Simplicial edge representation of protein structures and alpha contact potential with confidence measure

Abstract

Protein representation and potential function are two important ingredients for studying protein folding, equilibrium thermodynamics, and sequence design. We introduce a novel geometric representation of protein contact interactions using the edge simplices from the alpha shape of the protein structure. This representation can eliminate implausible neighbors that are not in physical contact, and can avoid spurious contact between two residues when a third residue is between them. We developed statistical alpha contact potential using an odds-ratio model. A studentized bootstrap method was then introduced to assess the 95% confidence intervals for each of the 210 propensity parameters. We found, with confidence, that there is significant long-range propensity (>30 residues apart) for hydrophobic interactions. We tested alpha contact potential for native structure discrimination using several sets of decoy structures, and found that it often performs comparably with atom-based potentials requiring many more parameters. We also show that accurate geometric representation is important, and that alpha contact potential has better performance than potential defined by cutoff distance between geometric centers of side chains. Hierarchical clustering of alpha contact potentials reveals natural grouping of residues. To explore the relationship between shape and physicochemical representations, we tested the minimum alphabet size necessary for native structure discrimination. We found that there is no significant difference in performance of discrimination when alphabet size varies from 7 to 20, if geometry is represented accurately by alpha simplicial edges. This result suggests that the geometry of packing plays an important role, but the specific residue types are often interchangeable.

Empirical potential function for simplified protein models: Combining contact and local sequence–structure descriptors

“…Conversely, since the extractable information from a particular structure are limited by the representation, the consideration of descriptors always affect the choice of representation. Many new descriptors incorporating a variety of different types of information have been developed, such as atomic pair-wise contact calculated by alpha-shape method [15] or Voronoi tessellation [9], distance dependent contact instead of simple distance cut-off [7,12,72], contact order dependent contact [46], and secondary structure dependent contact [73]. We replaced the 210 contact descriptors by distance-dependent contact descriptors with several different distance intervals, but did not observe any noticeable improvement.…”

“…Despite the dramatic changes in sequence, the folding rates of the protein encoded by the reduced alphabet are very close to that of the naturally occurring SH3 domain [32]. Various reduced amino acid alphabets have been obtained previously based on the analysis of amino acid substitution matrix, contact propensity, or information theory [15,[32][33][34][35][36]. The resulting reduced amino acid alphabets are useful in protein folding studies and in identifying consensus sequences from multiple alignment [37,38].…”

“…Performance of CALSP on these decoy sets is listed in Table IV. We compare CALSP with three other residuebased potential functions, namely, TE13, LL [15], and MJ. Performance of CALSP in general is better or comparable to other potential functions.…”

Knowledge-Based Energy Functions for Computational Studies of Proteins

“…Another class of knowledge-based statistical potentials is based on the computation of various geometric constructs that reflect the shape of the protein molecules more accurately. These geometric constructs include the Voronoi diagram (McConkey et al, 2003), the Delaunay triangulation (Singh et al, 1996a;Zheng et al, 1997a;Carter Jr. et al, 2001;Krishnamoorthy and Tropsha, 2003), and the alpha shape (Li et al, 2003;Li and Liang, 2005b,a) of the protein molecules. Geometric potential functions has achieved significant successes in many fields.…”

“…See Section 4.6 for the url links to download several folding and docking decoy sets. A variety of knowledge-based potential functions have been developed and their performance in decoy discrimination have steadily improved (Zhou and Zhou, 2002;Lu and Skolnick, 2001;Li et al, 2003). Figure 4.5 shows an example of decoy discrimination on the 4-state-reduced decoy set.…”