UNIQUNESS OF THE ALGEBRE OF POLYNOMIAL FUNCTIONS ON A FINITE GROUP

Article信州大学教養部紀要. 第二部, 自然科学 9: 7-10(1975)departmental bulletin pape

A Note on the Dimension Subgroups

Article信州大学教養部紀要. 第二部, 自然科学 8: 1-4(1974)departmental bulletin pape

COCLEFT MODULE COALGEBRAS FOR A BIALGEBRA

Article信州大学教養部紀要. 第一部, 人文科学. 第二部, 自然科学 21: 143-150(1987)departmental bulletin pape

ON THE CORRESPONDENCE OF GROUP EXTENSIONS WITH THE SECOND COHOMOLOGY CLASSES

Article信州大学教養部紀要. 第二部, 自然科学 11: 73-76(1977)departmental bulletin pape

ON THE GROUP ISOMORPHISM OF E(C,A) WITH H¹(G,HOM_K(C,A))

Article信州大学教養部紀要. 第二部, 自然科学 9: 1-5(1975)departmental bulletin pape

Further examples of cocleft module coalgebras

Article信州大学教養部紀要. 第一部, 人文科学. 第二部, 自然科学 22: 203-206(1988)departmental bulletin pape

Properties of contact matrices induced by pairwise interactions in proteins

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 a contact matrix, C-matrix) and a sequence-dependent energy parameter (an element of a contact energy matrix, 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; the E-matrix is expanded in a series of eigenspaces with an additional constant term, which corresponds to a threshold of contact energy that approximately separates native contacts from non-native ones. These relationships are confirmed in 182 representatives from each family of the SCOP database by examining inner products between the principal eigenvector of the C-matrix, that of the E-matrix evaluated with a statistical contact potential, and a contact number vector. In addition, the spectral representation of C- and E-matrices reveals that pairwise residue-residue interactions, which depends 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 the unique lowest energy conformations.Comment: Errata in DOI:10.1103/PhysRevE.77.051910 has been corrected in the present versio