Nonlinear Enhancement of Oxygen Evolution in Thylakoid Membranes

J. Phys. Chem. B 2005, 109, 14707-14714

14707

Nonlinear Enhancement of Oxygen Evolution in Thylakoid Membranes: Modeling the Effect of Light Intensity and β-Cyclodextrin Concentration Ma´ rio Fragata* and Subhan Dudekula† UniVersite´ du Que´ bec a` Trois-RiVie` res, De´ partement de Chimie-Biologie, Section de Chimie et Biochimie, Trois-RiVie` res, Que´ bec G9A 5H7, Canada ReceiVed: May 11, 2005; In Final Form: June 10, 2005

Electron transport through photosystem II, measured as oxygen evolution (OE), was investigated in isolated thylakoid membranes treated with β-cyclodextrin (β-CD, a cyclic oligosaccharide constituted of seven R-Dglucose residues linked by R-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 β-CD concentration. Second, we showed that under conditions of irradiation with white light of saturating intensity (∼5000 µmol of photons/m2‚s) β-CD enhances the oxygen evolution in the thylakoid membranes according to a sigmoid function displaying a sharp inflection point, or transition. Unexpectedely, this β-CD effect is not observed at irradiances of less than ∼300 µmol of photons/ m2‚s. We attempted a theoretical analysis of the combined effect of irradiance and β-CD concentration on oxygen evolution (OEth). For this purpose, the effect of irradiance (I) was modeled with a hyperbola (i) and the β-CD concentration (C) contribution with a Hill equation, that is, a sigmoid function (ii). The mathematical simulations generated the following general expressions: (i) OEth ) [OEmax(0) G1(C)]I/[L1/2(0) G2(C) + I] and (ii) Gi(C) ) 1 + p[Cn/(K1/2n + Cn)], where OEmax(0) is the OE maximum (OEmax) in the absence of β-CD, L1/2(0) is the photon flux density giving OEmax/2 in the absence of β-CD, G1(C) or G2(C) is obtained from Gi(C) where i is 1 or 2, n is the Hill coefficient, p is a parameter to account for the β-CD-mediated maximum OE increase, and K1/2 is the β-CD concentration giving half-maximal OE activity. The results of the calculations yielded the expression (iii) OEth ) 151[1 + 3.3C4.8/(13.14.8 + C4.8)]I/{97.5[1 + 5.2C7.8/ (14.87.8 + C7.8)] + 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 β-CD. We conclude that eq iii is a good approximation of the combined effect of irradiance and β-CD concentration, meaning that the model has a significant value for predicting the outcome of associated photochemical and biochemical reactions.

I. Introduction The cyclodextrins (CDs), a group of cyclic oligosaccharides constituted of various units of D-glucose linked by R-1,4 bonds,1,2 are currently used in various fundamental and applied aspects of the chemical and biomedical sciences.1-4 The CDs have a truncated cone geometry with a narrower rim (nR) and a wider rim (wR), where the primary 6-hydroxyl groups are located on the nR side and the secondary 2- and 3-hydroxyls on the wR side.1,2 This molecular arrangement renders the external surface of the CDs hydrophilic, whereas the internal cavity is less polar or hydrophobic. The low polarity of the cyclodextrin interior favors their interaction with the hydrophobic moieties of neutral or ionic molecules of small size, therefore facilitating the formation of a wide variety of inclusion complexes which are the framework of their mode of action. In the past few years, the cyclodextrins were applied successfully to the study of the photosynthetic activity in the thylakoid membrane of plant chloroplasts.5-10 It was shown that β-CD, a cyclodextrin containing seven D-glucose units, affects the spectroscopic characteristics and the electron transport * Corresponding author. Phone: 819-3765011. Fax: 819-3765057. E-mail: [email protected]. † Present address: Center for Cellular and Molecular Biology, Habsiguda, Hyderabad, Andhrapradesh 500007, India.

properties of isolated thylakoid membranes.7-10 In short, β-CD induces a red-shift from 681 to 683 nm in the absorption and second derivative spectra of the thylakoids7 which is assigned to perturbations affecting the QY(0,0) electronic transition in the plane of the chlorophyll (Chl) a molecule (see refs 11 and 12). However, the molecular interactions underlying this spectral shift are still not completely understood. A plausible explanation is to attribute the spectral shift to cyclodextrin interactions with the π-electron system of the Chl tetrapyrrole macrocycle in the pigments-proteins of photosystem II (PSII). However, a recent study using a combination of UV-vis absorption, circular dichroism, NMR, and steady-state and time-resolved fluorescence measurements does not seem to support this argument, since it showed that heptakis(2,3,6tri-O-methyl)-β-CD and hydroxypropyl-β-CD in aqueous solution with Chl a form, respectively, 1:1 and 1:2 inclusion complexes with the phytyl chain of the pigment.13 In the thylakoid membrane, a more effective role of β-CD is a molecular or structural membrane rearrangement causing new pigment-pigment interactions that would give rise to the QY(0,0) electronic transition changes at the origin of the spectral shift discussed above. Another line of evidence favoring the structural aspect of the β-CD effect comes from a study of the fluorescence induction

10.1021/jp052445l CCC: $30.25 © 2005 American Chemical Society Published on Web 07/13/2005

