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The functions of biological structures are related to the dynamics of the structures, especially various kinds of large-amplitude molecular motions. With some assumptions, those motions can be investigated by Normal Mode Analysis (NMA) and Gaussian Network Model (GNM). However, despite their contributions to many applications, the relationship between NMA and GNM requires a further discussion. In this work, we review the Normal Mode Analysis and Gaussian Network Model and address their common applications in structural biology. We evaluate the GNM, based on how well it predicts the structural fluctuations, compared to experimental data for a large set of protein structures. Then, we propose several ways of coarse-graining for NMA on protein residue-level structural fluctuations by choosing different approaches to represent the amino acids and the forces between them. Using backbone atoms such as Cα, C, N , and Cβ, single-atom representations are considered. Combinations of some of these atoms are also tested as a representative point for the residue. The force constants between the representative atoms are extracted from the Hessian matrix of the potential energy and used 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 residue-level GNM based on the choice of different kinds of representative backbone atoms. The coarse-grained methods perform more efficiently than all-atom normal mode analysis, and also agree better with the B-factors. B-factor correlations are comparable or better than with those estimated with conventional GNM. The extracted force constants are surveyed for different pairs of residues with different extents of separation in sequence. The statistical averages are used to build a finer-grained GNM here called nonhomogeneous GNM, which is able to predict residue-level mean square fluctuations significantly better than conventional GNM for many test cases.

On coarse-grained Normal Mode Analysis and refined Gaussian Network Model for protein structure fluctuations