J. Phys. Chem. B 2007, 111, 3315-3320
3315
Theoretical Consideration of the Use of a Langmuir Adsorption Isotherm To Describe the Effect of Light Intensity on Electron Transfer in Photosystem II Ma´ rio Fragata,* Venkataramanaiah Viruvuru, 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: December 7, 2006; In Final Form: January 23, 2007
Electron transport through photosystem II (PSII), measured as oxygen evolution, was investigated in isolated PSII particles and thylakoid membranes irradiated with white light of intensities (I) of 20 to about 4000 µmol of photons/(m2‚s). In steady-state conditions, the evolution of oxygen varies with I according to the hyperbolic expression OEth ) OEth(max)I/(L1/2 + I) (eq i) where OEth is the theoretical oxygen evolution, OEth(max) is the maximum oxygen evolution, and L1/2 is the light intensity giving OEth(max)/2. In this work, the mathematical derivation of this relationship was performed by using the Langmuir adsorption isotherm and assuming that the photon interaction with the chlorophyll (Chl) in the PSII reaction center is a heterogeneous reaction in which the light is represented as a stream of particles instead of an electromagnetic wave (see discussion in Turro, N. J. Modern Molecular Photochemistry; University Science Books: Mill Valley, CA, 1991). In accordance with this approximation, the Chl molecules (P680) were taken as the adsorption surfaces (or heterogeneous catalysts), and the incident (or exciting) photons as the substrate, or the reagent. Using these notions, we demonstrated that eq i (Langmuir equation) is a reliable interpretation of the photon-P680 interaction and 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 structural information that is apparent in the definition of OEth(max) as a measure of the maximal number of PSII reaction centers open for photochemistry, and L1/2 as the equilibrium between the electron transfer from Pheto 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) and L1/2 are affected differently by exogenous PSII stimulators of oxygen evolution (Fragata, M.; Dudekula, S. J. Phys. Chem. B 2005, 109, 14707). Finally, an unexpected new concept, implicit in eq i, is the consideration of the photon as the substrate in the photochemical reactions taking place in the PSII reaction center. We conclude that the Langmuir equation (eq i) is a novel mathematical formulation of energy and electron transfer in photosystem II.
I. Introduction In oxygenic photosynthesis the photosystem II (PSII) complex catalyzes the oxidation of water at the Mn4Ca cluster. This gives rise to the evolution of oxygen and the transfer of electrons to the primary (QA) and secondary (QB) quinone acceptors in respectively the D2 and the D1 proteins.1-3 First, there is formation of an excited-state chlorophyll (Chl), i.e., P680*, in the PSII reaction center upon absorption of photons via energy transfer from the antenna Chl. Second, an electron is transferred from P680* to the oxidized peophytin (Phe) with concomitant formation of P680+. Then, Phe- reduces the primary quinone QA, a plastoquinone (PQ) tightly bound noncovalently to the QA site in the PSII complex. In the next step, QA-• reduces the mobile plastoquinone QB to the semiquinone QB-• which has a high affinity to the QB site.4 Upon a second reduction and a protonation, QB-• becomes PQH2 (plastoquinol), which is rapidly exchanged for an oxidized plastoquinone from the PQ pool.4-6 Finally, the steady-state function of the PSII electron transport chain is maintained by the two remaining redox steps. * Address correspondence to this author. Phone: 819-3765011. Fax: 8193765057. E-mail:
[email protected]. † Present address: Department of Chemistry, National Cheng Kung University, Tainan-70101, Taiwan.
That is, the reduction of P680+ by the Tyr 161 in the D1 protein and the transfer of an electron from the Mn4Ca cluster to the oxidized 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 low I followed, at high irradiance, by a gradual decrease of the dOE/ dI rate to what has been often described as the upper steady OE limit, or maximum oxygen evolution (see, e.g., refs 8-19). The mathematical formulation of the photosynthetic activity dependence on the light intensity was attempted in a wide variety of plant materials (see review of earlier work in ref 20, and more recent studies in refs 16 and 19). Although these investigations have a practical value in the prediction of the biomass productivity, their significance as phenomenological descriptions of the photosynthetic mechanisms is in general rather limited. In a different perspective, the shape of the lightresponse curves was examined in a few works with the aim of providing fundamental descriptions of the light intensity effect on photosyntyhesis using either an exponential function applied to the hypothesis of a cumulative one-hit Poisson probability distribution21-23 or a hyperbolic expression derived from the steady-state approximation of coupled reactions where slow and fast kinetics alternate.18
10.1021/jp0684271 CCC: $37.00 © 2007 American Chemical Society Published on Web 03/06/2007
3316 J. Phys. Chem. B, Vol. 111, No. 12, 2007
Fragata et al.
