we propose a novel graph-based approach for switching dynamical systems, GRAph Switching dynamical Systems (GRASS), in which we use a dynamic graph to characterize interactions between objects and learn both intra-object and inter-object mode-switching behaviour. We introduce two new datasets for this setting, a synthesized ODE-driven particles dataset and a real-world Salsa Couple Dancing dataset. Experiments show that GRASS can consistently outperforms previous state-of-the-art methods.

During developmental processes such as embryogenesis, how a group of cells fold into specific structures, is a central question in biology that defines how living organisms form. Establishing tissue-level morphology critically relies on how every single cell decides to position itself relative to its neighboring cells. Despite its importance, it remains a major challenge to understand and predict the behavior of every cell within the living tissue over time during such intricate processes. To tackle this question, we propose a geometric deep learning model that can predict multicellular folding and embryogenesis, accurately capturing the highly convoluted spatial interactions among cells. We demonstrate that multicellular data can be represented with both granular and foam-like physical pictures through a unified graph data structure, considering both cellular interactions and cell junction networks. We successfully use our model to achieve two important tasks, interpretable 4-D morphological sequence alignment, and predicting local cell rearrangements before they occur at single-cell resolution. Furthermore, using an activation map and ablation studies, we demonstrate that cell geometries and cell junction networks together regulate local cell rearrangement which is critical for embryo morphogenesis. This approach provides a novel paradigm to study morphogenesis, highlighting a unified data structure and harnessing the power of geometric deep learning to accurately model the mechanisms and behaviors of cells during development. It offers a pathway toward creating a unified dynamic morphological atlas for a variety of developmental processes such as embryogenesis.

The capacity to precisely edit genomes has outpaced our ability to predict the consequences. A cell can be genetically perfect and therapeutically useless: edited exactly as intended, yet unstable, drifting toward unintended fates, or selected for properties that compromise safety. This paradox reflects a deeper gap in how we evaluate biological intervention. Current frameworks excel at measuring what was done to a cell but remain blind to what the cell has become. We argue that this blindness stems from treating cells as collections of independent variables rather than as dynamical systems occupying positions on high-dimensional state manifolds. Drawing on Waddington's epigenetic landscape, we propose geometric stability as a missing axis of evaluation: the directional coherence of cellular responses to perturbation. This metric distinguishes interventions that guide cells coherently toward stable states from those that scatter them across the state manifold. Validation across diverse perturbation datasets reveals that geometric stability captures regulatory architecture invisible to conventional metrics, discriminating pleiotropic master regulators from lineage-specific factors without prior biological annotation. As precision medicine increasingly relies on cellular reprogramming, the question shifts from ``did the intervention occur?'' to ``is the resulting state stable?'' Geometric stability provides a framework for answering.

Learning the continuous dynamics of a system from snapshots of its temporal marginals is a problem which appears throughout natural sciences and machine learning, including in quantum systems, single-cell biological data, and generative modeling. In these settings, we assume access to cross-sectional samples that are uncorrelated over time, rather than full trajectories of samples. In order to better understand the systems under observation, we would like to learn a model of the underlying process that allows us to propagate samples in time and thereby simulate entire individual trajectories. In this work, we propose Action Matching, a method for learning a rich family of dynamics using only independent samples from its time evolution. We derive a tractable training objective, which does not rely on explicit assumptions about the underlying dynamics and does not require back-propagation through differential equations or optimal transport solvers. Inspired by connections with optimal transport, we derive extensions of Action Matching to learn stochastic differential equations and dynamics involving creation and destruction of probability mass. Finally, we showcase applications of Action Matching by achieving competitive performance in a diverse set of experiments from biology, physics, and generative modeling.

We investigate a new dynamical system that describes tumor-host interaction. The equation that describes the untreated tumor growth is based on non-extensive statistical mechanics. Recently, this model has been shown to fit successfully exponential, Gompertz, logistic, and power-law tumor growths. We have been able to include as many hallmarks of cancer as possible. We study also the dynamic response of cancer under therapy. Using our model, we can make predictions about the different outcomes when we change the parameters, and/or the initial conditions. We can determine the importance of different factors to influence tumor growth. We discover synergistic therapeutic effects of different treatments and drugs. Cancer is generally untreatable using conventional monotherapy. We consider conventional therapies, oncogene-targeted therapies, tumor-suppressors gene-targeted therapies, immunotherapies, anti-angiogenesis therapies, virotherapy, among others. We need therapies with the potential to target both tumor cells and the tumors' microenvironment. Drugs that target oncogenes and tumor-suppressor genes can be effective in the treatment of some cancers. However, most tumors do reoccur. We have found that the success of the new therapeutic agents can be seen when used in combination with other cancer-cell-killing therapies. Our results have allowed us to design a combinational therapy that can lead to the complete eradication of cancer.

Cellular form and function emerge from complex mechanochemical systems within the cytoplasm. No systematic strategy currently exists to infer large-scale physical properties of a cell from its many molecular components. This is a significant obstacle to understanding biophysical processes such as cell adhesion and migration. Here, we develop a data-driven biophysical modeling approach to learn the mechanical behavior of adherent cells. We first train neural networks to predict forces generated by adherent cells from images of cytoskeletal proteins. Strikingly, experimental images of a single focal adhesion protein, such as zyxin, are sufficient to predict forces and generalize to unseen biological regimes. This protein field alone contains enough information to yield accurate predictions even if forces themselves are generated by many interacting proteins. We next develop two approaches - one explicitly constrained by physics, the other more agnostic - that help construct data-driven continuum models of cellular forces using this single focal adhesion field. Both strategies consistently reveal that cellular forces are encoded by two different length scales in adhesion protein distributions. Beyond adherent cell mechanics, our work serves as a case study for how to integrate neural networks in the construction of predictive phenomenological models in cell biology, even when little knowledge of the underlying microscopic mechanisms exist.

Modeling cellular states and predicting their responses to perturbations are central challenges in computational biology and the development of virtual cells. Existing foundation models for single-cell transcriptomics provide powerful static representations, but they do not explicitly model the distribution of cellular states for generative simulation. Here, we introduce Lingshu-Cell, a masked discrete diffusion model that learns transcriptomic state distributions and supports conditional simulation under perturbation. By operating directly in a discrete token space that is compatible with the sparse, non-sequential nature of single-cell transcriptomic data, Lingshu-Cell captures complex transcriptome-wide expression dependencies across approximately 18,000 genes without relying on prior gene selection, such as filtering by high variability or ranking by expression level. Across diverse tissues and species, Lingshu-Cell accurately reproduces transcriptomic distributions, marker-gene expression patterns and cell-subtype proportions, demonstrating its ability to capture complex cellular heterogeneity. Moreover, by jointly embedding cell type or donor identity with perturbation, Lingshu-Cell can predict whole-transcriptome expression changes for novel combinations of identity and perturbation. It achieves leading performance on the Virtual Cell Challenge H1 genetic perturbation benchmark and in predicting cytokine-induced responses in human PBMCs. Together, these results establish Lingshu-Cell as a flexible cellular world model for in silico simulation of cell states and perturbation responses, laying the foundation for a new paradigm in biological discovery and perturbation screening.

Practitioners frequently aim to infer an unobserved population trajectory using sample snapshots at multiple time points. For instance, in single-cell sequencing, scientists would like to learn how gene expression evolves over time. But sequencing any cell destroys that cell. So we cannot access any cell's full trajectory, but we can access snapshot samples from many cells. Stochastic differential equations are commonly used to analyze systems with full individual-trajectory access; since here we have only sample snapshots, these methods are inapplicable. The deep learning community has recently explored using Schr\"odinger bridges (SBs) and their extensions to estimate these dynamics. However, these methods either (1) interpolate between just two time points or (2) require a single fixed reference dynamic within the SB, which is often just set to be Brownian motion. But learning piecewise from adjacent time points can fail to capture long-term dependencies. And practitioners are typically able to specify a model class for the reference dynamic but not the exact values of the parameters within it. So we propose a new method that (1) learns the unobserved trajectories from sample snapshots across multiple time points and (2) requires specification only of a class of reference dynamics, not a single fixed one. In particular, we suggest an iterative projection method inspired by Schr\"odinger bridges; we alternate between learning a piecewise SB on the unobserved trajectories and using the learned SB to refine our best guess for the dynamics within the reference class. We demonstrate the advantages of our method via a well-known simulated parametric model from ecology, simulated and real data from systems biology, and real motion-capture data.

High-content screening (HCS) assays based on high-throughput microscopy techniques such as Cell Painting have enabled the interrogation of cells' morphological responses to perturbations at an unprecedented scale. The collection of such data promises to facilitate a better understanding of the relationships between different perturbations and their effects on cellular state. Towards achieving this goal, recent advances in cross-modal contrastive learning could, in theory, be leveraged to learn a unified latent space that aligns perturbations with their corresponding morphological effects. However, the application of such methods to HCS data is not straightforward due to substantial differences in the semantics of Cell Painting images compared to natural images, and the difficulty of representing different classes of perturbations (e.g., small molecule vs CRISPR gene knockout) in a single latent space. In response to these challenges, here we introduce CellCLIP, a cross-modal contrastive learning framework for HCS data. CellCLIP leverages pre-trained image encoders coupled with a novel channel encoding scheme to better capture relationships between different microscopy channels in image embeddings, along with natural language encoders for representing perturbations. Our framework outperforms current open-source models, demonstrating the best performance in both cross-modal retrieval and biologically meaningful downstream tasks while also achieving significant reductions in computation time.

Molecular dynamics (MD) is a central computational tool in physics, chemistry, and biology, enabling quantitative prediction of experimental observables as expectations over high-dimensional molecular distributions such as Boltzmann distributions and transition densities. However, conventional MD is fundamentally limited by the high computational cost required to generate independent samples. Generative molecular dynamics (GenMD) has recently emerged as an alternative, learning surrogates of molecular distributions either from data or through interaction with energy models. While these methods enable efficient sampling, their transferability across molecular systems is often limited. In this work, we show that incorporating auxiliary sources of information can improve the data efficiency and generalization of transferable implicit transfer operators (TITO) for molecular dynamics. We find that coarse-grained TITO models are substantially more data-efficient than Boltzmann Emulators, and that incorporating protein language model (pLM) embeddings further improves out-of-distribution generalization. Our approach, PLaTITO, achieves state-of-the-art performance on equilibrium sampling benchmarks for out-of-distribution protein systems, including fast-folding proteins. We further study the impact of additional conditioning signals -- such as structural embeddings, temperature, and large-language-model-derived embeddings -- on model performance.

The dynamics of biomolecules are crucial for our understanding of their functioning in living systems. However, current 3D imaging techniques, such as cryogenic electron microscopy (cryo-EM), require freezing the sample, which limits the observation of their conformational changes in real time. The innovative liquid-phase electron microscopy (liquid-phase EM) technique allows molecules to be placed in the native liquid environment, providing a unique opportunity to observe their dynamics. In this paper, we propose TEMPOR, a Temporal Electron MicroscoPy Object Reconstruction algorithm for liquid-phase EM that leverages an implicit neural representation (INR) and a dynamical variational auto-encoder (DVAE) to recover time series of molecular structures. We demonstrate its advantages in recovering different motion dynamics from two simulated datasets, 7bcq and Cas9. To our knowledge, our work is the first attempt to directly recover 3D structures of a temporally-varying particle from liquid-phase EM movies. It provides a promising new approach for studying molecules' 3D dynamics in structural biology.

Molecular Dynamics (MD) is a powerful computational microscope for probing protein functions. However, the need for fine-grained integration and the long timescales of biomolecular events make MD computationally expensive. To address this, several generative models have been proposed to generate surrogate trajectories at lower cost. Yet, these models typically learn a fixed-lag transition density, causing the training signal to be dominated by frequent but uninformative transitions. We introduce a new class of generative models, MSM Emulators, which instead learn to sample transitions across discrete states defined by an underlying Markov State Model (MSM). We instantiate this class with Markov Space Flow Matching (MarS-FM), whose sampling offers more than two orders of magnitude speedup compared to implicit- or explicit-solvent MD simulations. We benchmark Mars-FM ability to reproduce MD statistics through structural observables such as RMSD, radius of gyration, and secondary structure content. Our evaluation spans protein domains (up to 500 residues) with significant chemical and structural diversity, including unfolding events, and enforces strict sequence dissimilarity between training and test sets to assess generalization. Across all metrics, MarS-FM outperforms existing methods, often by a substantial margin.

Many natural dynamic processes -- such as in vivo cellular differentiation or disease progression -- can only be observed through the lens of static sample snapshots. While challenging, reconstructing their temporal evolution to decipher underlying dynamic properties is of major interest to scientific research. Existing approaches enable data transport along a temporal axis but are poorly scalable in high dimension and require restrictive assumptions to be met. To address these issues, we propose \textbf{Multi-Marginal temporal Schr\"odinger Bridge Matching} (MMtSBM) for video generation from unpaired data, extending the theoretical guarantees and empirical efficiency of Diffusion Schr\"odinger Bridge Matching (arXiv:archive/2303.16852) by deriving the Iterative Markovian Fitting algorithm to multiple marginals in a novel factorized fashion. Experiments show that MMtSBM retains theoretical properties on toy examples, achieves state-of-the-art performance on real world datasets such as transcriptomic trajectory inference in 100 dimensions, and for the first time recovers couplings and dynamics in very high dimensional image settings. Our work establishes multi-marginal Schr\"odinger bridges as a practical and principled approach for recovering hidden dynamics from static data.