14708 J. Phys. Chem. B, Vol. 109, No. 30, 2005

Fragata and Dudekula

in isolated thylakoid membranes.8 It was shown that β-CD enhances the transfer of electrons between the excited state of the reaction center Chl of PSII (P680*) and the oxidized pheophytin (Phe) and then from Phe- to the primary quinone QA. An explanation of these observations is the increase of light absorption by P680 and the reactivation of closed photochemical centers upon treatment of the thylakoid membranes with the cyclodextrin.8 We emphasize, in this respect, that the oxygen evolution yield is dependent on the number of open photochemical centers, or traps, in the thylakoid membrane and is functionally related to the photochemical efficiency of the chlorophyll absorption of excitation photons.14 A novel finding is the observation that the electron transport through photosystem II, measured as oxygen evolution, varies with the β-CD concentration according to an S-shaped, or sigmoid, function displaying a sharp inflection point, or transition.9 The nonlinearity of the β-CD concentration-response curves has been justified on the grounds of an augmentation of the structural and functional cooperativity between PSII units. It is important to note, however, that the experiments reported in ref 9 were performed with isolated thylakoid membranes irradiated with white light of saturating intensity, that is, about 5000 µmol of photons/m2‚s. What is more, it has been argued in previous works that the linear and nonlinear effects observed in photosynthesis are brought about mainly by differences in the light intensity levels used to irradiate the plant material.15-17 To examine further this question, we recall that the relationship between electron transport through PSII measured as the rate of oxygen evolution (νO2) and the quantum yield of PSII (ΦPSII) is expressed as18-20

νO2 ) I[RC]ΦPSII

(1)

where I is the rate of photon absorption per PSII unit, [RC] the concentration of reaction centers, that is, the density of PSII units, and ΦPSII the (Fm - F0)/Fm ratio obtained from Chl a fluorescence induction (FI) measurements. In FI experiments, F0 is the minimal level of chlorophyll fluorescence when all PSII centers are open after dark adaptation of the plant material and Fm is the maximal level of fluorescence when all PSII centers are closed after a saturating light flash.20,21 Generally, νO2 in eq 1 ought to be a linear function of any of the independent variables on the right-hand side of the equation. Nevertheless, eq 1 was shown to be linear at high irradiance but not under low light intensity conditions where significant deviations from linearity are observed.15-20,22 This is an intriguing question that so far has not been solved satisfactorily. In this perspective, we examine hereunder the effect of β-CD on the oxygen evolution in thylakoid membranes irradiated with a broad range of light intensities and put special emphasis on nonsaturating low irradiance conditions. In the first part of this work (section III), we investigate whether the nonlinear effect of the β-CD concentration on the oxygen evolution in thylakoid membranes irradiated with white light of saturating intensity9 is also seen upon irradiating the membranes with low light intensities. In the second part of this work (section IV), we modeled the combined effect of light intensity and β-CD concentration on oxygen evolution with a set of mathematical expressions where the effect of irradiance is represented with a hyperbolic function, and the β-CD effect is fitted with an equation of the Hill type for the hypothesis of an allosteric transition with many binding sites (see the discussions in ref 23). We show that the results of the calculations agree well with the experimental data, therefore confirming the quality of the model. The article ends with some

remarks on the phenomenological significance of the mathematical conclusions (section V). II. Materials and Methods Chemicals. β-Cyclodextrin was purchased from FlukaChemie (Buchs, Switzerland), and 2,6-dichloro-p-benzoquinone (DCBQ) was obtained from Pfaltz and Bauer (Waterbury, CT). All other chemicals were from Fisher Scientific Company (Fair Lawn, NJ). Isolation of Thylakoid Membranes. Primary leaves from 6-8 day old barley seedlings were used to isolate thylakoids from chloroplasts according to procedures described before.24,25 Briefly, the leaves were homogenized in a buffer containing 50 mM tricine-NaOH (N-tris[hydroxymethyl]-methylglycineNaOH) (pH 7.8), 400 mM sorbitol, 10 mM NaCl, and 5 mM MgCl2 (buffer A) at 273 K. The resultant slurry was filtered through eight layers of cheesecloth. The filtrate was centrifuged at 1000g for 5 min at 277 K to precipitate the chloroplasts which were centrifuged again upon suspension in buffer A. This chloroplast preparation was collected in a buffer containing 50 mM tricine-NaOH (pH 7.8), 10 mM NaCl, and 5 mM MgCl2 (buffer B) and centrifuged immediately at 1000g for 5 min at 277 K. The pellet contained the thylakoid membranes which were dispersed in a buffer containing 20 mM MES-NaOH (2[N-morpholino]ethanesulfonic acid-NaOH) (pH 6.5), 400 mM sucrose, 15 mM NaCl, and 5 mM MgCl2 (buffer C) and was centrifuged at 1000g for 5 min at 277 K. The final pellet was diluted in buffer C to give a final chlorophyll concentration of 2 mg/mL and stored at 143 K. The chlorophyll concentration in the thylakoid preparations was measured in 80% (v/v) acetone.26 The polypeptide composition of the isolated thylakoid membranes was analyzed by sodium dodecyl sulfate-polyacrylamide gel electrophoresis.27 The standard proteins and the thylakoid polypeptides were resolved on a linear gradient gel as described in ref 28 that gives also the procedures for staining and destaining the electrophoresis gels. To estimate the molecular mass of the proteins, a set of markers was used (RPN 800 kit from Amersham International plc, Buckinghamshire, England). Treatment of Isolated Thylakoid Membranes with β-Cyclodextrin. The thylakoid membranes used in oxygen evolution experiments were treated with β-CD as reported in refs 7 and 8. Briefly, β-CD was solubilized in an incubation buffer (pH 6.5) containing 20 mM MES-NaOH and 400 mM sorbitol to yield concentrations of 2-16 mg/mL upon addition of the thylakoid membrane sample (50 µg of Chl/mL). These suspensions were incubated at 273 K for 10 min in darkness followed immediately by a centrifugation at 8000g for 5 min at 277 K to precipitate the thylakoid membranes, thus eliminating unbound β-CD. The control untreated thylakoid membranes and the β-CD-treated samples were resuspended in a measurement buffer containing 20 mM MES-NaOH, 400 mM sucrose, 15 mM NaCl, and 10 mM MgCl2 (pH 6.5) to perform oxygen evolution determinations. Electron Transport Measurements and Irradiation of the Thylakoid Membranes. Electron transport through photosystem II estimated as oxygen evolution was measured with a Hansatech oxygen electrode (Hansatech Instruments Ltd., Norfolk, U.K.) connected to a temperature controlled water circulator at 298 K. The assay mixtures contained untreated or β-CD-treated samples of thylakoid membranes (12.5 µg of Chl/mL) in a oxygen evolution measurement buffer (pH 6.5) constituted of 20 mM MES-NaOH, 400 mM sucrose, 15 mM NaCl, 5 mM

