Gaussian Network Model Revisited: Effects of Mutation and Ligand Binding on Protein Behavior

Abstract

The coarse-grained Gaussian Network model, GNM, considers only the alpha carbons of the folded protein. Therefore it is not directly applicable to the study of mutation or ligand binding problems where atomic detail is required. This shortcoming is improved by including the local effect of heavy atoms in the neighborhood of each alpha carbon into the Kirchoff Adjacency Matrix. The presence of other atoms in the coordination shell of each alpha carbon diminishes the magnitude of fluctuations of that alpha carbon. But more importantly, it changes the graph-like connectivity structure, i.e., the Kirchoff Adjacency Matrix of the whole system which introduces amino acid specific and position specific information into the classical coarse-grained GNM which was originally modelled in analogy with phantom network theory of rubber elasticity. With this modification, it is now possible to make predictions on the effects of mutation and ligand binding on residue fluctuations and their pair-correlations. We refer to the new model as all-atom GNM. Using examples from published data we show that the all-atom GNM applied to in silico mutated proteins and to their laboratory mutated structures gives similar results. Thus, loss and gain of correlations, which may be related to loss and gain of function, may be studied by using simple in silico mutations only.