Modeling implicit reorganization in continuum descriptions of protein-protein interactions

The determination of free energies that govern protein-protein recognition is essential for a detailed molecular understanding of biological specificity. Continuum models of macromolecular interactions, in which the solvent is treated by an implicit representation and the proteins are treated semi-microscopically, are computationally tractable for estimating free energies, yet many questions remain concerning their accuracy. This article reports a continuum analysis of the free-energy changes underlying the binding of 31 interfacial alanine substitutions of two complexes of the antihen egg white lysozyme (HEL) antibody D1.3 bound with HEL or the antibody E5.2. Two implicit schemes for modeling the effects of protein and solvent relaxation were examined, in which the protein environment was treated as either homogeneous with a "protein dielectric constant" of epsilon(p) = 4 or inhomogeneous, with epsilon(p) = 4 for neutral residues and epsilon(p) = 25 for ionized residues. The results showed that the nonuniform dielectric model reproduced the experimental differences better, with an average absolute error of +/-1.1 kcal/mol, compared with +/-1.4 kcal/mol for the uniform model. More importantly, the error for charged residues in the nonuniform model is +/-0.8 kcal/mol and is nearly half of that corresponding to the uniform model. Several substitutions were clearly problematic in determining qualitative trends and probably required explicit structural reorganization at the protein-protein interface.