ON THE CALCULATION OF BINDING FREE-ENERGIES USING CONTINUUM METHODS -APPLICATION TO MHC CLASS-I PROTEIN-PEPTIDE INTERACTIONS

This paper describes a methodology to calculate the binding free energ y (Delta G) of a protein-ligand complex using a continuum model of the solvent. A formal thermodynamic cycle is used to decompose the bindin g free energy into electrostatic and non-electrostatic contributions. In this cycle, the reactants are discharged in water, associated as pu rely nonpolar entities, and the final complex is then recharged. The t otal electrostatic free energies of the protein, the ligand, and the c omplex in water are calculated with the finite difference Poisson-Bolt zmann (FDPB) method. The nonpolar (hydrophobic) binding free energy is calculated using a free energy-surface area relationship, with a sing le alkane/water surface tension coefficient (gamma(aw)). The loss in b ackbone and side-chain configurational entropy upon binding is estimat ed and added to the electrostatic and the nonpolar components of Delta G. The methodology is applied to the binding of the murine MHC class I protein H-2K(b) with three distinct peptides, and to the human MHC c lass I protein HLA-A2 in complex with five different peptides. Despite significant differences in the amino acid sequences of the different peptides, the experimental binding free energy differences (Delta Delt a G(exp)) are quite small (<0.3 and <2.7 kcal/mol for the H-2K(b) and HLA-A2 complexes, respectively). For each protein, the calculations ar e successful in reproducing a fairly small range of values for Delta D elta G(calc) (<4.4 and <5.2 kcal/mol, respectively) although the relat ive peptide binding affinities of K-2K(b) and HLA-A2 are not reproduce d. For all protein-peptide complexes that were treated, it was found t hat electrostatic interactions oppose binding whereas nonpolar interac tions drive complex formation. The two types of interactions appear to be correlated in that larger nonpolar contributions to binding are ge nerally opposed by increased electrostatic contributions favoring diss ociation. The factors that drive the binding of peptides to MHC protei ns are discussed in light of our results.