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

TL;DR

This work addresses the challenge of modeling disease progression at the pathway level when longitudinal measurements in individuals are difficult to obtain. It introduces Graph Pseudotime Analysis (GPA) to order graphs of molecular pathways constructed via a biology-informed graph-forming method, and uses neural stochastic differential equations (SDEs) to quantify pathway stability and detect disease bifurcation points along trajectories, enabling a formal analysis of dynamical transitions. The JR5558 mouse dataset is curated to form 343 pathway-nodes per graph and identify disease-sensitive pathways (SPs) through graph regression, followed by temporal GCN modeling of transitions between disease stages, with extensions to interacting pathways. The framework reveals biologically interpretable retinal degeneration dynamics, identifies critical transitions and potential therapeutic targets, and offers a generalizable approach for exploring pathway-level dynamics in complex diseases and precision medicine.

Abstract

Understanding disease progression at the molecular pathway level usually requires capturing both structural dependencies between pathways and the temporal dynamics of disease evolution. In this work, we solve the former challenge by developing a biologically informed graph-forming method to efficiently construct pathway graphs for subjects from our newly curated JR5558 mouse transcriptomics dataset. We then develop Graph-level Pseudotime Analysis (GPA) to infer graph-level trajectories that reveal how 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 disease stage transitions. In addition, we measure changes in pathway features using neural stochastic differential equations (SDEs), which enables us to formally define and compute pathway stability and disease bifurcation points (points of no return), two fundamental problems in disease progression research. We further extend our theory to the case when pathways can interact with each other, enabling a more comprehensive and multi-faceted characterization of disease phenotypes. The comprehensive experimental results demonstrate the effectiveness of our framework in reconstructing the dynamics of the pathway, identifying critical transitions, and providing novel insights into the mechanistic understanding of disease evolution.

Figures (3)

• Figure 1: Illustration of the key steps of the quantification method. (A) A circular region of interest (ROI) with a 283$\mu m$ radius centered on the optic nerve head was defined. (B) The image was converted to 8-bit grayscale, the background was removed using a 200$\mu m$ rolling ball algorithm, and lesions within the ROI were manually outlined using the freehand selection tool. (C) A threshold was applied to accurately segment the lesion areas. (D) The selected lesions were verified in the original color fundus image.
• Figure 2: Illustration on how the pathway graphs are formed and how SPs are identified through two types of graph regressions.
• Figure 3: Process of generating graph trajectory via GPA. (a): Graph dimensionality reduction and clustering; (b): Minimum spanning tree; (c): Trajectory estimation using shortest distance method.

Theorems & Definitions (8)

• Lemma 1: informal
• Definition 1: Point of No Return
• Lemma 2: Full Verison of Lemma \ref{['lem:stability']}
• proof
• Remark 1
• Corollary 1: GPS
• proof
• Definition 2: Graph-Interacted Point of No Return