Theoretical Consideration of the Use of a Langmuir Adsorption Isotherm To Describe theEffect of Light Intensity on Electron Transfer in Photosystem II

Mario Fragata,* Venkataramanaiah Viruvuru, and Subhan Dudekula†

UniVersitedu Quebec aTrois-RiVieres, Departement de Chimie-Biologie, Section de Chimie et Biochimie,Trois-RiVieres, Que´bec, G9A 5H7, Canada

ReceiVed: December 7, 2006; In Final Form: January 23, 2007

Electron transport through photosystem II (PSII), measured as oxygen evolution, was investigated in isolatedPSII particles and thylakoid membranes irradiated with white light of intensities (I) of 20 to about 4000µmolof photons/(m2‚s). In steady-state conditions, the evolution of oxygen varies withI according to the hyperbolicexpression OEth ) OEth(max)I/(L1/2 + I) (eq i) where OEth is the theoretical oxygen evolution, OEth(max) isthe maximum oxygen evolution, andL1/2 is the light intensity giving OEth(max)/2. In this work, the mathematicalderivation of this relationship was performed by using the Langmuir adsorption isotherm and assuming thatthe photon interaction with the chlorophyll (Chl) in the PSII reaction center is a heterogeneous reaction inwhich the light is represented as a stream of particles instead of an electromagnetic wave (see discussion inTurro, N. J.Modern Molecular Photochemistry; University Science Books: Mill Valley, CA, 1991). Inaccordance with this approximation, the Chl molecules (P680) were taken as the adsorption surfaces (orheterogeneous catalysts), and the incident (or exciting) photons as the substrate, or the reagent. Using thesenotions, we demonstrated that eq i (Langmuir equation) is a reliable interpretation of the photon-P680 interactionand the subsequent electron transfer from the excited state P680, i.e., P680*, to the oxidized pheophytin(Phe), then from Phe- to the primary quinone QA. First, eq i contains specific functional and structuralinformation that is apparent in the definition of OEth(max) as a measure of the maximal number of PSIIreaction centers open for photochemistry, andL1/2 as the equilibrium between the electron transfer from Phe-

to QA and the formation of reduced Phe in the PSII reaction center by electrons in provenance from P680*.Second, a physiological control mechanism in eq i is proved by the observation that the magnitudes of OEth-(max) andL1/2 are affected differently by exogenous PSII stimulators of oxygen evolution (Fragata, M.;Dudekula, S.J. Phys. Chem. B2005, 109, 14707). Finally, an unexpected new concept, implicit in eq i, is theconsideration of the photon as the substrate in the photochemical reactions taking place in the PSII reactioncenter. We conclude that the Langmuir equation (eq i) is a novel mathematical formulation of energy andelectron transfer in photosystem II.

I. Introduction

In oxygenic photosynthesis the photosystem II (PSII) complexcatalyzes the oxidation of water at the Mn4Ca cluster. This givesrise to the evolution of oxygen and the transfer of electrons tothe primary (QA) and secondary (QB) quinone acceptors inrespectively the D2 and the D1 proteins.1-3 First, there isformation of an excited-state chlorophyll (Chl), i.e., P680*, inthe PSII reaction center upon absorption of photons via energytransfer from the antenna Chl. Second, an electron is transferredfrom P680* to the oxidized peophytin (Phe) with concomitantformation of P680+. Then, Phe- reduces the primary quinoneQA, a plastoquinone (PQ) tightly bound noncovalently to theQA site in the PSII complex. In the next step, QA

-• reduces themobile plastoquinone QB to the semiquinone QB-• which has ahigh affinity to the QB site.4 Upon a second reduction and aprotonation, QB-• becomes PQH2 (plastoquinol), which israpidly exchanged for an oxidized plastoquinone from the PQpool.4-6 Finally, the steady-state function of the PSII electrontransport chain is maintained by the two remaining redox steps.

That is, the reduction of P680+ by the Tyr 161 in the D1 proteinand the transfer of an electron from the Mn4Ca cluster to theoxidized Tyr 161 (for structural details see, e.g., ref 7).