Nonlinear Enhancement of OE in Thylakoid Membranes

J. Phys. Chem. B, Vol. 109, No. 30, 2005 14709 Hereunder, we use two mathematical models, that is, an exponential function (model I) or a hyperbola (model II), which have relevant phenomenological significance. That is, in model I, we determine the best mathematical fit with the hypothesis of the cumulative one-hit Poisson probability distribution,14 and in model II, we use the steady-state approximation for the case of alternating slow and fast reactions.33 Model I. The experimental data displayed in Figure 1 are fitted with an exponential expression for OEth, that is, the theoretical oxygen evolution as a function of I, the photon flux density,

OEth ) OEth(max)(1 - e-kI)

Figure 1. Effect of the light intensity (µmol of photons/m2‚s) on the oxygen evolution in isolated thylakoid membranes. The theoretical curves were obtained with Origin 5.0 (see Materials and Methods). Chl, chlorophyll; I, photon flux density.

MgCl2, and 350 µM 2,6-dichloro-p-benzoquinone which accepts electrons at the QA site, that is, the primary quinone acceptor of PSII.29 Irradiation of the thylakoid membrane suspensions was performed with white light from a Fiber-Lite high intensity illuminator, model 180, from Dolan-Jenner Industries Inc. (Lawrence, MA). Incident photon flux densities were measured with a quantum photometer, model LI-185B, from LI-COR, Inc. (Lincoln, NE) which was equipped with an LI-190SB quantum sensor. Photon flux densities of 60-1100 µmol of photons/m2‚ s were obtained with a series of calibrated optical neutral density filters (Tiffen Optical Co., Roslyn Heights, LI, NY). The uniformity of the spectral characteristics of the neutral density filters was checked by registering the absorbance of chlorophyll a solutions in diethyl ether. Data Analysis. The theoretical curves displayed in sections III and IV are fits of the experimental data with mathematical expressions discussed in refs 14, 23, 30, and 31. The software programs used are Origin, version 5, from Microcal Software, Inc. (Northampton, MA), Maple V, release 5.1, from Waterloo Maple Inc. (Waterloo, ON, Canada), and Mathematica, version 4.0.1, from Wolfram Research (Champaign, IL). For several other calculations, we used the QuickBasic programming language, version 4.0, from Microsoft Corporation. III. Results and Discussion Light-Response Curves of Oxygen Evolution in the Thylakoid Membrane. Figure 1 displays the oxygen evolution (OE) observed in thylakoid membranes irradiated with white light of photon flux densities (I) between 60 and 1000 µmol‚m-2‚s-1. We note first that the variation of OE with I is characterized by a sharp increase at low light intensities followed by a quite lower dOE/dI rate at high irradiance. This trend has usually been reported in the literature (see, e.g., refs 18 and 32). The first question addressed here is to investigate which mathematical model is the best representation (or mathematical solution) of the experimental OE versus I data. This is especially important for the study of the combined effect of light intensity and β-CD concentration on the oxygen evolution in the thylakoid membrane undertaken in section IV.

(2)

where OEth(max), the maximum oxygen evolution, is given in µmol of oxygen evolution/(mg of Chl‚h), I in µmol of photons/ m2‚s, and k ()cross section for absorption of a photon × duration of illumination) in m2‚(µmol of photons)-1‚s. The best fit of OEth versus I is the theoretical light-response curve shown in Figure 1. The mathematical simulations performed with the curve fitting tool of the Origin software (see Materials and Methods) yielded the expression

OEth ) 132.9 ((3.6) (1 - e-0.0082((0.0007)I)

(3)

that clearly cannot represent adequately the experimental oxygen evolution data obtained with light intensities between 60 and 1000 µmol of photons/m2‚s. It is interesting that eq 2 is similar to the mathematical expression for the cumulative one-hit Poisson probability distribution developed by Mauzerall and Greenbaum,14 that is,

Y(z) ) Yo(z)(1 - e-σ(z)E)

(4)

where Y(z) is the yield of a photoproduct, Yo(z) is the yield of the photoproduct per hit or closing of a reaction center, σ(z) is the optical cross section for absorption of a photon by a unit forming z, E is the fluence, that is, the photons per unit area, and the term e-σ(z)E gives the fraction of targets which were not hit. A simple transformation of eq 2 to change -kI into -ko(z)It, where the term It, with t ) duration of irradiation, is the fluence (or E in eq 4), shows that ko(z) is the equivalent of the optical cross section for absorption of a photon by a unit forming z, or σ(z) (eq 4). The above discussions and the theoretical result displayed in Figure 1 are a good indication that the cumulative one-hit Poisson probability distribution14 does not yield a reliable representation of the experimental data. This conclusion is further illustrated upon comparing the results in Figure 1 (untreated thylakoid membranes) with data obtained with β-CDtreated thylakoid membranes (Figure 2 and Table 1). Figure 2 shows the light-response curves of oxygen evolution in thylakoid membranes treated with β-CD concentrations from 10 to 14 mM. For comparison purposes, the figure also contains the results obtained with control (untreated) preparations. Figure 2 shows that all β-CD concentrations used enhance considerably the oxygen evolution. Furthermore, the dOE/dI rate varies according to a trend which is similar to the one observed in control (untreated) thylakoid membranes. The results of the calculations are summarized in Table 1. The table collects (i) the oxygen evolution data obtained experimentally, OEobs, upon irradiating untreated and β-CD-treated thylakoids thylakoid membranes with white light of saturating intensity, that is, ∼5000 µmol of photons/m2‚s, (ii) the theoretical oxygen evolution maxima, OEth(max), computed for β-CD concentra-



