On the calculation of binding free energies using continuum methods: Application to MHC class I protein-peptide interactions

Nicolas Froloff, Andreas Windemuth, Barry Honig
1997 Protein Science  
This paper describes a methodology to calculate the binding free energy (AG) of a protein-ligand complex using a continuum model of the solvent. A formal thermodynamic cycle is used to decompose the binding free energy into electrostatic and non-electrostatic contributions. In this cycle, the reactants are discharged in water, associated as purely nonpolar entities, and the final complex is then recharged. The total electrostatic free energies of the protein, the ligand, and the complex in
more » ... are calculated with the finite difference Poisson-Boltzmann (FDPB) method. The nonpolar (hydrophobic) binding free energy is calculated using a free energy-surface area relationship, with a single alkane/water surface tension coefficient (yaw). The loss in backbone and side-chain configurational entropy upon binding is estimated and added to the electrostatic and the nonpolar components of AG. The methodology is applied to the binding of the murine MHC class I protein H-2Kb with three distinct peptides, and to the human MHC class 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 (AAGexp) are quite small (<0.3 and <2.7 kcal/mol for the H-2Kb and HLA-A2 complexes, respectively). For each protein, the calculations are successful in reproducing a fairly small range of values for AAGCalc (<4.4 and <5.2 kcal/mol, respectively) although the relative peptide binding affinities of H-2Kb and HLA-A2 are not reproduced. For all protein-peptide complexes that were treated, it was found that electrostatic interactions oppose binding whereas nonpolar interactions drive complex formation. The two types of interactions appear to be correlated in that larger nonpolar contributions to binding are generally opposed by increased electrostatic contributions favoring dissociation. The factors that drive the binding of peptides to MHC proteins are discussed in light of our results. . Abbreviations and symbols: FDPB method, finite difference Poisson-Boltzmann method; MHC, Major Histocompatibility Complex; PDB, Brookhaven Protein Data Bank; RMS, root mean square; KD, equilibrium dissociation constant; AGexp. experimental binding free energy; AGb, theoretical binding free energy; AG"l" calculated binding free energy; AGc"l, Coulomb contribution to binding; AGwlv, reaction field (solvation) contribution to binding; Ace" electrostatic contribution to binding (sum of AGcou, and AGs"lv); AG." nonpolar (hydrophobic) contribution to binding; AG""" change in conformational free energy of both the receptor and the ligand upon binding; AS" and AS" loss of configurational entropy due to the freezing of backbone and side-chain torsional angles upon binding; A&, loss of translational and rotational degrees of freedom upon binding; A, solvent-accessible surface area; yaw, microscopic surface tension associated with the transfer of alkane from liquid alkane to water: E" dielectric constant of water; 6 , dielectric constant of macromolecular interior. 1293
doi:10.1002/pro.5560060617 pmid:9194189 pmcid:PMC2143728 fatcat:zs7oujejyraivp7odhfcp6umku