The general trend of the variation of oxygen evolution (OE)with the light intensity (I) is first a sharp OE increase at lowIfollowed, at high irradiance, by a gradual decrease of the dOE/dI rate to what has been often described as the upper steadyOE limit, or maximum oxygen evolution (see, e.g., refs 8-19).The mathematical formulation of the photosynthetic activitydependence on the light intensity was attempted in a wide varietyof plant materials (see review of earlier work in ref 20, andmore recent studies in refs 16 and 19). Although theseinvestigations have a practical value in the prediction of thebiomass productivity, their significance as phenomenologicaldescriptions of the photosynthetic mechanisms is in generalrather limited. In a different perspective, the shape of the light-response curves was examined in a few works with the aim ofproviding fundamental descriptions of the light intensity effecton photosyntyhesis using either an exponential function appliedto the hypothesis of a cumulative one-hit Poisson probabilitydistribution21-23 or a hyperbolic expression derived from thesteady-state approximation of coupled reactions where slow andfast kinetics alternate.18

* Address correspondence to this author. Phone: 819-3765011. Fax: 819-3765057. E-mail: fragata@uqtr.ca.

† Present address: Department of Chemistry, National Cheng KungUniversity, Tainan-70101, Taiwan.

3315J. Phys. Chem. B2007,111,3315-3320

10.1021/jp0684271 CCC: $37.00 © 2007 American Chemical SocietyPublished on Web 03/06/2007

First, the cumulative one-hit Poisson probability distributionis usually represented by the general equation22

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, andE is the fluence, i.e., the photons per unit area.Moreover, the term e-σ(z)E in eq 1 is the fraction of targets whichwere not hit. This type of mathematical representation was alsoused in ref 18 to simulate the oxygen evolution as a functionof I in isolated thylakoid membranes, i.e.,

where OEth is the theoretical oxygen evolution inµmol ofoxygen evolution/(mg of Chl.h), OEth(max) is the maximumoxygen evolution, andk (cross section for absorption of a photon× duration of illumination) is given in m2‚(µmol of photons)-1‚s.

Second, application of the steady-state approximation24 to theoxygen evolution in isolated thylakoid membranes under variouslight intensity conditions yielded the hyperbola18

where OEth, OEth(max), andI are defined above, andL1/2 is theirradiance giving OEth(max)/2. It was also found18 that the trendof the light-response curves is not affected in thylakoidmembranes incubated withâ-cyclodextrin, an efficient exog-enous stimulator of oxygen evolution in photosystem II.

Most interestingly, we showed in ref 18 that only thehyperbolic model represented by eq 3 is a relevant descriptionof the effect of light intensity on the electron transport throughPSII in isolated thylakoid membranes. However, we note thatboth eqs 1 and 3 are supported by appropriate fundamentalconcepts.18,22 This is an intriguing question that so far has notbeen explained satisfactorily. An attractive prospect is tointegrate the Poisson and the hyperbolic models in a singlegeneral equation, meaning in that case that one needs to developmore detailed analyses of their underlying principles. As a steptoward this end, we use in the present work the Langmuiradsorption isotherm25 to examine the theoretical bases of thehyperbolic model.

In the first part of this work (section III), we determinedwhether the hyperbolic model is adequate to describe theelectron transfer through photosystem II, estimated as oxygenevolution, in isolated PSII particles. In the second part of thework (section IV), the Langmuir adsorption isotherm is appliedto the energy transfer from the excited state Chla in the PSIIantenna to P680 on the one hand, and the electron transfer fromP680* to Phe on the other hand. Implicitly, the question of thephoton as the substrate26 in the photochemical reactions takingplace in the PSII reaction center shall be discussed. The workends (section V) with some comments on this new applicationof the Langmuir adsorption isotherm, i.e., a novel mathematicaldescription of energy and electron transfer in photosystem II.

II. Experimental Section

Chemicals. The chemicals used in the present work wereobtained from Sigma Chemical Company (St. Louis, MO) andFisher Scientific Company (Fair Lawn, NJ).

Isolation of Thylakoid Membranes and Photosystem IIParticles. Primary leaves from 6 to 8 day old seedlings frombarley (HordeumVulgare) were used throughout this work. The

methods used below to isolate the thylakoid membranes andthe PSII particles are those described in refs 18, 27, and 28.

