Nonlinear Enhancement of Oxygen Evolution in Thylakoid Membranes:  Modeling the Effect of Light Intensity and β-Cyclodextrin Concentration

Abstract

Electron transport through photosystem II, measured as oxygen evolution (OE), was investigated in isolated thylakoid membranes treated with beta-cyclodextrin (beta-CD, a cyclic oligosaccharide constituted of seven alpha-d-glucose residues linked by alpha-1,4 glycosidic bonds) and irradiated with white light of variable intensity. First, we found that the light-response curves of oxygen evolution are well fitted with a hyperbolic function, the shape of which is not affected by the beta-CD concentration. Second, we showed that under conditions of irradiation with white light of saturating intensity ( approximately 5000 mumol of photons/m(2).s) beta-CD enhances the oxygen evolution in the thylakoid membranes according to a sigmoid function displaying a sharp inflection point, or transition. Unexpectedely, this beta-CD effect is not observed at irradiances of less than approximately 300 mumol of photons/m(2).s. We attempted a theoretical analysis of the combined effect of irradiance and beta-CD concentration on oxygen evolution (OE(th)). For this purpose, the effect of irradiance (I) was modeled with a hyperbola (i) and the beta-CD concentration (C) contribution with a Hill equation, that is, a sigmoid function (ii). The mathematical simulations generated the following general expressions: (i) OE(th) = [OE(max)(0) G(1)(C)]I/[L(1/2)(0) G(2)(C) + I] and (ii) G(i)()(C) = 1 + p[C(n)()/(K(1/2)(n)() + C(n)())], where OE(max)(0) is the OE maximum (OE(max)) in the absence of beta-CD, L(1/2)(0) is the photon flux density giving OE(max)/2 in the absence of beta-CD, G(1)(C) or G(2)(C) is obtained from G(i)()(C) where i is 1 or 2, n is the Hill coefficient, p is a parameter to account for the beta-CD-mediated maximum OE increase, and K(1/2) is the beta-CD concentration giving half-maximal OE activity. The results of the calculations yielded the expression (iii) OE(th) = 151[1 + 3.3C(4.8)/(13.1(4.8) + C(4.8))]I/{97.5[1 + 5.2C(7.8)/(14.8(7.8) + C(7.8))] + I} which agrees well with the experimental data for a broad range of I and C. Note that, for C = 0, eq iii reverts to the light-response curve of oxygen evolution in the absence of beta-CD. We conclude that eq iii is a good approximation of the combined effect of irradiance and beta-CD concentration, meaning that the model has a significant value for predicting the outcome of associated photochemical and biochemical reactions.

Photochemical cooperativity in photosystem II. Characterization of oxygen evolution discontinuities in the light-response curves

“…[18][19][20] but the theoretical discussion of those observations was not attempted. In two former papers, 13,14 we showed that the variation of oxygen evolution with the light intensity in PSII in steady state conditions can be formulated according to the Langmuir adsorption isotherm for heterogeneous catalysis where 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. However, we show here that eqn (1) is but a special case of a more general mathematical expression for a number n of interaction (or binding) sites of the photons in the PSII reaction center, that is, a cooperative interaction of incident photons with the chlorophylls, and most likely also the pheophytins, in the PSII reaction center.…”

“…In two former papers, 13,14 it was shown that in steady state conditions of coupled reactions where slow and fast kinetics alternate 15 the dependence of oxygen evolution in PSII particles on the incident light intensity is well described by the Langmuir adsorption isotherm for heterogeneous catalysis. 16 In this approximation, the Chl molecules in the PSII reaction center are the adsorption surfaces (or heterogeneous catalysts) and the incident photons the substrate, or the reagent, in accordance with Turro's concept 17 of light being represented in photochemical reactions as a stream of particles instead of an electromagnetic wave.…”

USING A NONANALYTICAL APPROACH TO MODEL NONLINEAR DYNAMICS IN PHOTOSYNTHESIS AT THE PHOTOSYSTEM LEVEL1

“…The equations in Table 1 are dynamically linear because changes in a particular property of a PSII population, such as the PSII functional crosssection, have a direct and proportional effect on photosynthetic rates and yields. Recent studies, however, suggest that the photosynthetic light reactions are not so clearly linear in this manner but rather can exhibit strong nonlinear dynamics (Nedbal and Březina 2002, Nedbal et al 2003, Fragata and Dudekula 2005, Rascher and Nedbal 2006. If the capture and uptake of photons at the photosystem level is sufficiently nonlinear in a dynamical sense, then small changes in a particular PSII property Dashed lines indicate simulations where the effect of PSII connectivity was ignored and p was fixed to 0.…”

“…Recent studies, however, suggest that the photosynthetic light reactions are not so clearly linear in this manner but rather can exhibit strong nonlinear dynamics (Nedbal and Březina 2002, Nedbal et al. 2003, Fragata and Dudekula 2005, Rascher and Nedbal 2006). If the capture and uptake of photons at the photosystem level is sufficiently nonlinear in a dynamical sense, then small changes in a particular PSII property may actually have a disproportionately strong effect on light‐harvesting rates or yields, which would not occur in a dynamically linear system.…”

“…A range of feedback, threshold, and lagged behaviors have been identified (e.g., Nedbal and Březina 2002, Nedbal et al. 2003, Fragata and Dudekula 2005) that indicate strong nonlinear dynamics in light harvesting at the photosystem level. In other physiological systems, such behaviors are known to reflect important modes of regulation (Glass 2001, Strogatz 2001), and a reasonable hypothesis is that nonlinear dynamics at the photosystem level may introduce similarly important but as of yet unexamined effects on photosynthetic rates or yields.…”