Nonlinear Enhancement of Oxygen Evolution in Thylakoid Membranes: Modeling theEffect of Light Intensity and â-Cyclodextrin Concentration

Mario Fragata* and Subhan Dudekula†

UniVersitedu Quebec aTrois-RiVieres, Departement de Chimie-Biologie, Section de Chimie et Biochimie,Trois-RiVieres, 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 isolatedthylakoid membranes treated withâ-cyclodextrin (â-CD, a cyclic oligosaccharide constituted of sevenR-D-glucose residues linked byR-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, theshape of which is not affected by theâ-CD concentration. Second, we showed that under conditions ofirradiation with white light of saturating intensity (∼5000µmol of photons/m2‚s) â-CD enhances the oxygenevolution in the thylakoid membranes according to a sigmoid function displaying a sharp inflection point, ortransition. Unexpectedely, thisâ-CD effect is not observed at irradiances of less than∼300µmol of photons/m2‚s. We attempted a theoretical analysis of the combined effect of irradiance andâ-CD concentration onoxygen evolution (OEth). For this purpose, the effect of irradiance (I) was modeled with a hyperbola (i) andtheâ-CD concentration (C) contribution with a Hill equation, that is, a sigmoid function (ii). The mathematicalsimulations 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/(K1/2

n + Cn)], where OEmax(0) is the OE maximum (OEmax) in the absence ofâ-CD, L1/2(0) is the photon flux density giving OEmax/2 in the absence ofâ-CD, G1(C) or G2(C) is obtainedfrom Gi(C) where i is 1 or 2,n is the Hill coefficient,p is a parameter to account for theâ-CD-mediatedmaximum OE increase, andK1/2 is theâ-CD concentration giving half-maximal OE activity. The results ofthe 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 ofI andC. Note that,for C ) 0, eq iii reverts to the light-response curve of oxygen evolution in the absence ofâ-CD. We concludethat eq iii is a good approximation of the combined effect of irradiance andâ-CD concentration, meaningthat the model has a significant value for predicting the outcome of associated photochemical and biochemicalreactions.

I. Introduction

The cyclodextrins (CDs), a group of cyclic oligosaccharidesconstituted of various units ofD-glucose linked byR-1,4bonds,1,2 are currently used in various fundamental and appliedaspects of the chemical and biomedical sciences.1-4 The CDshave a truncated cone geometry with a narrower rim (nR) anda wider rim (wR), where the primary 6-hydroxyl groups arelocated on the nR side and the secondary 2- and 3-hydroxylson the wR side.1,2 This molecular arrangement renders theexternal surface of the CDs hydrophilic, whereas the internalcavity is less polar or hydrophobic. The low polarity of thecyclodextrin interior favors their interaction with the hydro-phobic moieties of neutral or ionic molecules of small size,therefore facilitating the formation of a wide variety of inclusioncomplexes which are the framework of their mode of action.

In the past few years, the cyclodextrins were appliedsuccessfully to the study of the photosynthetic activity in thethylakoid membrane of plant chloroplasts.5-10 It was shown thatâ-CD, a cyclodextrin containing sevenD-glucose units, affectsthe spectroscopic characteristics and the electron transport

properties of isolated thylakoid membranes.7-10 In short,â-CDinduces a red-shift from 681 to 683 nm in the absorption andsecond derivative spectra of the thylakoids7 which is assignedto perturbations affecting the QY(0,0) electronic transition inthe plane of the chlorophyll (Chl)a molecule (see refs 11 and12). However, the molecular interactions underlying this spectralshift are still not completely understood.

A plausible explanation is to attribute the spectral shift tocyclodextrin interactions with theπ-electron system of the Chltetrapyrrole macrocycle in the pigments-proteins of photosys-tem II (PSII). However, a recent study using a combination ofUV-vis absorption, circular dichroism, NMR, and steady-stateand time-resolved fluorescence measurements does not seemto support this argument, since it showed that heptakis(2,3,6-tri-O-methyl)-â-CD and hydroxypropyl-â-CD in aqueous solu-tion with Chl a form, respectively, 1:1 and 1:2 inclusioncomplexes with the phytyl chain of the pigment.13 In thethylakoid membrane, a more effective role ofâ-CD is amolecular or structural membrane rearrangement causing newpigment-pigment interactions that would give rise to the QY-(0,0) electronic transition changes at the origin of the spectralshift discussed above.

Another line of evidence favoring the structural aspect of theâ-CD effect comes from a study of the fluorescence induction

* Corresponding author. Phone: 819-3765011. Fax: 819-3765057.E-mail: fragata@uqtr.ca.

† Present address: Center for Cellular and Molecular Biology, Habsiguda,Hyderabad, Andhrapradesh 500007, India.

