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 all atom pairs within the coordination shell of each other into the Kirchoff Adjacency Matrix. Counting all contacts rather than only alpha carbon contacts diminishes the magnitude of fluctuations in the system. But more importantly, it changes the graph-like connectivity structure, i.e., the Kirchoff Adjacency Matrix of the protein. This change depends on amino acid type which introduces amino acid specific and position specific information into the classical coarse-grained GNM which was originally modelled in analogy with the phantom network model of rubber elasticity. With this modification, it is now possible to explain the consequences of mutation and ligand binding on residue fluctuations, their pair-correlations and mutual information (MI) shared by each pair. We refer to the new model as ‘all-atom GNM’. Using examples from published data we show that the all-atom GNM gives B-factors that are in better agreement with experiment, can explain effects of mutation on long range communication in PDZ domains and can predict effects of GDP and GTP binding on the dimerization of KRAS.

Mutual information analysis of mutation, nonlinearity, and triple interactions in proteins

“…given by Equation 7 may be used where the correlations may be obtained from the elastic net model of a protein. 32 Moment-based Hermite series expansion is a convenient method for calculating all levels of nonlinearities in MI. Nonlinearities arise from two sources, from (i) nonlinearities of interaction potentials which are present even in the local dynamics of the protein, and…”

“…A plot for MI between D357 and all other residues is presented in These observations reflect and support the main theme of the work of Raman et al 28 where mutations that are neutral confer It is to be noted that the present study addresses changes in MI upon various mutations and does not give information on the changes in the ligand-binding affinities which is the subject of another study. 32 MI between a pair of residues is a static property and shows the maximum amount of information that may be transferred between the two residues. 1 The actual amount of information transferred between the two residues can be estimated from entropy transfer calculations and is always less than MI.…”