Elastic network normal modes provide a basis for protein structure refinement

Abstract

It is well recognized that thermal motions of atoms in the protein native state, the fluctuations about the minimum of the global free energy, are well reproduced by the simple elastic network models (ENMs) such as the anisotropic network model (ANM). Elastic network models represent protein dynamics as vibrations of a network of nodes (usually represented by positions of the heavy atoms or by the C(α) atoms only for coarse-grained representations) in which the spatially close nodes are connected by harmonic springs. These models provide a reliable representation of the fluctuational dynamics of proteins and RNA, and explain various conformational changes in protein structures including those important for ligand binding. In the present paper, we study the problem of protein structure refinement by analyzing thermal motions of proteins in non-native states. We represent the conformational space close to the native state by a set of decoys generated by the I-TASSER protein structure prediction server utilizing template-free modeling. The protein substates are selected by hierarchical structure clustering. The main finding is that thermal motions for some substates, overlap significantly with the deformations necessary to reach the native state. Additionally, more mobile residues yield higher overlaps with the required deformations than do the less mobile ones. These findings suggest that structural refinement of poorly resolved protein models can be significantly enhanced by reduction of the conformational space to the motions imposed by the dominant normal modes.

Figure 1

Scheme of construction of the deformation matrix between two structures. Structures are superimposed, and then the i-th element of deformation matrix T is taken as a difference between the coordinates of two corresponding positions. On the picture Q indicates query, and the M modeled structure so that T = Q – M.

Figure 2

Distributions and comparisons of various structure quality metrics. Upper triangle: Spearman correlation coefficients between: RMSD, TM-score, LG-score, and Max-Sub score. Diagonal: Density distributions. Lower triangle: Pairwise correlations plots between each measure. Red lines (lower triangle) are averages over all points in bins on abscissa. Red dots correspond to decoys for which TM-score ≥ 0.5, and black dots for these with TM-score ≤ 0.5. Plots are generated for all cluster medoids (see Sec. 2).

Figure 3

An example case for an overlap between thermal motion of decoy structure and deformation from the native state. Picture presents best medoid of 1di2A protein. Native structure is in cartoon representation, colored according its secondary structure elements (purple – helix; yellow – β strand; light green – hairpin; white – loop), and decoy in represented as a blue tube. Combination of the three lowest normal modes in presented as red arrows. In boxes mark two worst modeled structure elements: loop from 14 Gly to 18 Pro and hairpin from 27 Gly to 32 Arg.

Figure 4

Distributions and comparisons of RMSD, sizes and cumulative overlaps. Upper triangle: Spearman correlation coefficients for: RMSD, Length, COV(20), and COV(5%). Diagonal: The density distributions for each quantity. Lower triangle: Pairwise correlations plots between each measure. Red lines (lower triangle) are averages over all points in bins on abscissa. Red dots correspond to decoys for which TM-score ≥ 0.5, and black dots for cases with TM-score ≤ 0.5. Plots are generated for all cluster medoids (see Sec. 2).