Quantifying Differences in Gene Networks via Graph Curvature

Abstract: Fast improvements of technologies for the acquirement of large genomic data through single cell RNA-sequencing have led to a need for new mathematical methods for the analysis of such data. One approach of representing this data that has emerged over the last couple of decades is through graph representations, i.e. as networks that describes how genes interact with each other. There has since then been a development of a multitude of methods based on these so-called co-expression networks for gene analysis. More recently, a notion of curvature has provided a methodology for quantifying differences and similarities in these large graphs, but better understanding of the methods are still needed, especially when the networks considered grows larger and larger. Pompe disease is a rare genetic disorder caused due to mutations in the GAA gene which codes the enzyme acid alpha glucosidase (GAA). Current treatment involves enzyme replacement therapy and the side effects vary between patients. Here we develop an approach to identify genes and pathways that can reduce the disease pathology by utilizing concominant treatments or reduce the immunogenicity of current treatments. In this project we use single cell RNA-sequencing of hundreds of cells from real patients to generate networks describing gene interactions. The Ollivier-Ricci curvature is calculated for the large networks using entropy-regulated optimal mass transport. The top genes we identify by our method have a strong presence in prior literature in association with lysosomal and mitochondrial diseases. This positive verification from scientific literature makes this methodology for narrowing down genes of interest promising.