Semi-continuum electrostatic calculations of redox potentials in photosystem I

The midpoint redox potentials (E-m) of all cofactors in photosystem I from Synechococcus elongatus as well as of the iron-sulfur (Fe4S4) clusters in two soluble ferredoxins from Azotobacter vinelandii and Clostridium acidiurici were calculated within the framework of a semi-continuum dielectric approach. The widely used treatment of proteins as uniform media with single dielectric permittivity is oversimplified, particularly, because permanent charges are considered both as a source for intraprotein electric field and as a part of dielectric polarizability. Our approach overcomes this inconsistency by using two dielectric constants: optical epsilon(o) = 2.5 for permanent charges pre-existing in crystal structure, and static epsilon(s) for newly formed charges. We also take into account a substantial dielectric heterogeneity of photosystem I revealed by photoelectric measurements and a liquid junction potential correction for Em values of relevant redox cofactors measured in aprotic solvents. We show that calculations based on a single permittivity have the discrepancy with experimental data larger than 0.7 V, whereas E-m values calculated within our approach fall in the range of experimental estimates. The electrostatic analysis combined with quantum chemistry calculations shows that (i) the energy decrease upon chlorophyll dimerization is essential for the downhill mode of primary charge separation between the special pair P-700 and the primary acceptor A(0); (ii) the primary donor is apparently P700 but not a pair of accessory chlorophylls; (iii) the electron transfer from the A branch quinone Q(A) to the iron-sulfur cluster F-X is most probably downhill, whereas that from the B branch quinone Q(B) to F-X is essentially downhill.