TABLE 1: Comparison of Oxygen Evolution Observed in Isolated Thylakoid Membranes (OEobs)a,b with Data Obtained from Theoretical Simulations (OEth)c,d L1/2, µmol of photons/m2‚s

oxygen evolution, µmol of O2/(mg of Chl‚h) β-CD, mΜ

OEobse

0

155.4

OEth(max) 132.9c 151.0d

10

282.9 218.1c 255.0d

12

364.9 278.2c 342.9d

14

427.2 349.4c 449.4d

SE

Cvarf

3.3 3.6 3.8 9.5 4.9 7.4 15.2 7.2 8.4 16.5 4.9 11.4

2.1 2.7 2.5 3.4 2.2 2.9 4.2 2.6 2.4 3.9 1.4 2.5

L1/2

SE

Cvar

97.5

9.0

9.2

118.7

11.5

9.7

209.1

15.3

7.3

295.5

20.6

7.0

k, m2‚(µmol of photons)-1‚s k

SE

Cvar

0.008 20

0.000 70

8.5

0.007 36

0.000 51

6.9

0.004 75

0.000 37

7.8

0.003 73

0.000 16

4.3

a Abbreviations: β-CD, β-cyclodextrin; I, light intensity in µmol of photons/m2‚s; k, cross section for absorption of a photon × duration of illumination (see model I below); L1/2, light intensity giving OEth(max)/2 (see model II below); OEth(max), theoretical oxygen evolution maximum; SD, standard deviation; SE, standard error. b The isolated thylakoid membranes were irradiated with white light of saturating intensity (∼5000 µmol of photons/m2‚s). c Model I (see text, section III): OEth ) OEth(max)(1 - e-kI). d Model II (see text, section III): OEth ) OEth(max)I/(L1/2 + I). e Experimental data of Figure 3. f The coefficient of variation (Cvar) is given as a percentage, that is, SD × 100/mean.

Figure 2. Effect of the light intensity (µmol of photons/m2‚s) and the β-cyclodextrin (β-CD) concentration on the oxygen evolution in isolated thylakoid membranes. The theoretical curves were obtained with Origin 5.0 (see Materials and Methods). Chl, chlorophyll.

tions between 10 and 14 mM, and (iii) the values of the parameter k (see eq 2). Table 1 shows that the OEth(max) values calculated according to model I are quite different from the OEobs values. For example, in thylakoid membranes treated with 12 mM β-CD, one gets OEth(max) ) 278.2 ( 7.2 µmol of O2 evolution/(mg of Chl‚h) which is about 24% smaller than OEobs at the same β-CD concentration, that is, 364.9 ( 15.2 µmol of O2 evolution/ (mg of Chl‚h) (cf. Table 2). In brief, one sees in Table 2 that the estimated errors in the calculations of OEth(max) with eq 2 vary between about 15 and 24%. Model II. We show in Figure 1 that the experimental data obtained with light intensities from 60 to 1100 µmol of photons/ m2‚s are well fitted with the hyperbolic expression

OEth ) OEth(max)I/(L1/2 + I)

(5)

where OEth(max) is the theoretical oxygen evolution maximum that would be observed at very high irradiance (i.e., when the maximum possible number of PSII reaction centers is open),

L1/2 is the irradiance giving OEth(max)/2, and I is defined above. OEth(max) and L1/2 for control thylakoid membranes (i.e., not treated with β-CD) were computed with eq 5 using the curve fitting tool of the Origin software (see Materials and Methods). First, Table 1 shows that calculation of the data obtained with control (not treated) thylakoid membranes yields OEth(max) ) 151.0 ( 3.8 µmol of O2 evolution/(mg of Chl‚h) and L1/2 ) 97.5 ( 9.0 µmol of photons/m2‚s. We note that the OEth(max) value is quite close to the OEobs value which is about the maximum oxygen evolution obtained under experimental conditions of high irradiance. Second, Table 1 collects the result of calculations of data obtained with thylakoid membranes treated with 10-14 mM β-CD. In addition, Table 2 reveals that the estimated error in the determination of OEth(max) with eq 5 is between 0.7 and 12% which is significantly smaller than the error observed with the exponential function of eq 2 (model I), that is, between 14 and 24% (see the discussion above). We conclude therefore that, under the conditions of our experiments, the steady-state approximation33 expressed by the hyperbolic function of eq 5 is a better representation of the effect of light intensity on the electron transport through PSII in isolated thylakoid membranes than the exponential model of eq 2 for the cumulative one-hit Poisson probability distribution.14 Furthermore, we note that none of the β-CD concentrations used in the experiments reported here change the hyperbolic shape of the light-response curves displayed in Figure 2. This corroborates the argument that model II is a valid representation of the variation of oxygen evolution with the light intensity. Finally, it is interesting to remark that some experimental data published in the literature can also be correctly fitted with a hyperbolic function (see note 34). Toward a Phenomenological Interpretation of Model II. The OEth dependence on I seen in Figure 1 is explained hereunder in terms of the steady-state approximation33 of the electron transfer kinetics which is consistent with the conditions of our experiments. An attractive aspect of the steady-state approximation is that it permits the mathematical representation of a series of coupled sequences of reactions where slow and fast kinetics (or vice versa) alternate. This concept is applied in Scheme 1 to describe the energy transfer from an excited chlorophyll from the PSII antenna, that is, Chl aII*, to the PSII reaction center Chl (i.e., P680) followed by the transfer of an electron from P680* to an oxidized peophytin (Phe) (reaction 1) and then from Phe- to the primary quinone QA (reaction 2). For the sake of a


