  Optimizing amino-acid mutations has been a most challenging task in modern
bio- industrial enzyme designing. 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 correlation effects between mutations. The method is based on the
molecular dynamic simulations and the amino-acid network clique analysis that
simply examines if two single mutation sites belong to some 3-clique. 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 with less correlation or additive mutations. We also
applied the model to the protein Eglin c whose topology is significantly
distinct 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 correlation effects may heavily depend on
topology relationship among mutation sites, which can be quantitatively
characterized 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 physico-chemistry interactions
might be considered with the network model for better understanding of the
elusive mutation-correlation principle.