Simulating trajectories of multi-particle systems on complex energy landscapes is a central task in molecular dynamics (MD) and drug discovery, but remains challenging at scale due to computationally expensive and long simulations. Previous approaches leverage techniques such as flow or Schrödinger bridge matching to implicitly learn joint trajectories through data snapshots. However, many systems, including biomolecular systems and heterogeneous cell populations, undergo dynamic interactions that evolve over their trajectory and cannot be captured through static snapshots. To close this gap, we introduce Entangled Schrödinger Bridge Matching (EntangledSBM), a framework that learns the first- and second-order stochastic dynamics of interacting, multi-particle systems where the direction and magnitude of each particle's path depend dynamically on the paths of the other particles. We define the Entangled Schrödinger Bridge (EntangledSB) problem as solving a coupled system of bias forces that entangle particle velocities. We show that our framework accurately simulates heterogeneous cell populations under perturbations and rare transitions in high-dimensional biomolecular systems.

Cell painting is a popular technique for creating human-interpretable, high-contrast images of cell morphology. There are two major issues with cell paint: (1) it is labor-intensive and (2) it requires chemical fixation, making the study of cell dynamics impossible. We train a diffusion model (Morphological Observation Neural Enhancement Tool, or MONET) on a large dataset to predict cell paint channels from brightfield images. We show that model quality improves with scale. The model uses a consistency architecture to generate time-lapse videos, despite the impossibility of obtaining cell paint video training data. In addition, we show that this architecture enables a form of in-context learning, allowing the model to partially transfer to out-of-distribution cell lines and imaging protocols. Virtual cell painting is not intended to replace physical cell painting completely, but to act as a complementary tool enabling novel workflows in biological research.

Cell migration in vivo is often guided by chemical signals. Such chemotaxis, such as performed by immune cells migrating to a wound site, is complicated by the complex geometry inside living tissues. In this study, we extend our theoretical model of branched-cell migration on a network by introducing chemokine sources to explore the cellular response. The model predicts a speed-accuracy tradeoff, whereby slow cells are significantly more accurate and able to follow efficiently a weak chemoattractant signal. We then compare the model's predictions with experimental observations of neutrophils migrating to the site of laser-inflicted wound in a zebrafish larva fin, and migrating in-vitro inside a regular lattice of pillars. We find that the model captures the details of the sub-cellular response to the chemokine gradient, as well as the large-scale migration response. This comparison suggests that the neutrophils behave as fast cells, compromising their chemotaxis accuracy, which explains the functionality of these immune cells.

High-resolution brain imaging can now capture not just synapse locations but their molecular composition, with the cost of such mapping falling exponentially. Yet such ultrastructural data has so far told us little about local neuronal physiology - specifically, the parameters (e.g., synaptic efficacies, local conductances) that govern neural dynamics. We propose to translate molecularly annotated ultrastructure into physiology, introducing the concept of an ultrastructure-to-dynamics compiler: a learned mapping from molecularly annotated ultrastructure to simulator-ready, uncertainty-aware physiological parameters. The requirement is paired training data, with jointly acquired ultrastructure from imaging, and dynamical responses to perturbations from physiological experiments. With this data we can train models that predict local physiology directly from structure. Such a compiler would support biophysical simulations by turning anatomical maps into models of circuit dynamics, shifting structure-to-function from a descriptive program to a predictive one and opening routes to understanding neural computation and forecasting intervention effects.

As Large Language Models (LLMs) rapidly evolve, their influence in science is becoming increasingly prominent. The emerging capabilities of LLMs in task generalization and free-form dialogue can significantly advance fields like chemistry and biology. However, the field of single-cell biology, which forms the foundational building blocks of living organisms, still faces several challenges. High knowledge barriers and limited scalability in current methods restrict the full exploitation of LLMs in mastering single-cell data, impeding direct accessibility and rapid iteration. To this end, we introduce ChatCell, which signifies a paradigm shift by facilitating single-cell analysis with natural language. Leveraging vocabulary adaptation and unified sequence generation, ChatCell has acquired profound expertise in single-cell biology and the capability to accommodate a diverse range of analysis tasks. Extensive experiments further demonstrate ChatCell's robust performance and potential to deepen single-cell insights, paving the way for more accessible and intuitive exploration in this pivotal field. Our project homepage is available at https://zjunlp.github.io/project/ChatCell.

The generation of sustained, open-ended complexity from local interactions remains a fundamental challenge in artificial life. Differentiable multi-agent systems, such as Petri Dish Neural Cellular Automata (PD-NCA), exhibit rich self-organization driven purely by spatial competition; however, they are highly sensitive to hyperparameters and frequently collapse into uninteresting patterns and dynamics, such as frozen equilibria or structureless noise. In this paper, we introduce PBT-NCA, a meta-evolutionary algorithm that evolves a population of PD-NCAs subject to a composite objective that rewards both historical behavioral novelty and contemporary visual diversity. Driven by this continuous evolutionary pressure, PBT-NCA spontaneously generates a plethora of emergent lifelike phenomena over extended horizons-a hallmark of true open-endedness. Strikingly, the substrate autonomously discovers diverse morphological survival and self-organization strategies. We observe highly regular, coordinated periodic waves; spore-like scattering where homogeneous groups eject cell-like clusters to colonize distant territories; and fluid, shape-shifting macro-structures that migrate across the substrate, maintaining stable outer boundaries that enclose highly active interiors. By actively penalizing monocultures and dead states, PBT-NCA sustains a state of effective complexity that is neither globally ordered nor globally random, operating persistently at the "edge of chaos".

Virtual cell modeling represents an emerging frontier at the intersection of artificial intelligence and biology, aiming to predict quantities such as responses to diverse perturbations quantitatively. However, autonomously building computational models for virtual cells is challenging due to the complexity of biological systems, the heterogeneity of data modalities, and the need for domain-specific expertise across multiple disciplines. Here, we introduce CellForge, an agentic system that leverages a multi-agent framework that transforms presented biological datasets and research objectives directly into optimized computational models for virtual cells. More specifically, given only raw single-cell multi-omics data and task descriptions as input, CellForge outputs both an optimized model architecture and executable code for training virtual cell models and inference. The framework integrates three core modules: Task Analysis for presented dataset characterization and relevant literature retrieval, Method Design, where specialized agents collaboratively develop optimized modeling strategies, and Experiment Execution for automated generation of code. The agents in the Design module are separated into experts with differing perspectives and a central moderator, and have to collaboratively exchange solutions until they achieve a reasonable consensus. We demonstrate CellForge's capabilities in single-cell perturbation prediction, using six diverse datasets that encompass gene knockouts, drug treatments, and cytokine stimulations across multiple modalities. CellForge consistently outperforms task-specific state-of-the-art methods. Overall, CellForge demonstrates how iterative interaction between LLM agents with differing perspectives provides better solutions than directly addressing a modeling challenge. Our code is publicly available at https://github.com/gersteinlab/CellForge.

Predicting the intermediate trajectories between an initial and target distribution is a central problem in generative modeling. Existing approaches, such as flow matching and Schr\"odinger Bridge Matching, effectively learn mappings between two distributions by modeling a single stochastic path. However, these methods are inherently limited to unimodal transitions and cannot capture branched or divergent evolution from a common origin to multiple distinct outcomes. To address this, we introduce Branched Schr\"odinger Bridge Matching (BranchSBM), a novel framework that learns branched Schr\"odinger bridges. BranchSBM parameterizes multiple time-dependent velocity fields and growth processes, enabling the representation of population-level divergence into multiple terminal distributions. We show that BranchSBM is not only more expressive but also essential for tasks involving multi-path surface navigation, modeling cell fate bifurcations from homogeneous progenitor states, and simulating diverging cellular responses to perturbations.

This paper presents a mathematical framework for optimizing drug delivery in cancer treatment using a nonlocal model of solid tumor growth. We present a coupled system of partial differential equations that incorporate long-range cellular interactions through integral terms and drug-induced cell death. The model accounts for spatial heterogeneity in both tumor cell density and drug concentration while capturing the complex dynamics of drug resistance development. We first establish the well-posedness of the coupled system by proving the existence and uniqueness of a solution under appropriate regularity conditions. The optimal control problem is then formulated to minimize tumor size while accounting for drug toxicity constraints. Using variational methods, we derive the necessary optimality conditions and characterize the optimal control through an adjoint system. Theoretical results can help to design effective chemotherapy schedules that balance treatment efficacy with adverse effects.

We characterise the dynamics of neuronal activity, in terms of field theory, using neural units placed on a 2D-lattice modelling the cortical surface. The electrical activity of neuronal units was analysed with the aim of deriving a neural field model with a simple functional form that still able to predict or reproduce empirical findings. Each neural unit was modelled using a neural mass and the accompanying field theory was derived in the continuum limit. The field theory comprised coupled (real) Klein-Gordon fields, where predictions of the model fall within the range of experimental findings. These predictions included the frequency spectrum of electric activity measured from the cortex, which was derived using an equipartition of energy over eigenfunctions of the neural fields. Moreover, the neural field model was invariant, within a set of parameters, to the dynamical system used to model each neuronal mass. Specifically, topologically equivalent dynamical systems resulted in the same neural field model when connected in a lattice; indicating that the fields derived could be read as a canonical cortical field theory. We specifically investigated non-dispersive fields that provide a structure for the coding (or representation) of afferent information. Further elaboration of the ensuing neural field theory, including the effect of dispersive forces, could be of importance in the understanding of the cortical processing of information.

While the use of combination therapy is increasing in prevalence for cancer treatment, it is often difficult to predict the exact interactions between different treatment forms, and their synergistic/antagonistic effects on patient health and therapy outcome. In this research, a system of ordinary differential equations is constructed to model nonlinear dynamics between tumor cells, immune cells, and three forms of therapy: chemotherapy, immunotherapy, and radiotherapy. This model is then used to generate optimized combination therapy plans using optimal control theory. In-silico experiments are conducted to simulate the response of the patient model to various treatment plans. This is the first mathematical model in current literature to introduce radiotherapy as an option alongside immuno- and chemotherapy, permitting more flexible and effective treatment plans that reflect modern therapeutic approaches.

Segmenting cells and tracking their motion over time is a common task in biomedical applications. However, predicting accurate instance-wise segmentation and cell motions from microscopy imagery remains a challenging task. Using microstructured environments for analyzing single cells in a constant flow of media adds additional complexity. While large-scale labeled microscopy datasets are available, we are not aware of any large-scale dataset, including both cells and microstructures. In this paper, we introduce the trapped yeast cell (TYC) dataset, a novel dataset for understanding instance-level semantics and motions of cells in microstructures. We release 105 dense annotated high-resolution brightfield microscopy images, including about 19k instance masks. We also release 261 curated video clips composed of 1293 high-resolution microscopy images to facilitate unsupervised understanding of cell motions and morphology. TYC offers ten times more instance annotations than the previously largest dataset, including cells and microstructures. Our effort also exceeds previous attempts in terms of microstructure variability, resolution, complexity, and capturing device (microscopy) variability. We facilitate a unified comparison on our novel dataset by introducing a standardized evaluation strategy. TYC and evaluation code are publicly available under CC BY 4.0 license.

Breast Cancer is a major public health problem and the most common diagnosed malignancy in woman. There have been significant developments in clinical approaches and theoretical experimental to understand the interactions of cancer cells dynamics with the immune system, also developments on analytical and computational models to help provide insights into clinical observations for a better understanding of cancer cells, but more are needed, especially at the genetic and molecular levels mathematically. Treatments such as immunotherapy, chemotherapy, hormone therapy, radiotherapy, and gene therapy are the main strategies in the fight against breast cancer. The present study aims at investigating the effects of estrogen derived from recent models, but this time combined with immunotherapy as a way to treat or inhibit the cancer growth by a mathematical model of breast cancer in situ, governed by a simplified model of nonlinear-coupled ordinary differential equations, that combines important interactions between natural cells, tumor cells, immune cells, ketogenic diet in the presence of an anticancer drug. Another contribution was to introduce the inhibition effect epsilon for new results and conclusions, A qualitative study was performed and biological interpretations were included to understand the conditions of stability in a realistic way.

Recent advances in machine learning and large-scale biological data collections have revived the prospect of building a virtual cell, a computational model of cellular behavior that could accelerate biological discovery. One of the most compelling promises of this vision is the ability to perform in silico phenotypic screens, in which a model predicts the effects of cellular perturbations in unseen biological contexts. This task combines heterogeneous textual inputs with diverse phenotypic outputs, making it particularly well-suited to LLMs and agentic systems. Yet, no standard benchmark currently exists for this task, as existing efforts focus on narrower molecular readouts that are only indirectly aligned with the phenotypic endpoints driving many real-world drug discovery workflows. In this work, we present AssayBench, a benchmark for phenotypic screen prediction, built from 1,920 publicly available CRISPR screens spanning five broad classes of cellular phenotypes. We formulate the screen prediction task as a gene rank prediction for each screen and introduce the adjusted nDCG, a continuous metric for comparing performance across heterogeneous assays. Our extensive evaluation shows that existing methods remain far from empirically estimated performance ceilings and zero-shot generalist LLMs outperform biology-specific LLMs and trainable baselines. Optimization techniques such as fine-tuning, ensembling, and prompt optimization can further improve LLM performance on this task. Overall, AssayBench offers a practical testbed for measuring progress toward in silico phenotypic screening and, more broadly, virtual cell models.

