Nonlinear enhancement of oxygen evolution in thylakoid membranes: modeling the effect of light intensity and beta-cyclodextrin concentration.
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.