In response to charge separation or transfer, polar liquids respond in a simple linear fashion. A similar linear response for proteins might be expected from the central limit theorem and is postulated in widely used theories of protein electrostatics, including the Marcus electron transfer theory and dielectric continuum theories. Although these theories are supported by a variety of experimental data, the exact validity of a linear protein dielectric response has been difficult to determine. Molecular dynamics simulations are presented that establish a linear dielectric response of both protein and surrounding solvent over the course of a biologically relevant electron transfer reaction: oxido-reduction of yeast cytochrome c in solution. Using an umbrella-sampling free energy approach with long simulations, an accurate treatment of long-range electrostatics and both classical and quantum models of the heme, good agreement is obtained with experiment for the redox potential relative to a heme-octapeptide complex. We obtain a reorganization free energy that is only half that for heme-octapeptide and is reproduced with a dielectric continuum model where the heme vicinity has a dielectric constant of only 1.1. This value implies that the contribution of protein reorganization to the electron transfer free energy barrier is reduced almost to the theoretical limit (a dielectric of one), and that the fluctuations of the electrostatic potential on the heme have a simple harmonic form, in accord with Marcus theory, even though the fluctuations of many individual protein groups (especially at the protein surface) are anharmonic.
Chemical events in proteins often involve charge separation or transfer: enzyme reactions, photoexcitation of bound chromophores, proton binding and release, and electron transfer (1, 2). In response to such an event, the protein and solvent undergo dielectric relaxation, or reorganization, in the form of electronic polarization and displacement of atomic groups. Thus, enzyme reaction rates and driving forces are sensitive to the dielectric properties of the active site (3). An important goal in biophysics is to find models that can describe the dielectric properties of proteins (3-7). In the case of small molecules in aqueous solution, simple behavior is observed: the reorganization of the solvent is approximately a linear function of the solute charge rearrangement (8)(9)(10)(11)(12). This is consistent with simple models, like the dielectric continuum model (4, 13), or a model where the solvent fluctuations are assumed to be gaussian (14-16).Proteins are much more complex. They are heterogeneous polymers, and fluctuations around their folded structure are governed by an anharmonic, rugged energy surface (17, 18). The average polarity and flexibility of a folded protein are much lower than those of water, so the dielectric properties vary strongly across the protein-solvent interface. Recent experimental studies have used spectroscopic probes (19-23) whose optical absorption and emission are s...