To isolate thylakoids membranes the barley leaves werehomogenized in a buffer containing 50 mM Tricine-NaOH (N-tris[hydroxymethyl]-methylglycine-NaOH) (pH 7.8), 400 mMsorbitol, 10 mM NaCl, and 5 mM MgCl2 (buffer A) at 273 K.The resultant slurry was filtered through eight layers ofcheesecloth. The filtrate was centrifuged at 2460 g for 5 min at277 K to precipitate the chloroplasts which were centrifugedagain upon suspension in buffer A. This chloroplast preparationwas collected in a buffer containing 50 mM Tricine-NaOH (pH7.8), 10 mM NaCl, and 5 mM MgCl2 (buffer B), and centrifugedimmediately at 2460 g for 5 min at 277 K. The pellet containedthe thylakoid membranes which were dispersed in a buffercontaining 20 mM MES-NaOH (2-[N-morpholino]ethanesul-fonic acid-NaOH) (pH 6.5), 400 mM sucrose, 15 mM NaCl,and 5 mM MgCl2 (buffer C), and centrifuged at 2200 g for 5min at 277 K. The final pellet was diluted in buffer C to givea final chlorophyll concentration of 2 mg/mL, and stored at193 K.

To isolate PSII particles, 10 mL of the stock solution ofthylakoid membranes (2 mg Chl/mL; see above) was mixedwith 5 mL of buffer C and kept on ice. With very slow mixingof the thylakoids using flea and stirrer, 8% Triton X-100 (5mL) was added carefully drop by drop to a final Chl:TritonX-100 concentration ratio of 20:1. The suspension was incubatedfor 10 min in the dark and immediately centrifuged at 2200 gfor 3 min at 277 K. The supernatant was transferred to prechilledcentrifuge tubes and centrifuged at 35 300 g for 20 min at 277K. The pellet was dissolved in a minimal volume of buffer C,using brush and vortex, and then about 10 to 15 mL of bufferC was added followed by centrifugation at 35 300 g for 20 minat 277 K. The resultant pellet was dissolved in a minimal volumeof buffer C (2 mL). The PSII particles thus obtained were storedeither in a deep freezer (193 K) or in liquid nitrogen.

The chlorophyll concentration of the isolated thylakoidmembranes and PSII particles was measured in 80% acetone(v/v) according to the method described in ref 29, and theirpolypeptide composition was analyzed by SDS-polyacrylamidegel electrophoresis according to standard procedures describedin refs 18 and 28.

Measurement of Electron Transport through PhotosystemII. Electron transport through photosystem II, estimated asoxygen evolution, was measured with a Hansatech OxygenElectrode (Hansatech Instruments Ltd., Norfolk, UK) connectedto a temperature-controlled water circulator at 298 K. The assaymixtures contained samples of isolated PSII particles or thyla-koid membranes (12.5µg Chl/mL) suspended in a oxygenevolution measurement buffer (pH 6.5) constituted of 20 mMMES-NaOH, 400 mM sucrose, 15 mM NaCl, 5 mM MgCl2,and 350 µM 2,6-dichloro-p-benzoquinone as the electronacceptor.18

Irradiation Conditions and Measurement of Photon FluxDensities.Irradiation of the suspensions of thylakoid membraneor PSII particles was performed with artificial white light froma Fiber-Lite High Intensity Illuminator, model 180, from Dolan-Jenner Industries Inc. (Lawrence, MA). The light source of thisilluminator is a EKE lamp that has a spectral range spanningthe ultraviolet (UV), the visible, and the near-infrared (NIR)regions (see http://www.spectralproducts.com). We note firstthat in the conditions of our experiments (i) the UV light iseliminated by the glass walls of the oxygen evolution chamberand (ii) the NIR radiation is not used by the photosyntheticsystems and, in addition, cannot be detected by the LI-190SB

Y(z) ) Yo(z)(1 - e-σ(z)E) (1)

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

OEth ) OEth(max)I/(L1/2 + I) (3)

3316 J. Phys. Chem. B, Vol. 111, No. 12, 2007 Fragata et al.

quantum sensor described below. Therefore, the photosyntheti-cally active radiation (PAR) of the EKE lamp, i.e., from about380 to 720 nm, coincides with the absorption of visible lightby the chlorophyll and pheophytin pigments present in theantenna and reaction center complexes.