J. Phys. Chem. B, Vol. 109, No. 30, 2005 14711

TABLE 2: Estimated Error in the Determination of Oxygen Evolution with Model I and Model II in Relation to the Observed Oxygen Evolution in Thylakoid Membranes Untreated and Treated with Various β-Cyclodextrin Concentrationsa %∆OEth(5K)b or %∆OEth(max)c

µmol of O2 evolution/(mg of Chl‚h) β-CD, mM

model

0

10

12

14

0

10

12

14

Ie IIf I II

155.4 132.9 148.1 132.9 151.0

282.9 218.1 249.1 218.1 255.0

364.9 278.2 329.1 278.2 342.9

427.2 349.4 424.3 349.4 449.4

14.5 4.7 14.5 2.8

22.9 12.0 22.9 9.9

23.8 9.8 23.8 6.0

18.2 0.7 18.2 -5.2

OEobsd OEth(5K) OEth(max)

a Abbreviations: β-CD, β-cyclodextrin; I, light intensity in µmol of photons/m2‚s; k, cross section for absorption of a photon × duration of illumination (see model I below); L1/2, light intensity giving OEth(max)/2 (see model II below); OEobs, oxygen evolution observed; OEth(max), theoretical oxygen evolution maximum; OEth(5K), theoretical oxygen evolution computed for an irradiance of 5000 µmol of photons/m2‚s. b %∆OEth(5K) ) [OEobs - OEth(5K)] × 100/OEth(5K). c %∆OEth(max) ) [OEobs - OEth(max)] × 100/OEth(max). d The thylakoid membranes were irradiated with white light of saturating intensity (∼5000 µmol of photons/m2‚s). e Model I (see text, section III): OEth ) OEth(max)(1 e-kI). f Model II (see text, section III): OEth ) OEth(max)I/(L1/2 + I).

SCHEME 1: Electron Transfer through Photosystem II

more comprehensible photochemical context, we have also represented in Scheme 1 the pathway of P680+ reduction by electrons originating in the H2O photolysis and transferred to the oxidized Mn cluster (MnC+) and then from MnC to the tyrosine YZ (Tyr161) in the D1 protein (see, e.g., ref 35). In Scheme 1, k1 ) [P680+][Phe-]/[P680*][Phe] (reaction 1) and k2 ) [Phe][QA-]/[Phe-][QA] (reaction 2). One sees that reaction 1 is slow (6-10 ns) compared with reaction 2 which takes place in less than 400 ps. This means that Phe- never attains a significant concentration during the course of the reaction, since as it is formed, it reacts rapidly with the primary quinone QA to produce the reduced form QA-. Hence, the velocity of reaction 1 is about identical to the velocity of reaction 2, that is, -

k1[P680*][Phe] = k2[Phe ][QA]

(6)

According to the steady-state approximation, equilibria such as the one described by eq 6 have mathematical solutions which are usually represented by hyperbolic functions.33 This is the case of the hyperbola of eq 5 where consequently OEth(max) and L1/2 contain specific functional and structural information. A direct interpretation is to take (i) OEth(max) as a measure of the maximum number of PSII reaction centers open for electron transport through PSII and (ii) L1/2 as the k2/k1 ratio, that is, the equilibrium between the electron transfer from Phe- to the primary quinone QA and the formation of the reduced Phe molecule in the PSII reaction center (see also note 38). Nonlinearity of the β-CD Concentration Curves of Oxygen Evolution. We show in Figure 3 that the effect of the β-CD concentration on oxygen evolution in isolated thylakoid membranes irradiated with white light of saturation intensity (∼5000 µmol of photons/m2‚s) is the enhancement of oxygen evolution according to a sigmoid curve displaying a sharp inflection point, or transition. The theoretical representation of the nonlinear enhancement of oxygen evolution brought about by increasing

Figure 3. Effect of the concentration of β-cyclodextrin (β-CD) on the oxygen evolution (OE) in isolated thylakoid membranes irradiated with white light of saturating intensity (∼5000 µmol of photons/m2‚s). OE is 155.4 ( 3.3 µmol of O2/(mg of Chl‚hr) in the absence of β-CD. The experimental data are given as “mean ( SE”. The theoretical curve was obtained from mathematical simulations performed according to the Hill equation with Origin 5.0 (see text and Materials and Methods). Chl, chlorophyll; SE, standard error.

β-CD concentration was attempted previously9 with a mathematical expression for the hypothesis of an allosteric transition with many binding sites (see discussions in refs 23, 30, and 31). The theoretical dose-response curve is the Hill equation

OEth ) OEth(max)[Cn/(K1/2n + Cn)]

(7)

where OEth is the steady-state rate of oxygen evolution at various β-CD concentrations, OEth(max) the maximum oxygen-evolving activity, C the cyclodextrin concentration, K1/2 the concentration of cyclodextrin that resulted in half-maximal oxygen-evolving activity, that is, OEth(max)/2, and n the Hill coefficient, that is, the number of cyclodextrin binding sites. In eq 7, the term [Cn/ (K1/2n + Cn)] is the fraction of active cyclodextrin receptors in the thylakoid membrane. It is noted that the theoretical upper limit of oxygen evolution in Figure 3, that is, OEth(max) = 453 µmol of O2 evolution/(mg of Chl‚h), can only be attained at β-CD concentrations higher than 20 mM which are out of the solubility range of the cyclodextrins. However, the oxygen evolution observed in thylakoid membranes treated with 14 mM β-CD, that is, 427.2 µmol of O2 evolution/(mg of Chl‚h), is quite close to the theoretical maximum.


