Oxygen evolution in photosynthesis: simple analytical solution for the Kok model.

The light-induced oxidation of water by Photosystem II (PS II) of higher plants, algae, and cyanobacteria, is the main source of atmospheric oxygen. The discovery of the flash-induced period four oscillations in the oxygen evolution made by Pierre Joliot in 1969 has a lasting impact on current photosynthesis research. Bessel Kok explained such oscillations by introducing the cycle of flash-induced transitions of states (S-states) of an oxygen-evolving complex governed by the values of miss and double hit. Although this Kok model has been successfully used over 30 years for interpretation of experimental data in photosynthesis, until now there has been no simple analytical solution for it. Such an analytical solution for individual S-states and for oxygen evolution is presented here. When only the S(1) state is present before flash series, and when both the miss and double hit are zero, the oxygen evolved by the PSII after the n(th) flash, Y(n), is given by the following equation: 4Y(n)=1 + (-1)(n-1)-2 cos((n-1)pi/2). It is found here that binary oscillations of the secondary acceptor semiquinone at the acceptor side of the reaction center of PS II and release of reducing equivalents from reaction center to b(6)f complex can also be determined in the framework of the Kok model. The simple solutions found here for individual S-states, semiquinone, and oxygen evolution provide a basis for quantitative description of the charge accumulation processes at the donor and acceptor sides of PSII. It also provides a rare example of a significant problem in biology, which can be solved analytically.