The measurement of the photon flux densities (µmol ofphotons/(m2‚s)) was done with a Quantum Photometer, modelLI-185B, from LI-COR, Inc. (Lincoln, NE), which was equippedwith a LI-190SB quantum sensor. This sensor measures PARlight in the wavelength range from 400 to 700 nm (see Figure4 in the LI-COR Terrestrial Radiation Sensors, Type SBInstruction Manual). It is important to remark that the PAR rangeof the LI-190SB quantum sensor covers the absorption spectraof the photosynthetic pigments therefore in accord with thecharacteristics of the Dolan-Jenner illuminator, model 180,described above.

Data Analysis. The software programs used to fit theexperimental data in this work with the mathematical expres-sions discussed in section III are Origin, version 5, fromMicrocal Software, Inc. (Northampton, MA), and Maple V,release 5.1, from Waterloo Maple Inc. (Waterloo, ON, Canada).

III. Light-Response Curves of Oxygen Evolution inPhotosystem II

Figure 1 displays the oxygen evolution observed in isolatedPSII particles and thylakoid membranes irradiated with whitelight of photon flux densities (I) from 22 to about 4000µmolof photons/(m2‚s). The trend of the OE variation withI is firsta sharp increase at low light intensities followed by a quite lowerdOE/dI rate at high irradiance in accord with what has beenreported in the literature (see Introduction). Figure 1 shows alsothat the experimental data are well represented with thehyperbola OEth ) OEth(max)I/(L1/2 + I), where OEth, OEth(max),andL1/2 are defined above (see eq 3). The calculated oxygenevolution inµmol of O2 evolution/(mg of Chl.h) in isolated PSIIparticles, OEth(p), and thylakoid membranes, OEth(tm), isexpressed respectively by eqs 4 and 5 below:

The experimental data of Figure 1 are plotted in Figure 2 as1/OEth(p) vs 1/I and 1/OEth(tm) vs 1/I, that is, the Lineweaver-Burk representations. The linear graphics shown in Figure 2were computed with the theoretical data yielded by eqs 4 and5, using the curve-fitting tool of the Origin software (seeExperimental Section). One sees that the agreement betweentheory and experiment is in general excellent except for theoxygen evolution data obtained at very low light intensities.These deviations from linearity originate most likely in theuncertainties inherent to the measurement of low oxygenconcentrations. The theoretical expressions of 1/OEth(p) and1/OEth(tm) are given here by eqs 6 and 7.

We conclude therefore that, in the conditions of our experi-ments, the hyperbolic function of eq 3 is a reliable representationof the effect of light intensity on the electron transport throughPSII, estimated as oxygen evolution, in isolated PSII particlesand thylakoid membranes.

IV. Theoretical Description of the Langmuir AdsorptionIsotherm Model

Although the representation of the effect of light intensityon oxygen evolution (or carbon dioxide consumption) in wholeplant materials and isolated membranes (or membrane frag-ments) was attempted in several instances with a hyperbola orwith hyperbolic-like expressions (see, e.g., refs 16, 19, and 20),no mathematical derivation of the relationship between experi-ment and the hyperbolic model has been formulated. As a steptoward this end, we consider in the approximation describedhere that the interaction of a photon with P680 in the PSIIreaction center is a heterogeneous reaction. This premise isjustified by the knowledge that the formation of the excited stateP680*, i.e., P680+ hν f P680*, is a process involving morethan one phase. That is to say, the Chla molecules (P680) whichare thereby the adsorption surfaces (or heterogeneous catalysts)on the one hand and the phase constituted of incident (orexciting) photons on the other hand. Among the possiblemathematical solutions of systems of this kind, we note thatthe Langmuir equation was often shown to yield consistentdescriptions of the kinetics of heterogeneous catalysis.25 In thisperspective, the Langmuir adsorption isotherm is used in thefollowing section to deduce the hyperbolic expressions whichwere applied previously to represent the effect of the lightintensity on oxygen evolution in photosystem II.

