Uncovering critical transitions and molecule mechanisms in disease progressions using Gaussian graphical optimal transport

Understanding disease progression is crucial for detecting critical transitions and finding trigger molecules, facilitating early diagnosis interventions. However, the high dimensionality of data and the lack of aligned samples across disease stages have posed challenges in addressing these tasks. We present a novel framework, Gaussian Graphical Optimal Transport (GGOT), for analyzing disease progressions. The proposed GGOT uses Gaussian graphical models, incorporating protein interaction networks, to characterize the data distributions at different disease stages. Then we use population-level optimal transport to calculate the Wasserstein distances and transport maps between stages, enabling us to detect critical transitions. By analyzing the per-molecule transport distance, we quantify the importance of each molecule and identify trigger molecules. Moreover, GGOT predicts the occurrence of critical transitions in unseen samples and visualizes the disease progression process. We apply GGOT to the simulation dataset and six disease datasets with varying disease progression rates, to show its effectiveness for detecting critical transitions and identifying trigger molecules. ### Competing Interest Statement The authors have declared no competing interest.