Mapping Cell Fate Transition in Space and Time.

Cell fate transition is fundamentally a spatiotemporal process, but previous work has largely neglected the spatial dimension. Incorporating both space and time into models of cell fate transition would be a key step toward characterizing how interactions among neighboring cells, the presence of local niche factors, and physical migration of cells contribute to tissue development. To realize this potential, we propose topological velocity inference (TopoVelo), a model for jointly inferring spatial and temporal dynamics of cell fate transition from spatial transcriptomic data. TopoVelo extends the RNA velocity framework to model single-cell gene expression dynamics of an entire tissue with spatially coupled differential equations. Our principled probabilistic approach enables the incorporation of time point labels and multiple slices. We further introduce the idea of cell velocity, which is defined as the physical direction of cell maturation and migration. Simulated data analysis indicates that incorporating spatial coordinates significantly improves the accuracy of velocity and time inference. When evaluated on real Slide-Seq and Stereo-Seq data, TopoVelo significantly improves the spatial coherence of inferred cell ordering compared to previous methods. Furthermore, TopoVelo accurately recovers the expected directions of cell differentiation and migration in the embryonic mouse cerebral cortex, gut, and lung. Our work introduces a new dimension into the study of cell fate transitions and lays a foundation for modeling the collective dynamics of cells comprising an entire tissue. ### Competing Interest Statement The authors have declared no competing interest.