First, the cumulative one-hit Poisson probability distribution is usually represented by the general equation22
Y(z) ) Yo(z)(1 - e-σ(z)E)
(1)
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, and E 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 which were not hit. This type of mathematical representation was also used in ref 18 to simulate the oxygen evolution as a function of I in isolated thylakoid membranes, i.e.,
OEth ) OEth(max)(1 - e-kI)
(2)
where OEth is the theoretical oxygen evolution in µmol of oxygen evolution/(mg of Chl.h), OEth(max) is the maximum oxygen evolution, and k (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 the oxygen evolution in isolated thylakoid membranes under various light intensity conditions yielded the hyperbola18
OEth ) OEth(max)I/(L1/2 + I)
(3)
where OEth, OEth(max), and I are defined above, and L1/2 is the irradiance giving OEth(max)/2. It was also found18 that the trend of the light-response curves is not affected in thylakoid membranes incubated with β-cyclodextrin, an efficient exogenous stimulator of oxygen evolution in photosystem II. Most interestingly, we showed in ref 18 that only the hyperbolic model represented by eq 3 is a relevant description of the effect of light intensity on the electron transport through PSII in isolated thylakoid membranes. However, we note that both eqs 1 and 3 are supported by appropriate fundamental concepts.18,22 This is an intriguing question that so far has not been explained satisfactorily. An attractive prospect is to integrate the Poisson and the hyperbolic models in a single general equation, meaning in that case that one needs to develop more detailed analyses of their underlying principles. As a step toward this end, we use in the present work the Langmuir adsorption isotherm25 to examine the theoretical bases of the hyperbolic model. In the first part of this work (section III), we determined whether the hyperbolic model is adequate to describe the electron transfer through photosystem II, estimated as oxygen evolution, in isolated PSII particles. In the second part of the work (section IV), the Langmuir adsorption isotherm is applied to the energy transfer from the excited state Chl a in the PSII antenna to P680 on the one hand, and the electron transfer from P680* to Phe on the other hand. Implicitly, the question of the photon as the substrate26 in the photochemical reactions taking place in the PSII reaction center shall be discussed. The work ends (section V) with some comments on this new application of the Langmuir adsorption isotherm, i.e., a novel mathematical description of energy and electron transfer in photosystem II. II. Experimental Section Chemicals. The chemicals used in the present work were obtained from Sigma Chemical Company (St. Louis, MO) and Fisher Scientific Company (Fair Lawn, NJ). Isolation of Thylakoid Membranes and Photosystem II Particles. Primary leaves from 6 to 8 day old seedlings from barley (Hordeum Vulgare) were used throughout this work. The
methods used below to isolate the thylakoid membranes and the PSII particles are those described in refs 18, 27, and 28. To isolate thylakoids membranes the barley leaves were homogenized in a buffer containing 50 mM Tricine-NaOH (Ntris[hydroxymethyl]-methylglycine-NaOH) (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 2460 g 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 2460 g 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 centrifuged at 2200 g 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 193 K. To isolate PSII particles, 10 mL of the stock solution of thylakoid membranes (2 mg Chl/mL; see above) was mixed with 5 mL of buffer C and kept on ice. With very slow mixing of the thylakoids using flea and stirrer, 8% Triton X-100 (5 mL) was added carefully drop by drop to a final Chl:Triton X-100 concentration ratio of 20:1. The suspension was incubated for 10 min in the dark and immediately centrifuged at 2200 g for 3 min at 277 K. The supernatant was transferred to prechilled centrifuge tubes and centrifuged at 35 300 g for 20 min at 277 K. The pellet was dissolved in a minimal volume of buffer C, using brush and vortex, and then about 10 to 15 mL of buffer C was added followed by centrifugation at 35 300 g for 20 min at 277 K. The resultant pellet was dissolved in a minimal volume of buffer C (2 mL). The PSII particles thus obtained were stored either in a deep freezer (193 K) or in liquid nitrogen. The chlorophyll concentration of the isolated thylakoid membranes and PSII particles was measured in 80% acetone (v/v) according to the method described in ref 29, and their polypeptide composition was analyzed by SDS-polyacrylamide gel electrophoresis according to standard procedures described in refs 18 and 