Cell instance segmentation in fluorescence microscopy images is becoming essential for cancer dynamics and prognosis. Data extracted from cancer dynamics allows to understand and accurately model different metabolic processes such as proliferation. This enables customized and more precise cancer treatments. However, accurate cell instance segmentation, necessary for further cell tracking and behavior analysis, is still challenging in scenarios with high cell concentration and overlapping edges. Within this framework, we propose a novel cell instance segmentation approach based on the well-known U-Net architecture. To enforce the learning of morphological information per pixel, a deep distance transformer (DDT) acts as a back-bone model. The DDT output is subsequently used to train a top-model. The following top-models are considered: a three-class (e.g., foreground, background and cell border) U-net, and a watershed transform. The obtained results suggest a performance boost over traditional U-Net architectures. This opens an interesting research line around the idea of injecting morphological information into a fully convolutional model.

Identifying subtle phenotypic variations in cellular images is critical for advancing biological research and accelerating drug discovery. These variations are often masked by the inherent cellular heterogeneity, making it challenging to distinguish differences between experimental conditions. Recent advancements in deep generative models have demonstrated significant potential for revealing these nuanced phenotypes through image translation, opening new frontiers in cellular and molecular biology as well as the identification of novel biomarkers. Among these generative models, diffusion models stand out for their ability to produce high-quality, realistic images. However, training diffusion models typically requires large datasets and substantial computational resources, both of which can be limited in biological research. In this work, we propose a novel approach that leverages pre-trained latent diffusion models to uncover subtle phenotypic changes. We validate our approach qualitatively and quantitatively on several small datasets of microscopy images. Our findings reveal that our approach enables effective detection of phenotypic variations, capturing both visually apparent and imperceptible differences. Ultimately, our results highlight the promising potential of this approach for phenotype detection, especially in contexts constrained by limited data and computational capacity.

The simulation of the metabolism in mammalian cells becomes a severe problem if spatial distributions must be taken into account. Especially the cytoplasm has a very complex geometric structure which cannot be handled by standard discretization techniques. In the present paper we propose a homogenization technique for computing effective diffusion constants. This is accomplished by using a two-step strategy. The first step consists of an analytic homogenization from the smallest to an intermediate scale. The homogenization error is estimated by comparing the analytic diffusion constant with a numerical estimate obtained by using real cell geometries. The second step consists of a random homogenization. Since no analytical solution is known to this homogenization problem, a numerical approximation algorithm is proposed. Although rather expensive this algorithm provides a reasonable estimate of the homogenized diffusion constant.

We study growth of solid tumors in a partial differential equation model introduced by Hillen et al for the interaction between tumor cells (TCs) and cancer stem cells (CSCs). We find that invasion into the cancer-free state may be separated into two regimes, depending on the death rate of tumor cells. In the first, staged invasion regime, invasion into the cancer-free state is lead by tumor cells, which are then subsequently invaded at a slower speed by cancer stem cells. In the second, TC extinction regime, cancer stem cells directly invade the cancer-free state. Relying on recent results establishing front selection propagation under marginal stability assumptions, we use geometric singular perturbation theory to establish existence and selection properties of front solutions which describe both the primary and secondary invasion processes. With rigorous predictions for the invasion speeds, we are then able to heuristically predict how the total cancer mass as a function of time depends on the TC death rate, finding in some situations a tumor invasion paradox, in which increasing the TC death rate leads to an increase in the total cancer mass. Our methods give a general approach for verifying linear determinacy of spreading speeds of invasion fronts in systems with fast-slow structure.

Cells that collide with each other repolarize away from contact, in a process called contact inhibition of locomotion (CIL), which is necessary for correct development of the embryo. CIL can occur even when cells make a micron-scale contact with a neighbor - much smaller than their size. How precisely can a cell sense cell-cell contact and repolarize in the correct direction? What factors control whether a cell recognizes it has contacted a neighbor? We propose a theoretical model for the limits of CIL where cells recognize the presence of another cell by binding the protein ephrin with the Eph receptor. This recognition is made difficult by the presence of interfering ligands that bind nonspecifically. Both theoretical predictions and simulation results show that it becomes more difficult to sense cell-cell contact when it is difficult to distinguish ephrin from the interfering ligands, or when there are more interfering ligands, or when the contact width decreases. However, the error of estimating contact position remains almost constant when the contact width changes. This happens because the cell gains spatial information largely from the boundaries of cell-cell contact. We study using statistical decision theory the likelihood of a false positive CIL event in the absence of cell-cell contact, and the likelihood of a false negative where CIL does not occur when another cell is present. Our results suggest that the cell is more likely to make incorrect decisions when the contact width is very small or so large that it nears the cell's perimeter. However, in general, we find that cells have the ability to make reasonably reliable CIL decisions even for very narrow (micron-scale) contacts, even if the concentration of interfering ligands is ten times that of the correct ligands.

There is a widening recognition that cancer cells are products of complex developmental processes. Carcinogenesis and metastasis formation are increasingly described as systems-level, network phenomena. Here we propose that malignant transformation is a two-phase process, where an initial increase of system plasticity is followed by a decrease of plasticity at late stages of carcinogenesis as a model of cellular learning. We describe the hallmarks of increased system plasticity of early, tumor initiating cells, such as increased noise, entropy, conformational and phenotypic plasticity, physical deformability, cell heterogeneity and network rearrangements. Finally, we argue that the large structural changes of molecular networks during cancer development necessitate a rather different targeting strategy in early and late phase of carcinogenesis. Plastic networks of early phase cancer development need a central hit, while rigid networks of late stage primary tumors or established metastases should be attacked by the network influence strategy, such as by edgetic, multi-target, or allo-network drugs. Cancer stem cells need special diagnosis and targeting, since their dormant and rapidly proliferating forms may have more rigid, or more plastic networks, respectively. The extremely high ability to change their rigidity/plasticity may be a key differentiating hallmark of cancer stem cells. The application of early stage-optimized anti-cancer drugs to late-stage patients may be a reason of many failures in anti-cancer therapies. Our hypotheses presented here underlie the need for patient-specific multi-target therapies applying the correct ratio of central hits and network influences -- in an optimized sequence.

Cell type annotation is a key task in analyzing the heterogeneity of single-cell RNA sequencing data. Although recent foundation models automate this process, they typically annotate cells independently, without considering batch-level cellular context or providing explanatory reasoning. In contrast, human experts often annotate distinct cell types for different cell clusters based on their domain knowledge. To mimic this workflow, we introduce the CellPuzzles task, where the objective is to assign unique cell types to a batch of cells. This benchmark spans diverse tissues, diseases, and donor conditions, and requires reasoning across the batch-level cellular context to ensure label uniqueness. We find that off-the-shelf large language models (LLMs) struggle on CellPuzzles, with the best baseline (OpenAI's o1) achieving only 19.0% batch-level accuracy. To fill this gap, we propose Cell-o1, a 7B LLM trained via supervised fine-tuning on distilled reasoning traces, followed by reinforcement learning with batch-level rewards. Cell-o1 achieves state-of-the-art performance, outperforming o1 by over 73% and generalizing well across contexts. Further analysis of training dynamics and reasoning behaviors provides insights into batch-level annotation performance and emergent expert-like reasoning. Code and data are available at https://github.com/ncbi-nlp/cell-o1.

Genome engineering has achieved remarkable sequence-level precision, yet predicting the transcriptomic state that a cell will occupy after perturbation remains an open problem. Single-cell CRISPR screens measure how far cells move from their unperturbed state, but this effect magnitude ignores a fundamental question: do the cells move together? Two perturbations with identical magnitude can produce qualitatively different outcomes if one drives cells coherently along a shared trajectory while the other scatters them across expression space. We introduce a geometric stability metric, Shesha, that quantifies the directional coherence of single-cell perturbation responses as the mean cosine similarity between individual cell shift vectors and the mean perturbation direction. Across five CRISPR datasets (2,200+ perturbations spanning CRISPRa, CRISPRi, and pooled screens), stability correlates strongly with effect magnitude (Spearman ρ=0.75-0.97), with a calibrated cross-dataset correlation of 0.97. Crucially, discordant cases where the two metrics decouple expose regulatory architecture: pleiotropic master regulators such as CEBPA and GATA1 pay a "geometric tax," producing large but incoherent shifts, while lineage-specific factors such as KLF1 produce tightly coordinated responses. After controlling for magnitude, geometric instability is independently associated with elevated chaperone activation (HSPA5/BiP; ρ_{partial}=-0.34 and -0.21 across datasets), and the high-stability/high-stress quadrant is systematically depleted. The magnitude-stability relationship persists in scGPT foundation model embeddings, confirming it is a property of biological state space rather than linear projection. Perturbation stability provides a complementary axis for hit prioritization in screens, phenotypic quality control in cell manufacturing, and evaluation of in silico perturbation predictions.

Can a micron sized sack of interacting molecules understand, and adapt to a constantly-fluctuating environment? Cellular life provides an existence proof in the affirmative, but the principles that allow for life's existence are far from being proven. One challenge in engineering and understanding biochemical computation is the intrinsic noise due to chemical fluctuations. In this paper, we draw insights from machine learning theory, chemical reaction network theory, and statistical physics to show that the broad and biologically relevant class of detailed balanced chemical reaction networks is capable of representing and conditioning complex distributions. These results illustrate how a biochemical computer can use intrinsic chemical noise to perform complex computations. Furthermore, we use our explicit physical model to derive thermodynamic costs of inference.

In single-cell research, tracing and analyzing high-throughput single-cell differentiation trajectories is crucial for understanding biological processes. Key to this is the robust modeling of hierarchical structures that govern cellular development. Traditional methods face limitations in computational cost, performance, and stability. VAE-based approaches have made strides but still require branch-specific network modules, limiting their scalability and stability, while often suffering from posterior collapse. To overcome these challenges, we introduce HDTree, a generative modeling framework designed for robust lineage inference. HDTree captures tree relationships within a hierarchical latent space using a unified hierarchical codebook and employs a quantized diffusion process to model continuous cell state transitions. By aligning the generative process with the Waddington landscape, this method not only improves stability and scalability but also enhances the biological plausibility of inferred lineages. HDTree's effectiveness is demonstrated through comparisons on both general-purpose and single-cell datasets, where it outperforms existing methods in lineage inference accuracy, reconstruction quality, and hierarchical consistency. These contributions enable accurate and efficient modeling of cellular differentiation paths, offering reliable insights for biological discovery.\footnote{Code is available at https://github.com/zangzelin/code\_HDTree\_icml.

Molecular dynamics (MD) is a powerful technique for studying microscopic phenomena, but its computational cost has driven significant interest in the development of deep learning-based surrogate models. We introduce generative modeling of molecular trajectories as a paradigm for learning flexible multi-task surrogate models of MD from data. By conditioning on appropriately chosen frames of the trajectory, we show such generative models can be adapted to diverse tasks such as forward simulation, transition path sampling, and trajectory upsampling. By alternatively conditioning on part of the molecular system and inpainting the rest, we also demonstrate the first steps towards dynamics-conditioned molecular design. We validate the full set of these capabilities on tetrapeptide simulations and show that our model can produce reasonable ensembles of protein monomers. Altogether, our work illustrates how generative modeling can unlock value from MD data towards diverse downstream tasks that are not straightforward to address with existing methods or even MD itself. Code is available at https://github.com/bjing2016/mdgen.

Cell identity encompasses various semantic aspects of a cell, including cell type, pathway information, disease information, and more, which are essential for biologists to gain insights into its biological characteristics. Understanding cell identity from the transcriptomic data, such as annotating cell types, has become an important task in bioinformatics. As these semantic aspects are determined by human experts, it is impossible for AI models to effectively carry out cell identity understanding tasks without the supervision signals provided by single-cell and label pairs. The single-cell pre-trained language models (PLMs) currently used for this task are trained only on a single modality, transcriptomics data, lack an understanding of cell identity knowledge. As a result, they have to be fine-tuned for downstream tasks and struggle when lacking labeled data with the desired semantic labels. To address this issue, we propose an innovative solution by constructing a unified representation of single-cell data and natural language during the pre-training phase, allowing the model to directly incorporate insights related to cell identity. More specifically, we introduce LangCell, the first Language-Cell pre-training framework. LangCell utilizes texts enriched with cell identity information to gain a profound comprehension of cross-modal knowledge. Results from experiments conducted on different benchmarks show that LangCell is the only single-cell PLM that can work effectively in zero-shot cell identity understanding scenarios, and also significantly outperforms existing models in few-shot and fine-tuning cell identity understanding scenarios.

Large language models (LLMs) and emerging agentic frameworks are beginning to transform single-cell biology by enabling natural-language reasoning, generative annotation, and multimodal data integration. However, progress remains fragmented across data modalities, architectures, and evaluation standards. LLM4Cell presents the first unified survey of 58 foundation and agentic models developed for single-cell research, spanning RNA, ATAC, multi-omic, and spatial modalities. We categorize these methods into five families-foundation, text-bridge, spatial, multimodal, epigenomic, and agentic-and map them to eight key analytical tasks including annotation, trajectory and perturbation modeling, and drug-response prediction. Drawing on over 40 public datasets, we analyze benchmark suitability, data diversity, and ethical or scalability constraints, and evaluate models across 10 domain dimensions covering biological grounding, multi-omics alignment, fairness, privacy, and explainability. By linking datasets, models, and evaluation domains, LLM4Cell provides the first integrated view of language-driven single-cell intelligence and outlines open challenges in interpretability, standardization, and trustworthy model development.

