DERIVATION AND TESTING OF PAIR POTENTIALS FOR PROTEIN-FOLDING - WHEN IS THE QUASI-CHEMICAL APPROXIMATION CORRECT

Many existing derivations of knowledge-based statistical pair potentia ls invoke the quasichemical approximation to estimate the expected sid e-chain contact frequency if there were no amino acid pair-specific in teractions. At first glance, the quasichemical approximation that trea ts the residues in a protein as being disconnected and expresses the s ide-chain contact probability as being proportional to the product of the mole fractions of the pair of residues would appear to be rather s evere. To investigate the validity of this approximation, we introduce two new reference states in which no specific pair interactions betwe en amino acids are allowed, but in which the connectivity of the prote in chain is retained, The first estimates the expected number of side- chain contacts by treating the protein as a Gaussian random coil polym er. The second, more realistic reference state includes the effects of chain connectivity, secondary structure, and chain compactness by est imating the expected side-chain contact probability by placing the seq uence of interest in each member of a library of structures of compara ble compactness to the native conformation. The side-chain contact map s are not allowed to readjust to the sequence of interest, i.e., the s ide chains cannot repack. This situation would hold rigorously if all amino acids were the same size. Both reference states effectively perm it the factorization of the side-chain contact probability into sequen ce-dependent and structure-dependent terms. Then, because the sequence distribution of amino acids in proteins is random, the quasichemical approximation to each of these reference states is shown to be excelle nt. Thus, the range of validity of the quasichemical approximation is determined by the magnitude of the side-chain repacking term, which is , at present, unknown. Finally, the performance of these two sets of p air interaction potentials as well as side-chain contact fraction-base d interaction scales is assessed by inverse folding tests both without and with allowing for gaps.