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

in isolated thylakoid membranes.8 It was shown thatâ-CDenhances the transfer of electrons between the excited state ofthe reaction center Chl of PSII (P680*) and the oxidizedpheophytin (Phe) and then from Phe- to the primary quinoneQA. An explanation of these observations is the increase of lightabsorption by P680 and the reactivation of closed photochemicalcenters upon treatment of the thylakoid membranes with thecyclodextrin.8 We emphasize, in this respect, that the oxygenevolution yield is dependent on the number of open photo-chemical centers, or traps, in the thylakoid membrane and isfunctionally related to the photochemical efficiency of thechlorophyll absorption of excitation photons.14

A novel finding is the observation that the electron transportthrough photosystem II, measured as oxygen evolution, varieswith the â-CD concentration according to an S-shaped, orsigmoid, function displaying a sharp inflection point, or transi-tion.9 The nonlinearity of theâ-CD concentration-responsecurves has been justified on the grounds of an augmentation ofthe structural and functional cooperativity between PSII units.It is important to note, however, that the experiments reportedin ref 9 were performed with isolated thylakoid membranesirradiated with white light of saturating intensity, that is, about5000µmol of photons/m2‚s. What is more, it has been arguedin previous works that the linear and nonlinear effects observedin photosynthesis are brought about mainly by differences inthe light intensity levels used to irradiate the plant material.15-17

To examine further this question, we recall that the relationshipbetween electron transport through PSII measured as the rateof oxygen evolution (νO2) and the quantum yield of PSII (ΦPSII)is expressed as18-20

whereI is the rate of photon absorption per PSII unit, [RC] theconcentration of reaction centers, that is, the density of PSIIunits, andΦPSII the (Fm - F0)/Fm ratio obtained from Chlafluorescence induction (FI) measurements. In FI experiments,F0 is the minimal level of chlorophyll fluorescence when allPSII centers are open after dark adaptation of the plant materialand Fm is the maximal level of fluorescence when all PSIIcenters are closed after a saturating light flash.20,21

Generally,νO2 in eq 1 ought to be a linear function of anyof the independent variables on the right-hand side of theequation. Nevertheless, eq 1 was shown to be linear at highirradiance but not under low light intensity conditions wheresignificant deviations from linearity are observed.15-20,22 Thisis an intriguing question that so far has not been solvedsatisfactorily. In this perspective, we examine hereunder theeffect ofâ-CD on the oxygen evolution in thylakoid membranesirradiated with a broad range of light intensities and put specialemphasis on nonsaturating low irradiance conditions.

In the first part of this work (section III), we investigatewhether the nonlinear effect of theâ-CD concentration on theoxygen evolution in thylakoid membranes irradiated with whitelight of saturating intensity9 is also seen upon irradiating themembranes with low light intensities. In the second part of thiswork (section IV), we modeled the combined effect of lightintensity andâ-CD concentration on oxygen evolution with aset of mathematical expressions where the effect of irradianceis represented with a hyperbolic function, and theâ-CD effectis fitted with an equation of the Hill type for the hypothesis ofan allosteric transition with many binding sites (see thediscussions in ref 23). We show that the results of thecalculations agree well with the experimental data, thereforeconfirming the quality of the model. The article ends with some

remarks on the phenomenological significance of the math-ematical conclusions (section V).

II. Materials and Methods

Chemicals. â-Cyclodextrin was purchased from Fluka-Chemie (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 (FairLawn, NJ).

Isolation of Thylakoid Membranes. Primary leaves from6-8 day old barley seedlings were used to isolate thylakoidsfrom chloroplasts according to procedures described before.24,25

Briefly, the leaves were homogenized in a buffer containing50 mM tricine-NaOH (N-tris[hydroxymethyl]-methylglycine-NaOH) (pH 7.8), 400 mM sorbitol, 10 mM NaCl, and 5 mMMgCl2 (buffer A) at 273 K. The resultant slurry was filteredthrough eight layers of cheesecloth. The filtrate was centrifugedat 1000g for 5 min at 277 K to precipitate the chloroplasts whichwere centrifuged again upon suspension in buffer A. Thischloroplast preparation was collected in a buffer containing 50mM tricine-NaOH (pH 7.8), 10 mM NaCl, and 5 mM MgCl2

(buffer B) and centrifuged immediately at 1000g for 5 min at277 K. The pellet contained the thylakoid membranes whichwere dispersed in a buffer containing 20 mM MES-NaOH (2-[N-morpholino]ethanesulfonic acid-NaOH) (pH 6.5), 400 mMsucrose, 15 mM NaCl, and 5 mM MgCl2 (buffer C) and wascentrifuged at 1000g for 5 min at 277 K. The final pellet wasdiluted in buffer C to give a final chlorophyll concentration of2 mg/mL and stored at 143 K. The chlorophyll concentrationin the thylakoid preparations was measured in 80% (v/v)acetone.26

The polypeptide composition of the isolated thylakoidmembranes was analyzed by sodium dodecyl sulfate-polyacry-lamide gel electrophoresis.27 The standard proteins and thethylakoid polypeptides were resolved on a linear gradient gelas described in ref 28 that gives also the procedures for stainingand destaining the electrophoresis gels. To estimate the molec-ular mass of the proteins, a set of markers was used (RPN 800kit from Amersham International plc, Buckinghamshire, En-gland).

