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

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 under various conditions of interest. Our approach combines three distinct yet seamlessly integrated modelling schemes: i) we first leverage Prior-Knowledge Networks (PKNs) derived from comprehensive and established databases to reconstruct their topology using genomic and transcriptomic data via mathematical programming optimization, ii) we apply causal learning via Additive Noise Models (ANMs) to further prune the optimized networks, and iii) we apply tailored Graph Convolutional Networks (GCNs) to classify each network as a single data point at graph-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. We demonstrate the framework in the DNA damage and repair pathway using the TP53 regulon in a pancancer study, classifying Gene Regulatory Networks (GRNs) across different TP53 mutation types. This scalable approach enables the classification of diverse conditions while addressing the multifactorial nature of diseases. It disentangles their polygenic complexity and reveals new functional patterns through a causal representation.