Calculation of redox properties: understanding short- and long-range effects in rubredoxin

In this computational study we show that for rubredoxin, a small and comparatively simple iron-sulfur protein, it is possible to combine a full ab initio description of the electronic structure of the protein in explicit solvent with sampling of the relevant time scale of the protein dynamics by using a hybrid method based on a force field molecular dynamics/density functional theory scheme. Applying this scheme within the framework of Marcus theory we are able to reproduce the experimental redox potential difference of 60 mV between a mesophilic and thermophilic rubredoxin within an accuracy of 20 mV and explain it in terms of short-range contributions from a few residues close to the metal center. We also compute the reorganization free energy for oxidation of the protein obtaining 720 meV for the mesophilic and 590 meV for thermophilic variant. Decomposition of the reorganization energy by using the classical force field shows that this quantity is largely determined by the solvent, with both short-range (an oxidation induced change of coordination number) and long-range (dielectric) contributions. The 130 meV higher value for the mesophilic form is analyzed in terms of detailed differences in the solvent structure around the metal center and the dielectric response. These results underline the importance of a molecular description of the solvent and of a correct inclusion of the polarization effects.