Multivariate stochastic modeling for transcriptional dynamics with cell-specific latent time using SDEvelo

Recently, RNA velocity has driven a paradigmatic change in single-cell RNA sequencing (scRNA-seq) studies, allowing the reconstruction and prediction of directed trajectories in cell differentiation and state transitions. Most existing methods of dynamic modeling use ordinary differential equations (ODE) for individual genes without applying multivariate approaches. However, this modeling strategy inadequately captures the intrinsically stochastic nature of transcriptional dynamics governed by a cell-specific latent time across multiple genes, potentially leading to erroneous results. Here, we present SDEvelo, a generative approach to inferring RNA velocity by modeling the dynamics of unspliced and spliced RNAs via multivariate stochastic differential equations (SDE). Uniquely, SDEvelo explicitly models inherent uncertainty in transcriptional dynamics while estimating a cell-specific latent time across genes. Using both simulated and four scRNA-seq and spatial transcriptomics datasets, we show that SDEvelo can model the random dynamic patterns of mature-state cells while accurately detecting carcinogenesis. Additionally, the estimated gene-shared latent time can facilitate many downstream analyses for biological discovery. We demonstrate that SDEvelo is computationally scalable and applicable to both scRNA-seq and sequencing-based spatial transcriptomics data.