Polarizability of the Active Site in Enzymatic Catalysis: Cytochrome c

Anisotropic polarizability of the heme in cytochrome c is found to be a major factor in suppressing the activation barrier of protein electron transfer (catalytic effect). Polarizability couples to the electric field of protein and water to enhance fluctuations of the electron-transfer energy gap and the corresponding variance reorganization energy λ^var. The reorganization energy observable by kinetic measurements λ^r = (λ^St)²/λ^var is composed of λ^var and the Stokes-shift reorganization energy λ^St. It is lowered compared to the usually reported λ^St due to polarizability of the active site leading to λ^var > λ^St. The coupling of electrostatic protein-water fluctuations to the polarizable active site is accounted for here by empirical valence-bond diagonalization of the active-site Hamiltonian along the simulation trajectory. We show that recent simulations employing this technique, which failed to find the effect of polarizability on electron-transfer kinetics, were erroneous in neglecting the diagonal dipole moments in the Hamiltonian matrix and failing to rotate the electric field produced by the protein-water medium into the molecular frame of the active site. We find that anisotropy of the tensor of polarizability difference in the two oxidation states of the heme matches anisotropy of the second-rank tensor constructed from the electric field at the active site. Exposure of the heme to water from only one side carries significant catalytic function, directly leading to the field anisotropy and the corresponding depression of the activation barrier.