Normal modes for predicting protein motions: a comprehensive database assessment and associated Web tool

Abstract

We carry out an extensive statistical study of the applicability of normal modes to the prediction of mobile regions in proteins. In particular, we assess the degree to which the observed motions found in a comprehensive data set of 377 nonredundant motions can be modeled by a single normal-mode vibration. We describe each motion in our data set by vectors connecting corresponding atoms in two crystallographically known conformations. We then measure the geometric overlap of these motion vectors with the displacement vectors of the lowest-frequency mode, for one of the conformations. Our study suggests that the lowest mode contains useful information about the parts of a protein that move most (i.e., have the largest amplitudes) and about the direction of this movement. Based on our findings, we developed a Web tool for motion prediction (available from http://molmovdb.org/nma) and apply it here to four representative motions--from bacteriorhodopsin, calmodulin, insulin, and T7 RNA polymerase.

Figure 1.

Notations used in the paper. R_ij is the vector connecting atom i to atom j in the experimental (initial) structure. Δ_j is the difference vector between atom i in the displaced (final) structure and the same atom in the initial structure. D_j is the lowest normal mode displacement vector for atom j in the initial conformation. θ_j is the angle between vectors D_j and Δ_j for atom j.

Figure 2.

An illustration of the scheme that was used to identify the data set of nonredundant domain motions.

Figure 3.

Distribution of RMSD scores (in Å) for the nonredundant set of domain motions.

Figure 4.

Histogram of S² statistic and the corresponding average θ_j angle. Values are shown for 100% (dotted), 10% (dashed), and 2.5% (solid) of selected Cα-atoms based on the motion amplitudes in the nonredundant data set of domain motions. Selection of the most moving atoms results in larger values of S² (the larger values of S and S² correspond to the lower average angle between the two sets of vectors). Dotted line points to the location of equal to 54.7°, the average angle between two randomly θ_j generated vectors.

Figure 5.

S-statistic as a function of percentage of the largest selected Cα displacements for single-domain and multidomain protein motions.

Figure 6.

Real motion (red) and NMA-predicted (blue) vectors for the motion of (A) insulin (d7insb_SCOP domain), (B) calmodulin (d2bbm_domain), (C) bacteriorhodopsin (d1c8sa_SCOP domain), and (D) T7 polymerase (elongation complex). In D, labels 1, 2 , 3, and 4 represent residues THR 596, VAL 597, THR 598, and GLY 603, respectively. Arrows indicate only the directions of the motion.

Figure 7.

Histogram of the average angle between the lowest-frequency normal mode vectors and the corresponding observed displacement vectors for the selected Cα with the largest B-factors in the nonredundant data set of domain motions. θ₄^(B) distribution is represented by the solid line, and θ₁^(B) by the dashed line.

Figure 8.

Screenshot of the NMA motion and flexibility prediction server: (A) input page and (B) results page.