Estimation of effective interresidue contact energies from protein crystal structures: quasi-chemical approximation

ABSTRACT: Effective interresidue contact energies for proteins in solution are estimated from the numbers of residue-residue contacts observed in crystal structures of globular proteins by means of the quasi-chemical approximation with an approximate treatment of the effects of chain connectivity. Employing a lattice model, each residue of a protein is assumed to occupy a site in a lattice and vacant sites are regarded to be occupied by an effective solvent molecule whose size is equal to the average size of a residue. A basic assumption is that the average characteristics of residue-residue contacts formed in a large number of protein crystal structures reflcct actual differences of interactions among residues, as if there were no significant contribution from the specific amino acid sequence in each protein as well as intraresidue and short-range interactions. Then, taking account of the effects of the chain connectivity only as imposing a limit to the size of the system, Le., the number of lattice sites or the number of effective solvent molecules in the system, the system is regarded to be the mixture of unconnected residues and effective solvent molecules. The quasi-chemical approximation, that contact pair formation resembles a chemical reaction, is applied to this system to obtain formulas that relate the statistical averages of the numbers of contacts to the contact energies. The number of effective solvent molecules for each protein is chosen to yield the total number of residue-residue contacts equal to its expected value for the hypothetical case of hard sphere interactions among residues and effective solvent