Internal and interfacial dielectric properties of cytochrome c from molecular dynamics in aqueous solution

The dielectric properties of proteins are central to their stability and activity. We use the Fröhlich-Kirkwood theory of dielectrics to analyze two 1-ns molecular dynamics simulations of ferro- and ferricytochrome c in spherical droplets of 1400 water molecules. Protein and solvent are idealized as a series of concentric, spherical, dielectric media. Analysis results depend strongly on the treatment of the charged protein side chains at the protein/solvent interface. If charged side chains are viewed as part of the protein medium, then the protein dipole fluctuations are dominated by large, mutually uncorrelated, anisotropic, motions of the charged side chains. It is then incorrect to view the protein region as a single, homogeneous dielectric material. If one does take this view, estimates of the protein "dielectric constant" vary from 16 to 37, depending on the exact choice of model parameters. In contrast, if the charged portions of the charged side chains are viewed as part of the solvent medium, then theory and simulation are consistent: the protein dipole fluctuations excluding charged side chains are roughly those of a homogeneous, isotropic dielectric medium, with a dielectric constant of 4.7 +/- 1.0 (ferro) or 3.4 +/- 1.0 (ferri), in agreement with powder experiments. Statistical uncertainty and sensitivity to model parameters are small. Analysis of the radial dependence of the dipole fluctuations suggests that the inner half of the protein has a somewhat lower dielectric constant of 1.5-2, consistent with its biological function in electron transfer. These results suggest that Poisson-Boltzmann models could treat the protein bulk as a low-dielectric medium and the charged surface groups as part of the solvent region.