Treatment of Isolated Thylakoid Membranes with â-Cy-clodextrin. The thylakoid membranes used in oxygen evolutionexperiments were treated withâ-CD as reported in refs 7 and8. Briefly, â-CD was solubilized in an incubation buffer (pH6.5) containing 20 mM MES-NaOH and 400 mM sorbitol toyield concentrations of 2-16 mg/mL upon addition of thethylakoid membrane sample (50µg of Chl/mL). These suspen-sions were incubated at 273 K for 10 min in darkness followedimmediately by a centrifugation at 8000g for 5 min at 277 K toprecipitate the thylakoid membranes, thus eliminating unboundâ-CD. The control untreated thylakoid membranes and theâ-CD-treated samples were resuspended in a measurementbuffer containing 20 mM MES-NaOH, 400 mM sucrose, 15mM NaCl, and 10 mM MgCl2 (pH 6.5) to perform oxygenevolution determinations.

Electron Transport Measurements and Irradiation of theThylakoid Membranes.Electron transport through photosystemII estimated as oxygen evolution was measured with a Hansatechoxygen electrode (Hansatech Instruments Ltd., Norfolk, U.K.)connected to a temperature controlled water circulator at 298K. The assay mixtures contained untreated orâ-CD-treatedsamples of thylakoid membranes (12.5µg of Chl/mL) in aoxygen evolution measurement buffer (pH 6.5) constituted of20 mM MES-NaOH, 400 mM sucrose, 15 mM NaCl, 5 mM

νO2 ) I[RC]ΦPSII (1)

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

MgCl2, and 350µM 2,6-dichloro-p-benzoquinone which acceptselectrons at the QA site, that is, the primary quinone acceptorof PSII.29

Irradiation of the thylakoid membrane suspensions wasperformed with white light from a Fiber-Lite high intensityilluminator, model 180, from Dolan-Jenner Industries Inc.(Lawrence, MA). Incident photon flux densities were measuredwith a quantum photometer, model LI-185B, from LI-COR, Inc.(Lincoln, NE) which was equipped with an LI-190SB quantumsensor. Photon flux densities of 60-1100µmol of photons/m2‚s were obtained with a series of calibrated optical neutral densityfilters (Tiffen Optical Co., Roslyn Heights, LI, NY). Theuniformity of the spectral characteristics of the neutral densityfilters was checked by registering the absorbance of chlorophylla solutions in diethyl ether.

Data Analysis.The theoretical curves displayed in sectionsIII and IV are fits of the experimental data with mathematicalexpressions discussed in refs 14, 23, 30, and 31. The softwareprograms used are Origin, version 5, from Microcal Software,Inc. (Northampton, MA), Maple V, release 5.1, from WaterlooMaple Inc. (Waterloo, ON, Canada), and Mathematica, version4.0.1, from Wolfram Research (Champaign, IL). For severalother calculations, we used the QuickBasic programminglanguage, version 4.0, from Microsoft Corporation.

III. Results and Discussion

Light-Response Curves of Oxygen Evolution in the Thy-lakoid Membrane. Figure 1 displays the oxygen evolution (OE)observed in thylakoid membranes irradiated with white lightof photon flux densities (I) between 60 and 1000µmol‚m-2‚s-1.We note first that the variation of OE withI is characterized bya sharp increase at low light intensities followed by a quite lowerdOE/dI rate at high irradiance. This trend has usually beenreported in the literature (see, e.g., refs 18 and 32). The firstquestion addressed here is to investigate which mathematicalmodel is the best representation (or mathematical solution) ofthe experimental OE versusI data. This is especially importantfor the study of the combined effect of light intensity andâ-CDconcentration on the oxygen evolution in the thylakoid mem-brane undertaken in section IV.

Hereunder, we use two mathematical models, that is, anexponential function (model I) or a hyperbola (model II), whichhave relevant phenomenological significance. That is, in modelI, we determine the best mathematical fit with the hypothesisof the cumulative one-hit Poisson probability distribution,14 andin model II, we use the steady-state approximation for the caseof alternating slow and fast reactions.33

Model I. The experimental data displayed in Figure 1 arefitted with an exponential expression for OEth, that is, thetheoretical oxygen evolution as a function ofI, the photon fluxdensity,

where OEth(max), the maximum oxygen evolution, is given inµmol 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 bestfit of OEth versusI is the theoretical light-response curve shownin Figure 1. The mathematical simulations performed with thecurve fitting tool of the Origin software (see Materials andMethods) yielded the expression

that clearly cannot represent adequately the experimental oxygenevolution data obtained with light intensities between 60 and1000µmol of photons/m2‚s.

