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

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

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.

Dynamic Landscape Analysis of cell fate decisions provides predictive models of neural development from single-cell data

Building a mechanistic understanding of cell fate decisions remains a fundamental goal of developmental biology, with implications for stem cell therapies, regenerative medicine and understanding disease mechanisms. Single-cell transcriptomics provides a detailed picture of the cellular states observed during these decisions, but building dynamic and predictive models from these data remains a challenge. Here, we present dynamic landscape analysis (DLA), an integrative framework that applies dynamical systems theory to identify stable cell states, map transition pathways, and generate a predictive cell fate decision landscape from single-cell data. Applying this framework to vertebrate neural tube development revealed that progenitor specification by Sonic Hedgehog (Shh) can be captured in a landscape with an unexpected topology in which initially divergent lineages converge to the same fate through multiple distinct routes. The model accurately predicted cellular responses and cell fate allocation for unseen dynamic signalling regimes. Cross-species validation using human embryonic organoid data demonstrated conservation of this decision-making architecture. By modelling the dynamic responses that drive cell fate decisions, the DLA framework provides a quantitative and generative framework for extracting mechanistic insights from high-dimensional single-cell data.

ResolVI: addressing noise and bias in spatial transcriptomics

Technologies for estimating RNA expression at high throughput, in intact tissue slices and with high spatial resolution (spatial transcriptomics) shed new light on how cells communicate and tissues function. A fundamental step in analyzing data generated by subcellular resolution spatial transcriptomics technologies is quantification, namely, segmenting the plane into regions, each approximating a cell, and then collating the molecules inside each region to estimate the cellular expression profile. Despite many advances in this area, a persistent problem is that of the incorrect assignment of molecules to cells, which limits many current applications to the level of a priori-defined cell subsets and complicates the discovery of novel cell states. Here we develop resolVI, a model that operates downstream of any segmentation algorithm to generate a probabilistic representation, correcting for the misassignment of molecules, as well as for batch effects and other nuisance factors. We demonstrate that resolVI improves our ability to distinguish between cell states, identify subtle expression changes in space and perform integrated analysis across datasets. ResolVI is available as open source software within scvi-tools.

Benchmarking gene expression reconstruction from single-cell latent representations

Single-cell transcriptomics is typically modeled in low-dimensional latent representations that improve the signal-to-noise ratio of the data. Such representations underpin data integration, cell state discovery, and perturbation prediction, with applications ranging from large-scale organ atlases to latent trajectory modeling. Recent virtual cell approaches further leverage these representations to predict cellular responses as distributional shifts in latent space. Each of these applications ultimately requires faithful gene expression reconstruction from latent spaces for biological interpretation, enabling gene-level analysis of predicted perturbed or batch-corrected cells. Yet representation choice is typically treated as an implementation detail rather than a primary modeling decision, with no systematic evaluation of how well latent representations support gene expression reconstruction. Here, we introduce ReconEval, a benchmark for evaluating gene expression reconstruction from single-cell latent spaces. We benchmark two classes of latent representations: end-to-end trained models such as PCA, autoencoders, and variational autoencoders, and pretrained single-cell foundation model embeddings coupled to newly trained decoders. Reconstruction is evaluated both directly and after latent-space perturbation prediction. Across perturbational and observational datasets totaling over 100 million cells, our metric suite quantifies statistical fidelity; biological signal preservation, including differential expression, coexpression, cell-cycle structure, cytokine response and pathway activity; and perturbation-specific effects. We find that autoencoders achieve the strongest stand-alone reconstruction at low dimensionality, while variational regularization does not improve generalization in reconstruction. Frozen foundation model embeddings retain recoverable gene-level information, with reconstruction quality depending strongly on decoder architecture and pretraining objective. In latent perturbation modeling, high-dimensional PCA matches foundation model embeddings, while low-dimensional AE embeddings are optimal for flow-based generative models. Overall, reconstruction depends critically on the interplay between representation and downstream model, and simpler representations can outperform complex alternatives given appropriate capacity. Our benchmark establishes reconstruction as a critical evaluation axis for single-cell foundation models. We envision it improving the biological interpretability of latent-space modeling, a prerequisite for future virtual cell models to be validated by domain experts and grounded in biology. ### Competing Interest Statement F.J.T. consults for Immunai, CytoReason, Valinor Industries, Bioturing and Phylo Inc., and has ownership interest in RN.AI Therapeutics, Dermagnostix, and Cellarity. The remaining authors declare no competing interests.

The evolving concept of cell identity in the single cell era

Summary: This Spotlight explores emerging technologies that are enabling the systematic and unbiased quantification of cell identity, and how these efforts will enable the construction of high-resolution, dynamic cell atlases.

Embryo-scale reverse genetics at single-cell resolution

The maturation of single-cell transcriptomic technologies has facilitated the generation of comprehensive cellular atlases from whole embryos1–4. A majority of these data, however, has been collected from wild-type embryos without an appreciation for the latent variation that is present in development. Here we present the ‘zebrafish single-cell atlas of perturbed embryos’: single-cell transcriptomic data from 1,812 individually resolved developing zebrafish embryos, encompassing 19 timepoints, 23 genetic perturbations and a total of 3.2 million cells. The high degree of replication in our study (eight or more embryos per condition) enables us to estimate the variance in cell type abundance organism-wide and to detect perturbation-dependent deviance in cell type composition relative to wild-type embryos. Our approach is sensitive to rare cell types, resolving developmental trajectories and genetic dependencies in the cranial ganglia neurons, a cell population that comprises less than 1% of the embryo. Additionally, time-series profiling of individual mutants identified a group of brachyury-independent cells with strikingly similar transcriptomes to notochord sheath cells, leading to new hypotheses about early origins of the skull. We anticipate that standardized collection of high-resolution, organism-scale single-cell data from large numbers of individual embryos will enable mapping of the genetic dependencies of zebrafish cell types, while also addressing longstanding challenges in developmental genetics, including the cellular and transcriptional plasticity underlying phenotypic diversity across individuals.

