(456h) Visualization and Characterization of Protein Conformational Space Via Geometric Techniques

Short Abstract For efficient protein structure modeling and analysis, it is important to understand the restricted nature of the protein local conformational space. Visualization of the conformational space has remained a challenge mainly due to the lack of unilateral descriptors of protein structures. Protein structure analysis has conventionally been based on pair-wise alignment of structures. We first map the local conformations in a fixed dimensional space by using a carefully selected suite of geometric invariants (GI's) as unilateral descriptors of structure. We then reduce the number of dimensions via principal component analysis (PCA). Of the four significant principal components (PC's), the first PC separates the extended structures from compact ones while the second PC separates the regular structures from the irregular ones. Note that the PCA methodology automatically computes the weights of GI's towards the PC's to provide maximum separation between the dominant structure forms-alpha-helices, beta-strands and loops-without the prior knowledge of these structure categories. Distribution of the conformations in the space spanned by the first four PC's is visualized in the form of conditional bi-variate probability distribution plots, where the peaks correspond to the preferred conformations. The peak corresponding to the alpha-helix structure is sharper and taller than that for the beta-strand. This agrees well with the known fact that the beta-strands have a greater tolerance for deviation from regularity than helices. Separate peaks are identifiable for the kinked-helix and several canonical loop structures. The locations of the different canonical structures in the PC-space have been interpreted in the context of the eigenvectors of the first four PC's. We find that the number of preferred local conformations is several orders of magnitude smaller than that suggested previously. These results will substantially reduce the search space in ab initio and homology based protein structure modeling. Further, this work provides a systematic framework for the analysis of protein structures using geometric invariant theory.

Long Abstract: Protein local conformations have conventionally been classified into alpha-helix, beta-strand and loop. Helix and strand are characterized by their regularity in their backbone torsion angles while loops can potentially occupy a vast conformational continuum. Ramchandran plot was the first step in demarcating the feasible and infeasible regions of conformational space even for loops(1). More recently, loops have been systematically classified based on structural similarity(2-6). Several of these loop classification methods begin by looking at the secondary structural elements that flank a loop on the two sides. Thus, the loops that join two beta-strands are classified separately from those that join an alpha-helix and a beta-strand. Regardless of the method of classification, loop classification has important implications in interpreting the electron density maps or in protein structure modeling (7, 8).

We have previously shown that the protein conformation space is biased in favor of a finite number of conformations(9). Here we present a visual map of the restricted protein local conformational space using geometric invariant theory. We have selected octapeptide as a unit of protein local conformation and represented each octapeptide with its C-alpha geometry(10). We have drawn approximately 1.7 million overlapping octapeptides from ASTRAL-95 dataset, version 1.67 (11). Each octapeptide is described with a suite of geometric invariants(9) followed by dimension reduction via Principal Component Analysis. Note that the closeness in the geometric invariant space guarantees that the two structures are superimposable without having to compute the superimposing transform(12). The conformational space is then visualized in the form of conditional bi-variate probability distribution plots, which contain peaks of varying size, corresponding to the different preferred conformations. The peak corresponding to alpha-helix is sharper and taller than that of beta-strand. A Separate peak is identifiable for the kinked helix and several others for loops. The octapeptide fragments were subjected to k-means clustering to detect clusters of similar geometry. The clusters and peaks in the conditional bivariate distribution plots share a one-to-one correspondence. We observe that the number of preferred local conformations is far less than that predicted previously.

It has been previously reported that the protein local conformation space is highly restricted; however, visualization of the conformational space has remained a challenge. Conventional methods of pairwise comparison and alignment of available protein structures are inadequate for the task of visualization of conformational space. Unilateral representation of the local conformations using geometric invariants followed by dimension reduction via principal component analysis allowed us to achieve the visualization. The conditional bivariate distribution plots provide a visual map of allowed and disallowed protein conformations.

The method presented here can have applications in protein structure prediction and validation. The current protein structure prediction algorithms search a vast protein conformational space using a computationally expensive energy minimization protocol. Visualizing the allowed and disallowed regions in the conformational space provides a useful method for eliminating the disallowed conformations with significant savings in computational time. Moreover, the peak size in the distribution is indicative of the likelihood of the structure occurring in a randomly selected natural protein. This can be useful in checking the integrity of both predicted and experimentally deduced structures.

References:

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