Theoretical investigation of the rates of electron transfer processes Q − I + Q II → Q I + Q − II and Q − I + Q − II → Q I + Q 2− II in photosynthesis

A theoretical investigation on the rates of electron‐transfer processes Q − I + Q II → Q − I + Q − II and Q − I + Q − II → Q I + Q 2− II was carried out by using the Marcus theory of long‐range electron transfer in solution. The molecular reorganizational parameter λ, the free‐energy change Δ G 0 for the overall reaction, and the electronic matrix element H DA for these two processes were calculated from the INDO‐optimized geometries of molecules Q I , Q II , and histidine. Q I and Q II are plastoquinones (PQ) which are hydrogen‐bonded to a histidine each, and the two histidines may or may not be coordinated to a Fe 2+ ion. The plastoquinone representing Q I is additionally flanked by two peptide fragments. Each of the species (Pep) 2 Q I · His and His · Q II has been considered to be immersed in a dielectric continuum that represents the surrounding molecules and protein folds. INDO calculations confirm the standard reduction potential for the first process (calculated 0.127 V; observed 0.13 V) and predict a midpoint potential of 0.174 V for the second process at 300 K at pH 7 (experimental value remains uncertain but is known to be close to 0.13 V). The plastoquinone fragment carries almost all the net charge (about 95.7%) in [PQ · His] − and the net charge in [PQH · His] − . The electron is transferred effectively from the plastoquinone part of [(Pep) 2 Q I · His] − to the plastoquinone moiety of Q II · His in the first step and to the plastoquinone fragment of HisH + · Q − II in the second step. Therefore, we made use of the formula for the rate of through‐space electron transfer from Q I to Q II (and to Q − II ). The plastoquinones are, of course, electronically coupled to histidines, and the transfer is, in reality, through the molecular bridge consisting of histidines and also Fe 2+ . The through‐bridge effect is inherent in our calculation of Δ G 0 , H DA , and the reorganization parameter λ. We investigated the correlation between half‐times for the transfer and ( D −1 op − D −1 s ), where D op and D s are, respectively, optical and static dielectric constants of the condensed phase in the vicinity of the plastoquinones. We found that with reasonable values of D op (2.6) and D s (8.5) the experimental rates are adequately explained in terms of transfers from the plastoquinone moiety of Q I to that of Q II . The t 1/2 values calculated for the two processes are 247 and 472 μs in the absence of Fe 2+ and 134 and 181 μs in the presence of Fe 2+ . These are in good agreement with the observed values which are ≈ 100 and ≈ 200 μs when Fe 2+ is present in the matrix and which are known to be almost twice as large when the Fe 2+ is evicted from the matrix. The present work also shows that the Marcus‐Hush theory of long‐range electron transfers can be successfully applied to the investigation of processes occurring in a semirigid condensed phase like the thylakoid membrane region. © 1997 John Wiley & Sons, Inc.