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

Abstract

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 water 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. 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. KeywordsThe accurate calculation of ligand-protein binding free energies is a difficult problem for which no general solution has been forthcoming. Molecular dynamics simulations including the explicit treatment of solvent molecules have encountered a number of striking successes (see, e.g., Bash et al

Poisson–Boltzmann model analysis of binding mRNA cap analogues to the translation initiation factor eIF4E

“…It should be noted that the uncertainty in the estimated non-electrostatic terms may be quite substantial, although it is difficult to provide their accurate estimate. For computation of non-electrostatic terms we adapted methods described by Honig and coworkers [39,10] and by Beveridge and coworkers [40]. Both groups have found that the estimated total free energies of binding were overestimated.…”

“…(2) describes the electrostatic effects on binding affinity, within approximation of a single (macro)molecular conformation fixed in a given protonation state. PB calculations usually show that the electrostatic contribution to binding is unfavourable due to the large desolvation penalty of charged and polar groups which is not sufficiently compensated by the direct charge-charge interactions at the protein-ligand interface [1,10,11,12,13]. The unfavourable electrostatic contribution to the free energy of binding is usually obtained when the dielectric boundary is specified as the solvent exclusion (SE) surface along with solute dielectric constant in the range of about 2 to 4.…”

“…Additional contributions to the binding free energy were estimated using a method described elsewhere [10]. The equation for ∆G bind used in this report is as follows:…”

“…The side chain term in Eq. (6) was estimated following [10], where an average value of 2 kcal/mole had been ascribed to every residue buried in the interface between the interacting molecules.…”

“…(3), ∆G strain and −T ∆S t,r , give positive contributions to the total free energy of association. The upper limit for ∆G strain is 10 kcal/mole, which is the free energy of folding of a typical protein [10]. To calculate the −T ∆S t,r , the range of residual motion in the complex must be known.…”