Coarse grained normal mode analysis vs. refined Gaussian Network Model for protein residue-level structural fluctuations

Abstract

We investigate several approaches to coarse grained normal mode analysis on protein residual-level structural fluctuations by choosing different ways of representing the residues and the forces among them. Single-atom representations using the backbone atoms C(α), C, N, and C(β) are considered. Combinations of some of these atoms are also tested. The force constants between the representative atoms are extracted from the Hessian matrix of the energy function and served as the force constants between the corresponding residues. The residue mean-square-fluctuations and their correlations with the experimental B-factors are calculated for a large set of proteins. The results are compared with all-atom normal mode analysis and the residue-level Gaussian Network Model. The coarse-grained methods perform more efficiently than all-atom normal mode analysis, while their B-factor correlations are also higher. Their B-factor correlations are comparable with those estimated by the Gaussian Network Model and in many cases better. The extracted force constants are surveyed for different pairs of residues with different numbers of separation residues in sequence. The statistical averages are used to build a refined Gaussian Network Model, which is able to predict residue-level structural fluctuations significantly better than the conventional Gaussian Network Model in many test cases.

Fig. 1

The picture on the left shows the C_α trace of 1HEL. The one on the right shows all connections between C_α nodes for 1HEL to indicate the nature of the elastic network analyzed by GNM (Cui and Bahar 2006).

Fig. 2

This is an example of a contact matrix.

Fig. 3

(a) The residue mean-square-fluctuations calculated by GNM(C_α) for 1HJE are compared with the experimental B-factors of C_α. (b) The residue mean-square-fluctuations calculated by cgNMA(M) for 1HJE are compared with the experimental B-factors of C_α. (c) The residue mean-square-fluctuations calculated by NMA for 1HJE are compared with the experimental B-factors of C_α

Fig. 4

(a) The residue mean-square-fluctuations calculated by GNM(C_α) for 2BF9 are compared with the experimental B-factors of C_α. (b) The residue mean-square-fluctuations calculated by cgNMA(M) for 2BF9 are compared with the experimental B-factors of C_α. (c) The residue mean-square-fluctuations calculated by NMA for 2BF9 are compared with the experimental B-factors of C_α

Fig. 5

(a) The residue mean-square-fluctuations calculated by GNM(C_α) for 2HQK are compared with the experimental B-factors of C_α. (b) The residue mean-square-fluctuations calculated by cgNMA(M) for 2HQK are compared with the experimental B-factors of C_α. (c) The residue mean-square-fluctuations calculated by NMA for 2HQK are compared with the experimental B-factors of C_α

Fig. 6

The distributions of the force constants for pairs of residues separated by 0,1,2,3 residues in sequence.

Fig. 7

An example of an nhGNM contact matrix.