The Extent of Cooperativity of Protein Motions Observed with Elastic Network Models Is Similar for Atomic and Coarser-Grained Models

Abstract

Coarse-grained elastic network models have been successful in determining functionally relevant collective motions. The level of coarse-graining, however, has usually focused on the level of one point per residue. In this work, we compare the applicability of elastic network models over a broader range of representational scales. We apply normal mode analysis for multiple scales on a highresolution protein data set using various cutoff radii to define the residues considered to be interacting, or the extent of cooperativity of their motions. These scales include the residue-, atomic-, proton-, and explicit solvent-levels. Interestingly, atomic, proton, and explicit solvent level calculations all provide similar results at the same cutoff value, with the computed mean-square fluctuations showing only a slightly higher correlation (0.61) with the experimental temperature factors from crystallography than the results of the residue-level coarse-graining. The qualitative behavior of each level of coarse graining is similar at different cutoff values. The correlations between these fluctuations and the number of internal contacts improve with increased cutoff values. Our results demonstrate that atomic level elastic network models provide an improved representation for the collective motions of proteins compared to the coarse-grained models.

Protein elastic network models and the ranges of cooperativity

“…Kundu et al (10) studied 113 X-ray protein structures and found that GNM is able to predict the experimental B-factors well, yielding an average correlation between prediction and experiment of Ϸ0.59. The results of Sen et al showed that the correlations between experimental B-factors and the GNMpredicted values are quite similar at either coarse-grained or atomic levels (12), which is consistent with its being overall an entropy model. The ANM can also be used for B-factor predictions, although, in reproducing the isotropic B-factors, it was noted that ANM generally performs slightly worse than GNM (10).…”

“…A number of computational and statistical approaches has been proposed to predict protein B-factors from protein sequence (1-7), atomic coordinates (8)(9)(10)(11)(12)(13), and electron density maps (14). The atomic coordinate-based methods such as molecular dynamics (MD) (15)(16)(17)(18) and normal mode analysis (NMA) (19)(20)(21)(22) are computationally expensive, and thus, in the past decade, the elastic network model (ENM), with NMA, using a single parameter harmonic potential, usually coarse-grained, has been widely used for studying protein dynamics including B-factor predictions.…”

Elastic network models capture the motions apparent within ensembles of RNA structures

“…ENMs, in particular the anisotropic network model (ANM), a type of ENM that provides the directions of motions in addition to relative mobility, have proven useful for obtaining the dominant functional motions of proteins in many studies (Bahar and Rader 2005;Ma 2005;Zheng and Brooks 2005;Sen et al 2006;Tama and Brooks 2006;Jernigan and Kloczkowski 2007;Yang et al 2007Yang et al , 2008. It has been shown that the motions computed using ENMs correspond well to the principal components of molecular dynamics (MD) trajectories (Hayward and de Groot 2008), can aid in molecular structure determination (Wu and Ma 2004), refining of structural models (Delarue and Dumas 2004), and in flexible docking (May and Zacharias 2008;Gerek and Ozkan 2010).…”

Chain dimensions and fluctuations in elastomeric networks in which the junctions alternate regularly in their functionality

“…Most important, these new results may have significant impact on the well-known elastic network models of proteins 23,27,28 and the characterization of other biological structures. Elastic network models originated from the phantom network models of polymers in general, by a direct application of Eq.…”