Mathematical Programming and Graph Neural Networks illuminate functional heterogeneity of pathways in disease

Abstract

We employ a computationally intensive framework that integrates mathematical programming and graph neural networks to elucidate functional phenotypic heterogeneity in disease by classifying entire pathways of interest under various conditions. Our approach combines two distinct yet seamlessly integrated mathematical modelling schemes: (i) we first leverage Prior-Knowledge gene regulatory Networks (PKNs) derived from comprehensive and established databases to reconstruct and optimize their topology using genomic and transcriptomic data and mathematical programming optimization, and (ii) we apply tailored Graph Convolutional Networks (GCNs) to classify each network as a single data point atgraph-level, using Mode of Regulation (MoR) and gene activity profiles as node embeddings. These networks may vary in their biological or molecular annotations, which serves as a labelling scheme for their supervised classification. As a case study, we investigate the DNA damage and repair pathway using theTP53regulon in a pancancer study, classifying gene networks across differentTP53mutation types. Our findings pave the way for a systematic, causality-driven approach to classify stimuli or stress conditions and their functional implications, thereby advancing drug discovery and precision medicine.