It is interesting that eq 2 is similar to the mathematicalexpression for the cumulative one-hit Poisson probabilitydistribution developed by Mauzerall and Greenbaum,14 that is,

whereY(z) is the yield of a photoproduct,Yo(z) is the yield ofthe photoproduct per hit or closing of a reaction center,σ(z) isthe optical cross section for absorption of a photon by a unitforming 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 werenot hit. A simple transformation of eq 2 to change-kI into-ko(z)It, where the termIt, with t ) duration of irradiation, isthe fluence (orE in eq 4), shows thatko(z) is the equivalent ofthe optical cross section for absorption of a photon by a unitforming z, or σ(z) (eq 4).

The above discussions and the theoretical result displayed inFigure 1 are a good indication that the cumulative one-hitPoisson probability distribution14 does not yield a reliablerepresentation of the experimental data. This conclusion isfurther illustrated upon comparing the results in Figure 1(untreated thylakoid membranes) with data obtained withâ-CD-treated thylakoid membranes (Figure 2 and Table 1). Figure 2shows the light-response curves of oxygen evolution in thylakoidmembranes treated withâ-CD concentrations from 10 to 14mM. For comparison purposes, the figure also contains theresults obtained with control (untreated) preparations.

Figure 2 shows that allâ-CD concentrations used enhanceconsiderably the oxygen evolution. Furthermore, the dOE/dI ratevaries according to a trend which is similar to the one observedin control (untreated) thylakoid membranes. The results of thecalculations are summarized in Table 1. The table collects (i)the oxygen evolution data obtained experimentally, OEobs, uponirradiating untreated andâ-CD-treated thylakoids thylakoidmembranes with white light of saturating intensity, that is,∼5000 µmol of photons/m2‚s, (ii) the theoretical oxygenevolution maxima, OEth(max), computed forâ-CD concentra-

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

OEth ) OEth(max)(1- e-kI) (2)

OEth ) 132.9 ((3.6) (1- e-0.0082((0.0007)I) (3)

Y(z) ) Yo(z)(1 - e-σ(z)E) (4)

Nonlinear Enhancement of OE in Thylakoid Membranes J. Phys. Chem. B, Vol. 109, No. 30, 200514709

tions between 10 and 14 mM, and (iii) the values of theparameterk (see eq 2).

Table 1 shows that the OEth(max) values calculated accordingto model I are quite different from the OEobs values. Forexample, in thylakoid membranes treated with 12 mMâ-CD,one gets OEth(max) ) 278.2( 7.2 µmol of O2 evolution/(mgof Chl‚h) which is about 24% smaller than OEobs at the sameâ-CD concentration, that is, 364.9( 15.2µmol of O2 evolution/(mg of Chl‚h) (cf. Table 2). In brief, one sees in Table 2 thatthe estimated errors in the calculations of OEth(max) with eq 2vary between about 15 and 24%.

Model II. We show in Figure 1 that the experimental dataobtained with light intensities from 60 to 1100µmol of photons/m2‚s are well fitted with the hyperbolic expression

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

L1/2 is the irradiance giving OEth(max)/2, andI is defined above.OEth(max) andL1/2 for control thylakoid membranes (i.e., nottreated withâ-CD) were computed with eq 5 using the curvefitting tool of the Origin software (see Materials and Methods).

First, Table 1 shows that calculation of the data obtained withcontrol (not treated) thylakoid membranes yields OEth(max))151.0( 3.8 µmol of O2 evolution/(mg of Chl‚h) andL1/2 )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 themaximum oxygen evolution obtained under experimental condi-tions of high irradiance. Second, Table 1 collects the result ofcalculations of data obtained with thylakoid membranes treatedwith 10-14 mM â-CD. In addition, Table 2 reveals that theestimated error in the determination of OEth(max) with eq 5 isbetween 0.7 and 12% which is significantly smaller than theerror 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 ourexperiments, the steady-state approximation33 expressed by thehyperbolic function of eq 5 is a better representation of the effectof light intensity on the electron transport through PSII inisolated thylakoid membranes than the exponential model ofeq 2 for the cumulative one-hit Poisson probability distribution.14

Furthermore, we note that none of theâ-CD concentrations usedin the experiments reported here change the hyperbolic shapeof the light-response curves displayed in Figure 2. Thiscorroborates the argument that model II is a valid representationof the variation of oxygen evolution with the light intensity.Finally, it is interesting to remark that some experimental datapublished in the literature can also be correctly fitted with ahyperbolic function (see note 34).

