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. 2009 May 1;75(2):453-67.
doi: 10.1002/prot.22256.

Shape complementarity of protein-protein complexes at multiple resolutions

Qing Zhang  1 , Michel Sanner, Arthur J Olson
Affiliations

Shape complementarity of protein-protein complexes at multiple resolutions

Qing Zhang et al. Proteins. .

Abstract

Biological complexes typically exhibit intermolecular interfaces of high shape complementarity. Many computational docking approaches use this surface complementarity as a guide in the search for predicting the structures of protein-protein complexes. Proteins often undergo conformational changes to create a highly complementary interface when associating. These conformational changes are a major cause of failure for automated docking procedures when predicting binding modes between proteins using their unbound conformations. Low resolution surfaces in which high frequency geometric details are omitted have been used to address this problem. These smoothed, or blurred, surfaces are expected to minimize the differences between free and bound structures, especially those that are due to side chain conformations or small backbone deviations. Despite the fact that this approach has been used in many docking protocols, there has yet to be a systematic study of the effects of such surface smoothing on the shape complementarity of the resulting interfaces. Here we investigate this question by computing shape complementarity of a set of 66 protein-protein complexes represented by multiresolution blurred surfaces. Complexed and unbound structures are available for these protein-protein complexes. They are a subset of complexes from a nonredundant docking benchmark selected for rigidity (i.e. the proteins undergo limited conformational changes between their bound and unbound states). In this work, we construct the surfaces by isocontouring a density map obtained by accumulating the densities of Gaussian functions placed at all atom centers of the molecule. The smoothness or resolution is specified by a Gaussian fall-off coefficient, termed "blobbyness." Shape complementarity is quantified using a histogram of the shortest distances between two proteins' surface mesh vertices for both the crystallographic complexes and the complexes built using the protein structures in their unbound conformation. The histograms calculated for the bound complex structures demonstrate that medium resolution smoothing (blobbyness = -0.9) can reproduce about 88% of the shape complementarity of atomic resolution surfaces. Complexes formed from the free component structures show a partial loss of shape complementarity (more overlaps and gaps) with the atomic resolution surfaces. For surfaces smoothed to low resolution (blobbyness = -0.3), we find more consistency of shape complementarity between the complexed and free cases. To further reduce bad contacts without significantly impacting the good contacts we introduce another blurred surface, in which the Gaussian densities of flexible atoms are reduced. From these results we discuss the use of shape complementarity in protein-protein docking.

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Figures

Figure 1
Figure 1
Comparison of shape functions: Gaussian density functions with blobbyness = −0.10, −0.50, −1.50, and hard sphere density function. The values of the shape functions are plotted on a one-dimension coordinate between −5.0 and 5.0 Å for simplicity. Top: Shape functions of a single atom that has a radius of 1.0 Å and is located at coordinate 0.0. Bottom: Shape functions of two close atoms that have the same radius of 1.0 Å and are located at coordinate 0.0 and 3.0, respectively.
Figure 2
Figure 2
Isocontouring value (mean and standard deviation) as a function of blobbyness based on all the molecules in the protein-protein complexes used in this work. An isocontouring value is optimized to reproduce the molecular surface volume of a protein.
Figure 3
Figure 3
A protein molecule represented as Blur surfaces at blobbyness −0.1 (a), −0.3 (b), −0.5 (c), −0.9 (d), and −3.0 (e) as well as a molecular surface (f).
Figure 4
Figure 4
Illustration of FlexBlur surface building. A molecule's crystal structure is shown in ball-and-stick render and colored by (a) atom types, (b) constraints with red for strong constraints and blue for weak constraints, and (c) weights with red for weight 1.0 and blue for weight<1.0. (d) Comparison between a FlexBlur surface in red and a Blur surface as blue mesh (both at blobbyness −0.9).
Figure 5
Figure 5
Histograms of interface distances based on the molecular surfaces of all bound-bound complexes of Rigid Group (top) and Slightly Flexible Group (bottom).
Figure 6
Figure 6
Sources of interface overlaps based on the molecular surfaces of all bound-bound complexes of Rigid Group.
Figure 7
Figure 7
Histograms of interface distances based on the Blur surfaces of Rigid Group bound-bound complexes at blobbyness −0.1 (a), −0.3 (b), −0.9 (c), and −3.0 (d).
Figure 8
Figure 8
Partial interface between an enzyme (red) and its inhibitor (blue) represented using different surfaces. (a) Molecular surfaces (white mesh) vs. Blur surface at blobbyness −3.0 (red and blue transparent surfaces). (b) Blur surfaces at blobbyness −3.0 (red and blue transparent surfaces) vs. −0.9 (white mesh). (c) Blur surfaces at −0.9 (red and blue transparent surfaces) vs. −0.3 (white mesh).
Figure 9
Figure 9
Ratio of total interface vertex pairs between the Blur surface and the molecular surface as a function of blobbyness. The interface pairs are from all the bound-bound complexes in Rigid Group.
Figure 10
Figure 10
Ratio of total interface overlaps between the Blur surface and the molecular surface as a function of blobbyness. The interface overlaps are from all the bound-bound complexes in Rigid Group.
Figure 11
Figure 11
Interface distance histograms of Rigid Group and Slightly Flexible Group. The histograms are based on the molecular surfaces of the bound-bound complexes (a-b; the former for Rigid Group and the latter for Slightly Flexible Group), the molecular surfaces of the unbound-unbound complexes (c-d), the Blur surfaces at blobbyness −0.3 of the unbound-unbound complexes (e-f), and the FlexBlur surfaces at blobbyness −0.9 of the unbound-unbound complexes (g-h).
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