Time-lapse fluorescent microscopy (TLFM) combined with predictive mathematical modelling is a powerful tool to study the inherently dynamic processes of life on the single-cell level. Such experiments are costly, complex and labour intensive. A complimentary approach and a step towards in silico experimentation, is to synthesise the imagery itself. Here, we propose Multi-StyleGAN as a descriptive approach to simulate time-lapse fluorescence microscopy imagery of living cells, based on a past experiment. This novel generative adversarial network synthesises a multi-domain sequence of consecutive timesteps. We showcase Multi-StyleGAN on imagery of multiple live yeast cells in microstructured environments and train on a dataset recorded in our laboratory. The simulation captures underlying biophysical factors and time dependencies, such as cell morphology, growth, physical interactions, as well as the intensity of a fluorescent reporter protein. An immediate application is to generate additional training and validation data for feature extraction algorithms or to aid and expedite development of advanced experimental techniques such as online monitoring or control of cells. Code and dataset is available at https://git.rwth-aachen.de/bcs/projects/tp/multi-stylegan.

Sparse autoencoders (SAEs) have lately been used to uncover interpretable latent features in large language models. Here, we explore their potential for decomposing latent representations in complex and high-dimensional biological data, where the underlying variables are often unknown. On simulated data we show that generative hidden variables can be captured in learned representations in the form of superpositions. The degree to which they are learned depends on the completeness of the representations. Superpositions, however, are not identifiable if these generative variables are unknown. SAEs can to some extent recover these variables, yielding interpretable features. Applied to single-cell multi-omics data, we show that an SAE can uncover key biological processes such as carbon dioxide transport and ion homeostasis, which are crucial for red blood cell differentiation and immune function. Our findings highlight how SAEs can be used in advancing interpretability in biological and other scientific domains.

Markov jump processes are continuous-time stochastic processes which describe dynamical systems evolving in discrete state spaces. These processes find wide application in the natural sciences and machine learning, but their inference is known to be far from trivial. In this work we introduce a methodology for zero-shot inference of Markov jump processes (MJPs), on bounded state spaces, from noisy and sparse observations, which consists of two components. First, a broad probability distribution over families of MJPs, as well as over possible observation times and noise mechanisms, with which we simulate a synthetic dataset of hidden MJPs and their noisy observation process. Second, a neural network model that processes subsets of the simulated observations, and that is trained to output the initial condition and rate matrix of the target MJP in a supervised way. We empirically demonstrate that one and the same (pretrained) model can infer, in a zero-shot fashion, hidden MJPs evolving in state spaces of different dimensionalities. Specifically, we infer MJPs which describe (i) discrete flashing ratchet systems, which are a type of Brownian motors, and the conformational dynamics in (ii) molecular simulations, (iii) experimental ion channel data and (iv) simple protein folding models. What is more, we show that our model performs on par with state-of-the-art models which are finetuned to the target datasets.

We put forward the dynamical study of a novel higher-order small network of Chialvo neurons arranged in a ring-star topology, with the neurons interacting via linear diffusive couplings. This model is perceived to imitate the nonlinear dynamical properties exhibited by a realistic nervous system where the neurons transfer information through higher-order multi-body interactions. We first analyze our model using the tools from nonlinear dynamics literature: fixed point analysis, Jacobian matrix, and bifurcation patterns. We observe the coexistence of chaotic attractors, and also an intriguing route to chaos starting from a fixed point, to period-doubling, to cyclic quasiperiodic closed invariant curves, to ultimately chaos. We numerically observe the existence of codimension-1 bifurcation patterns: saddle-node, period-doubling, and Neimark Sacker. We also qualitatively study the typical phase portraits of the system and numerically quantify chaos and complexity using the 0-1 test and sample entropy measure respectively. Finally, we study the collective behavior of the neurons in terms of two synchronization measures: the cross-correlation coefficient, and the Kuramoto order parameter.

Large language models excel at interpreting complex natural language instructions, enabling them to perform a wide range of tasks. In the life sciences, single-cell RNA sequencing (scRNA-seq) data serves as the "language of cellular biology", capturing intricate gene expression patterns at the single-cell level. However, interacting with this "language" through conventional tools is often inefficient and unintuitive, posing challenges for researchers. To address these limitations, we present InstructCell, a multi-modal AI copilot that leverages natural language as a medium for more direct and flexible single-cell analysis. We construct a comprehensive multi-modal instruction dataset that pairs text-based instructions with scRNA-seq profiles from diverse tissues and species. Building on this, we develop a multi-modal cell language architecture capable of simultaneously interpreting and processing both modalities. InstructCell empowers researchers to accomplish critical tasks-such as cell type annotation, conditional pseudo-cell generation, and drug sensitivity prediction-using straightforward natural language commands. Extensive evaluations demonstrate that InstructCell consistently meets or exceeds the performance of existing single-cell foundation models, while adapting to diverse experimental conditions. More importantly, InstructCell provides an accessible and intuitive tool for exploring complex single-cell data, lowering technical barriers and enabling deeper biological insights.

Large language models (LLMs) are increasingly applied in scientific research, offering new capabilities for knowledge discovery and reasoning. In single-cell biology, however, evaluation practices for both general and specialized LLMs remain inadequate: existing benchmarks are fragmented across tasks, adopt formats such as multiple-choice classification that diverge from real-world usage, and rely on metrics lacking interpretability and biological grounding. We present SC-ARENA, a natural language evaluation framework tailored to single-cell foundation models. SC-ARENA formalizes a virtual cell abstraction that unifies evaluation targets by representing both intrinsic attributes and gene-level interactions. Within this paradigm, we define five natural language tasks (cell type annotation, captioning, generation, perturbation prediction, and scientific QA) that probe core reasoning capabilities in cellular biology. To overcome the limitations of brittle string-matching metrics, we introduce knowledge-augmented evaluation, which incorporates external ontologies, marker databases, and scientific literature to support biologically faithful and interpretable judgments. Experiments and analysis across both general-purpose and domain-specialized LLMs demonstrate that (i) under the Virtual Cell unified evaluation paradigm, current models achieve uneven performance on biologically complex tasks, particularly those demanding mechanistic or causal understanding; and (ii) our knowledge-augmented evaluation framework ensures biological correctness, provides interpretable, evidence-grounded rationales, and achieves high discriminative capacity, overcoming the brittleness and opacity of conventional metrics. SC-Arena thus provides a unified and interpretable framework for assessing LLMs in single-cell biology, pointing toward the development of biology-aligned, generalizable foundation models.

We extend our previously proposed image reconstruction method, which allows confocal microscopes to capture periodically moving objects at frequencies beyond their frame rates, to three-dimensional and two-dimensional wide-field imaging. This extension is achieved by implementing a synchronization scheme between a confocal laser scanning microscope and a function generator to ensure consistent initial phase alignment across image sequences acquired at different focal depths or fields of view. The method was demonstrated by visualizing the three-dimensional motion of silica particles attached to an aluminum bar oscillating at 100 Hz and the two-dimensional wide-field response of colloidal particles subjected to periodic pulsed excitation. Quantitative single-particle analysis confirmed that the reconstructed images accurately captured the underlying particle dynamics. The extended approach requires no additional specialized hardware and can be readily integrated with conventional confocal microscopes. Thus, it extends the applicability of confocal imaging to the fast dynamics of periodic processes in biological and soft-matter systems.

Dynamic Mode Decomposition (DMD) is an equation-free method that aims at reconstructing the best linear fit from temporal datasets. In this paper, we show that DMD does not provide accurate approximation for datasets describing oscillatory dynamics, like spiral waves and relaxation oscillations, or spatio-temporal Turing instability. Inspired from the classical "divide and conquer" approach, we propose a piecewise version of DMD (pDMD) to overcome this problem. The main idea is to split the original dataset in N submatrices and then apply the exact (randomized) DMD method in each subset of the obtained partition. We describe the pDMD algorithm in detail and we introduce some error indicators to evaluate its performance when N is increased. Numerical experiments show that very accurate reconstructions are obtained by pDMD for datasets arising from time snapshots of some reaction-diffusion PDE systems, like the FitzHugh-Nagumo model, the lambda-omega system and the DIB morpho-chemical system for battery modeling.

We report a new system of artificial life called Lenia (from Latin lenis "smooth"), a two-dimensional cellular automaton with continuous space-time-state and generalized local rule. Computer simulations show that Lenia supports a great diversity of complex autonomous patterns or "lifeforms" bearing resemblance to real-world microscopic organisms. More than 400 species in 18 families have been identified, many discovered via interactive evolutionary computation. They differ from other cellular automata patterns in being geometric, metameric, fuzzy, resilient, adaptive, and rule-generic. We present basic observations of the system regarding the properties of space-time and basic settings. We provide a broad survey of the lifeforms, categorize them into a hierarchical taxonomy, and map their distribution in the parameter hyperspace. We describe their morphological structures and behavioral dynamics, propose possible mechanisms of their self-propulsion, self-organization and plasticity. Finally, we discuss how the study of Lenia would be related to biology, artificial life, and artificial intelligence.

Quantifying cell morphology using images and machine learning has proven to be a powerful tool to study the response of cells to treatments. However, models used to quantify cellular morphology are typically trained with a single microscopy imaging type. This results in specialized models that cannot be reused across biological studies because the technical specifications do not match (e.g., different number of channels), or because the target experimental conditions are out of distribution. Here, we present CHAMMI-75, an open access dataset of heterogeneous, multi-channel microscopy images from 75 diverse biological studies. We curated this resource from publicly available sources to investigate cellular morphology models that are channel-adaptive and can process any microscopy image type. Our experiments show that training with CHAMMI-75 can improve performance in multi-channel bioimaging tasks primarily because of its high diversity in microscopy modalities. This work paves the way to create the next generation of cellular morphology models for biological studies.

Computational microscopy, in which hardware and algorithms of an imaging system are jointly designed, shows promise for making imaging systems that cost less, perform more robustly, and collect new types of information. Often, the performance of computational imaging systems, especially those that incorporate machine learning, is sample-dependent. Thus, standardized datasets are an essential tool for comparing the performance of different approaches. Here, we introduce the Berkeley Single Cell Computational Microscopy (BSCCM) dataset, which contains over ~12,000,000 images of 400,000 of individual white blood cells. The dataset contains images captured with multiple illumination patterns on an LED array microscope and fluorescent measurements of the abundance of surface proteins that mark different cell types. We hope this dataset will provide a valuable resource for the development and testing of new algorithms in computational microscopy and computer vision with practical biomedical applications.

Predicting how cells respond to genetic perturbations is fundamental to understanding gene function, disease mechanisms, and therapeutic development. While recent deep learning approaches have shown promise in modeling single-cell perturbation responses, they struggle to generalize across cell types and perturbation contexts due to limited contextual information during generation. We introduce PT-RAG (Perturbation-aware Two-stage Retrieval-Augmented Generation), a novel framework that extends Retrieval-Augmented Generation beyond traditional language-model applications to cellular biology. Unlike standard RAG systems designed for text retrieval with pre-trained LLMs, perturbation retrieval lacks established similarity metrics and requires learning what constitutes relevant context, making differentiable retrieval essential. PT-RAG addresses this through a two-stage pipeline: first, retrieving candidate perturbations K using GenePT embeddings, then adaptively refining the selection through Gumbel-Softmax discrete sampling conditioned on both the cell state and the input perturbation. This cell-type-aware differentiable retrieval enables end-to-end optimization of the retrieval objective jointly with generation. On the Replogle-Nadig single-gene perturbation dataset, we demonstrate that PT-RAG outperforms both STATE and vanilla RAG under identical experimental conditions, with the strongest gains in distributional similarity metrics (W_1, W_2). Notably, vanilla RAG's dramatic failure is itself a key finding: it demonstrates that differentiable, cell-type-aware retrieval is essential in this domain, and that naive retrieval can actively harm performance. Our results establish retrieval-augmented generation as a promising paradigm for modelling cellular responses to gene perturbation. The code to reproduce our experiments is available at https://github.com/difra100/PT-RAG_ICLR.

The fields of Origin of Life and Artificial Life both question what life is and how it emerges from a distinct set of "pre-life" dynamics. One common feature of most substrates where life emerges is a marked shift in dynamics when self-replication appears. While there are some hypotheses regarding how self-replicators arose in nature, we know very little about the general dynamics, computational principles, and necessary conditions for self-replicators to emerge. This is especially true on "computational substrates" where interactions involve logical, mathematical, or programming rules. In this paper we take a step towards understanding how self-replicators arise by studying several computational substrates based on various simple programming languages and machine instruction sets. We show that when random, non self-replicating programs are placed in an environment lacking any explicit fitness landscape, self-replicators tend to arise. We demonstrate how this occurs due to random interactions and self-modification, and can happen with and without background random mutations. We also show how increasingly complex dynamics continue to emerge following the rise of self-replicators. Finally, we show a counterexample of a minimalistic programming language where self-replicators are possible, but so far have not been observed to arise.

Planning effective interventions in biological systems requires treatment-effect models that adapt to unseen biological contexts by identifying their specific underlying mechanisms. Yet single-cell perturbation datasets span only a handful of biological contexts, and existing methods cannot leverage new interventional evidence at inference time to adapt beyond their training data. To meta-learn a perturbation effect estimator, we present MapPFN, a prior-data fitted network (PFN) pretrained on synthetic data generated from a prior over causal perturbations. Given a set of experiments, MapPFN uses in-context learning to predict post-perturbation distributions, without gradient-based optimization. Despite being pretrained on in silico gene knockouts alone, MapPFN identifies differentially expressed genes, matching the performance of models trained on real single-cell data. Our code and data are available at https://github.com/marvinsxtr/MapPFN.

