Protein dynamics modulated electron transfer kinetics in early stage photosynthesis.

A recent experiment has probed the electron transfer kinetics in the early stage of photosynthesis in Rhodobacter sphaeroides for the reaction center of wild type and different mutants [Science 316, 747 (2007)]. By monitoring the changes in the transient absorption of the donor-acceptor pair at 280 and 930 nm, both of which show non-exponential temporal decay, the experiment has provided a strong evidence that the initial electron transfer kinetics is modulated by the dynamics of protein backbone. In this work, we present a model where the electron transfer kinetics of the donor-acceptor pair is described along the reaction coordinate associated with the distance fluctuations in a protein backbone. The stochastic evolution of the reaction coordinate is described in terms of a non-Markovian generalized Langevin equation with a memory kernel and Gaussian colored noise, both of which are completely described in terms of the microscopics of the protein normal modes. This model provides excellent fits to the transient absorption signals at 280 and 930 nm associated with protein distance fluctuations and protein dynamics modulated electron transfer reaction, respectively. In contrast to previous models, the present work explains the microscopic origins of the non-exponential decay of the transient absorption curve at 280 nm in terms of multiple time scales of relaxation of the protein normal modes. Dynamic disorder in the reaction pathway due to protein conformational fluctuations which occur on time scales slower than or comparable to the electron transfer kinetics explains the microscopic origin of the non-exponential nature of the transient absorption decay at 930 nm. The theoretical estimates for the relative driving force for five different mutants are in close agreement with the experimental estimates obtained using electrochemical measurements.