Molecular dynamics simulation of electron transfer in proteins. Theory and application to Q_A → Q_B transfer in the photosynthetic reaction center

Electron transfer (ET) from the primary menaquinone Q_A to the secondary ubiquinone Q_B, i.e., Q_A^-Q_B → Q_AQ_B^-, in the photosynthetic reaction center of Rhodopseudomonas viridis has been simulated by using the method of molecular dynamics accounting for the classical motion of a protein's nuclear degrees of freedom, the redistribution of charge accompanying electron transfer being described quantum chemically. We outline the role of classical nuclear degrees of freedom in electron transfer, identifying the essential dynamic properties that should be determined from molecular dynamics simulations in order to characterize electron transfer. These quantities, all related to the energy difference ΔE(t) = E_P(t) - E_R(t) of virtual forward (electron tries to jump forward before ET) and backward (electron tries to jump backward after ET) electron transfer, R and P denoting the states Q_A^-Q_B and Q_AQ_B^-, respectively, are as follows: the variance of ΔE(t) and the average value of ΔE(t) before and after transfer, i.e., Σ_R (6.9 kcal/mol), 〈ΔE〉_R (22 kcal/mol) and Σ_P (8.8 kcal/mol), 〈ΔE〉_P (-25 kcal/mol), respectively; the relaxation time of the energy-energy correlation function 〈(ΔE(t) - 〈ΔE〉_R)(ΔE(0) - 〈ΔE〉_R)〉_R (120 fs); the time describing the relaxation of ΔE(t) from an average value 〈ΔE〉_R to an average value 〈ΔE〉_P immediately after electron transfer (200 fs). The quantities in brackets are the respective simulation results. We determined also the free enthalpy difference of the transfer Q_A^-Q_B → Q_AQ_B^- (-3.4 kcal/mol). Our simulations indicate that the motion of the non-heme iron of the reaction center is not coupled to the Q_A^-Q_B → Q_AQ_B^- transfer. Interaction energies of Q_B in different charge states with the protein environment have been calculated and reflect a stronger binding of Q_B^- and Q_B^2- compared to that of Q_B.