Single-cell RNA sequencing (scRNA-seq) data analysis is crucial for biological research, as it enables the precise characterization of cellular heterogeneity. However, manual manipulation of various tools to achieve desired outcomes can be labor-intensive for researchers. To address this, we introduce CellAgent (http://cell.agent4science.cn/), an LLM-driven multi-agent framework, specifically designed for the automatic processing and execution of scRNA-seq data analysis tasks, providing high-quality results with no human intervention. Firstly, to adapt general LLMs to the biological field, CellAgent constructs LLM-driven biological expert roles - planner, executor, and evaluator - each with specific responsibilities. Then, CellAgent introduces a hierarchical decision-making mechanism to coordinate these biological experts, effectively driving the planning and step-by-step execution of complex data analysis tasks. Furthermore, we propose a self-iterative optimization mechanism, enabling CellAgent to autonomously evaluate and optimize solutions, thereby guaranteeing output quality. We evaluate CellAgent on a comprehensive benchmark dataset encompassing dozens of tissues and hundreds of distinct cell types. Evaluation results consistently show that CellAgent effectively identifies the most suitable tools and hyperparameters for single-cell analysis tasks, achieving optimal performance. This automated framework dramatically reduces the workload for science data analyses, bringing us into the "Agent for Science" era.

Recurrent neural networks (RNNs) provide a powerful approach in neuroscience to infer latent dynamics in neural populations and to generate hypotheses about the neural computations underlying behavior. However, past work has focused on relatively simple, input-driven, and largely deterministic behaviors - little is known about the mechanisms that would allow RNNs to generate the richer, spontaneous, and potentially stochastic behaviors observed in natural settings. Modeling with Hidden Markov Models (HMMs) has revealed a segmentation of natural behaviors into discrete latent states with stochastic transitions between them, a type of dynamics that may appear at odds with the continuous state spaces implemented by RNNs. Here we first show that RNNs can replicate HMM emission statistics and then reverse-engineer the trained networks to uncover the mechanisms they implement. In the absence of inputs, the activity of trained RNNs collapses towards a single fixed point. When driven by stochastic input, trajectories instead exhibit noise-sustained dynamics along closed orbits. Rotation along these orbits modulates the emission probabilities and is governed by transitions between regions of slow, noise-driven dynamics connected by fast, deterministic transitions. The trained RNNs develop highly structured connectivity, with a small set of "kick neurons" initiating transitions between these regions. This mechanism emerges during training as the network shifts into a regime of stochastic resonance, enabling it to perform probabilistic computations. Analyses across multiple HMM architectures - fully connected, cyclic, and linear-chain - reveal that this solution generalizes through the modular reuse of the same dynamical motif, suggesting a compositional principle by which RNNs can emulate complex discrete latent dynamics.

Many examples of cooperation exist in biology. In chemical systems however, which can sometimes be quite complex, we do not appear to observe intricate cooperative interactions. A key question for the origin of life, is then how can molecular cooperation first arise in an abiotic system prior to the emergence of biological replication. We postulate that selection at the molecular level is a driving force behind the complexification of chemical systems, particularly during the origins of life. In the theory of multilevel selection the two selective forces are: within-group and between-group, where the former tends to favor "selfish" replication of individuals and the latter favor cooperation between individuals enhancing the replication of the group as a whole. These forces can be quantified using the Price equation, which is a standard tool used in evolutionary biology to quantify evolutionary change. Our central claim is that replication and heredity in chemical systems are subject to selection, and quantifiable using the multilevel Price equation. We demonstrate this using the Graded Autocatalysis Replication Domain computer model, describing simple protocell composed out of molecules and its replication, which respectively analogue to the group and the individuals. In contrast to previous treatments of this model, we treat the lipid molecules themselves as replicating individuals and the protocells they form as groups of individuals. Our goal is to demonstrate how evolutionary biology tools and concepts can be applied in chemistry and we suggest that molecular cooperation may arise as a result of group selection. Further, the biological relation of parent-progeny is proposed to be analogue to the reactant-product relation in chemistry, thus allowing for tools from evolutionary biology to be applied to chemistry and would deepen the connection between chemistry and biology.

Large-scale cell microscopy screens are used in drug discovery and molecular biology research to study the effects of millions of chemical and genetic perturbations on cells. To use these images in downstream analysis, we need models that can map each image into a feature space that represents diverse biological phenotypes consistently, in the sense that perturbations with similar biological effects have similar representations. In this work, we present the largest foundation model for cell microscopy data to date, a new 1.9 billion-parameter ViT-G/8 MAE trained on over 8 billion microscopy image crops. Compared to a previous published ViT-L/8 MAE, our new model achieves a 60% improvement in linear separability of genetic perturbations and obtains the best overall performance on whole-genome biological relationship recall and replicate consistency benchmarks. Beyond scaling, we developed two key methods that improve performance: (1) training on a curated and diverse dataset; and, (2) using biologically motivated linear probing tasks to search across each transformer block for the best candidate representation of whole-genome screens. We find that many self-supervised vision transformers, pretrained on either natural or microscopy images, yield significantly more biologically meaningful representations of microscopy images in their intermediate blocks than in their typically used final blocks. More broadly, our approach and results provide insights toward a general strategy for successfully building foundation models for large-scale biological data.

Collectives of actively-moving particles can spontaneously separate into dilute and dense phases -- a fascinating phenomenon known as motility-induced phase separation (MIPS). MIPS is well-studied for randomly-moving particles with no directional bias. However, many forms of active matter exhibit collective chemotaxis, directed motion along a chemical gradient that the constituent particles can generate themselves. Here, using theory and simulations, we demonstrate that collective chemotaxis strongly competes with MIPS -- in some cases, arresting or completely suppressing phase separation, or in other cases, generating fundamentally new dynamic instabilities. We establish quantitative principles describing this competition, thereby helping to reveal and clarify the rich physics underlying active matter systems that perform chemotaxis, ranging from cells to robots.

High-throughput screening techniques, such as microscopy imaging of cellular responses to genetic and chemical perturbations, play a crucial role in drug discovery and biomedical research. However, robust perturbation screening for de novo cell lines remains challenging due to the significant morphological and biological heterogeneity across cell lines. To address this, we propose a novel framework that integrates external biological knowledge into existing pretraining strategies to enhance microscopy image profiling models. Our approach explicitly disentangles perturbation-specific and cell line-specific representations using external biological information. Specifically, we construct a knowledge graph leveraging protein interaction data from STRING and Hetionet databases to guide models toward perturbation-specific features during pretraining. Additionally, we incorporate transcriptomic features from single-cell foundation models to capture cell line-specific representations. By learning these disentangled features, our method improves the generalization of imaging models to de novo cell lines. We evaluate our framework on the RxRx database through one-shot fine-tuning on an RxRx1 cell line and few-shot fine-tuning on cell lines from the RxRx19a dataset. Experimental results demonstrate that our method enhances microscopy image profiling for de novo cell lines, highlighting its effectiveness in real-world phenotype-based drug discovery applications.

Understanding protein dynamics is critical for elucidating their biological functions. The increasing availability of molecular dynamics (MD) data enables the training of deep generative models to efficiently explore the conformational space of proteins. However, existing approaches either fail to explicitly capture the temporal dependencies between conformations or do not support direct generation of time-independent samples. To address these limitations, we introduce ConfRover, an autoregressive model that simultaneously learns protein conformation and dynamics from MD trajectories, supporting both time-dependent and time-independent sampling. At the core of our model is a modular architecture comprising: (i) an encoding layer, adapted from protein folding models, that embeds protein-specific information and conformation at each time frame into a latent space; (ii) a temporal module, a sequence model that captures conformational dynamics across frames; and (iii) an SE(3) diffusion model as the structure decoder, generating conformations in continuous space. Experiments on ATLAS, a large-scale protein MD dataset of diverse structures, demonstrate the effectiveness of our model in learning conformational dynamics and supporting a wide range of downstream tasks. ConfRover is the first model to sample both protein conformations and trajectories within a single framework, offering a novel and flexible approach for learning from protein MD data.

The static synaptic connectivity of neuronal circuits stands in direct contrast to the dynamics of their function. As in changing community interactions, different neurons can participate actively in various combinations to effect behaviors at different times. We introduce an unsupervised approach to learn the dynamic affinities between neurons in live, behaving animals, and to reveal which communities form among neurons at different times. The inference occurs in two major steps. First, pairwise non-linear affinities between neuronal traces from brain-wide calcium activity are organized by non-negative tensor factorization (NTF). Each factor specifies which groups of neurons are most likely interacting for an inferred interval in time, and for which animals. Finally, a generative model that allows for weighted community detection is applied to the functional motifs produced by NTF to reveal a dynamic functional connectome. Since time codes the different experimental variables (e.g., application of chemical stimuli), this provides an atlas of neural motifs active during separate stages of an experiment (e.g., stimulus application or spontaneous behaviors). Results from our analysis are experimentally validated, confirming that our method is able to robustly predict causal interactions between neurons to generate behavior. Code is available at https://github.com/dyballa/dynamic-connectomes.

Molecular dynamics (MD) provides insights into atomic-scale processes by integrating over time the equations that describe the motion of atoms under the action of interatomic forces. Machine learning models have substantially accelerated MD by providing inexpensive predictions of the forces, but they remain constrained to minuscule time integration steps, which are required by the fast time scale of atomic motion. In this work, we propose FlashMD, a method to predict the evolution of positions and momenta over strides that are between one and two orders of magnitude longer than typical MD time steps. We incorporate considerations on the mathematical and physical properties of Hamiltonian dynamics in the architecture, generalize the approach to allow the simulation of any thermodynamic ensemble, and carefully assess the possible failure modes of such a long-stride MD approach. We validate FlashMD's accuracy in reproducing equilibrium and time-dependent properties, using both system-specific and general-purpose models, extending the ability of MD simulation to reach the long time scales needed to model microscopic processes of high scientific and technological relevance.

Continuous cellular automata are rocketing in popularity, yet developing a theoretical understanding of their behaviour remains a challenge. In the case of Lenia, a few fundamental open problems include determining what exactly constitutes a soliton, what is the overall structure of the parameter space, and where do the solitons occur in it. In this abstract, we present a new method to automatically classify Lenia systems into four qualitatively different dynamical classes. This allows us to detect moving solitons, and to provide an interactive visualization of Lenia's parameter space structure on our website https://lenia-explorer.vercel.app/. The results shed new light on the above-mentioned questions and lead to several observations: the existence of new soliton families for parameters where they were not believed to exist, or the universality of the phase space structure across various kernels.

Image-based or morphological profiling is a rapidly expanding field wherein cells are "profiled" by extracting hundreds to thousands of unbiased, quantitative features from images of cells that have been perturbed by genetic or chemical perturbations. The Cell Painting assay is the most popular imaged-based profiling assay wherein six small-molecule dyes label eight cellular compartments and thousands of measurements are made, describing quantitative traits such as size, shape, intensity, and texture within the nucleus, cytoplasm, and whole cell (Cimini et al., 2023). We have created the Cell Painting Gallery, a publicly available collection of Cell Painting datasets, with granular dataset descriptions and access instructions. It is hosted by AWS on the Registry of Open Data (RODA). As of January 2024, the Cell Painting Gallery holds 656 terabytes (TB) of image and associated numerical data. It includes the largest publicly available Cell Painting dataset, in terms of perturbations tested (Joint Undertaking for Morphological Profiling or JUMP (Chandrasekaran et al., 2023)), along with many other canonical datasets using Cell Painting, close derivatives of Cell Painting (such as LipocyteProfiler (Laber et al., 2023) and Pooled Cell Painting (Ramezani et al., 2023)).

The objective of personalized medicine is to tailor interventions to an individual patient's unique characteristics. A key technology for this purpose involves medical digital twins, computational models of human biology that can be personalized and dynamically updated to incorporate patient-specific data collected over time. Certain aspects of human biology, such as the immune system, are not easily captured with physics-based models, such as differential equations. Instead, they are often multi-scale, stochastic, and hybrid. This poses a challenge to existing model-based control and optimization approaches that cannot be readily applied to such models. Recent advances in automatic differentiation and neural-network control methods hold promise in addressing complex control problems. However, the application of these approaches to biomedical systems is still in its early stages. This work introduces dynamics-informed neural-network controllers as an alternative approach to control of medical digital twins. As a first use case for this method, the focus is on agent-based models, a versatile and increasingly common modeling platform in biomedicine. The effectiveness of the proposed neural-network control method is illustrated and benchmarked against other methods with two widely-used agent-based model types. The relevance of the method introduced here extends beyond medical digital twins to other complex dynamical systems.

We introduce Biomaker CA: a Biome Maker project using Cellular Automata (CA). In Biomaker CA, morphogenesis is a first class citizen and small seeds need to grow into plant-like organisms to survive in a nutrient starved environment and eventually reproduce with variation so that a biome survives for long timelines. We simulate complex biomes by means of CA rules in 2D grids and parallelize all of its computation on GPUs through the Python JAX framework. We show how this project allows for several different kinds of environments and laws of 'physics', alongside different model architectures and mutation strategies. We further analyze some configurations to show how plant agents can grow, survive, reproduce, and evolve, forming stable and unstable biomes. We then demonstrate how one can meta-evolve models to survive in a harsh environment either through end-to-end meta-evolution or by a more surgical and efficient approach, called Petri dish meta-evolution. Finally, we show how to perform interactive evolution, where the user decides how to evolve a plant model interactively and then deploys it in a larger environment. We open source Biomaker CA at: https://tinyurl.com/2x8yu34s .

