The Effect of Protein Relaxation on Charge-Charge Interactions and Dielectric Constants of Proteins

The effect of the reorganization of the protein polar groups on charge-charge interaction and the corresponding effective dielectric constant (∈ eff) is examined by the semimicroscopic version of the Protein Dipole Langevin Dipoles (PDLD/S) method within the framework of the Linear Response Approximation (LRA). This is done by evaluating the interactions between ionized residues in the reaction center of Rhodobacter sphaeroides, while taking into account the protein reorganization energy. It is found that an explicit consideration of the protein relaxation leads to a significant increase in ∈ eff and that semimicroscopic models that do not take this relaxation into account force one to use a large value for the so-called “protein dielectric constant,” ∈ p, of the Poisson-Boltzmann model or for the corresponding ∈ in in the PDLD/S model. An additional increase in ∈ eff is expected from the reorganization of ionized residues and from changes in the degree of water penetration. This finding provides further support for the idea that ∈ in (or ∈ p) represents contributions that are not considered explicitly. The present study also provides a systematic illustration of the nature of ∈ eff, supporting our previously reported view that charge-charge interactions correspond to a large value of this “dielectric constant,” even in protein interiors. It is also pointed out that ∈ eff for the interaction between ionizable groups in proteins is very different from the effective dielectric constant, ∈′ eff, that determines the free energy of ion pairs in proteins (∈′ eff reflects the effect of preoriented protein dipoles). Finally, the problems associated with the search for a general ∈ in are discussed. It is clarified that the ∈ in that reproduces the effect of protein relaxation on charge-charge interaction is not equal to the ∈ in that reproduces the corresponding effect upon formation of individual charges. This reflects fundamental inconsistencies in attempts to cast microscopic concepts in a macroscopic model. Thus one should either use a large ∈ in for charge-charge interactions and a small ∈ in for charge-dipole interactions or consider the protein relaxation microscopically.