A Poisson-Boltzmann study of charge insertion in an enzyme active site: The effect of dielectric relaxation

Continuum solvent models are playing an increasing role in the study of aqueous solutions, particularly those involving protein solutes. To estimate the magnitude of dielectric relaxation and clarify the microscopic meaning of the protein dielectric constant, charge insertion in the active site of the enzyme aspartyl-tRNA synthetase (AspRS) is analyzed using finite-difference Poisson-Boltzmann calculations. The insertion process is a simplified model that mimics qualitatively the mutation of substrate Asp into Asn, studied earlier by free; energy simulations. A two-step insertion path gives the relaxation and nonrelaxation ("static") free energy components separately. The assumption of linear response leads to a linear relation between the two components, connecting the explicit structural differences between reactant and product structures with the relaxation free energy calculated from either structure. This relation is verified here only if protein dielectric constants of 1 and 4-8 are used for the static and relaxation free energies, respectively. These are also the only conditions that give reasonable agreement with the Asp --> Asn free energy simulated earlier and with a molecular dynamics/linear response estimate of the present charging free energy. The use of two protein dielectric constants represents a significant departure from standard continuum models. The values obtained are physically reasonable: a protein dielectric of 4-8 for relaxation indicates that the active site of AspRS, though highly polar, is only moderately polarizable. A dielectric of one for the static term indicates that the charge set, optimized for explicit solvent simulations, reproduces the equilibrium potential without the need for additional, implicit protein polarization. In contrast to simple charge insertion, the binding free energies of Asp and Asn to AspRS are best calculated with a more standard protocol that uses a single protein dielectric of 4, accurately reproducing free energy simulation results. For this and other binding processes, additional fi ee energy components are involved, related to desolvation of the binding site; the optimal dielectric constant represents an empirical compromise among these. A multistep component analysis could also be used to analyze the role of relaxation in these more complex processes. It is suggested that the use of more than one dielectric constant in continuum models will lead to a more consistent and robust description of dielectric phenomena in solution.