We propose a novel nonlinear bidirectionally coupled heterogeneous chain network whose dynamics evolve in discrete time. The backbone of the model is a pair of popular map-based neuron models, the Chialvo and the Rulkov maps. This model is assumed to proximate the intricate dynamical properties of neurons in the widely complex nervous system. The model is first realized via various nonlinear analysis techniques: fixed point analysis, phase portraits, Jacobian matrix, and bifurcation diagrams. We observe the coexistence of chaotic and period-4 attractors. Various codimension-1 and -2 patterns for example saddle-node, period-doubling, Neimark-Sacker, double Neimark-Sacker, flip- and fold-Neimark Sacker, and 1:1 and 1:2 resonance are also explored. Furthermore, the study employs two synchronization measures to quantify how the oscillators in the network behave in tandem with each other over a long number of iterations. Finally, a time series analysis of the model is performed to investigate its complexity in terms of sample entropy.

Within the complex neuroarchitecture of the brain, astrocytes play crucial roles in development, structure, and metabolism. These cells regulate neural activity through tripartite synapses, directly impacting cognitive processes such as learning and memory. Despite the growing recognition of astrocytes' significance, traditional Spiking Neural Network (SNN) models remain predominantly neuron-centric, overlooking the profound influence of astrocytes on neural dynamics. Inspired by these biological insights, we have developed an Astrocyte-Modulated Spiking Unit (AM-SU), an innovative framework that integrates neuron-astrocyte interactions into the computational paradigm, demonstrating wide applicability across various hardware platforms. Our Astrocyte-Modulated Spiking Neural Network (AstroSNN) exhibits exceptional performance in tasks involving memory retention and natural language generation, particularly in handling long-term dependencies and complex linguistic structures. The design of AstroSNN not only enhances its biological authenticity but also introduces novel computational dynamics, enabling more effective processing of complex temporal dependencies. Furthermore, AstroSNN shows low latency, high throughput, and reduced memory usage in practical applications, making it highly suitable for resource-constrained environments. By successfully integrating astrocytic dynamics into intelligent neural networks, our work narrows the gap between biological plausibility and neural modeling, laying the groundwork for future biologically-inspired neural computing research that includes both neurons and astrocytes.

Complex cell signaling systems -- governed by varying protein abundances and interactions -- generate diverse cell types across organs. These systems evolve under influences such as age, sex, diet, environmental exposures, and diseases, making them challenging to decode given the involvement of tens of thousands of genes and proteins. Recently, hundreds of millions of single-cell omics data have provided a robust foundation for understanding these signaling networks within various cell subpopulations and conditions. Inspired by the success of large foundation models (for example, large language models and large vision models) pre-trained on massive datasets, we introduce OmniCellTOSG, the first dataset of cell text-omic signaling graphs (TOSGs). Each TOSG represents the signaling network of an individual or meta-cell and is labeled with information such as organ, disease, sex, age, and cell subtype. OmniCellTOSG offers two key contributions. First, it introduces a novel graph model that integrates human-readable annotations -- such as biological functions, cellular locations, signaling pathways, related diseases, and drugs -- with quantitative gene and protein abundance data, enabling graph reasoning to decode cell signaling. This approach calls for new joint models combining large language models and graph neural networks. Second, the dataset is built from single-cell RNA sequencing data of approximately 120 million cells from diverse tissues and conditions (healthy and diseased) and is fully compatible with PyTorch. This facilitates the development of innovative cell signaling models that could transform research in life sciences, healthcare, and precision medicine. The OmniCellTOSG dataset is continuously expanding and will be updated regularly. The dataset and code are available at https://github.com/FuhaiLiAiLab/OmniCellTOSG.

This paper presents advancements in automated early-stage prediction of the success of reprogramming human induced pluripotent stem cells (iPSCs) as a potential source for regenerative cell therapies.The minuscule success rate of iPSC-reprogramming of around 0.01% to 0.1% makes it labor-intensive, time-consuming, and exorbitantly expensive to generate a stable iPSC line. Since that requires culturing of millions of cells and intense biological scrutiny of multiple clones to identify a single optimal clone. The ability to reliably predict which cells are likely to establish as an optimal iPSC line at an early stage of pluripotency would therefore be ground-breaking in rendering this a practical and cost-effective approach to personalized medicine. Temporal information about changes in cellular appearance over time is crucial for predicting its future growth outcomes. In order to generate this data, we first performed continuous time-lapse imaging of iPSCs in culture using an ultra-high resolution microscope. We then annotated the locations and identities of cells in late-stage images where reliable manual identification is possible. Next, we propagated these labels backwards in time using a semi-automated tracking system to obtain labels for early stages of growth. Finally, we used this data to train deep neural networks to perform automatic cell segmentation and classification. Our code and data are available at https://github.com/abhineet123/ipsc_prediction.

Sparse autoencoders (SAEs) emerged as a promising tool for mechanistic interpretability of transformer-based foundation models. Very recently, SAEs were also adopted for the visual domain, enabling the discovery of visual concepts and their patch-wise attribution to tokens in the transformer model. While a growing number of foundation models emerged for medical imaging, tools for explaining their inferences are still lacking. In this work, we show the applicability of SAEs for hematology. We propose CytoSAE, a sparse autoencoder which is trained on over 40,000 peripheral blood single-cell images. CytoSAE generalizes to diverse and out-of-domain datasets, including bone marrow cytology, where it identifies morphologically relevant concepts which we validated with medical experts. Furthermore, we demonstrate scenarios in which CytoSAE can generate patient-specific and disease-specific concepts, enabling the detection of pathognomonic cells and localized cellular abnormalities at the patch level. We quantified the effect of concepts on a patient-level AML subtype classification task and show that CytoSAE concepts reach performance comparable to the state-of-the-art, while offering explainability on the sub-cellular level. Source code and model weights are available at https://github.com/dynamical-inference/cytosae.

The liquid state machine (LSM) combines low training complexity and biological plausibility, which has made it an attractive machine learning framework for edge and neuromorphic computing paradigms. Originally proposed as a model of brain computation, the LSM tunes its internal weights without backpropagation of gradients, which results in lower performance compared to multi-layer neural networks. Recent findings in neuroscience suggest that astrocytes, a long-neglected non-neuronal brain cell, modulate synaptic plasticity and brain dynamics, tuning brain networks to the vicinity of the computationally optimal critical phase transition between order and chaos. Inspired by this disruptive understanding of how brain networks self-tune, we propose the neuron-astrocyte liquid state machine (NALSM) that addresses under-performance through self-organized near-critical dynamics. Similar to its biological counterpart, the astrocyte model integrates neuronal activity and provides global feedback to spike-timing-dependent plasticity (STDP), which self-organizes NALSM dynamics around a critical branching factor that is associated with the edge-of-chaos. We demonstrate that NALSM achieves state-of-the-art accuracy versus comparable LSM methods, without the need for data-specific hand-tuning. With a top accuracy of 97.61% on MNIST, 97.51% on N-MNIST, and 85.84% on Fashion-MNIST, NALSM achieved comparable performance to current fully-connected multi-layer spiking neural networks trained via backpropagation. Our findings suggest that the further development of brain-inspired machine learning methods has the potential to reach the performance of deep learning, with the added benefits of supporting robust and energy-efficient neuromorphic computing on the edge.

Learning and decision making in the brain are key processes critical to survival, and yet are processes implemented by non-ideal biological building blocks which can impose significant error. We explore quantitatively how the brain might cope with this inherent source of error by taking advantage of two ubiquitous mechanisms, redundancy and synchronization. In particular we consider a neural process whose goal is to learn a decision function by implementing a nonlinear gradient dynamics. The dynamics, however, are assumed to be corrupted by perturbations modeling the error which might be incurred due to limitations of the biology, intrinsic neuronal noise, and imperfect measurements. We show that error, and the associated uncertainty surrounding a learned solution, can be controlled in large part by trading off synchronization strength among multiple redundant neural systems against the noise amplitude. The impact of the coupling between such redundant systems is quantified by the spectrum of the network Laplacian, and we discuss the role of network topology in synchronization and in reducing the effect of noise. A range of situations in which the mechanisms we model arise in brain science are discussed, and we draw attention to experimental evidence suggesting that cortical circuits capable of implementing the computations of interest here can be found on several scales. Finally, simulations comparing theoretical bounds to the relevant empirical quantities show that the theoretical estimates we derive can be tight.

Biological nervous systems are created in a fundamentally different way than current artificial neural networks. Despite its impressive results in a variety of different domains, deep learning often requires considerable engineering effort to design high-performing neural architectures. By contrast, biological nervous systems are grown through a dynamic self-organizing process. In this paper, we take initial steps toward neural networks that grow through a developmental process that mirrors key properties of embryonic development in biological organisms. The growth process is guided by another neural network, which we call a Neural Developmental Program (NDP) and which operates through local communication alone. We investigate the role of neural growth on different machine learning benchmarks and different optimization methods (evolutionary training, online RL, offline RL, and supervised learning). Additionally, we highlight future research directions and opportunities enabled by having self-organization driving the growth of neural networks.

This review presents the elastic theory of low-dimensional (one- and two-dimensional) continua and its applications in bio- and nano-structures. First, the curve and surface theory, as the geometric representation of the low-dimensional continua, is briefly described through Cartan moving frame method. The elastic theory of Kirchhoff rod, Helfrich rod, bending-soften rod, fluid membrane, and solid shell is revisited. Secondly, the application and availability of the elastic theory of low-dimensional continua in bio-structures, including short DNA rings, lipid membranes, and cell membranes, are discussed. The kink stability of short DNA rings is addressed by using the theory of Kirchhoff rod, Helfrich rod, and bending-soften rod. The lipid membranes obey the theory of fluid membrane. A cell membrane is simplified as a composite shell of lipid bilayer and membrane skeleton, which is a little similar to the solid shell. It is found that the membrane skeleton enhances highly the mechanical stability of cell membranes. Thirdly, the application and availability of the elastic theory of low-dimensional continua in nano-structures, including graphene and carbon nanotubes, are discussed. A revised Lenosky lattice model is proposed based on the local density approximation. Its continuum form up to the second order terms of curvatures and strains is the same as the free energy of 2D solid shells. Several typical mechanical properties of carbon nanotubes are revisited and investigated based on this continuum form. It is possible to avoid introducing the controversial concepts, the Young's modulus and thickness of graphene and single-walled carbon nanotubes, with this continuum form.

We investigate the time evolution of the Boltzmann entropy of a dilute gas of N particles, N>>1, as it undergoes a free expansion doubling its volume. The microstate of the system, a point in the 4N dimensional phase space, changes in time via Hamiltonian dynamics. Its entropy, at any time t, is given by the logarithm of the phase space volume of all the microstates giving rise to its macrostate at time t. The macrostates that we consider are defined by coarse graining the one-particle phase space into cells Δ_α. The initial and final macrostates of the system are equilibrium states in volumes V and 2V, with the same energy E and particle number N. Their entropy per particle is given, for sufficiently large systems, by the thermodynamic entropy as a function of the particle and energy density, whose leading term is independent of the size of the Δ_α. The intermediate (non-equilibrium) entropy does however depend on the size of the cells Δ_α. Its change with time is due to (i) dispersal in physical space from free motion and to (ii) the collisions between particles which change their velocities. The former depends strongly on the size of the velocity coarse graining Δv: it produces entropy at a rate proportional to Δv. This dependence is investigated numerically and analytically for a dilute two-dimensional gas of hard discs. It becomes significant when the mean free path between collisions is of the same order or larger than the length scale of the initial spatial inhomogeneity. In the opposite limit, the rate of entropy production is essentially independent of Δv and is given by the Boltzmann equation for the limit Δvrightarrow 0. We show that when both processes are active the time dependence of the entropy has a scaling form involving the ratio of the rates of its production by the two processes.

Molecular dynamics (MD) simulation is a widely used technique to simulate molecular systems, most commonly at the all-atom resolution where equations of motion are integrated with timesteps on the order of femtoseconds (1fs=10^{-15}s). MD is often used to compute equilibrium properties, which requires sampling from an equilibrium distribution such as the Boltzmann distribution. However, many important processes, such as binding and folding, occur over timescales of milliseconds or beyond, and cannot be efficiently sampled with conventional MD. Furthermore, new MD simulations need to be performed for each molecular system studied. We present Timewarp, an enhanced sampling method which uses a normalising flow as a proposal distribution in a Markov chain Monte Carlo method targeting the Boltzmann distribution. The flow is trained offline on MD trajectories and learns to make large steps in time, simulating the molecular dynamics of 10^{5} - 10^{6}:fs. Crucially, Timewarp is transferable between molecular systems: once trained, we show that it generalises to unseen small peptides (2-4 amino acids) at all-atom resolution, exploring their metastable states and providing wall-clock acceleration of sampling compared to standard MD. Our method constitutes an important step towards general, transferable algorithms for accelerating MD.

