Discrete curvatures of biological networks

Biological networks, such as protein-protein and gene-gene networks, are crucial to the physiology and function of organisms. High-throughput technology has led to significant progress in understanding individual biological entities, but comprehending the interactions between them remains challenging due to the complexity and vastness of these networks. To address this, we explore the use of network curvature as a mathematical concept that measures the natural behaviors of a graph, including diffusion, information flow, and network resilience. Analyzing biological networks with network curvature allows for insights into the fundamental structure and dynamics of networks under biological phenomena, which can lead to a better understanding of disease mechanisms and treatment options. We investigate the application of well-defined curvatures, including Ollivier-Ricci, Balanced Forman, Diffusion, and Bakry-Emery, on protein and gene networks. Our findings provide new insights into the structure and dynamics of these networks, with potential implications for understanding disease mechanisms and identifying effective treatments. In particular, Ollivier-Ricci curvature can be used to measure network clustering, Balanced Forman curvature can identify critical genes and proteins, Diffusion curvature can study disease spread and intervention effectiveness, and Bakry-Emery curvature can identify key metabolic pathways. Our work contributes to the development of network curvature as a valuable tool for understanding biological networks.

Discrete curvature

gene-gene network

protein-protein network 

Mid-Level

Machine Learning

Symposium on Data Science and Statistics (SDSS) 2023