A fundamental matter arising from the foregoing discussionis the question of the photon as the substrate in the photochemi-cal reactions taking place in the PSII reaction center. This notionhas emerged from an argumentation initiated by Turro26 on thenature of the photon as a reagent in chemical reactions in whichlight is represented as a stream of particles instead of anelectromagnetic wave. In accordance with this view, the photonis the reagent for starting up a photoreaction as in the absorptionof light, and the product is the resultant emitted photon orelectron. These concepts were followed in the derivationsformulated here where the photon is taken as the substrate inits interaction with P680, and the reaction product is implicitlythe electron transferred from P680* to the oxidized Phe.

Figure 1. Effect of light intensity on oxygen evolution in isolatedPSII particles and thylakoid membranes. The experimental data aregiven as “mean( SD”. The theoretical curves were obtained frommathematical simulations performed with Origin 5.0 and Maple V (seethe Experimental Section). Chl, chlorophyll; PSII, photosystem II; SD,standard deviation.

OEth(p) ) (802( 8)I/[(836 ( 19) + I] (4)

OEth(tm) ) (203( 16)I/[(365 ( 7) + I] (5)

1/OEth(p) ) 0.00127+ 1.02532(1/I) (6)

1/OEth(tm) ) 0.00488+ 1.78049(1/I) (7)

Effect of Light Intensity on Electron Transfer J. Phys. Chem. B, Vol. 111, No. 12, 20073317

A. The Langmuir Adsorption Isotherm Applied to Elec-tron Transfer through PSII. In this approximation24,25the firststep is the interaction, or collision, of the photons in provenancefrom the PSII antenna with the reaction center chlorophylls(P680). This is depicted in eq 8 below:

wherehν is the excitation quantum, (P680*‚Phe) the transientcomplex between the excited state Chl (i.e., P680*) and Phe,and

where I is the concentration of incident quantahν, i.e., thenumber of photons that hit the Chl molecules available forphotochemistry in the PSII reaction centers.

The electron transfer shown in eq 8 is followed by the transferof an electron from Phe- to QA, which is much faster. In brief,the lifetime of the electron-transfer reaction of eq 8 is lessthan 1 ns,30-32 and between 200 ps34 and 400 ps30,31 for thereaction

In other words, the Phe reduction is much slower than theelectron transfer from Phe- to QA. Thus, Phe- never attains asignificant concentration as it reacts rapidly with the primaryquinone QA to form QA

-•. Consequently, the function of theelectron-transfer chain in the thylakoid membrane is not limitedby the formation of reduced pheophytin.

The Langmuir Adsorption Isotherm Equations.In the chainof reactions displayed in eq 8, the evolution of the transientelectron-transfer complex P680+‚Phe- in the course of time is

expressed as

where k1[P680‚Phe]I is the rate of P680+‚Phe- formation,k2[P680+‚Phe-] is the rate of P680+‚Phe- breakdown, and

is the velocity of electron transfer. Moreover, for steady-state(or quasisteady-state) conditions d[P680+‚Phe-]/dt = 0.24,25

Hence,

From this, the following equilibria are deduced

and

or

whereL1/2 ) (k2 + k3)/k1. It is noted, furthermore, that in thecourse of the reaction the concentration of P680‚Phe availablefor photochemistry is given by

where [P680‚Phe]T is the total concentration of P680‚Phe and[P680+‚Phe-] the concentration of P680‚Phe that underwentelectron transfer. Combining eqs 15 and 16 gives

Upon multiplication of each term of eq 19 byk3, we get

and

sinceV ) k3[P680+‚Phe-] (cf. eq 11 above) andVmax ) k3-[P680‚Phe]T.

It is worth noting that the termI/(L1/2 + I) in eq 21 is a usefulmeasure of the fraction of the total number of open PSII centersavailable for photochemistry as it equals about 0 in low lightintensity conditions and is close to 1 at high irradiance.

