Dielectric relaxation in proteins: A continuum electrostatics model incorporating dielectric heterogeneity of the protein and time-dependent charges

A boundary element formulation of continuum electrostatics is used to exami ne time-independent dielectric relaxation and screening in two proteins, an d time-dependent relaxation in two simpler solutes. Cytochrome c oxidation is modeled by inserting partial charges on the heme, using one to three die lectric regions in the protein. It was suggested recently that for charge i nsertion on a protein-bound ligand, all or part of the ligand should be tre ated as a cavity within the protein medium. Here, the effect of an internal cavity surrounding the central heme atoms is examined, considering separat ely the static and relaxation (or reorganization) free energies. The former is the free energy to remove the redox electron while maintaining the rest of the structure and charge distribution fixed; the latter is the free ene rgy associated with the relaxation into the product state after the corresp onding constraints are released. The effect of the cavity is found to be sm all for the static free energy, while for the relaxation free energy it is large, as polarization of groups immediately around the heme dominates the relaxation. If the protein surface groups are treated as a distinct medium with a dielectric of 25 las suggested by recent molecular dynamics simulati ons), the relaxation free energy decreases significantly (from -37.0 to -43 .9 kcal/mol), compared to a model where the whole protein has a dielectric constant of two. Therefore, with this model, although polarization of group s immediately around the heme still dominates the relaxation, polar groups near the protein surface also contribute significantly, and solvent negligi bly. The screening of an applied field within myoglobin is calculated, with the protein surrounded by either a low-dielectric or a high-dielectric gla ss. In the vicinity of the CO ligand, the screening is approximately isotro pic with a low-dielectric glass. It is anisotropic with a high-dielectric g lass, but the applied and local fields are still approximately parallel. Th is has implications for experiments that probe dielectric screening in prot eins with the newly developed technique of vibrational Stark spectroscopy: with a high-dielectric glass, a single, rotationally averaged screening fac tor can be used, the local field being about 1.65 times the applied field. Finally, we calculate the time-dependent relaxation in response to instanta neous charge insertion within a spherical cavity in a Debye solvent, and to photoexcitation of a tryptophan solute, illustrating the extension of the boundary element formulation to time-dependent problems. (C) 2001 John Wile y & Sons, Inc.