A unified network systems approach uncovers a core program underlying T follicular helper cell differentiation

Characterizing multi-scale processes underlying immune-state progression is critical for defining their function. This becomes pertinent for functionally diverse and plastic immune cells, such as T follicular helper (Tfh) cells. Here, we adopt a multi-scale network-systems approach that incorporates both regulatory and protein-protein interactions. This approach integrates diverse data types, captures regulation across levels of immune system organization, and recapitulates known Tfh differentiation drivers. Further, we present CoreNet, a core Tfh gene set that is conserved between humans and mice, across tissue types and disease contexts, and is consistent across data modalities. Using CoreNet, we implicate NR3C1 and interleukin (IL)-12 in the regulation of Tfh differentiation. Notably, IL-12 is permissive for differentiation of Tfh precursors but blocks differentiation into germinal center Tfh cells. Overall, this work elucidates networks with unexplored roles governing Tfh differentiation across species and tissues, while providing a generalizable framework. CoreNet is accessible through an interactive web server: https://pitt-csi.shinyapps.io/tfhcorenet/.

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

Mathematical biology has long relied on mechanistic models, including ordinary and partial differential equations, stochastic systems, and agent-based models, to study biological processes across scales. These approaches remain central because they provide structure, interpretability, and biological insight. However, modern biological and biomedical data, including longitudinal clinical records, medical imaging, and multi-omics measurements, are often high-dimensional, noisy, heterogeneous, and incomplete. These features make model calibration, simulation, and uncertainty quantification increasingly difficult. As a result, artificial intelligence (AI) and machine learning (ML) are playing a growing role in mathematical biology, not as replacements for mechanistic modeling, but as complementary tools that can support prediction, hybrid modeling, inference, and control. In this review, we organize these uses of AI from a mathematical biology perspective and examine how data-driven and mechanistic approaches interact across different modeling tasks. The selected examples span biomedical, epidemiological, ecological, evolutionary, biochemical, and population-level systems, while the review is intended to be representative rather than exhaustive. We emphasize recurring challenges that strongly affect biological credibility and practical usefulness, including interpretability, identifiability, generalization, and uncertainty quantification. Our goal is to clarify the roles AI can play in mathematical biology and to highlight the opportunities and limitations that arise when flexible learning methods are integrated with biologically grounded modeling.

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.

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.

Dynamical independence: Discovering emergent macroscopic processes in complex dynamical systems

We introduce a notion of emergence for macroscopic variables associated with highly multivariate microscopic dynamical processes. Dynamical independence instantiates the intuition of an emergent macroscopic process as one possessing the characteristics of a dynamical system ``in its own right,'' with its own dynamical laws distinct from those of the underlying microscopic dynamics. We quantify (departure from) dynamical independence by a transformation-invariant Shannon information-based measure of dynamical dependence. We emphasize the data-driven discovery of dynamically independent macroscopic variables, and introduce the idea of a multiscale ``emergence portrait'' for complex systems. We show how dynamical dependence may be computed explicitly for linear systems in both time and frequency domains, facilitating discovery of emergent phenomena across spatiotemporal scales, and outline application of the linear operationalization to inference of emergence portraits for neural systems from neurophysiological time-series data. We discuss dynamical independence for discrete- and continuous-time deterministic dynamics, with potential application to Hamiltonian mechanics and classical complex systems such as flocking and cellular automata.

A multimodal perturbation atlas defines the phenotypic resolution of cellular morphology

Because cells are complex dynamical systems, modeling cellular behaviors requires methods that capture how cells evolve across time, environments, and interventions. Microscopy is uniquely suited to this goal in that it can be applied to living cells in their native context. However, the phenotypic resolving power of live-cell microscopy remains incompletely characterized, particularly relative to molecular assays. Here, we present a multimodal perturbation atlas of 1,000 pooled CRISPR knockouts in A549 cells, profiled by fluorescence microscopy (39 live, 13 fixed markers), label-free phase imaging of the same live cells, and single-cell RNA sequencing (scRNA-seq). Totaling ∼57 million single-cell profiles, our data yield rich cell-biological signatures that map individual gene function. We find that phase imaging matches — and, with sufficient cell coverage, exceeds — the phenotypic resolution of fluorescence imaging and scRNA-seq, while capturing higher-order pathway organization that scRNA-seq does not resolve. These results establish intrinsic morphology as a high-precision readout of cellular state, and lay a foundation for live-cell profiling of phenotypic trajectories. ### Competing Interest Statement The authors have declared no competing interest. Biohub, Redwoood City, CA, USA

Rectangle: robust and scalable multiscale deconvolution informed by single-cell RNA sequencing data

Bulk RNA-seq enables effective profiling of large cohorts and complex experimental designs, but current single-cell-informed deconvolution methods incompletely resolve closely related cell phenotypes, do not scale efficiently to large single-cell datasets, or fail to account for cellular content not represented in the reference. Here, we present Rectangle, an scverse Python framework for single-cell-informed deconvolution of bulk RNA-seq data.

On cell types and cell states

The advent of single-cell genomics has brought about new efforts to characterize and catalog all of the cell types in the human body. Despite these efforts, the very definition of a “cell type” is under debate. In this post, I will discuss a conceptual framework for defining cell types as subsets of states in an underlying cellular state space. Moreover, I will link the cellular state space to biomedical ontologies that attempt to capture biological knowledge regarding cell types.