Toward a Phenomenological Interpretation of Model II.TheOEth dependence onI seen in Figure 1 is explained hereunderin terms of the steady-state approximation33 of the electrontransfer kinetics which is consistent with the conditions of ourexperiments. An attractive aspect of the steady-state approxima-tion is that it permits the mathematical representation of a seriesof coupled sequences of reactions where slow and fast kinetics(or vice versa) alternate. This concept is applied in Scheme 1to describe the energy transfer from an excited chlorophyll fromthe PSII antenna, that is, ChlaII*, to the PSII reaction centerChl (i.e., P680) followed by the transfer of an electron fromP680* to an oxidized peophytin (Phe) (reaction 1) and then fromPhe- to the primary quinone QA (reaction 2). For the sake of a

TABLE 1: Comparison of Oxygen Evolution Observed in Isolated Thylakoid Membranes (OEobs)a,b with Data Obtained fromTheoretical Simulations (OEth)c,d

oxygen evolution,µmol of O2/(mg of Chl‚h) L1/2, µmol of photons/m2‚s k, m2‚(µmol of photons)-1‚s

â-CD, mΜ OEobse OEth(max) SE Cvarf L1/2 SE Cvar k SE Cvar

0 155.4 3.3 2.1132.9c 3.6 2.7 0.008 20 0.000 70 8.5151.0d 3.8 2.5 97.5 9.0 9.2

10 282.9 9.5 3.4218.1c 4.9 2.2 0.007 36 0.000 51 6.9255.0d 7.4 2.9 118.7 11.5 9.7

12 364.9 15.2 4.2278.2c 7.2 2.6 0.004 75 0.000 37 7.8342.9d 8.4 2.4 209.1 15.3 7.3

14 427.2 16.5 3.9349.4c 4.9 1.4 0.003 73 0.000 16 4.3449.4d 11.4 2.5 295.5 20.6 7.0

a Abbreviations: â-CD, â-cyclodextrin; I, light intensity inµmol of photons/m2‚s; k, cross section for absorption of a photon× duration ofillumination (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 (∼5000µmol 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 theâ-cyclodextrin (â-CD) concentration on the oxygen evolution in isolatedthylakoid membranes. The theoretical curves were obtained with Origin5.0 (see Materials and Methods). Chl, chlorophyll.

OEth ) OEth(max)I/(L1/2 + I) (5)

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more comprehensible photochemical context, we have alsorepresented in Scheme 1 the pathway of P680+ reduction byelectrons originating in the H2O photolysis and transferred tothe oxidized Mn cluster (MnC+) and then from MnC to thetyrosine 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 thatreaction 1 is slow (6-10 ns) compared with reaction 2 whichtakes place in less than 400 ps. This means that Phe- neverattains a significant concentration during the course of thereaction, since as it is formed, it reacts rapidly with the primaryquinone QA to produce the reduced form QA

-. Hence, thevelocity of reaction 1 is about identical to the velocity of reaction2, that is,

According to the steady-state approximation, equilibria suchas the one described by eq 6 have mathematical solutions whichare usually represented by hyperbolic functions.33 This is thecase of the hyperbola of eq 5 where consequently OEth(max)andL1/2 contain specific functional and structural information.A direct interpretation is to take (i) OEth(max) as a measure ofthe maximum number of PSII reaction centers open for electrontransport through PSII and (ii)L1/2 as thek2/k1 ratio, that is, theequilibrium between the electron transfer from Phe- to theprimary quinone QA and the formation of the reduced Phemolecule in the PSII reaction center (see also note 38).

Nonlinearity of the â-CD Concentration Curves of OxygenEvolution. We show in Figure 3 that the effect of theâ-CDconcentration on oxygen evolution in isolated thylakoid mem-branes irradiated with white light of saturation intensity (∼5000µmol of photons/m2‚s) is the enhancement of oxygen evolutionaccording to a sigmoid curve displaying a sharp inflection point,or transition. The theoretical representation of the nonlinearenhancement of oxygen evolution brought about by increasing

â-CD concentration was attempted previously9 with a math-ematical expression for the hypothesis of an allosteric transitionwith many binding sites (see discussions in refs 23, 30, and31). The theoretical dose-response curve is the Hill equation

where OEth is the steady-state rate of oxygen evolution at variousâ-CD concentrations, OEth(max) the maximum oxygen-evolvingactivity, C the cyclodextrin concentration,K1/2 the concentrationof cyclodextrin that resulted in half-maximal oxygen-evolvingactivity, that is, OEth(max)/2, andn the Hill coefficient, that is,the number of cyclodextrin binding sites. In eq 7, the term [Cn/(K1/2

n + Cn)] is the fraction of active cyclodextrin receptors inthe thylakoid membrane. It is noted that the theoretical upperlimit of oxygen evolution in Figure 3, that is, OEth(max)= 453µmol of O2 evolution/(mg of Chl‚h), can only be attained atâ-CD concentrations higher than 20 mM which are out of thesolubility range of the cyclodextrins. However, the oxygenevolution observed in thylakoid membranes treated with 14 mMâ-CD, that is, 427.2µmol of O2 evolution/(mg of Chl‚h), isquite close to the theoretical maximum.

