Self-consistent estimation of inter-residue protein contact energies basedon an equilibrium mixture approximation of residues

Pairwise contact energies for 20 types of residues are estimated self-consi stently from the actual observed frequencies of contacts with regression co efficients that are obtained by comparing "input" and predicted values with the Bathe approximation for the equilibrium mixtures of residues interacti ng. This is premised on the fact that correlations between the "input" and the predicted values are sufficiently high although the regression coeffici ents themselves can depend to some extent on protein structures as well as interaction strengths. Residue coordination numbers are optimized to obtain the best correlation between "input" and predicted values for the partitio n energies. The contact energies self-consistently estimated this way indic ate that the partition energies predicted with the Bethe approximation shou ld be reduced by a factor of about 0.3 and the intrinsic pairwise energies by a factor of about 0.6. The observed distribution of contacts can be appr oximated with a small relative error of only about 0.08 as an equilibrium m ixture of residues, if many proteins were employed to collect more than 20, 000 contacts. Including repulsive packing interactions and secondary struct ure interactions further reduces the relative errors. These new contact ene rgies are demonstrated by threading to have improved their ability to discr iminate native structures from other non-native folds. (C) 1999 Wiley-Liss, Inc.