Leveraging spectrum of graph sheaf Laplacian as a genome-architecture-aware measure of microbiome diversity.

Motivation: Measures of microbial diversity that can be derived directly from metagenomic sequencing data offer a valuable summary view of the underlying complex systems. Prior work has shown that both taxonomic composition and abundances that are captured by standard diversity measures (e.g., Shannon entropy), and structural variation within the metagenome due to gene duplications, losses and horizontal transfers (HGT), can correlate with the host's health. However, there are no diversity measures available that simultaneously account for the genome architecture and taxonomic composition within the sample. Thus, in this work we propose the spectral energy of a graph sheaf Laplacian as such a measure, and justify its applicability through a simulation study and analysis of biological data. Results: First, we describe a theoretical framework that allows us to combine the features of genome graphs with the taxonomic data. Then, we explore the sensitivity of the proposed diversity measure to genome rearrangements and HGT events in a simulation study. Finally, we explore applicability of our proposed measure to characterization of diversity of human gut metagenomes. We find our proposed measure to offer better discrimination between healthy controls and inflammatory bowel disease (IBD) patients' samples ( Availability and Implementation: https://github.com/nsapoval/bd-gsl.