Abstract
New experimental and computational methods use genetic or gene expression observations with single cell resolution to study the relationship between single-cell molecular profiles and developmental trajectories. Most tissues contain spatially contiguous regions that develop as a unit, such as follicles in the ovary, or tubules and glomeruli in the kidney. We find that existing approaches designed to use time series spatial transcriptomics (ST) data produce biologically incoherent trajectories that fail to maintain these structural units over time. We present Spatiotemporal Optimal transport with Contiguous Structures (SOCS), an Optimal Transport-based trajectory inference method for time-series ST that produces trajectory inferences preserving the structural integrity of contiguous biologically meaningful units, along with gene expression similarity and global geometric structure. We show that SOCS produces more plausible trajectory estimates, maintaining the spatial coherence of biological structures across time, enabling more accurate trajectory inference and biological insight than other approaches.