SpaGRD deciphers signaling architectures in spatial transcriptomics using graph reaction-diffusion systems

The rapid emergence of spatial transcriptomics offers unprecedented opportunities to study cell-cell communication (CCC) by capturing gene expression alongside spatial context. However, existing CCC inference methods often rely on static, heuristic models that overlook the inherently spatiotemporal dynamics and mechanistic complexity of intercellular signaling, limiting both accuracy and biological interpretability. Here, we present SpaGRD, a first-principles-based method that explicitly models ligand-receptor interactions through partial differential equations derived from Fick law of diffusion and the mass action law. Leveraging graph signal processing techniques, SpaGRD solves these equations on spatial graphs, providing a principled and generalizable approach to CCC inference. Through extensive simulations, SpaGRD demonstrates superior accuracy and robustness compared to existing methods. Applications to multiple datasets across diverse tissues and platforms reveal dynamic CCC patterns with spatially resolved signaling heterogeneity, providing biologically meaningful insights into cellular coordination and developmental processes. By bridging physical modeling with spatial transcriptomics, SpaGRD provides an accurate, interpretable, and mechanistically grounded framework for advancing quantitative studies of spatiotemporal cell-cell communication.