TABLE 2: Estimated Error in the Determination of Oxygen Evolution with Model I and Model II in Relation to the ObservedOxygen Evolution in Thylakoid Membranes Untreated and Treated with Various â-Cyclodextrin Concentrationsa

µmol of O2 evolution/(mg of Chl‚h) %∆OEth(5K)b or %∆OEth(max)c

â-CD, mM model 0 10 12 14 0 10 12 14

OEobsd 155.4 282.9 364.9 427.2

OEth(5K) Ie 132.9 218.1 278.2 349.4 14.5 22.9 23.8 18.2II f 148.1 249.1 329.1 424.3 4.7 12.0 9.8 0.7

OEth(max) I 132.9 218.1 278.2 349.4 14.5 22.9 23.8 18.2II 151.0 255.0 342.9 449.4 2.8 9.9 6.0 -5.2

a Abbreviations: â-CD, â-cyclodextrin; I, light intensity inµmol of photons/m2‚s; k, cross section for absorption of a photon× duration ofillumination (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 5000µmol 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 membraneswere 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

k1[P680*][Phe]= k2[Phe-][QA] (6)

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

OEth ) OEth(max)[Cn/(K1/2n + Cn)] (7)

Nonlinear Enhancement of OE in Thylakoid Membranes J. Phys. Chem. B, Vol. 109, No. 30, 200514711

To determine the characteristics of theâ-CD effect atirradiances far from the saturating light conditions of Figure 3we performed experiments under low light intensity conditionsand at irradiances up to 1100µmol of photons/m2‚s. The three-dimensional graph in Figure 4 presents the combined effect ofirradiance (60-1100µmol of photons/m2‚s) andâ-CD concen-tration (6-14 mM) on oxygen evolution in isolated thylakoidmembranes. We remark first that all light-response curves ofoxygen evolution in Figure 4 were shown to be well fitted withhyperbolic functions (cf. Table 1). Unexpectedly, however,Figure 4 reveals that a neat S-shaped (sigmoid) curve of oxygenevolution enhancement with increasingâ-CD concentration ofthe type seen in Figure 3 is observed only at irradiances higherthan approximately 300µmol of photons/m2‚s.

At photon flux densities lower than about 300µmol ofphotons/m2‚s, the oxygen evolution variation withâ-CD con-centration is small. This is best seen in Figure 5 which displaysthe oxygen evolution observed inâ-CD-treated thylakoidmembranes irradiated with light intensities of 66, 100, and 1000µmol of photons/m2‚s. We note at first that the shape of thelow light intensity curves is quite different from the sigmoidshape seen at high light intensity. In short, the oxygen evolutionincreases to a maximum atâ-CD concentrations between 10and 12 mM and then decreases to a lower steady level.

IV. Modeling the Combined Effect of Irradiance andâ-CD Concentration

We examine in this section the constraints to be introducedin the light-response curves of oxygen evolution (Figure 2) inorder to include the sigmoid character of theâ-CD concentrationeffect as is seen in the OE evolution versusâ-CD concentrationcurve displayed in Figure 3. The aim is to deduce a mathematicalexpression more general than the hyperbolic function of eq 5to include the sigmoid aspect of theâ-CD concentration effecton oxygen evolution. In other words, the modified eq 5 mightdescribe completely the oxygen evolution data seen in the three-dimensional graph of Figure 4 for a broad range of irradiancesandâ-CD concentrations.

â-CD Effect on OEmax and L1/2 in Light-Response Curvesof Oxygen Evolution. The purpose here is to rewrite eq 5 in

order to correct the values of OEmax andL1/2 observed in controlthylakoid membranes (in the absence ofâ-CD), that is, OEmax-(0) andL1/2(0). To this end, OEmax(0) andL1/2(0) are multipliedby scale functions dependent on theâ-CD concentration (C),that is,G1(C) andG2(C), to transform eq 5 into eq 8

Determination of G1(C) and G2(C): Step 1.Analysis of thedata in Table 1 reveals that OEmax andL1/2 vary according tosigmoid functions of the type given by eq 7 according to thegeneral expression

whereGi(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 theâ-CD-mediated maximum increase of oxygen evolution, andK1/2 isdefined above (cf. eq 7). It is emphasized that, in the absenceof â-CD, that is, forC ) 0 in eq 9,Gi(C) is equal to 1 and eq8 reverts to the expression given by eq 5.