28. Measurement of Electron Transport through Photosystem II. Electron transport through photosystem II, estimated as oxygen evolution, was measured with a Hansatech Oxygen Electrode (Hansatech Instruments Ltd., Norfolk, UK) connected to a temperature-controlled water circulator at 298 K. The assay mixtures contained samples of isolated PSII particles or thylakoid membranes (12.5 µg Chl/mL) suspended in a oxygen evolution measurement buffer (pH 6.5) constituted of 20 mM MES-NaOH, 400 mM sucrose, 15 mM NaCl, 5 mM MgCl2, and 350 µM 2,6-dichloro-p-benzoquinone as the electron acceptor.18 Irradiation Conditions and Measurement of Photon Flux Densities. Irradiation of the suspensions of thylakoid membrane or PSII particles was performed with artificial white light from a Fiber-Lite High Intensity Illuminator, model 180, from DolanJenner Industries Inc. (Lawrence, MA). The light source of this illuminator is a EKE lamp that has a spectral range spanning the ultraviolet (UV), the visible, and the near-infrared (NIR) regions (see http://www.spectralproducts.com). We note first that in the conditions of our experiments (i) the UV light is eliminated by the glass walls of the oxygen evolution chamber and (ii) the NIR radiation is not used by the photosynthetic systems and, in addition, cannot be detected by the LI-190SB
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J. Phys. Chem. B, Vol. 111, No. 12, 2007 3317
OEth(tm) ) (203 ( 16)I/[(365 ( 7) + I]
(5)
The experimental data of Figure 1 are plotted in Figure 2 as 1/OEth(p) vs 1/I and 1/OEth(tm) vs 1/I, that is, the LineweaverBurk representations. The linear graphics shown in Figure 2 were computed with the theoretical data yielded by eqs 4 and 5, using the curve-fitting tool of the Origin software (see Experimental Section). One sees that the agreement between theory and experiment is in general excellent except for the oxygen evolution data obtained at very low light intensities. These deviations from linearity originate most likely in the uncertainties inherent to the measurement of low oxygen concentrations. The theoretical expressions of 1/OEth(p) and 1/OEth(tm) are given here by eqs 6 and 7.
Figure 1. Effect of light intensity on oxygen evolution in isolated PSII particles and thylakoid membranes. The experimental data are given as “mean ( SD”. The theoretical curves were obtained from mathematical simulations performed with Origin 5.0 and Maple V (see the Experimental Section). Chl, chlorophyll; PSII, photosystem II; SD, standard deviation.
quantum sensor described below. Therefore, the photosynthetically active radiation (PAR) of the EKE lamp, i.e., from about 380 to 720 nm, coincides with the absorption of visible light by the chlorophyll and pheophytin pigments present in the antenna and reaction center complexes. The measurement of the photon flux densities (µmol of photons/(m2‚s)) was done with a Quantum Photometer, model LI-185B, from LI-COR, Inc. (Lincoln, NE), which was equipped with a LI-190SB quantum sensor. This sensor measures PAR light in the wavelength range from 400 to 700 nm (see Figure 4 in the LI-COR Terrestrial Radiation Sensors, Type SB Instruction Manual). It is important to remark that the PAR range of the LI-190SB quantum sensor covers the absorption spectra of the photosynthetic pigments therefore in accord with the characteristics of the Dolan-Jenner illuminator, model 180, described above. Data Analysis. The software programs used to fit the experimental data in this work with the mathematical expressions discussed in section III are Origin, version 5, from Microcal Software, Inc. (Northampton, MA), and Maple V, release 5.1, from Waterloo Maple Inc. (Waterloo, ON, Canada). III. Light-Response Curves of Oxygen Evolution in Photosystem II Figure 1 displays the oxygen evolution observed in isolated PSII particles and thylakoid membranes irradiated with white light of photon flux densities (I) from 22 to about 4000 µmol of photons/(m2‚s). The trend of the OE variation with I is first a sharp increase at low light intensities followed by a quite lower dOE/dI rate at high irradiance in accord with what has been reported in the literature (see Introduction). Figure 1 shows also that the experimental data are well represented with the hyperbola OEth ) OEth(max)I/(L1/2 + I), where OEth, OEth(max), and L1/2 are defined above (see eq 3). The calculated oxygen evolution in µmol of O2 evolution/(mg of Chl.h) in isolated PSII particles, OEth(p), and thylakoid membranes, OEth(tm), is expressed respectively by eqs 4 and 5 below:
OEth(p) ) (802 ( 8)I/[(836 ( 19) + I]
(4)
1/OEth(p) ) 0.00127 + 1.02532(1/I)
(6)
1/OEth(tm) ) 0.00488 + 1.78049(1/I)
(7)
