How AI Can Advance Mathematical Biology: Opportunities, Challenges, and Future Directions

Selecting synthetic data for successful simulation-based transfer learning in dynamical biological systems

Accurate prediction of the temporal dynamics of biological systems is crucial for informing timely and effective interventions, e.g., in ecological or epidemiological contexts, or for treatment adjustments in therapy. While machine learning has proven its capabilities in generalizing the underlying non-linear dynamics of such systems, unlocking its predictive power is often restrained by the limited availability of large, curated datasets. To supplement real-world data, informing machine learning by transfer learning with synthetic data derived from simulations using ordinary differential equations has emerged as a promising solution. However, the success of this approach highly depends on the designed characteristics of the synthetic data.

The lost art of mathematical modelling

We provide a critique of mathematical biology in light of rapid developments in modern machine learning. We argue that out of the three modelling activities – (1) formulating models; (2) analysing models; and (3) fitting or comparing models to data – inherent to mathematical biology, researchers currently focus too much on activity (2) at the cost of (1). This trend, we propose, can be reversed by realising that any given biological phenomenon can be modelled in an infinite number of different ways, through the adoption of a pluralistic approach, where we view a system from multiple, different points of view. We explain this pluralistic approach using fish locomotion as a case study and illustrate some of the pitfalls – universalism, creating models of models, etc. – that hinder mathematical biology. We then ask how we might rediscover a lost art: that of creative mathematical modelling.

Gene regulatory networks: from correlative models to causal explanations

Gene regulatory networks (GRNs) explain how the genome controls cellular behaviour and tissue morphogenesis, serving to connect molecular mechanism to functional output. Single-cell technologies now provide descriptions of these networks with unprecedented detail, but this advance has also revealed gene regulatory systems that are too complex for our existing conceptual frameworks. GRNs, which should provide mechanistic explanations, are increasingly reduced to statistical correlations — ‘hairballs’ that fail to capture molecular causation. Here, we explore why this dilemma exists and propose a path forward. We argue that methods in ‘representation learning’ can be used to model GRNs, without needing to capture every molecular detail. For this framework, we advocate three linked principles: models must be inherently mechanistic, with structures grounded in cellular and evolutionary biology; molecular principles and constraints must be used to reduce the solution space for learning GRN models; and more sophisticated forms of experimental perturbation and synthetic biological engineering are needed to train models and test predictions. By reimagining GRNs through these principles, we can bridge the gap from data abundance to new conceptual understanding.

Agentic systems are adept at solving well-scoped, verifiable problems in computational biology

We introduce CompBioBench, a benchmark of 100 diverse tasks for evaluating agentic systems in computational biology. Unlike mathematics and programming, which more readily admit systematic verification, biological data are inherently noisy and open to interpretation.

Biohub releases a world model of protein biology

Open AI models used for a wide range of scientific applications, including accelerating the design of therapeutic molecules.

AI for Drug Discovery Needs Trustworthy Biological Data

To unleash the potential of AI in life sciences and drug discovery, biological datasets must be authenticated, validated, and supported by standardized metadata.

Quantifying cell-state densities in single-cell phenotypic landscapes using Mellon

Cell-state density characterizes the distribution of cells along phenotypic landscapes and is crucial for unraveling the mechanisms that drive diverse biological processes. Here, we present Mellon, an algorithm for estimation of cell-state densities from high-dimensional representations of single-cell data. We demonstrate Mellon’s efficacy by dissecting the density landscape of differentiating systems, revealing a consistent pattern of high-density regions corresponding to major cell types intertwined with low-density, rare transitory states. We present evidence implicating enhancer priming and the activation of master regulators in emergence of these transitory states. Mellon offers the flexibility to perform temporal interpolation of time-series data, providing a detailed view of cell-state dynamics during developmental processes. Mellon facilitates density estimation across various single-cell data modalities, scaling linearly with the number of cells. Our work underscores the importance of cell-state density in understanding the differentiation processes, and the potential of Mellon to provide insights into mechanisms guiding biological trajectories.

Temporal tissue dynamics from a spatial snapshot

Physiological and pathological processes such as inflammation and cancer emerge from interactions between cells over time1. However, methods to follow cell populations over time within the native context of a human tissue are lacking because a biopsy offers only a single snapshot. Here we present one-shot tissue dynamics reconstruction (OSDR), an approach to estimate a dynamical model of cell populations based on a single tissue sample. OSDR uses spatial proteomics to learn how the composition of cellular neighbourhoods influences division rate, providing a dynamical model of cell population change over time. We apply OSDR to human breast cancer data2–4, and reconstruct two fixed points of fibroblasts and macrophage interactions5,6. These fixed points correspond to hot and cold fibrosis7, in agreement with co-culture experiments that measured these dynamics directly8. We then use OSDR to discover a pulse-generating excitable circuit of T and B cells in the tumour microenvironment, suggesting temporal flares of anticancer immune responses. Finally, we study longitudinal biopsies from a triple-negative breast cancer clinical trial3, in which OSDR predicts the collapse of the tumour cell population in responders but not in non-responders, based on early-treatment biopsies. OSDR can be applied to a wide range of spatial proteomics assays to enable analysis of tissue dynamics based on patient biopsies.

