Photosynthetic Electron Transfer Controlled by Protein Relaxation: Analysis by Langevin Stochastic Approach

Abstract

Relaxation processes in proteins range in time from picoseconds to seconds. Correspondingly, biological electron transfer (ET) could be controlled by slow protein relaxation. We used the Langevin stochastic approach to describe this type of ET dynamics. Two different types of kinetic behavior were revealed, namely: oscillating ET (that could occur at picoseconds) and monotonically relaxing ET. On a longer time scale, the ET dynamics can include two different kinetic components. The faster one reflects the initial, nonadiabatic ET, whereas the slower one is governed by the medium relaxation. We derived a simple relation between the relative extents of these components, the change in the free energy ( ΔG), and the energy of the slow reorganization Λ. The rate of ET was found to be determined by slow relaxation at −Δ G ≤ Λ. The application of the developed approach to experimental data on ET in the bacterial photosynthetic reaction centers allowed a quantitative description of the oscillating features in the primary charge separation and yielded values of Λ for the slower low-exothermic ET reactions. In all cases but one, the obtained estimates of Λ varied in the range of 70–100 meV. Because the vast majority of the biological ET reactions are only slightly exothermic (Δ G ≥ −100 meV), the relaxationally controlled ET is likely to prevail in proteins.