Figure 4. Three-dimensional representation of the effect of the light intensity (µmol of photons/m2‚s) and the β-cyclodextrin (β-CD) concentration on the oxygen evolution in isolated thylakoid membranes. Chl, chlorophyll.

To determine the characteristics of the β-CD effect at irradiances far from the saturating light conditions of Figure 3 we performed experiments under low light intensity conditions and at irradiances up to 1100 µmol of photons/m2‚s. The threedimensional graph in Figure 4 presents the combined effect of irradiance (60-1100 µmol of photons/m2‚s) and β-CD concentration (6-14 mM) on oxygen evolution in isolated thylakoid membranes. We remark first that all light-response curves of oxygen evolution in Figure 4 were shown to be well fitted with hyperbolic functions (cf. Table 1). Unexpectedly, however, Figure 4 reveals that a neat S-shaped (sigmoid) curve of oxygen evolution enhancement with increasing β-CD concentration of the type seen in Figure 3 is observed only at irradiances higher than approximately 300 µmol of photons/m2‚s. At photon flux densities lower than about 300 µmol of photons/m2‚s, the oxygen evolution variation with β-CD concentration is small. This is best seen in Figure 5 which displays the oxygen evolution observed in β-CD-treated thylakoid membranes irradiated with light intensities of 66, 100, and 1000 µmol of photons/m2‚s. We note at first that the shape of the low light intensity curves is quite different from the sigmoid shape seen at high light intensity. In short, the oxygen evolution increases to a maximum at β-CD concentrations between 10 and 12 mM and then decreases to a lower steady level.


Figure 5. Comparison of theoretical and experimental data on the effect of β-cyclodextrin concentration and irradiance (66, 102, and 1000 µmol of photons/m2‚s) on oxygen evolution in isolated thylakoid membranes. The theoretical curves were obtained from mathematical simulations performed with Origin 5.0 (see Materials and Methods and eq 12). Chl, chlorophyll.

order to correct the values of OEmax and L1/2 observed in control thylakoid membranes (in the absence of β-CD), that is, OEmax(0) and L1/2(0). To this end, OEmax(0) and L1/2(0) are multiplied by scale functions dependent on the β-CD concentration (C), that is, G1(C) and G2(C), to transform eq 5 into eq 8

OEth ) [OEmax(0) G1(C)]I/[L1/2(0) G2(C) + I]

(8)

Determination of G1(C) and G2(C): Step 1. Analysis of the data in Table 1 reveals that OEmax and L1/2 vary according to sigmoid functions of the type given by eq 7 according to the general expression

Gi(C) ) 1 + p[Cn/(K1/2n + Cn)]

(9)

where Gi(C) is G1(C) or G2(C) in eq 8, n is the Hill coefficient (cf. eq 7), p is a parameter to take into account the β-CDmediated maximum increase of oxygen evolution, and K1/2 is defined above (cf. eq 7). It is emphasized that, in the absence of β-CD, that is, for C ) 0 in eq 9, Gi(C) is equal to 1 and eq 8 reverts to the expression given by eq 5. Determination of G1(C) and G2(C): Step 2. The results of the mathematical simulations are the following two expressions

IV. Modeling the Combined Effect of Irradiance and β-CD Concentration

G1(C) ) 1 + 3.3C4.8/(13.14.8 + C4.8)

(10)

We examine in this section the constraints to be introduced in the light-response curves of oxygen evolution (Figure 2) in order to include the sigmoid character of the β-CD concentration effect as is seen in the OE evolution versus β-CD concentration curve displayed in Figure 3. The aim is to deduce a mathematical expression more general than the hyperbolic function of eq 5 to include the sigmoid aspect of the β-CD concentration effect on oxygen evolution. In other words, the modified eq 5 might describe completely the oxygen evolution data seen in the threedimensional graph of Figure 4 for a broad range of irradiances and β-CD concentrations. β-CD Effect on OEmax and L1/2 in Light-Response Curves of Oxygen Evolution. The purpose here is to rewrite eq 5 in

G2(C) ) 1 + 5.2C7.8/(14.87.8 + C7.8)

(11)

Equations 10 and 11 show that the nonlinear variation of G1(C) and G2(C) is sigmoidal, as was expected from analysis of the OEmax(0) and L1/2(0) data in Table 1. However, the sigmoidicity is not identical, as is seen in the relative magnitudes of p, n, and K1/2 which, therefore, shall influence the data yielded by eq 8. Surface of Occupancy. The computed values of the Hill coefficients (n) in eqs 10 and 11 are largely different, that is, 4.8 in G1(C) and 7.8 in G2(C). We recall that the size of n is a mesure of the number of cyclodextrin binding sites in the thylakoid membrane.9 Therefore, the magnitude of n in eqs 10


Figure 6. Theoretical three-dimensional representation of the effect of the light intensity (µmol of photons/m2‚s) and the β-cyclodextrin (β-CD) concentration on the oxygen evolution in isolated thylakoid membranes. The mathematical simulations were performed with eq 12 (see text) using Origin 5.0 (see Materials and Methods). Chl, chlorophyll.

