Amino-Acid Network Clique Analysis of Protein Mutation Non-Additive Effects: A Case Study of Lysozyme

Optimizing amino-acid mutations in enzyme design has been a very challenging task in modern bio-industrial applications. It is well known that many successful designs often hinge on extensive correlations among mutations at different sites within the enzyme, however, the underpinning mechanism for these correlations is far from clear. Here, we present a topology-based model to quantitively characterize non-additive effects between mutations. The method is based on the molecular dynamic simulations and the amino-acid network clique analysis. It examines if the two mutation sites of a double-site mutation fall into to a 3-clique structure, and associates such topological property of mutational site spatial distribution with mutation additivity features. We analyzed 13 dual mutations of T4 phage lysozyme and found that the clique-based model successfully distinguishes highly correlated or non-additive double-site mutations from those additive ones whose component mutations have less correlation. We also applied the model to protein Eglin c whose structural topology is significantly different from that of T4 phage lysozyme, and found that the model can, to some extension, still identify non-additive mutations from additive ones. Our calculations showed that mutation non-additive effects may heavily depend on a structural topology relationship between mutation sites, which can be quantitatively determined using amino-acid network k-cliques. We also showed that double-site mutation correlations can be significantly altered by exerting a third mutation, indicating that more detailed physicochemical interactions should be considered along with the network clique-based model for better understanding of this elusive mutation-correlation principle.