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.