A Unified Geometric Framework for Developmental Analysis of Spatial Transcriptomic Data
This study addresses the challenge of reconstructing developmental trajectories from destructive spatial transcriptomics sampling by proposing a unified geometric framework. The method integrates gene expression and spatial proximity to construct graph representations, leveraging Gromov-Wasserstein embeddings, geodesic interpolation, and Ollivier-Ricci curvature to quantify spatiotemporal evolution. Validation on Drosophila datasets demonstrates that this framework accurately recapitulates curvature trends in developmental dynamics and exhibits high consistency with Co-Optimal Transport distances. By enabling cross-temporal network structure comparison and continuous interpolation, this work establishes a novel paradigm for elucidating complex developmental processes.