and 11 indicates the presence in the thylakoid membrane surface of at least two specific molecular targets, or binding sites, for β-CD which have quite different sizes. Taking into account that the cross section of a β-CD molecule is about 1.84 nm2 (cf. refs 1 and 2), a simple calculation shows that, for n ) 4.8, or say five β-CD molecules, one has a thylakoid membrane surface of occupancy of about 9.2 nm2, whereas, for n ) 7.8, or ∼8, the calculated surface of occupancy is approximately 14.7 nm2. These size differences of the molecular surface of docking of β-CD in the thylakoid membrane is likely at the origin of distinct structural and functional changes. Theoretical Representation of the Effect of Light Intensity and β-CD Concentration. Substitution of the expressions given by eqs 10 and 11 for G1(C) and G2(C) in eq 8 results in the following general expression (eq 12) for oxygen evolution in β-CD-treated thylakoid membranes irradiated with low and high photon flux densities

OEth ) 151[1 + 3.3C4.8/(13.14.8 + C4.8)]I/{97.5[1 + 5.2C7.8/(14.87.8 + C7.8)] + I} (12) The three-dimensional representation displayed in Figure 6 was obtained with OEmax(0) ) 151.0 µmol of O2 evolution/(mg of Chl‚h) and L1/2(0) ) 97.5 µmol of photons/m2‚s, as is indicated in eq 12 and Table 1. The theoretical representation of the oxygen evolution (OEth) as a function of I and C (Figure 6) was tested against the experimental data displayed in Figure 2 (OEobs). For this purpose, we used software written with the QuickBasic programming language, version 4.0, from Microsoft Corporation. The calculated percentage error (%OEr) is represented in Figure 7. One sees that the average %OEr is between 2 and 9% and in most cases not greater than 13%. Furthermore, the predictive value of the model was assayed for several sets of observed and theoretical data. For example, eq 12 yields OEth ) 198.4 µmol of O2 evolution/(mg of Chl‚h) for I ) 400 µmol of photons/m2‚s and C ) 10 mM, whereas for these same I and C values the observed oxygen evolution is 209 µmol of O2 evolution/(mg of Chl‚h) (cf. Figure 2), that is, an error of approximately 5.3% which is small enough to confirm the

J. Phys. Chem. B, Vol. 109, No. 30, 2005 14713

Figure 7. Error (%OEr) between theoretical and experimental data observed in the study of the effect of the light intensity (µmol of photons/m2‚s) and the β-cyclodextrin (β-CD) concentration on the oxygen evolution in isolated thylakoid membranes. The theoretical data were obtained with eq 12 (see text and Figure 6), and the experimental data are those given in Figure 2.

quality of the model. In general, the calculations performed with eq 12 show a notable convergence between theory and experiment. V. Concluding Remarks First, we showed that the light response of oxygen evolution in isolated thylakoid membranes irradiated with white light under steady-state conditions is well represented by a hyperbolic function (Figure 1 and Table 1), the shape of which is not affected by the β-CD concentration (Figure 2). We acknowledge, however, that this is at variance with the exponential functions, such as eq 4 (section III), which are used to describe the effect of light flashes of high intensity and very short duration on whole leaves and other plant materials. On one hand, Poisson statistics is mandatory for the interpretation of data obtained with optically thin samples irradiated with single turnover flashes of monochromatic light.14 On the other hand, the steady-state approximation applied to the kinetics of electron transport through PSII justifies the use of a hyperbolic representation instead of an exponential function. These apparent discrepancies indicate the need for further investigations. Second, we found that the sigmoid trend of the β-CD concentration effect on the oxygen evolution in thylakoid membranes irradiated with white light of saturating intensity, that is, about 5000 µmol of photons/m2‚s (Figure 3), is not seen under low light intensity conditions, for example, less than ∼300 µmol of photons/m2‚s (Figure 4). This dual aspect of the β-CD effect has some connection to the photosynthetic activity differences observed previously in plant materials irradiated with low and high light intensities.15-17 In this respect, it is particularly interesting that the differences between low and high irradiance are ascribed in ref 17 to dissimilarities in molecular organization, that is, to the presence in the photosynthetic membrane of at least two populations of PSII centers with distinct properties. This conclusion gives support to our previous suggestion that the cyclodextrins cause the cooperative association of PSII units.9

14714 J. Phys. Chem. B, Vol. 109, No. 30, 2005 A major issue in this work is the demonstration that the combined effect of light intensity and β-CD concentration on oxygen evolution (Figures 4 and 6) is well represented by eq 12 in which the irradiance effect on oxygen evolution is fitted with a hyperbolic function and the β-CD concentration effect is described by a mathematical expression for the hypothesis of an allosteric transition with many binding sites (see discussions in refs 23, 30, and 31). In the latter case, the theoretical β-CD dose-response curve is eq 7, that is, a Hill-type equation. We conclude that the theoretical result yielded by eq 12 is a reliable approximation of the combined effect of light intensity and β-CD concentration on oxygen evolution in isolated thylakoid membranes, therefore indicating that the model has a significant value for predicting the outcome of associated photochemical and biochemical reactions. Acknowledgment. This work was supported by grants to M.F. from the Natural Sciences and Engineering Research Council of Canada. We thank Dr. S. Govindachary, Mr. P.-O. He´bert-Mercier, and Mr. E. Richard for very helpful discussions and the reviewers for having called our attention to a few ambiguities in the text, thereby helping to improve the quality of the paper. References and Notes (1) Li, S.; Purdy, W. C. Chem. ReV. 1992, 92, 1457. (2) D’Souza, V.-T.; Lipkowitz, K. B. Chem. ReV. 1998, 98, 1741. (3) Szejtli, J. J. Cyclodextrin Technology; Springer: Berlin, 1988. (4) Mikami, B.; Hehre, E. J.; Sato, M.; Katsube, Y.; Hirose, M.; Morita, Y.; Sacchettini, J. C. Biochemistry 1993, 32, 6836. (5) Rawyler. A.; Siegenthaler, P.-A. Biochim. Biophys. Acta 1996, 1278, 89. (6) Ducheˆne, S.; Siegenthaler, P.-A. Lipids 2000, 37, 201. (7) Sridharan, G.; Gaudreau, S.; Dalstein, L.; Huiban, C.; Lejeune, A.; Fragata, M. Z. Naturforsch. 2001, 56c, 792. (8) Sridharan, G.; Daneau, E.; Fragata, M. Can. J. Bot. 2002, 80, 741. (9) Dudekula, S.; Sridharan, G.; Fragata, M. Can. J. Bot. 2005, 83, 320. (10) Fragata, M.; Dudekula, S. In Photosynthesis: Fundamental Aspects to Global PerspectiVes; van der Est, A., Bruce, D., Eds.; ACG Publishing: Lawrence, KS, 2005. (11) Fragata, M.; Nordeń, B.; Kurucsev, T. Photochem. Photobiol. 1988, 47, 133. (12) Nordeń, B.; Fragata, M.; Kurucsev, T. Aust. J. Chem. 1992, 45, 1559. (13) Dentuto, P. L.; Catucci, L.; Cosma, P.; Fini, P.; Agostiano, A.; D’Acolti, L.; Trevithick-Sutton, C. C.; Foote, C. S. J. Phys. Chem. B 2005, 109, 1313. (14) Mauzerall, D.; Greenbaum, N. L. Biochim. Biophys. Acta 1989, 974, 119. (15) van Wijk, K. J.; van Hasselt, P. R. Photosynth. Res. 1990, 25, 233. (16) Edwards, G. E.; Baker, N. R. Photosynth. Res. 1993, 37, 89. (17) Hormann, H.; Neubauer, C.; Schreiber, U. Photosynth. Res. 1994, 40, 93. (18) Genty, B.; Briantais, J.-M.; Baker, N. R. Biochim. Biophys. Acta 1989, 990, 87.

