Dynamical Effects in Protein Electrochemistry

Electrochemical measurements of electron transfer from an electrode to proteins immobilized at protective layers of varying thickness have shown the presence of two characteristic regimes: (i) exponential (tunneling) decay of the rate constant with the distance to the electrode and (ii) a plateau region where the rate is independent of the distance to the electrode. The reaction in the plateau region is viewed as friction-controlled electron transfer, with the rate constant inversely proportional to the medium relaxation time. Fitting the rates to established theories requires medium relaxation times far exceeding common estimates and relaxation times obtained from computer simulations of the Stokes-shift dynamics. There is a significant disconnect between experimental observations and theoretical expectations. This difficulty is resolved here by allowing additional dissipative dynamics consisting of protein's low-frequency oscillations in a soft harmonic potential describing binding of the protein to the substrate. Protein translational motions modulate the electrode-protein electronic coupling, leading to a new time-scale appearing, along with the Stokes-shift relaxation time, in the pre-exponential factor of the rate constant. The new model provides a consistent account of the experimental data. The anticipated range of friction-controlled kinetics is significantly extended, since the effective relaxation time entering the rate pre-exponential factor gains an exponential dependence on the mean-square displacement of the protein. Since the mean-square displacement is proportional to temperature, the enthalpy of activation acquires a significant and nontrivial temperature dependence. The possibility of a negative reaction enthalpy is predicted.