Application ofV ) VmaxI/(L1/2 + I) to Oxygen EVolution inPSII. To apply eq 21, i.e.,V ) VmaxI/(L1/2 + I), to electrontransfer through PSII, estimated as oxygen evolution,Vand Vmax are correlated to OEth and OEth(max) (cf. eq 3) byappropriate scale factors, sayR1 and R2, respectively. Thesecorrections yieldV ) R1OEth andVmax ) R2OEth(max), and eq

Figure 2. Lineweaver-Burk plots of the effect of light intensity onoxygen evolution in isolated PSII particles and thylakoid membranes.Chl, chlorophyll; PSII, photosystem II. The linear relationships wereobtained from the theoretical curves displayed in Figure 1 (see alsoeqs 4 and 5 in the text).

P680‚Phe+ hν f

(P680*.Phe){\}k1

k2P680+‚Phe- 98

k3P680+ + Phe- (8)

k1 ) [P680+‚Phe-]/[P680‚Phe]I (8a)

k2 ) [P680‚Phe]I/[P680+‚Phe-] (8b)

k3 ) [P680+][Phe-]/[P680+‚Phe-] (8c)

Phe- + QA f Phe+ QA-• (9)

d[P680+‚Phe-]/dt ) k1[P680‚Phe]I - k2[P680+‚Phe-] -

k3[P680+‚Phe-] (10)

V ) k3[P680+‚Phe-] (11)

d[P680+‚Phe-]/dt ) k1[P680‚Phe]I - k2[P680+‚Phe-] -

k3[P680+‚Phe-] = 0 (12)

k1 [P680‚Phe]I ) (k2 + k3)[P680+‚Phe-] (13)

[P680+‚Phe-] ) [P680‚Phe]I/{(k2 + k3)/k1} (14)

[P680+‚Phe-] ) [P680‚Phe]I/L1/2 (15)

[P680‚Phe]) [P680‚Phe]T - [P680+‚Phe-] (16)

[P680+‚Phe-] ) ([P680‚Phe]T - [P680+‚Phe-])I/L1/2 (17)

[P680+‚Phe-] ) [P680‚Phe]T{(I/L1/2)/(1 + I/L1/2)} (18)

[P680+‚Phe-] ) [P680‚Phe]T{I/(L1/2 + I)} (19)

k3[P680+‚Phe-] ) k3[P680‚Phe]T{I/(L1/2 + I)} (20)

V ) VmaxI/(L1/2 + I) (21)

3318 J. Phys. Chem. B, Vol. 111, No. 12, 2007 Fragata et al.

21 becomes

If the molecular mechanisms that affectR1 at V < Vmax aresimilar to those influencingR2 at Vmax or at electron-transfervelocities close toVmax, a conjecture that is reasonable, one mayconclude thatR1 and R2 are about identical. Then, eq 22 be-comes OEth ) OEth(max)I/(L1/2 + I), which is eq 3 (see sectionsI and III).

The above conjecture is justified for an ensemble of PSIIphotochemical centers presenting small or no differences, thatis, the steady-state approximation conditions of the experimentsdiscussed here. At the molecular and structural levels this meansthat in the ensemble of PSII particles and thylakoid membranesused in the work reported here the electron-transfer velocityVmight not change substantially in the electron sequence fromthe Mn4Ca cluster to the reduction of QA: first, in the transferof electrons from P680* to the oxidized Phe in the D1 proteinwith formation of P680+, second, in the electron transfer fromPhe- to QA in the protein D2, and finally, in the reduction ofP680+ by electrons from Tyr161 in the D1 protein, followedby the Tyr161 reduction by electrons originating in the Mn4Cacluster (see refs 1-3, and structural details in ref 7).

Therefore, it is reasonable to assume that the rate of oxygenevolution and the electron-transfer velocity in the ensemble ofPSII photochemical centers present in the PSII particles andthylakoid membranes might have comparable values. What ismore, this conclusion gives further support to the use of theLangmuir adsorption isotherm (eq 3) to represent the variationof oxygen evolution with the light intensity as is seen in Figure1 and elsewhere (see, e.g., refs 16, 18, and 19).

