Electrostatic contributions to protein-protein binding affinities: application to Rap/Raf interaction.

The challenge of evaluating absolute binding free energies of protein-protein complexes is addressed using the scaled Protein Dipoles Langevin Dipoles (PDLD/S) model in combination with the Linear Response Approximation (LRA). This is done by taking the complex between Rap1A (Rap) and the p21ras binding domain of c-Raf (Raf-RBD) (Nassar et al., Nature 375:554-560, 1995) as a model system. Several formulations and different thermodynamic cycles are explored taking advantage of the LRA method and considering the protein reorganization during complex formation. The performance of different approximations is examined by comparing the calculated and observed absolute binding energies for the native complex and some of its mutants. The evaluation of the contributions of individual residues to the binding free energy, which is referred to here as group contributions is also examined. Special attention is paid to the role of the "dielectric constant," epsilon(in) which is in fact a scaling factor that represents the contributions that are treated implicitly. It is found that explicit consideration of protein relaxation is crucial for obtaining reasonable results with small values of epsilon(in), but it is also found that such a treatment of protein-protein interactions is very challenging and does not always give stable results. This indicates that more advanced explicit calculations should be based on experimentally determined structures of both the complex and the isolated proteins. Nevertheless, it is demonstrated that the qualitative trend of the effect of mutations can be reproduced by considering the effect of protein reorganization implicitly, using epsilon(in) approximately 25 for ionized residues and epsilon(in) approximately 4 for polar residues. Thus, it is concluded that an explicit treatment of solvent relaxation (which is common to current continuum models) does not provide sufficient compensation for turning off the charges of ionized residues on the interaction surface of the Raf-RBD/Rap complex. Representing the missing contribution by large epsilon(in) can, of course, reproduce the observed effect of ionized residues, but now the contribution of uncharged residues will be largely underestimated. Regardless of these conceptual problems, it is established that a very simple nonrelaxed approach, where the relaxation of both the protein and the solvent are considered implicitly, can provide an effective qualitative way for evaluating group contributions, using large and small values for epsilon(in) of ionized and neutral residues, respectively. As much as the actual system studied is concerned we find that more residues than generally assumed play a role in Raf-RBD/Rap interaction. This includes residues that are not located at the protein-protein interaction surface. These residues contribute to the binding energy through direct charge-charge interaction without leading to drastic structural changes. The overall contribution of the surface residues is quite significant since Raf and Rap are positively and negatively charged, respectively, and their charges are distributed along the interaction site between the two proteins.