Microscopic Dielectric Properties of Cytochrome c from Molecular Dynamics Simulations in Aqueous Solution

The dielectric properties of proteins play an important role in biological charge transfer and catalysis. We investigate microscopic charge screening by the electron transfer protein cytochrome c in solution, using linear response and thermodynamic perturbation theory. Electronic relaxation is described using atomic point polarizabilities. Dipolar relaxation is described using a 1 ns molecular dynamics simulation of the protein in solution. Dielectric relaxation in response to perturbing charges is calculated from simulations of a single, unperturbed, reference state. This technique allows us to study the microscopic dielectric properties throughout the entire protein interior using a single simulation. We calculate relaxation free energies in response to a single test charge, located successively on each C_α of the protein backbone. For small test charges, these energies are given by the variance of the reference electrostatic potential at the test charge site. Protein and solvent contributions are nearly equal, and the total relaxation free energy is much smaller than either, due to protein–solvent coupling. The fluctuations of the reference electrostatic potential are approximately Gaussian, leading to a nearly linear dielectric response for perturbing charge magnitudes of ≤ e/4 and relaxation free energies of ≤4 kcal/mol. The electronic contribution to the relaxation free energies is spatially homogeneous and can be fit by a continuum model, with a dielectric constant of 2. The dipolar contribution is 1.5–2 times larger, is less homogeneous, and is fit only moderately well by a continuum model, with a dielectric constant of 4. The relaxation free energies increase smoothly by a factor of 2 when the test charge is moved from the protein center to its surface. The heme center is in a region where the relaxation is minimal. This correlates directly with the biological requirement to reduce the reorganization free energy for electron transfer to and from the heme.