Gromov-Wasserstein framework reveals gene network evolution from spatial transcriptomics

A team led by Shiying Li at UNC Chapel Hill has published a new framework that tackles a fundamental problem in biology: how to infer developmental trajectories when cells are destroyed during measurement. Existing optimal transport (OT) methods compare distributions of gene expression, but they ignore the relational structure between genes. This paper, titled "A Unified Geometric Framework for Developmental Analysis of Spatial Transcriptomic Data," instead embeds entire gene expression networks into Gromov-Wasserstein (GW) space — a mathematical space that measures how well two networks align in structure, not just position.

Using Drosophila spatiotemporal transcriptomic data, the framework builds a graph for each developmental stage that combines gene expression values with spatial proximity of cells. From these graphs, it computes GW geodesics to continuously interpolate between stages, effectively morphing one network into another to reveal how gene relationships evolve. The authors also apply Ollivier-Ricci curvature — a measure of local network geometry — to quantify whether connections are strengthening or weakening over time. Their interpolation reproduces empirical curvature trends, and agreement with higher-order Co-Optimal Transport (COOT) distances, which jointly capture spatial and temporal information, validates the approach. The 33-page paper (arXiv:2608.15306) demonstrates that hypernetwork representations successfully capture salient biological changes, providing a unified geometric framework for studying dynamic biological networks in any system.