Information flow and catalytic dyad in SARS-CoV2 main protease Mpro enzyme using embedded discrete Markov chains and centrality measures

Abstract

Abstract In this work, we use a network representation of the globular crystalline structure of a given protein as a graph structure with N nodes and E edges in order to analyze quantitatively the flow information and to identify key sites within the globular structure. Each node nj represents a $ C_{\alpha}^{i}$ carbon of the main backbone whereas the node’s degree ki is a measure of its physical interactions. In order to identify biologically relevant and active nodes, we compute local per residue closeness $ C_{c}(i)$, betweenness $ C_{b}(i)$ and eigenvector centralities $ C_{e}(i)$. Further analysis is done by embedding a stochastic dynamic discrete Markov chain in order to evaluate the dynamics of a set of normal random walkers (NRW’s) within the network. From this, we compute the mean first passage time matrix M and the stationary occupation probability vector ψi for each node. These two measures provide very useful information on the dynamical process embed within the $ C_{\alpha}$ network. We apply this to SARS-CoV2 Mpro main protease which is a key enzyme in the virus replication cycle. In particular, we focus our attention to the properties of the catalytic dyad integrated by His41-Cys145 in Mpro main protease since this active site has been under intense scrutiny as a pharmaceutical target. In addition, our results show the existence of additional relevant aminoacids that might play a fundamental role on signal propagation and allosteric pathways in SARS-CoV main proteases.