Electron transport through photosystem II (PSII), measured as oxygen evolution, was investigated in isolated PSII particles and thylakoid membranes irradiated with white light of intensities (I) of 20 to about 4000 micromol of photons/(m2.s). In steady-state conditions, the evolution of oxygen varies with I according to the hyperbolic expression OEth = OEth(max)I/(L1/2 + I) (eq i) where OEth is the theoretical oxygen evolution, OEth(max) is the maximum oxygen evolution, and L1/2 is the light intensity giving OEth(max)/2. In this work, the mathematical derivation of this relationship was performed by using the Langmuir adsorption isotherm and assuming that the photon interaction with the chlorophyll (Chl) in the PSII reaction center is a heterogeneous reaction in which the light is represented as a stream of particles instead of an electromagnetic wave (see discussion in Turro, N. J. Modern Molecular Photochemistry; University Science Books: Mill Valley, CA, 1991). In accordance with this approximation, the Chl molecules (P680) were taken as the adsorption surfaces (or heterogeneous catalysts), and the incident (or exciting) photons as the substrate, or the reagent. Using these notions, we demonstrated that eq i (Langmuir equation) is a reliable interpretation of the photon-P680 interaction and the subsequent electron transfer from the excited state P680, i.e., P680*, to the oxidized pheophytin (Phe), then from Phe- to the primary quinone QA. First, eq i contains specific functional and structural information that is apparent in the definition of OEth(max) as a measure of the maximal number of PSII reaction centers open for photochemistry, and L1/2 as the equilibrium between the electron transfer from Phe- to QA and the formation of reduced Phe in the PSII reaction center by electrons in provenance from P680*. Second, a physiological control mechanism in eq i is proved by the observation that the magnitudes of OEth(max) and L1/2 are affected differently by exogenous PSII stimulators of oxygen evolution (Fragata, M.; Dudekula, S. J. Phys. Chem. B 2005, 109, 14707). Finally, an unexpected new concept, implicit in eq i, is the consideration of the photon as the substrate in the photochemical reactions taking place in the PSII reaction center. We conclude that the Langmuir equation (eq i) is a novel mathematical formulation of energy and electron transfer in photosystem II.

In two previous papers (Fragata et al., J. Phys. Chem. B, 2005, 109, 14707-14714; Fragata et al., J. Phys. Chem. B, 2007, 111, 3315-3320), it was shown that the variation of oxygen evolution with the light intensity (I) in photosystem II (PSII) in steady state conditions can be formulated according to the Langmuir adsorption isotherm for heterogeneous catalysis. This yielded the expression OEth = OEth(max) I/(L1/2 + I), where OEth is the theoretical oxygen evolution, OEth(max) the maximum oxygen evolution, and L1/2 the irradiance giving OEth(max)/2. In this approximation, the photons interaction with the chlorophylls in the PSII reaction center is assumed to be a heterogeneous reaction in which the light is represented as a stream of particles instead of an electromagnetic wave. That is, the chlorophyll molecules are the adsorption surfaces (or heterogeneous catalysts), and the incident (or exciting) photons are the substrate, or the reagent. Recently, the examination of new experimental data obtained with 2,6-dichloro-p-benzoquinone (DCBQ) and p-benzoquinone (pBQ) as exogenous electron acceptors, disclosed the presence of oxygen evolution discontinuities (or transitions) in the light-response curves. The new data were fitted with a mathematical summation of hyperbola of order n(i) > 1, OEth = Sigma(i) [OEth(max)]iIn(i)/[(L1/2)i(n(i)) + I(n(i))], where the n(i)'s are the number of sites used by the incident photons in their interaction with the photosynthetic pigments in each population i of PSII centers open for photochemistry. The mathematical simulations yielded only three distinct n(i)'s, that is, 1.8, 4.8, 8.5 and 1.8, 4.2, 8.4 for isolated PSII particles incubated with DCBQ and pBQ, respectively. Implicitly, this means the simultaneous excitation of each PSII reaction center with more than one photon, that is, the excitation of more than one pigment molecule. It is suggested that these transitions have their origin in the cooperative interaction of the photons and the chlorophylls, and most likely also the pheophytins. This indicates that the discontinuities (or transitions) observed in the light-response curves of oxygen evolution are consistent with the hypothesis of photochemical cooperativity in photosystem II.

The temperature dependence of electron transport through photosystem II (PSII), measured as oxygen evolution, was investigated in thylakoid membranes irradiated with white light of 450 micromol of photons/(m(2) x s). The experiments were performed in steady-state conditions at temperatures between 273 and 303 K. The results show discontinuities, or thermal transitions, in the temperature-response curves of oxygen evolution. The experimental data was examined with the Marcus theory of electron transfer modified to take into account the oxygen evolution discontinuities. For this purpose, the Gibbs free energy of activation of the electron transfer reaction, DeltaG(o), is replaced in the classical Marcus equation with the expression DeltaH(o) - TDeltaS(o), where H(o) and DeltaS(o) are respectively the enthalpy and entropy of activation, and T is the temperature in kelvin. The result of the derivation is a summation of j Gaussian functions, or states, OE = 69 250 summation operator(j){(V(DA)(4)/lambdaT)(1/2) exp[-(T(max) - T)(2)/2Tsigma(o)(2)]}(j) (eq 1), where OE is expressed in micromol oxygen evolution.(mg Chl x h)(-1), and V(DA) is the electronic coupling matrix element between electron donor (D) and acceptor (A) wave functions, lambda the reorganization free energy, k(B) the Boltzmann constant, T(max) = (DeltaH(o) + lambda)/DeltaS(o), sigma(o) = (2k(B)lambda/DeltaS(o2))(1/2), and sigma = T(1/2)sigma(o) is the standard deviation of the Gaussian band. The mathematical simulations revealed the presence of six thermal transitions, or Gaussian bands with maxima at 275.3, 281.2, 286.4, 291.4, 297.1, and 302.4 K. The resolution of the Gaussian bands is about 0.55 owing to multiple band superpositions. The theoretical analyses showed that (i) the oxygen evolution in PSII is essentially dependent on V(DA)(2)/(lambdaT)(1/2) in the pre-exponential term of the modified Marcus equation (eq 1), and (ii) the reorganization energy, lambda, decreases exponentially with increasing temperature, and is also dependent on the electron donor-acceptor distance. It is concluded that the temperature dependence of the large enhancement of oxygen evolution observed in this work originates, at least partly, in heat-induced structural rearrangements in the photosystem II reaction center.

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