Fragata and Dudekula (19) Lavergne, J.; Trissl, H.-W. Biophys. J. 1995, 68, 2474. (20) Lavergne, J.; Briantais, J.-M. In Oxygenic Photosynthesis: The Light Reactions; Ort, D. R., Yocum, C. F., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1996; p 265. (21) Laza´r, D. Biochim. Biophys. Acta 1999, 1412, 1. (22) Falkowski, P. G.; Wyman, K.; Ley, A. C.; Mauzerall, D. C. Biochim. Biophys. Acta 1986, 849, 183. (23) Wyman, J.; Gill, S. J. Binding and Linkage. Functional Chemistry of Biological Macromolecules; University Science Books: Mill Valley, CA, 1990. (24) Berthold, D. A.; Babcock, G. T.; Yocum, C. F. FEBS Lett. 1981, 134, 231. (25) Neńoneńe´, E. K.; Fragata, M. J. Plant Physiol. 1990, 136, 615. (26) Arnon, D. I. Plant Physiol. 1949, 14, 552. (27) Chua, N. H. Methods Enzymol. 1980, 69, 434. (28) Neńoneńe´, E. K.; Me´thot, M.; Fragata, M. Z. Naturforsch. 1998, 53c, 39. (29) Mulo, P.; Laakso, S.; Maenpaa, P.; Aro, E.-M. Plant Physiol. 1998, 117, 483. (30) Krause, R. M.; Buisson, B.; Bertrand, S.; Corringer, P.-J.; Galzi, J.-L.; Changeux, J.-P.; Bertrand, D. Mol. Pharmacol. 1998, 53, 283. (31) Kimmel, J. L.; Reinhart, G. D. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 3844. (32) Kro¨mer, S.; Malmberg, G.; Gardestrom, P. Plant Physiol. 1993, 102, 947. (33) Tinoco, I., Jr.; Sauer, K.; Wang, J. C. Physical Chemistry. Principles and Applications in Biological Sciences, 3rd ed.; Prentice Hall: Englewood Cliffs, NJ, 1995. (34) The relationship between electron transport in photosynthetic membranes and the photon flux density has been reported often. For example, in Figure 2 of ref 18, experimental data are presented on the relation of the CO2 assimilation rate (µmol‚m-2‚s-1) in leaves of wild-type barley and the photon flux density (µmol of quanta/m2‚s). We performed the mathematical modeling of the empirical graphical representations given in ref 18 and showed that the data cannot be fitted with any of the several exponential functions studied. The best fit of the CO2 assimilation rate (y) was found to be the expression y ) 36.2(1 - e-0.003I), where I is the photon flux density. This equation is nevertheless clearly inadequate. On the contrary, a good representation of the experimental data in ref 18 is given by the hyperbolic function y ) 33.6I/(266 + I). (35) Hankamer, B.; Barber, J.; Boekema, E. J. Annu. ReV. Plant Physiol. Plant Mol. Biol. 1997, 48, 641. (36) Klimov, V. V.; Krasnovsky, A. A. Photosynthetica 1981, 15, 592. (37) Jursinic, P. A. In Light Emission by Plants and Bacteria; Govindjee, Amesz, I., Fork, D. C., Eds.; Academic Press: New York, 1986; p 291. (38) The application of the “steady-state approximation” to the reactions in Scheme 1 requires a set of boundary conditions which are simply delineated in the following generally accepted molecular equilibria (see, e.g., Figure 3 in ref 37) with rates k1 and k2: k1

k2

P680*‚Phe‚QA 98 P680+‚Phe-‚QA 98 P680+‚Phe‚QAIn this approximation, the sequence of photochemical and biochemical events is limited to the instant of the absorption of a photon by P680 and the subsequent electron transfer up to the oxidized form of QA. Interestingly, the final result of the mathematical deductions is invariably a hyperbolic expression of the type given by eq 5 with L1/2 ) k2/k1. A detailed account of this matter shall be presented in another paper.

Nonlinear Enhancement of Oxygen Evolution in Thylakoid Membranes

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