Computational analysis of molecular networks using spectral graph theory, complexity measures and information theory

Abstract

Molecular networks are described in terms of directed multigraphs, so-called network motifs. Spectral graph theory, reciprocal link and complexity measures were utilized to quantify network motifs. It was found that graph energy, reciprocal link and cyclomatic complexity can optimally specify network motifs with some degree of degeneracy. Biological networks are built up from a finite number of motif patterns; hence, a graph energy cutoff exists and the Shannon entropy of the motif frequency distribution is not maximal. Also, frequently found motifs are irreducible graphs.Network similarity was quantified by gauging their motif frequency distribution functions using Jensen-Shannon entropy. This method allows us to determine the distance between two networks regardless of their nodes' identities and network sizes.This study provides a systematic approach to dissect the complex nature of biological networks. Our novel method different from any other approach. The findings support the view that there are organizational principles underlying molecular networks. Biological networks and network motifsMolecular biological networks are the basis of biological processes, where the networks exhibit biological functions through interaction among the genetic elements.Each module is expected to perform specific functions, separable from the functions of other modules 1-3 . Such modular networks can be decomposed into smaller clusters, also known as network motifs. These motifs show interesting dynamical behaviors, in which cooperativity effects between the motif components play a critical role in human diseases.Essentially, network-based analysis falls into the following major categories: (1) motif identification and analysis, (2) global architecture study, (3) local topological properties, and (4) robustness of the network under different types of perturbations.For the first category, there are a number of publicly available network motif detection tools, namely MFINDER 4 , MAVISTO 5 , FANMOD 6 , NetMatch 7 and SNAVI 8 .

Geometry and symmetry in biochemical reaction systems

“…There has been some prior work on spectral graph theory applied to biochemical networks, see for instance MacArthur et al (2008), MacArthur andSánchez-García (2009), Sánchez-García (2020), Lesne (2006), Mason and Verwoerd (2007), Perkins and Langston (2009), Banerjee and Jost (2009), Huang et al (2019), and there is a growing literature on how to use hypergraphs for modelling biochemical networks. In Estrada and Rodríguez-Velázquez (2006), for example, the concepts of subgraph centrality and clustering are generalised to the case of hypergraphs, and various practical examples, including examples from biology, are given.…”