Comparison of molecular dynamics and superfamily spaces of protein domain deformation

Abstract

Background: It is well known the strong relationship between protein structure and flexibility, on one hand, and biological protein function, on the other hand. Technically, protein flexibility exploration is an essential task in many applications, such as protein structure prediction and modeling. In this contribution we have compared two different approaches to explore the flexibility space of protein domains: i) molecular dynamics (MD-space), and ii) the study of the structural changes within superfamily (SF-space).

Results: Our analysis indicates that the MD-space and the SF-space display a significant overlap, but are still different enough to be considered as complementary. The SF-space space is wider but less complex than the MD-space, irrespective of the number of members in the superfamily. Also, the SF-space does not sample all possibilities offered by the MD-space, but often introduces very large changes along just a few deformation modes, whose number tend to a plateau as the number of related folds in the superfamily increases.

Conclusion: Theoretically, we obtained two conclusions. First, that function restricts the access to some flexibility patterns to evolution, as we observe that when a superfamily member changes to become another, the path does not completely overlap with the physical deformability. Second, that conformational changes from variation in a superfamily are larger and much simpler than those allowed by physical deformability. Methodologically, the conclusion is that both spaces studied are complementary, and have different size and complexity. We expect this fact to have application in fields as 3D-EM/X-ray hybrid models or ab initio protein folding.

Figure 1

Workflow of the comparison between SF and MD-spaces of protein domain deformability done in the study.

Figure 2

Comparisons based on variance. a) Total variance for the performed decompositions: ISVD of the SF-space, SVD of the partial MD-space containing as many snapshots as members in the superfamily (average values for 100 windows), and SVD of the MD-space containing the entire MD trajectory. The domains in the x-axis are sorted by increasing number of aminoacids. b) Ratio of SF- and MD-space variances against the number residues in the reference domain. c) Ratio of SF- and MD-space variances against number of superfamily members (log scale).

Figure 3

Comparisons based on complexity. a) Vectors required to explain 90% of the variance for the performed decompositions: ISVD of the SF-space, SVD of the partial MD-space containing as many snapshots as members in the superfamily (average values for 100 windows), and SVD of the MD-space containing the entire MD trajectory. The domains in the x-axis are sorted by increasing number of superfamily members. b) Ratio of required vectors from SF- and MD-spaces to explain 90% of the variance against the number of superfamily members. c. Cumulative variance described by the SF singular vectors versus the size of the SF-space (normalized) and the number of SF-members. d. Cumulative variance described by the SF singular vectors versus the size of the SF-space (normalized) and number of aminoacids of the domain.

Figure 4

Coverage factors for the superfamily members (SF) in the essential MD-space, and coverage factors for the partial MD-space (MDp) in the essential MD-space. The x-axis is sorted by increasing number of members in the superfamily (the name of the reference member is written).

Figure 5

Comparisons based on space similarity. a) Hess metric applied using as many singular vectors as members in the superfamily. The x-axis is sorted by increasing number of members in the superfamily (the name of the reference member is written). b) Z-score of the Hess metric for a random model (See Methods for details). c) Z-score* of the Hess metric for a pseudo-random model (See Methods for details).

Figure 6

Examples of per residue B-factor and core quality of the reference domain against the aminoacid number in the core. The core quality q at a given core aminoacid is defined as the quotient of the number of times that this aminoacid has been structurally aligned and the number of superfamily members employed for the core. See Additional file 1. a) Example for superfamilies with low Hess index, H < 0.15. 1aps000. b) Example for superfamilies with n < 30 and H > 0.15. 1o08A01. c) Example for superfamilies with n > 30 and H > 0.25. 1b56000.

Figure 7

Structure and B-factor plot for 1a8h001 (red), the anticodon-binding domain of Methionyl-tRNA synthetase from Thermus thermophilus. According to MD, the loops depicted in green have high flexibility, with B-factors for MD higher than those obtained from superfamily information.

Figure 8

Structure and B-factor plot for 1fi2A00 (green), oxalate oxidase from Hordeum vulgare. The red region (aminoacids 174–184) is involved in forming dimers as part of the final hexamer that is the active complex. In this region the B-factors are higher for MD than for the superfamily alignment.

Figure 9

Example of structural alignment for a superfamily. All the domains are pairwise aligned against the reference domain. Purple discontinuous box: Domain excluded of the analysis because -ln(E) < 5. Red box: core of the alignment, composed by all the aminoacids of the reference domain aligned at least once and their correspondences. Blue box: Example of reference residue aligned with gaps (core quality: 1/6 = 17%). Green box: reference residue aligned without gaps (core quality: 6/6 = 100%). Black box: Reference residue that is not part of the core because there is not variation info for it (never aligned. Core quality 0/6 = 0%).

Figure 10

Example of coverage of the essential MD-space achieved by SF-space. The limits of the essential MD-space were determined by the smallest and largest projection values achieved during 10 ns trajectories (10000 structures, red). The essential MD-space was divided in 9 equivalent portions and coverage was evaluated as the number of portions of the essential MD-space visited by at least one superfamily structure (blue).