In contrast to entropy, which increases monotonically, the "complexity" or "interestingness" of closed systems seems intuitively to increase at first and then decrease as equilibrium is approached. For example, our universe lacked complex structures at the Big Bang and will also lack them after black holes evaporate and particles are dispersed. This paper makes an initial attempt to quantify this pattern. As a model system, we use a simple, two-dimensional cellular automaton that simulates the mixing of two liquids ("coffee" and "cream"). A plausible complexity measure is then the Kolmogorov complexity of a coarse-grained approximation of the automaton's state, which we dub the "apparent complexity." We study this complexity measure, and show analytically that it never becomes large when the liquid particles are non-interacting. By contrast, when the particles do interact, we give numerical evidence that the complexity reaches a maximum comparable to the "coffee cup's" horizontal dimension. We raise the problem of proving this behavior analytically.

Ultrafast electron microscopy (UEM) has found widespread applications in physics, chemistry, and materials science, enabling real-space imaging of dynamics on ultrafast timescales. Recent advances have pushed the temporal resolution of UEM into the attosecond regime, enabling the attomicroscopy technique to directly visualize electron motion. In this work, we extend the capabilities of this powerful imaging tool to investigate ultrafast electron dynamics in a biological system by imaging and controlling light induced electronic and chemical changes in the conductive network of multicellular cable bacteria. Using electron energy loss spectroscopy (EELS), we first observed a laser induced increase in {\pi}-electron density, accompanied by spectral peak broadening and a blueshift features indicative of enhanced conductivity and structural modification. We also traced the effect of ultrafast laser pumping on bulk plasmon electron oscillations by monitoring changes in the plasmon like resonance peak. Additionally, we visualized laser induced chemical structural changes in cable bacteria in real space. The imaging results revealed carbon enrichment alongside a depletion of nitrogen and oxygen, highlighting the controllability of chemical dynamics. Moreover, time resolved EELS measurements further revealed a picosecond scale decay and recovery of both {\pi}-electron and plasmonic features, attributed to electron phonon coupling. In addition to shedding light on the mechanism of electron motion in cable bacteria, these findings demonstrate ultrafast modulation and switching of conductivity, underscoring their potential as bio-optoelectronic components operating on ultrafast timescales.

Recent advances in microscopy have enabled the rapid generation of terabytes of image data in cell biology and biomedical research. Vision-language models (VLMs) offer a promising solution for large-scale biological image analysis, enhancing researchers' efficiency, identifying new image biomarkers, and accelerating hypothesis generation and scientific discovery. However, there is a lack of standardized, diverse, and large-scale vision-language benchmarks to evaluate VLMs' perception and cognition capabilities in biological image understanding. To address this gap, we introduce {\mu}-Bench, an expert-curated benchmark encompassing 22 biomedical tasks across various scientific disciplines (biology, pathology), microscopy modalities (electron, fluorescence, light), scales (subcellular, cellular, tissue), and organisms in both normal and abnormal states. We evaluate state-of-the-art biomedical, pathology, and general VLMs on {\mu}-Bench and find that: i) current models struggle on all categories, even for basic tasks such as distinguishing microscopy modalities; ii) current specialist models fine-tuned on biomedical data often perform worse than generalist models; iii) fine-tuning in specific microscopy domains can cause catastrophic forgetting, eroding prior biomedical knowledge encoded in their base model. iv) weight interpolation between fine-tuned and pre-trained models offers one solution to forgetting and improves general performance across biomedical tasks. We release {\mu}-Bench under a permissive license to accelerate the research and development of microscopy foundation models.

Modeling the dynamics of deformable objects is challenging due to their diverse physical properties and the difficulty of estimating states from limited visual information. We address these challenges with a neural dynamics framework that combines object particles and spatial grids in a hybrid representation. Our particle-grid model captures global shape and motion information while predicting dense particle movements, enabling the modeling of objects with varied shapes and materials. Particles represent object shapes, while the spatial grid discretizes the 3D space to ensure spatial continuity and enhance learning efficiency. Coupled with Gaussian Splattings for visual rendering, our framework achieves a fully learning-based digital twin of deformable objects and generates 3D action-conditioned videos. Through experiments, we demonstrate that our model learns the dynamics of diverse objects -- such as ropes, cloths, stuffed animals, and paper bags -- from sparse-view RGB-D recordings of robot-object interactions, while also generalizing at the category level to unseen instances. Our approach outperforms state-of-the-art learning-based and physics-based simulators, particularly in scenarios with limited camera views. Furthermore, we showcase the utility of our learned models in model-based planning, enabling goal-conditioned object manipulation across a range of tasks. The project page is available at https://kywind.github.io/pgnd .

Correlative computational microscopy is accelerating the mapping of dynamic biological systems by integrating morphological and molecular measurements across spatial scales, from organelles to entire organisms. Visualization, measurement, and prediction of interactions among the components of biological systems can be accelerated by generalist computational imaging frameworks that relax the trade-offs imposed by multiplex dynamic imaging. This work reports a generalist framework for wave optical imaging of the architectural order (waveOrder) among biomolecules for encoding and decoding multiple specimen properties from a minimal set of acquired channels, with or without fluorescent labels. waveOrder expresses material properties in terms of elegant physically motivated basis vectors directly interpretable as phase, absorption, birefringence, diattenuation, and fluorophore density; and it expresses image data in terms of directly measurable Stokes parameters. We report a corresponding multi-channel reconstruction algorithm to recover specimen properties in multiple contrast modes. With this framework, we implement multiple 3D computational microscopy methods, including quantitative phase imaging, quantitative label-free imaging with phase and polarization, and fluorescence deconvolution imaging, across scales ranging from organelles to whole zebrafish. These advances are available via an extensible open-source computational imaging library, waveOrder, and a napari plugin, recOrder.

Understanding the biological mechanism of disease is critical for medicine, and in particular drug discovery. AI-powered analysis of genome-scale biological data hold great potential in this regard. The increasing availability of single-cell RNA sequencing data has enabled the development of large foundation models for disease biology. However, existing foundation models either do not improve or only modestly improve over task-specific models in downstream applications. Here, we explored two avenues for improving the state-of-the-art. First, we scaled the pre-training dataset to 116 million cells, which is larger than those used by previous models. Second, we leveraged the availability of large-scale biological annotations as a form of supervision during pre-training. We trained the TEDDY family of models comprising six transformer-based state-of-the-art single-cell foundation models with 70 million, 160 million, and 400 million parameters. We vetted our models on two downstream evaluation tasks -- identifying the underlying disease state of held-out donors not seen during training and distinguishing healthy cells from diseased ones for disease conditions and donors not seen during training. Scaling experiments showed that performance improved predictably with both data volume and parameter count. Our models showed substantial improvement over existing work on the first task and more muted improvements on the second.

Modern life sciences research is increasingly relying on artificial intelligence approaches to model biological systems, primarily centered around the use of machine learning (ML) models. Although ML is undeniably useful for identifying patterns in large, complex data sets, its widespread application in biological sciences represents a significant deviation from traditional methods of scientific inquiry. As such, the interplay between these models and scientific understanding in biology is a topic with important implications for the future of scientific research, yet it is a subject that has received little attention. Here, we draw from an epistemological toolkit to contextualize recent applications of ML in biological sciences under modern philosophical theories of understanding, identifying general principles that can guide the design and application of ML systems to model biological phenomena and advance scientific knowledge. We propose that conceptions of scientific understanding as information compression, qualitative intelligibility, and dependency relation modelling provide a useful framework for interpreting ML-mediated understanding of biological systems. Through a detailed analysis of two key application areas of ML in modern biological research - protein structure prediction and single cell RNA-sequencing - we explore how these features have thus far enabled ML systems to advance scientific understanding of their target phenomena, how they may guide the development of future ML models, and the key obstacles that remain in preventing ML from achieving its potential as a tool for biological discovery. Consideration of the epistemological features of ML applications in biology will improve the prospects of these methods to solve important problems and advance scientific understanding of living systems.

In here presented in silico study we suggest a way how to implement the evolutionary principles into anti-cancer therapy design. We hypothesize that instead of its ongoing supervised adaptation, the therapy may be constructed as a self-sustaining evolutionary process in a dynamic fitness landscape established implicitly by evolving cancer cells, microenvironment and the therapy itself. For these purposes, we replace a unified therapy with the `therapy species', which is a population of heterogeneous elementary therapies, and propose a way how to turn the toxicity of the elementary therapy into its fitness in a way conforming to evolutionary causation. As a result, not only the therapies govern the evolution of different cell phenotypes, but the cells' resistances govern the evolution of the therapies as well. We illustrate the approach by the minimalistic ad hoc evolutionary model. Its results indicate that the resistant cells could bias the evolution towards more toxic elementary therapies by inhibiting the less toxic ones. As the evolutionary causation of cancer drug resistance has been intensively studied for a few decades, we refer to cancer as a special case to illustrate purely theoretical analysis.

We present DYMAG, a graph neural network based on a novel form of message aggregation. Standard message-passing neural networks, which often aggregate local neighbors via mean-aggregation, can be regarded as convolving with a simple rectangular waveform which is non-zero only on 1-hop neighbors of every vertex. Here, we go beyond such local averaging. We will convolve the node features with more sophisticated waveforms generated using dynamics such as the heat equation, wave equation, and the Sprott model (an example of chaotic dynamics). Furthermore, we use snapshots of these dynamics at different time points to create waveforms at many effective scales. Theoretically, we show that these dynamic waveforms can capture salient information about the graph including connected components, connectivity, and cycle structures even with no features. Empirically, we test DYMAG on both real and synthetic benchmarks to establish that DYMAG outperforms baseline models on recovery of graph persistence, generating parameters of random graphs, as well as property prediction for proteins, molecules and materials. Our code is available at https://github.com/KrishnaswamyLab/DYMAG.

The mobility of particles in fluid membranes is a fundamental aspect of many biological processes. In a 1975 paper [1], Saffman and Delbr\"uck demonstrated how the presence of external Stokesian solvents is crucial in regularising the apparently singular flow within an infinite flat membrane. In the present paper, we extend this classical work and compute the rotational mobility of a rigid finite-sized particle located inside a spherical membrane embedded in Stokesian solvents. Treating the particle as a spherical cap, we solve for the flow semi-analytically as a function of the Saffman-Delbr\"uck (SD) length (ratio of membrane to solvent viscosity) and the solid angle formed by the particle. We study the dependence of the mobility and flow on inclusion size and SD length, recovering the flat-space mobility as a special case. Our results will be applicable to a range of biological problems including rotational Brownian motion, the dynamics of lipid rafts, and the motion of aquaporin channels in response to water flow. Our method will provide a novel way of measuring a membrane's viscosity from the rotational diffusion of large inclusions, for which the commonly used planar Saffman-Delbr\"uck theory does not apply.

We introduce Tadpole, a novel foundation model for three-dimensional partial differential equations (PDEs) that addresses key challenges in transferability, scalability to high dimensionality, and multi-functionality. Tadpole is pre-trained as an autoencoder on synthetic 3D PDE data generated by an efficient online data-generation framework. This enables large-scale, diverse training without storage or I/O overhead, demonstrated by scaling to an equivalent of hundreds of terabytes of training data. By autoencoding single-channel spatial crops, Tadpole learns rich and transferable representations across heterogeneous physical systems with varying numbers of state variables and spatial resolutions. Although pre-trained solely as an autoencoder, Tadpole can be efficiently applied for multiple downstream tasks beyond reconstruction, including dynamics learning and generative modeling. For dynamics learning, we propose a novel parameter-efficient fine-tuning strategy that integrates low-rank adaptation, latent-space transformations, and reintroduced skip connections, achieving accurate temporal modeling with a minimal number of trainable parameters. Tadpole demonstrates strong fine-tuning performance across various downstream tasks, highlighting its versatility and effectiveness as a foundation model for 3D PDE learning. Source code and pre-trained weights of Tadpole are available at https://github.com/tum-pbs/tadpole

Microbial swarming on mucosal surfaces reshapes microbial communities and influences mucosal healing and antibiotic tolerance. Yet even with time-lapse microscopy and deep learning, analyses of swarming colonies remain descriptive and cannot forecast how their fronts reorganize in time. This limitation is significant because the advancing edge determines access to nutrients, host tissue and competing microbes. We recast the expansion of Enterobacter sp. SM3 swarms as a problem of morphological forecasting, and assemble SwarmEvo, a time-lapse dataset represented as boundary-resolved segmentations. TexPol--Net, a texture- and geometry-aware segmentation model, sharpens diffuse edges and preserves fingered fronts, creating a stable substrate for dynamics. On this representation, we develop Morpher, an autoregressive forecasting network with a ``Morphon'' memory that links local curvature to long-range temporal dependencies. Morpher outperforms leading video-prediction models in maintaining front localization and anisotropic branching, and modest segmentation improvements yield noticeably more stable forecasts. Ablations across sequence models, inference strategies and observation ratios show that attention-based architectures with structural memory best preserve dense-finger propagation. By uniting geometry-aware segmentation with morphology-level forecasting, this framework turns swarming expansion into a predictive dynamical system, enabling quantitative interrogation and potential control of microbial collectives during mucosal repair and gut ecosystem engineering.