B. On the Phenomenological Significance of the LangmuirEquation. In eq 3, OEth(max) andL1/2 are assumed to containfunctional and structural information if the OEth(max) magnitudeis interpreted as the maximal number of PSII reaction centersopen for photochemistry, andL1/2 as the equilibrium betweenthe electron transfer from Phe- to the primary quinone QA andthe formation of the reduced Phe molecule in the PSII reactioncenter by electrons in provenance from P680*. As a conse-quence, it is predictable that at least some molecular perturba-tions in the D1 and D2 proteins, or in their vicinity, where arelocalized the major components of the electron transport chain,namely, Tyr161, P680 Chl’s, Phe, QA, and QB, might affect thePSII function and thereby the oxygen evolution in the Mn4Cacluster, and this might be reflected in the Langmuir equation ifit is to keep its phenomenological significance. A demonstrationof this view was developed in ref 18 to explain the effect ofâ-cyclodextrin (â-CD) on oxygen evolution in isolated thylakoidmembranes.

For this purpose, eq 3 was rewritten to correct the values ofOEmax andL1/2 observed in thylakoid membranes incubated inthe absence ofâ-CD, i.e., OEmax(0) andL1/2(0). To achieve thisphysiological control, OEmax(0) andL1/2(0) are multiplied byscale functions dependent on theâ-CD concentration (C), i.e.,G1(C) andG2(C), to transform eq 3 into eq 23

where, in the conditions of the experiments reported in ref 18,one has

The comparison of theory and experiment performed in ref18 showed clearly that the theoretical result yielded by eq 23 isa reliable approximation of the combined effect of light intensityand â-CD concentration on oxygen evolution in isolatedthylakoid membranes. This indicates therefore that the modifiedLangmuir equation (eq 23) has a significant predictive value instructure-function studies.

Finally, it is worth noting that the afore discussed interpreta-tions are corroborated by earlier studies examined by Adamsonin ref 25 showing that the formulation of the temperature effecton the adsorption of a gas in a solid surface is well justifiedwith a Langmuir equation provided that one undertakes itscorrection with appropriate scale factors. What is more, thecorrections proposed by Adamson25 were performed in muchthe same way as we did above in eq 23 (see discussions in ref18).

V. Concluding Remarks

First, we showed that in steady-state conditions the effect oflight intensity on oxygen evolution in isolated PSII particlesand thylakoid membranes irradiated with white light is welldescribed by a hyperbolic function (eq 3). A major issue in thiswork is the demonstration that the Langmuir adsorption isothermfor heterogeneous catalysis is a reliable explanation of thephoton-chlorophyll (P680) interaction in the PSII reactioncenter and the subsequent electron transfer from P680* to theoxidized Phe, then from Phe- to the primary quinone QA. Inthe approximation represented by eq 3 (Langmuir equation),the P680 molecules are the adsorption surfaces (or heteroge-neous catalysts) and the incident (or exciting) photons thesubstrate. This notion has emerged from an argumentationinitiated by Turro26 on the nature of the photon as a reagent inchemical reactions in which light is represented as a stream ofparticles instead of an electromagnetic wave.

Second, we note that the phenomenological significance ofeq 3 is apparent in the interpretation of OEth(max) andL1/2 whichcontain specific functional and structural information (seediscussion in ref 18). In short, OEth(max) is a measure of themaximal number of PSII reaction centers open for photochem-istry, andL1/2 is the equilibrium between the electron transferfrom Phe- to QA and the formation of the reduced Phe moleculein the PSII reaction center. In addition, the function of aphysiological control inherent to eq 3 is demonstrated by thefinding that the magnitude of OEth(max) andL1/2 is affecteddifferently by exogenous stimulators of oxygen evolution inphotosystem II.18

From the above considerations, we conclude that the Lang-muir equation (eq 3) is a novel mathematical formulation ofenergy and electron transfer in photosystem II.

Acknowledgment. This work was supported by grants toM.F. from the Natural Sciences and Engineering ResearchCouncil of Canada. We thank Prof. N. J. Turro for helpfulcomments on the “photon as a reagent” concept. We are gratefulto the reviewers for several remarks that clarified some aspectsof the paper.

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Effect of Light Intensity on Electron Transfer J. Phys. Chem. B, Vol. 111, No. 12, 20073319

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