Integrated computational and in vivo models reveal Key Insights into macrophage behavior during bone healing

Myeloid-derived monocyte and macrophages are key cells in the bone that contribute to remodeling and injury repair. However, their temporal polarization status and control of bone-resorbing osteoclasts and bone-forming osteoblasts responses is largely unknown. In this study, we focused on two aspects of monocyte/macrophage dynamics and polarization states over time: 1) the injury-triggered pro- and anti-inflammatory monocytes/macrophages temporal profiles, 2) the contributions of pro- versus anti-inflammatory monocytes/macrophages in coordinating healing response. Bone healing is a complex multicellular dynamic process. While traditional in vitro and in vivo experimentation may capture the behavior of select populations with high resolution, they cannot simultaneously track the behavior of multiple populations. To address this, we have used an integrated coupled ordinary differential equations (ODEs)-based framework describing multiple cellular species to in vivo bone injury data in order to identify and test various hypotheses regarding bone cell populations dynamics. Our approach allowed us to infer several biological insights including, but not limited to,: 1) anti-inflammatory macrophages are key for early osteoclast inhibition and pro-inflammatory macrophage suppression, 2) pro-inflammatory macrophages are involved in osteoclast bone resorptive activity, whereas osteoblasts promote osteoclast differentiation, 3) Pro-inflammatory monocytes/macrophages rise during two expansion waves, which can be explained by the anti-inflammatory macrophages-mediated inhibition phase between the two waves. In addition, we further tested the robustness of the mathematical model by comparing simulation results to an independent experimental dataset. Taken together, this novel comprehensive mathematical framework allowed us to identify biological mechanisms that best recapitulate bone injury data and that explain the coupled cellular population dynamics involved in the process. Furthermore, our hypothesis testing methodology could be used in other contexts to decipher mechanisms in complex multicellular processes.

Mathematical Discovery of Potential Therapeutic Targets: Application to Rare Melanomas

Patients with rare types of melanoma such as acral, mucosal, or uveal melanoma, have lower survival rates than patients with cutaneous melanoma; these lower survival rates reflect the lower objective response rates to immunotherapy compared to cutaneous melanoma. Understanding tumor-immune dynamics in rare melanomas is critical for the development of new therapies and for improving response rates to current cancer therapies. Progress has been hindered by the lack of clinical data and the need for better preclinical models of rare melanomas. Canine melanoma provides a valuable comparative oncology model for rare types of human melanomas. We analyzed RNA sequencing data from canine melanoma patients and combined this with literature information to create a novel mechanistic mathematical model of melanoma-immune dynamics. Sensitivity analysis of the mathematical model indicated influential pathways in the dynamics, providing support for potential new therapeutic targets and future combinations of therapies. We share our learnings from this work, to help enable the application of this proof-of-concept workflow to other rare disease settings with sparse available data.

VAPOR: A variational autoencoder with transport operators to disentangle cellular gene expression dynamics of co-occurring biological processes in time and space

Abstract Single-cell and spatial transcriptomics enable the analysis of cellular states and dynamics in gene expression, revealing how diverse biological processes relate to these states over time and space. To study these dynamics, trajectory inference methods order cells along computationally inferred paths to reconstruct gradual transitions in cell states. However, by encouraging smooth and continuous trajectories, these approaches tend to conflate co-occurring processes-such as proliferation, maturation, and spatial organization-that are jointly reflected in gene expression, potentially overlooking process-specific gene expression dynamics. To address this, we developed VAPOR, which integrates a variational autoencoder with transport operators to model and disentangle cellular gene expression dynamics for potentially co-occurring biological processes. VAPOR inputs single-cell (or spatial) gene expression data into a variational autoencoder (VAE) to learn the latent states of cells and then models their latent dynamics as an ordinary differential equation. The latent dynamics are further decomposed into process-specific components parameterized by transport operators (TOs) and their corresponding process weights. Each TO defines a process-specific dynamics, and its weight for each cell quantifies the process's contribution to the cell dynamics. After assessment by simulation studies, we applied VAPOR with benchmarking to real data, including time-course scRNA-seq from postconceptual human brain development, spatial transcriptomics of the mouse hippocampus, and cross-species scRNA-seq spanning human and macaque first-trimester forebrain development. In these applications, VAPOR has identified a variety of temporal and spatial co-occurring processes, such as cell cycle, gliogenesis, neurogenesis, and neuronal migration, along with associated dynamic genes, including those species-specific to human and macaque development. VAPOR is available as an open-source tool for general-purpose use. ### Competing Interest Statement The authors have declared no competing interest.