Recent advances in 3D X-ray Computed Tomographic (CT) sensors have stimulated research efforts to unveil the extremely complex micro-scale processes that control the activity of soil microorganisms. Voxel-based description (up to hundreds millions voxels) of the pore space can be extracted, from grey level 3D CT scanner images, by means of simple image processing tools. Classical methods for numerical simulation of biological dynamics using mesh of voxels, such as Lattice Boltzmann Model (LBM), are too much time consuming. Thus, the use of more compact and reliable geometrical representations of pore space can drastically decrease the computational cost of the simulations. Several recent works propose basic analytic volume primitives (e.g. spheres, generalized cylinders, ellipsoids) to define a piece-wise approximation of pore space for numerical simulation of draining, diffusion and microbial decomposition. Such approaches work well but the drawback is that it generates approximation errors. In the present work, we study another alternative where pore space is described by means of geometrically relevant connected subsets of voxels (regions) computed from the curvilinear skeleton. Indeed, many works use the curvilinear skeleton (3D medial axis) for analyzing and partitioning 3D shapes within various domains (medicine, material sciences, petroleum engineering, etc.) but only a few ones in soil sciences. Within the context of soil sciences, most studies dealing with 3D medial axis focus on the determination of pore throats. Here, we segment pore space using curvilinear skeleton in order to achieve numerical simulation of microbial decomposition (including diffusion processes). We validate simulation outputs by comparison with other methods using different pore space geometrical representations (balls, voxels).

We derive an expression for the variation between parallel trajectories in phenotypic evolution, extending the well known result that predicts the mean evolutionary path in adaptive dynamics or quantitative genetics. We show how this expression gives rise to the notion of fluctuation domains - parts of the fitness landscape where the rate of evolution is very predictable (due to fluctuation dissipation) and parts where it is highly variable (due to fluctuation enhancement). These fluctuation domains are determined by the curvature of the fitness landscape. Regions of the fitness landscape with positive curvature, such as adaptive valleys or branching points, experience enhancement. Regions with negative curvature, such as adaptive peaks, experience dissipation. We explore these dynamics in the ecological scenarios of implicit and explicit competition for a limiting resource.

Learning the response of single-cells to various treatments offers great potential to enable targeted therapies. In this context, neural optimal transport (OT) has emerged as a principled methodological framework because it inherently accommodates the challenges of unpaired data induced by cell destruction during data acquisition. However, most existing OT approaches are incapable of conditioning on different treatment contexts (e.g., time, drug treatment, drug dosage, or cell type) and we still lack methods that unanimously show promising generalization performance to unseen treatments. Here, we propose the Conditional Monge Gap which learns OT maps conditionally on arbitrary covariates. We demonstrate its value in predicting single-cell perturbation responses conditional to one or multiple drugs, a drug dosage, or combinations thereof. We find that our conditional models achieve results comparable and sometimes even superior to the condition-specific state-of-the-art on scRNA-seq as well as multiplexed protein imaging data. Notably, by aggregating data across conditions we perform cross-task learning which unlocks remarkable generalization abilities to unseen drugs or drug dosages, widely outperforming other conditional models in capturing heterogeneity (i.e., higher moments) in the perturbed population. Finally, by scaling to hundreds of conditions and testing on unseen drugs, we narrow the gap between structure-based and effect-based drug representations, suggesting a promising path to the successful prediction of perturbation effects for unseen treatments.

Estimating single-cell responses across various perturbations facilitates the identification of key genes and enhances drug screening, significantly boosting experimental efficiency. However, single-cell sequencing is a destructive process, making it impossible to capture the same cell's phenotype before and after perturbation. Consequently, data collected under perturbed and unperturbed conditions are inherently unpaired. Existing methods either attempt to forcibly pair unpaired data using random sampling, or neglect the inherent relationship between unperturbed and perturbed cells during the modeling. In this work, we propose a framework based on Dual Diffusion Implicit Bridges (DDIB) to learn the mapping between different data distributions, effectively addressing the challenge of unpaired data. We further interpret this framework as a form of data augmentation. We integrate gene regulatory network (GRN) information to propagate perturbation signals in a biologically meaningful way, and further incorporate a masking mechanism to predict silent genes, improving the quality of generated profiles. Moreover, gene expression under the same perturbation often varies significantly across cells, frequently exhibiting a bimodal distribution that reflects intrinsic heterogeneity. To capture this, we introduce a more suitable evaluation metric. We propose Unlasting, dual conditional diffusion models that overcome the problem of unpaired single-cell perturbation data and strengthen the model's insight into perturbations under the guidance of the GRN, with a dedicated mask model designed to improve generation quality by predicting silent genes. In addition, we introduce a biologically grounded evaluation metric that better reflects the inherent heterogeneity in single-cell responses.

The deep neural nets of modern artificial intelligence (AI) have not achieved defining features of biological intelligence, including abstraction, causal learning, and energy-efficiency. While scaling to larger models has delivered performance improvements for current applications, more brain-like capacities may demand new theories, models, and methods for designing artificial learning systems. Here, we argue that this opportunity to reassess insights from the brain should stimulate cooperation between AI research and theory-driven computational neuroscience (CN). To motivate a brain basis of neural computation, we present a dynamical view of intelligence from which we elaborate concepts of sparsity in network structure, temporal dynamics, and interactive learning. In particular, we suggest that temporal dynamics, as expressed through neural synchrony, nested oscillations, and flexible sequences, provide a rich computational layer for reading and updating hierarchical models distributed in long-term memory networks. Moreover, embracing agent-centered paradigms in AI and CN will accelerate our understanding of the complex dynamics and behaviors that build useful world models. A convergence of AI/CN theories and objectives will reveal dynamical principles of intelligence for brains and engineered learning systems. This article was inspired by our symposium on dynamical neuroscience and machine learning at the 6th Annual US/NIH BRAIN Initiative Investigators Meeting.

This chapter provides a pedagogical introduction and overview of spatial and temporal correlation and fluctuation effects resulting from the fundamentally stochastic kinetics underlying chemical reactions and the dynamics of populations or epidemics. After reviewing the assumptions and mean-field type approximations involved in the construction of chemical rate equations for uniform reactant densities, we first discuss spatial clustering in birth-death systems, where non-linearities are introduced through either density-limiting pair reactions, or equivalently via local imposition of finite carrying capacities. The competition of offspring production, death, and non-linear inhibition induces a population extinction threshold, which represents a non-equilibrium phase transition that separates active from absorbing states. This continuous transition is characterized by the universal scaling exponents of critical directed percolation clusters. Next we focus on the emergence of depletion zones in single-species annihilation processes and spatial population segregation with the associated reaction fronts in two-species pair annihilation. These strong (anti-)correlation effects are dynamically generated by the underlying stochastic kinetics. Finally, we address noise-induced and fluctuation-stabilized spatio-temporal patterns in basic predator-prey systems, exemplified by spreading activity fronts in the two-species Lotka-Volterra model as well as spiral structures in the May-Leonard variant of cyclically competing three-species systems akin to rock-paper-scissors games.

Recent advancements in protein structure determination are revolutionizing our understanding of proteins. Still, a significant gap remains in the availability of comprehensive datasets that focus on the dynamics of proteins, which are crucial for understanding protein function, folding, and interactions. To address this critical gap, we introduce mdCATH, a dataset generated through an extensive set of all-atom molecular dynamics simulations of a diverse and representative collection of protein domains. This dataset comprises all-atom systems for 5,398 domains, modeled with a state-of-the-art classical force field, and simulated in five replicates each at five temperatures from 320 K to 413 K. The mdCATH dataset records coordinates and forces every 1 ns, for over 62 ms of accumulated simulation time, effectively capturing the dynamics of the various classes of domains and providing a unique resource for proteome-wide statistical analyses of protein unfolding thermodynamics and kinetics. We outline the dataset structure and showcase its potential through four easily reproducible case studies, highlighting its capabilities in advancing protein science.

Rayleigh-B\'enard convection (RBC) is a recurrent phenomenon in several industrial and geoscience flows and a well-studied system from a fundamental fluid-mechanics viewpoint. However, controlling RBC, for example by modulating the spatial distribution of the bottom-plate heating in the canonical RBC configuration, remains a challenging topic for classical control-theory methods. In the present work, we apply deep reinforcement learning (DRL) for controlling RBC. We show that effective RBC control can be obtained by leveraging invariant multi-agent reinforcement learning (MARL), which takes advantage of the locality and translational invariance inherent to RBC flows inside wide channels. The MARL framework applied to RBC allows for an increase in the number of control segments without encountering the curse of dimensionality that would result from a naive increase in the DRL action-size dimension. This is made possible by the MARL ability for re-using the knowledge generated in different parts of the RBC domain. We show in a case study that MARL DRL is able to discover an advanced control strategy that destabilizes the spontaneous RBC double-cell pattern, changes the topology of RBC by coalescing adjacent convection cells, and actively controls the resulting coalesced cell to bring it to a new stable configuration. This modified flow configuration results in reduced convective heat transfer, which is beneficial in several industrial processes. Therefore, our work both shows the potential of MARL DRL for controlling large RBC systems, as well as demonstrates the possibility for DRL to discover strategies that move the RBC configuration between different topological configurations, yielding desirable heat-transfer characteristics. These results are useful for both gaining further understanding of the intrinsic properties of RBC, as well as for developing industrial applications.

Virtual cell modeling predicts molecular state changes under genetic perturbations in silico, which is essential for biological mechanism studies. However, existing approaches suffer from unconstrained reasoning, uninterpretable predictions, and retrieval signals that are weakly aligned with regulatory topology. To address these limitations, we propose AROMA, an Augmented Reasoning Over a Multimodal Architecture for virtual cell genetic perturbation modeling. AROMA integrates textual evidence, graph-topology information, and protein sequence features to model perturbation-target dependencies, and is trained with a two-stage optimization strategy to yield predictions that are both accurate and interpretable. We also construct two knowledge graphs and a perturbation reasoning dataset, PerturbReason, containing more than 498k samples, as reusable resources for the virtual cell domain. Experiments show that AROMA outperforms existing methods across multiple cell lines, and remains robust under zero-shot evaluation on an unseen cell line, as well as in knowledge-sparse, long-tail scenarios. Overall, AROMA demonstrates that combining knowledge-driven multimodal modeling with evidence retrieval provides a promising pathway toward more reliable and interpretable virtual cell perturbation prediction. Model weights are available at https://huggingface.co/blazerye/AROMA. Code is available at https://github.com/blazerye/AROMA.

Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it. In this work, we introduce a novel generative modeling framework grounded in phase space dynamics, where a phase space is defined as {an augmented space encompassing both position and velocity.} Leveraging insights from Stochastic Optimal Control, we construct a path measure in the phase space that enables efficient sampling. {In contrast to DMs, our framework demonstrates the capability to generate realistic data points at an early stage of dynamics propagation.} This early prediction sets the stage for efficient data generation by leveraging additional velocity information along the trajectory. On standard image generation benchmarks, our model yields favorable performance over baselines in the regime of small Number of Function Evaluations (NFEs). Furthermore, our approach rivals the performance of diffusion models equipped with efficient sampling techniques, underscoring its potential as a new tool generative modeling.

Single-cell technologies generate high-dimensional point clouds of cells, enabling detailed characterization of complex patient states and treatment responses. Yet each patient is represented by an irregular point cloud rather than a simple vector, making it difficult to directly quantify and compare biological differences between individuals. Nonlinear methods such as kernels and neural networks achieve predictive accuracy but act as black boxes, offering little biological interpretability. To address these limitations, we adapt the Linear Optimal Transport (LOT) framework to this setting, embedding irregular point clouds into a fixed-dimensional Euclidean space while preserving distributional structure. This embedding provides a principled linear representation that preserves optimal transport geometry while enabling downstream analysis. It also forms a registration between any two patients, enabling direct comparison of their cellular distributions. Within this space, LOT enables: (i) accurate and interpretable classification of COVID-19 patient states, where classifier weights map back to specific markers and spatial regions driving predictions; and (ii) synthetic data generation for patient-derived organoids, exploiting the linearity of the LOT embedding. LOT barycenters yield averaged cellular profiles representing combined conditions or samples, supporting drug interaction testing. Together, these results establish LOT as a unified framework that bridges predictive performance, interpretability, and generative modeling. By transforming heterogeneous point clouds into structured embeddings directly traceable to the original data, LOT opens new opportunities for understanding immune variation and treatment effects in high-dimensional biological systems.

Single-cell transcriptomics enabled the study of cellular heterogeneity in response to perturbations at the resolution of individual cells. However, scaling high-throughput screens (HTSs) to measure cellular responses for many drugs remains a challenge due to technical limitations and, more importantly, the cost of such multiplexed experiments. Thus, transferring information from routinely performed bulk RNA HTS is required to enrich single-cell data meaningfully. We introduce chemCPA, a new encoder-decoder architecture to study the perturbational effects of unseen drugs. We combine the model with an architecture surgery for transfer learning and demonstrate how training on existing bulk RNA HTS datasets can improve generalisation performance. Better generalisation reduces the need for extensive and costly screens at single-cell resolution. We envision that our proposed method will facilitate more efficient experiment designs through its ability to generate in-silico hypotheses, ultimately accelerating drug discovery.

Biophysical modeling, particularly involving partial differential equations (PDEs), offers significant potential for tailoring disease treatment protocols to individual patients. However, the inverse problem-solving aspect of these models presents a substantial challenge, either due to the high computational requirements of model-based approaches or the limited robustness of deep learning (DL) methods. We propose a novel framework that leverages the unique strengths of both approaches in a synergistic manner. Our method incorporates a DL ensemble for initial parameter estimation, facilitating efficient downstream evolutionary sampling initialized with this DL-based prior. We showcase the effectiveness of integrating a rapid deep-learning algorithm with a high-precision evolution strategy in estimating brain tumor cell concentrations from magnetic resonance images. The DL-Prior plays a pivotal role, significantly constraining the effective sampling-parameter space. This reduction results in a fivefold convergence acceleration and a Dice-score of 95%