Graph Pseudotime Analysis and Neural Stochastic Differential Equations for Analyzing Retinal Degeneration Dynamics and Beyond

Understanding the progression of disease at the molecular level usually requires capturing both the structural dependencies between pathways and the temporal dynamics of how diseases evolve. In this work, we resolve the former challenge by developing a biologically informed graph-forming method to efficiently construct pathway graphs for subjects from our newly curated transcriptomic dataset of JR5558 mice that spontaneously develop neovascularization beneath their retinas. We then developed Graph-level Pseudotime Analysis (GPA) to infer graph-level trajectories that reveal how the disease progresses at the population level rather than in individual subjects. Based on the trajectories estimated by GPA, we identify the most sensitive pathways that drive transitions between disease stages. In addition, we measure changes in pathway features using neural stochastic differential equations (SDEs), which enable us to formally define and compute pathway stability and disease bifurcation points (points of no return)—two fundamental problems in research on disease progression. We have extended our theory to allow pathways to interact with each other, enabling a more comprehensive and multi-faceted characterization of disease phenotypes. Comprehensive experimental results demonstrate the effectiveness of our framework in reconstructing pathway dynamics, identifying critical transitions, and providing novel insights into the mechanistic understanding of the evolution of disease.