Determination of G1(C) and G2(C): Step 2.The results ofthe mathematical simulations are the following two expressions

Equations 10 and 11 show that the nonlinear variation ofG1-(C) andG2(C) is sigmoidal, as was expected from analysis ofthe OEmax(0) and L1/2(0) data in Table 1. However, thesigmoidicity is not identical, as is seen in the relative magnitudesof p, n, andK1/2 which, therefore, shall influence the data yieldedby eq 8.

Surface of Occupancy.The computed values of the Hillcoefficients (n) in eqs 10 and 11 are largely different, that is,4.8 in G1(C) and 7.8 inG2(C). We recall that the size ofn is amesure of the number of cyclodextrin binding sites in thethylakoid membrane.9 Therefore, the magnitude ofn in eqs 10

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

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

OEth ) [OEmax(0) G1(C)]I/[L1/2(0) G2(C) + I] (8)

Gi(C) ) 1 + p[Cn/(K1/2n + Cn)] (9)

G1(C) ) 1 + 3.3C4.8/(13.14.8 + C4.8) (10)

G2(C) ) 1 + 5.2C7.8/(14.87.8 + C7.8) (11)

14712 J. Phys. Chem. B, Vol. 109, No. 30, 2005 Fragata and Dudekula

and 11 indicates the presence in the thylakoid membrane surfaceof at least two specific molecular targets, or binding sites, forâ-CD which have quite different sizes. Taking into account thatthe cross section of aâ-CD molecule is about 1.84 nm2 (cf.refs 1 and 2), a simple calculation shows that, forn ) 4.8, orsay fiveâ-CD molecules, one has a thylakoid membrane surfaceof occupancy of about 9.2 nm2, whereas, forn ) 7.8, or∼8,the calculated surface of occupancy is approximately 14.7 nm2.These size differences of the molecular surface of docking ofâ-CD in the thylakoid membrane is likely at the origin of distinctstructural and functional changes.

Theoretical Representation of the Effect of Light Intensityand â-CD Concentration.Substitution of the expressions givenby eqs 10 and 11 forG1(C) and G2(C) in eq 8 results in thefollowing general expression (eq 12) for oxygen evolution inâ-CD-treated thylakoid membranes irradiated with low and highphoton flux densities

The three-dimensional representation displayed in Figure 6 wasobtained with OEmax(0) ) 151.0µmol of O2 evolution/(mg ofChl‚h) andL1/2(0) ) 97.5µmol of photons/m2‚s, as is indicatedin eq 12 and Table 1.

The theoretical representation of the oxygen evolution (OEth)as a function ofI and C (Figure 6) was tested against theexperimental data displayed in Figure 2 (OEobs). For thispurpose, we used software written with the QuickBasic pro-gramming language, version 4.0, from Microsoft Corporation.The calculated percentage error (%OEr) is represented in Figure7. One sees that the average %OEr is between 2 and 9% and inmost cases not greater than 13%. Furthermore, the predictivevalue of the model was assayed for several sets of observedand theoretical data. For example, eq 12 yields OEth ) 198.4µmol of O2 evolution/(mg of Chl‚h) for I ) 400 µmol ofphotons/m2‚s andC ) 10 mM, whereas for these sameI andCvalues the observed oxygen evolution is 209µmol of O2

evolution/(mg of Chl‚h) (cf. Figure 2), that is, an error ofapproximately 5.3% which is small enough to confirm the

quality of the model. In general, the calculations performed witheq 12 show a notable convergence between theory and experi-ment.

V. Concluding Remarks

First, we showed that the light response of oxygen evolutionin isolated thylakoid membranes irradiated with white lightunder steady-state conditions is well represented by a hyperbolicfunction (Figure 1 and Table 1), the shape of which is notaffected by theâ-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 effectof light flashes of high intensity and very short duration onwhole leaves and other plant materials. On one hand, Poissonstatistics is mandatory for the interpretation of data obtainedwith optically thin samples irradiated with single turnover flashesof monochromatic light.14 On the other hand, the steady-stateapproximation applied to the kinetics of electron transportthrough PSII justifies the use of a hyperbolic representationinstead of an exponential function. These apparent discrepanciesindicate the need for further investigations.

Second, we found that the sigmoid trend of theâ-CDconcentration effect on the oxygen evolution in thylakoidmembranes irradiated with white light of saturating intensity,that is, about 5000µmol of photons/m2‚s (Figure 3), is not seenunder low light intensity conditions, for example, less than∼300µmol of photons/m2‚s (Figure 4). This dual aspect of theâ-CDeffect has some connection to the photosynthetic activitydifferences observed previously in plant materials irradiated withlow and high light intensities.15-17 In this respect, it isparticularly interesting that the differences between low and highirradiance are ascribed in ref 17 to dissimilarities in molecularorganization, that is, to the presence in the photosyntheticmembrane of at least two populations of PSII centers withdistinct properties. This conclusion gives support to our previoussuggestion that the cyclodextrins cause the cooperative associa-tion of PSII units.9

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

Figure 7. Error (%OEr) between theoretical and experimental dataobserved in the study of the effect of the light intensity (µmol ofphotons/m2‚s) and theâ-cyclodextrin (â-CD) concentration on theoxygen evolution in isolated thylakoid membranes. The theoretical datawere obtained with eq 12 (see text and Figure 6), and the experimentaldata are those given in Figure 2.

