Coupling of Protein Motion to Electron Transfer in a Photosynthetic Reaction Center: Investigating the Low Temperature Behavior in the Framework of the Spin–Boson Model

1 The spin–boson model is applied to describe the coupling between protein motion and electron transfer for the primary electron transfer in the photosynthetic reaction center of Rps. viridis, a coupling which involves a very large number of degrees of freedom of the protein. For this purpose the relationship between the spectral function J(ω) characterizing the protein motion and the fluctuations of the protein contribution to the energy gap is derived. The relationship allows one to determine a suitable J(ω) from classical Molecular Dynamics simulations. Furthermore, we provide also an efficient numerical method to determine electron transfer rates in the framework of the spin–boson model. We also derive a high temperature approximation for the transfer rate which connects the spin–boson description with the well-known descriptions by Marcus and Hopfield. We determine then electron transfer rates both as a function of the redox energy difference and of temperature. The results show that for the system considered, the Marcus theory holds well at physiological temperatures. The low temperature behavior of the electron transfer rates is in qualitative agreement with observations in that electron transfer can accelerate with lowering the temperature, and that transfer rates can also slightly decrease with decreasing temperature.