A Unified Geometric Framework for Developmental Analysis of Spatial Transcriptomic Data

2026-08-15

AI Summary

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.

Abstract

High-throughput single-cell and spatial transcriptomic technologies provide high-resolution snapshots of heterogeneous cellular states, but their destructive nature prevents repeated measurements of the same cells over time. Consequently, temporal and spatial dynamics must be inferred from independently sampled, unaligned cell populations, making it challenging to reconstruct developmental trajectories. Optimal transport (OT) offers a geometric framework for aligning cell populations and inferring developmental trajectories, but many existing approaches focus on modeling the evolution of distributions of cells in gene expression space rather than the relational structure encoded by gene expression networks. To address this limitation, we introduce a geometric framework for analyzing the spatiotemporal evolution of gene expression networks through embeddings in Gromov--Wasserstein (GW) space. By representing each developmental stage as a graph combining gene expression and spatial proximity, our approach enables comparisons of network structure across time, continuous interpolation between developmental stages via GW geodesics, and quantification of network-level changes using Ollivier-Ricci curvature. We evaluate our framework on a spatiotemporal transcriptomic \textit{Drosophila} dataset and show that GW geodesic interpolations reproduce main trends in curvature dynamics observed in empirical gene expression networks. Agreement with higher-order Co-Optimal Transport (COOT) distances, which jointly represent spatial and temporal information, further validates the framework and suggests that hypernetwork representations successfully record salient biological changes across time. In general, our approach provides a unified geometric approach to study dynamically evolving biological networks.

Problem

• Spatial Transcriptomics
• Developmental Trajectory Inference
• Gene Expression Networks
• Optimal Transport

Innovation

• Gromov-Wasserstein space
• spatial transcriptomics
• gene expression networks
• Ollivier-Ricci curvature
• geodesic interpolation