DALI Learns Rules Generating Spatiotemporal Transcriptomics

Learning how molecular interactions dictate the self-organization of biological systems is a longstanding goal in developmental biology. Time-series spatial transcriptomics (spatiotemporal transcriptomics) provides data to interrogate such dynamic tissue processes. Existing computational methods for spatiotemporal transcriptomics focus on aligning cells and spatial regions across timepoints and learning the spatiotemporal determinants of cell-fate transitions, but do not identify interactions between local spatial processes that generate developmental patterns. To address this, we introduce \textit{Dynamical Analysis of Latent Interactions} (DALI), a framework that takes as input a time series of spatial transcriptomic snapshots and simultaneously fits a latent partial differential equation (PDE) and a spatial registration model to learn rules that generate tissue development. On two Stereo-seq datasets of Zebrafish and Mouse embryogenesis, DALI learns rules that predict gene expression from held-out tissue regions better than baseline approaches. We furthermore interpret these rules: the learned latent variables correspond to meaningful gene programs, and their learned interactions to developmentally important signaling interactions with previous causal evidence.