Comparing phenotypic manifolds with Kompot: Detecting differential abundance and gene expression at single-cell resolution

Single-cell studies are frequently designed to compare across conditions such as health and disease. However, existing computational approaches typically rely on grouping cells into discrete populations before making comparisons, which can limit resolution for detecting state-dependent changes. Here, we introduce Kompot, a statistical framework for comparative analysis of multi-condition single-cell data. Kompot quantifies both differential abundance, capturing how cells redistribute across the phenotypic space, and differential expression, identifying condition-specific transcriptional changes that may be localized, heterogeneous, or oppositely regulated across states. By modeling cell density and gene expression as continuous functions over a shared cell-state representation, Kompot enables single-cell–resolution inference with principled uncertainty estimates, without requiring predefined clusters or cell types. Applying Kompot to aging murine bone marrow, we identified a continuum of shifts in hematopoietic stem cell and mature cell states, transcriptional remodeling of monocytes independent of compositional changes, and divergent regulation of oxidative stress response genes across cell types. We demonstrate the utility of Kompot in disease settings by identifying cell-state and gene expression changes associated with improved efficacy of combinatorial immunotherapy in melanoma. Additionally, Kompot enables multi-sample comparative analysis by accounting for sample-to-sample heterogeneity. By capturing both global and cell-state–specific effects of perturbation, the Kompot framework is broadly applicable to dissecting condition-specific effects in complex single-cell landscapes. ### Competing Interest Statement The authors have declared no competing interest. National Institutes of Health, R35GM147125, R01CA292932, T32GM136534, S10OD028685 The Mark Foundation for Cancer Research, https://ror.org/00v7th354, Endeavor Award Edward P. Evans Foundation, https://ror.org/03h22gm35, Discovery Research Grant Brotman Baty Institute, https://ror.org/03jxvbk42, Pilot Award

GenBio ICML Workshop 2026

The 2026 workshop on Generative and Agentic AI for Biology at ICML 2026, Seoul, South Korea.

<i>In silico</i> models of bone remodeling from macro to nano—from organ to cell

Abstract Computational modeling is a tool through which researchers can achieve a greater understanding of the mechanisms governing biological systems. In the field of bone biology, a plethora of models exist which attempt to replicate and investigate bone's dynamic behavior at different scales. At organ level, models are continuum based and describe the variation of bone's apparent density as a function of both biological and external mechanical stimuli. At tissue level, models include bone microarchitecture and more descriptive parameters such as trabecular thickness, osteoclast resorption depth, and activation frequency. Finally, at cell level, models employ partial differential equations to describe complex cellular interactions in the temporal domain. Although informative, these models exist in isolation. Consequently, their interpretation is limited. In this review, we present an overview of the organ‐, tissue‐, and cell‐level models and assess their ability to reflect bone's metabolic processes reliably. Existing interscale synergies are then presented along with a computational framework which could be exploited to achieve a fully integrated, multiscale modeling approach. WIREs Syst Biol Med 2011 3 241–251 DOI: 10.1002/wsbm.115 This article is categorized under: Analytical and Computational Methods > Computational Methods Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models

Accelerating scientific discovery with Co-Scientist

Scientific discovery is driven by scientists generating novel hypotheses for complex problems that undergo rigorous experimental validation. To augment this process, we introduce Co-Scientist, a multi-agent AI system built on Gemini for structured scientific thinking and hypothesis generation. Co-Scientist aims to help scientists discover new original knowledge. Conditioned on their research objectives and prior scientific evidence, it formulates demonstrably novel research hypotheses for experimental verification. The system's design involves agents continuously generating, critiquing and refining hypotheses accelerated by scaling test-time compute. Key contributions include: (1) a multi-agent architecture with an asynchronous task execution framework for flexible compute scaling; (2) a tournament evolution process for self-improving hypotheses generation. Automated evaluations show continued benefits of test-time compute scaling, improving hypothesis quality over time. While general purpose, we focus the validation in three biomedical applications: drug repurposing, novel target discovery, and explaining mechanisms of anti-microbial resistance. Specifically, Co-Scientist helped identify new drug repurposing candidates and synergistic combination therapies for acute myeloid leukemia, which were validated through in vitro experiments. These real-world validations demonstrate the potential of Co-Scientist to accelerate scientific discovery and usher in an era of AI empowered scientists.