title: Properties of contact matrices induced by pairwise interactions in proteins.
abstract: The properties of contact matrices ( C matrices) needed for native proteins to be the lowest-energy conformations are considered in relation to a contact energy matrix ( E matrix). The total conformational energy is assumed to consist of pairwise interaction energies between atoms or residues, each of which is expressed as a product of a conformation-dependent function (an element of the C matrix) and a sequence-dependent energy parameter (an element of the E matrix). Such pairwise interactions in proteins force native C matrices to be in a relationship as if the interactions are a Go-like potential [N. Go, Annu. Rev. Biophys. Bioeng. 12, 183 (1983)] for the native C matrix, because the lowest bound of the total energy function is equal to the total energy of the native conformation interacting in a Go-like pairwise potential. This relationship between C and E matrices corresponds to (a) a parallel relationship between the eigenvectors of the C and E matrices and a linear relationship between their eigenvalues and (b) a parallel relationship between a contact number vector and the principal eigenvectors of the C and E matrices, where the E matrix is expanded in a series of eigenspaces with an additional constant term. The additional constant term in the spectral expansion of the E matrix is indicated by the lowest bound of the total energy function to correspond to a threshold of contact energy that approximately separates native contacts from non-native ones. Inner products between the principal eigenvector of the C matrix, that of the E matrix, and a contact number vector have been examined for 182 proteins, each of which is a representative from each family of the SCOP database [Murzin, J. Mol. Biol. 247, 536 (1995)], and the results indicate the parallel tendencies between those vectors. A statistical contact potential [S. Miyazawa and R. L. Jernigan, Proteins 34, 49 (1999); S. Miyazawa and R. L. Jernigan, Proteins50, 35 (2003)] estimated from protein crystal structures was used to evaluate pairwise residue-residue interactions in the proteins. In addition, the spectral representation of C and E matrices reveals that pairwise residue-residue interactions, which depend only on the types of interacting amino acids, but not on other residues in a protein, are insufficient and other interactions including residue connectivities and steric hindrance are needed to make native structures unique lowest-energy conformations.
authors.affiliation: Graduate School of Engineering, Gunma University, Kiryu, Gunma 376-8515, Japan. miyazawa@smlab.sci.gunma-u.ac.jp
authors.forename: Sanzo
authors.initials: S
authors.lastname: Miyazawa
authors.forename: Akira R
authors.initials: AR
authors.lastname: Kinjo
mesh_terms: D000595:Amino Acid Sequence; D001665:Binding Sites; D003198:Computer Simulation; D008956:Models, Chemical; D008958:Models, Molecular; D008969:Molecular Sequence Data; D011485:Protein Binding; D011487:Protein Conformation; D025941:Protein Interaction Mapping / Q000379:methods*; D011506:Proteins / Q000737:chemistry* / Q000648:ultrastructure*; D020539:Sequence Analysis, Protein / Q000379:methods*
chemical_list: D011506:Proteins