Applications of graph theory in studying protein structure, dynamics, and interactions.

Being a core tool, graph theory, as a mathematical formalism in mathematical chemistry, has become an essential approach for studying the complex behavior and interactions in protein systems. Here, we review recent advances in the field, particularly in our group, including the methods developed to access protein functions and their applications in disease biology. First, we provide the necessary background and definitions of graph-based structures and network centralities, and methodologies developed at the node-, subgraph- and pathway-levels. We then review the applications of how to use these algorithms to gain new biological insights, ranging from protein structures to protein dynamics, and interactions for linking genotypes and phenotypes. Furthermore, we discuss immediate challenges in the multilayer network, which is more realistic in the biological world, and hope to draw increasing attention from mathematicians, especially graph theorists, to reveal the basic principles of "networks of networks". [ABSTRACT FROM AUTHOR]