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)

Nonlinear Enhancement of OE in Thylakoid Membranes J. Phys. Chem. B, Vol. 109, No. 30, 200514713

A major issue in this work is the demonstration that thecombined effect of light intensity andâ-CD concentration onoxygen evolution (Figures 4 and 6) is well represented by eq12 in which the irradiance effect on oxygen evolution is fittedwith a hyperbolic function and theâ-CD concentration effectis described by a mathematical expression for the hypothesisof an allosteric transition with many binding sites (see discus-sions in refs 23, 30, and 31). In the latter case, the theoreticalâ-CD dose-response curve is eq 7, that is, a Hill-type equation.We conclude that the theoretical result yielded by eq 12 is areliable approximation of the combined effect of light intensityand â-CD concentration on oxygen evolution in isolatedthylakoid membranes, therefore indicating that the model has asignificant value for predicting the outcome of associatedphotochemical and biochemical reactions.

Acknowledgment. This work was supported by grants toM.F. from the Natural Sciences and Engineering ResearchCouncil of Canada. We thank Dr. S. Govindachary, Mr. P.-O.Hebert-Mercier, and Mr. E. Richard for very helpful discussionsand the reviewers for having called our attention to a fewambiguities in the text, thereby helping to improve the qualityof 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.Biochemistry1993, 32, 6836.(5) Rawyler. A.; Siegenthaler, P.-A.Biochim. Biophys. Acta1996, 1278,

89.(6) Duchene, 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. InPhotosynthesis: Fundamental Aspects

to Global PerspectiVes; van der Est, A., Bruce, D., Eds.; ACG Publishing:Lawrence, KS, 2005.

(11) Fragata, M.; Norde´n, B.; Kurucsev, T.Photochem. Photobiol.1988,47, 133.

(12) Norden, 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. B2005,109, 1313.

(14) Mauzerall, D.; Greenbaum, N. L.Biochim. Biophys. Acta1989,974, 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.

(19) Lavergne, J.; Trissl, H.-W.Biophys. J.1995, 68, 2474.(20) Lavergne, J.; Briantais, J.-M. InOxygenic Photosynthesis: The Light

Reactions; Ort, D. R., Yocum, C. F., Eds.; Kluwer Academic Publishers:Dordrecht, The Netherlands, 1996; p 265.

(21) Lazar, D. Biochim. Biophys. Acta1999, 1412, 1.(22) Falkowski, P. G.; Wyman, K.; Ley, A. C.; Mauzerall, D. C.Biochim.

Biophys. Acta1986, 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) Nenonene, 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) Nenonene, E. K.; Methot, 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) Kromer, 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: EnglewoodCliffs, NJ, 1995.

(34) The relationship between electron transport in photosyntheticmembranes and the photon flux density has been reported often. Forexample, in Figure 2 of ref 18, experimental data are presented on therelation of the CO2 assimilation rate (µmol‚m-2‚s-1) in leaves of wild-typebarley and the photon flux density (µmol of quanta/m2‚s). We performedthe mathematical modeling of the empirical graphical representations givenin ref 18 and showed that the data cannot be fitted with any of the severalexponential functions studied. The best fit of the CO2 assimilation rate (y)was found to be the expressiony ) 36.2(1- e-0.003I), whereI is the photonflux density. This equation is nevertheless clearly inadequate. On thecontrary, a good representation of the experimental data in ref 18 is givenby the hyperbolic functiony ) 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.Photosynthetica1981, 15, 592.(37) Jursinic, P. A. InLight 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 simplydelineated in the following generally accepted molecular equilibria (see,e.g., Figure 3 in ref 37) with ratesk1 andk2:

In this approximation, the sequence of photochemical and biochemicalevents is limited to the instant of the absorption of a photon by P680 andthe subsequent electron transfer up to the oxidized form of QA. Interestingly,the final result of the mathematical deductions is invariably a hyperbolicexpression of the type given by eq 5 withL1/2 ) k2/k1. A detailed accountof this matter shall be presented in another paper.

P680*‚Phe‚QA 98k1

P680+‚Phe-‚QA 98k2

P680+‚Phe‚QA-

14714 J. Phys. Chem. B, Vol. 109, No. 30, 2005 Fragata and Dudekula