Statistical significance of hierarchical multi‐body potentials based on Delaunay tessellation and their application in sequence‐structure alignment

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Abstract
Statistical potentials based on pairwise interactions between Cα atoms are commonly used in protein threading/fold‐recognition attempts. Inclusion of higher order interaction is a possible means of improving the specificity of these potentials. Delaunay tessellation of the Cα‐atom representation of protein structure has been suggested as a means of defining multi‐body interactions.A large number of parameters are required to define all four‐body interactions of 20 amino acid types (204 = 160,000). Assuming that residue order within a four‐body contact is irrelevant reduces this to a manageable 8,855 parameters, using a nonredundant dataset of 608 protein structures.Three lines of evidence support the significance and utility of the four‐body potential for sequence‐structure matching. First, compared to the four‐body model, all lower‐order interaction models (three‐body, two‐body, one‐body) are found statistically inadequate to explain the frequency distribution of residue contacts.Second, coherent patterns of interaction are seen in a graphic presentation of the four‐body potential. Many patterns have plausible biophysical explanations and are consistent across sets of residues sharing certain properties (e.g., size, hydrophobicity, or charge).Third, the utility of the multi‐body potential is tested on a test set of 12 same‐length pairs of proteins of known structure for two protocols: Sequence‐recognizes‐structure, where a query sequence is threaded (without gap) through the native and a non‐native structure; and structure‐recognizes‐sequence, where a query structure is threaded by its native and another non‐native sequence. Using cross‐validated training, protein sequences correctly recognized their native structure in all 24 cases. Conversely, structures recognized the native sequence in 23 of 24 cases. Further, the score differences between correct and decoy structures increased significantly using the three‐ or four‐body potential compared to potentials of lower order.