The balance between primary forward and back reactions in bacterial photosynthesis

The temperature dependence of the bacteriochlorophyll fluorescence and reaction center triplet yield in while cells of Rhodopseudomonas sphaeroides strain 2.4.1 and of the magnetic field-induced fluorescence increase are calculated, taking into account rate constants of losses in the antenna system and of charge separation and recombination in the reaction center. Triplet and singlet yield after recombination in the reaction center are described by the radical pair mechanism. Good fits of the theoretically calculated temperature dependence with published experimental results could be obtained, assuming that ks, the rate constant for recombination of the charges on the primary donor P+ and the reduced intermediate acceptor I- to the lowest excited singlet state P*I of the reaction center bacteriochlorophyll, is temperature-dependent via the Boltzmann factor Kso exp(-delta E/kT), where delta E is the energy difference between P*I and P+I- and kso is the frequency factor. kg and/or kt, the rate constants for recombination to the singlet ground and triplet states, respectively, were assumed to be temperature-independent, or temperature-dependent via their exothermicity factors ki = CiT-1/2 exp(-Ei/kT) with i = g, t. Depending on the particular choice for the temperature dependence of kg and kt, best fits were obtained for delta E = 45-75 meV and recombination rate constants at 300 K of ks = 0.4-0.8 ns-1, kg = 0.08-0.12 ns-1, and kt = 0.3-0.5 ns-1. The model predicts a lifetime of the radical pair P+I- that is somewhat larger than that of delayed fluorescence; a magnetic field increases both.