We conclude therefore that, in the conditions of our experiments, the hyperbolic function of eq 3 is a reliable representation of the effect of light intensity on the electron transport through PSII, estimated as oxygen evolution, in isolated PSII particles and thylakoid membranes. IV. Theoretical Description of the Langmuir Adsorption Isotherm Model Although the representation of the effect of light intensity on oxygen evolution (or carbon dioxide consumption) in whole plant materials and isolated membranes (or membrane fragments) was attempted in several instances with a hyperbola or with hyperbolic-like expressions (see, e.g., refs 16, 19, and 20), no mathematical derivation of the relationship between experiment and the hyperbolic model has been formulated. As a step toward this end, we consider in the approximation described here that the interaction of a photon with P680 in the PSII reaction center is a heterogeneous reaction. This premise is justified by the knowledge that the formation of the excited state P680*, i.e., P680 + hν f P680*, is a process involving more than one phase. That is to say, the Chl a molecules (P680) which are thereby the adsorption surfaces (or heterogeneous catalysts) on the one hand and the phase constituted of incident (or exciting) photons on the other hand. Among the possible mathematical solutions of systems of this kind, we note that the Langmuir equation was often shown to yield consistent descriptions of the kinetics of heterogeneous catalysis.25 In this perspective, the Langmuir adsorption isotherm is used in the following section to deduce the hyperbolic expressions which were applied previously to represent the effect of the light intensity on oxygen evolution in photosystem II. A fundamental matter arising from the foregoing discussion is the question of the photon as the substrate in the photochemical reactions taking place in the PSII reaction center. This notion has emerged from an argumentation initiated by Turro26 on the nature of the photon as a reagent in chemical reactions in which light is represented as a stream of particles instead of an electromagnetic wave. In accordance with this view, the photon is the reagent for starting up a photoreaction as in the absorption of light, and the product is the resultant emitted photon or electron. These concepts were followed in the derivations formulated here where the photon is taken as the substrate in its interaction with P680, and the reaction product is implicitly the electron transferred from P680* to the oxidized Phe.
3318 J. Phys. Chem. B, Vol. 111, No. 12, 2007
Fragata et al. expressed as
d[P680+‚Phe-]/dt ) k1[P680‚Phe]I - k2[P680+‚Phe-] k3[P680+‚Phe-] (10) where k1[P680‚Phe]I is the rate of P680+‚Phe- formation, k2[P680+‚Phe-] is the rate of P680+‚Phe- breakdown, and
V ) k3[P680+‚Phe-]
(11)
is the velocity of electron transfer. Moreover, for steady-state (or quasisteady-state) conditions d[P680+‚Phe-]/dt = 0.24,25 Hence,
d[P680+‚Phe-]/dt ) k1[P680‚Phe]I - k2[P680+‚Phe-] k3[P680+‚Phe-] = 0 (12) From this, the following equilibria are deduced Figure 2. Lineweaver-Burk plots of the effect of light intensity on oxygen evolution in isolated PSII particles and thylakoid membranes. Chl, chlorophyll; PSII, photosystem II. The linear relationships were obtained from the theoretical curves displayed in Figure 1 (see also eqs 4 and 5 in the text).
A. The Langmuir Adsorption Isotherm Applied to Electron Transfer through PSII. In this approximation24,25 the first step is the interaction, or collision, of the photons in provenance from the PSII antenna with the reaction center chlorophylls (P680). This is depicted in eq 8 below:
P680‚Phe + hν f k1
k3
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)
and
or
where L1/2 ) (k2 + k3)/k1. It is noted, furthermore, that in the course of the reaction the concentration of P680‚Phe available for photochemistry is given by
(P680*.Phe) {\ } P680+‚Phe- 98 P680+ + Phe- (8) k
[P680‚Phe] ) [P680‚Phe]T - [P680+‚Phe-]
2
(16)
where hν is the excitation quantum, (P680*‚Phe) the transient complex between the excited state Chl (i.e., P680*) and Phe, and
where [P680‚Phe]T is the total concentration of P680‚Phe and [P680+‚Phe-] the concentration of P680‚Phe that underwent electron transfer. Combining eqs 15 and 16 gives
k1 ) [P680+‚Phe-]/[P680‚Phe]I
(8a)
[P680+‚Phe-] ) ([P680‚Phe]T - [P680+‚Phe-])I/L1/2 (17)
k2 ) [P680‚Phe]I/[P680+‚Phe-]
(8b)
[P680+‚Phe-] ) [P680‚Phe]T{(I/L1/2)/(1 + I/L1/2)}
k3 ) [P680+][Phe-]/[P680+‚Phe-]
(8c)
where I is the concentration of incident quanta hν, i.e., the number of photons that hit the Chl molecules available for photochemistry in the PSII reaction centers. The electron transfer shown in eq 8 is followed by the transfer of an electron from Phe- to QA, which is much faster. In brief, the lifetime of the electron-transfer reaction of eq 8 is less than 1 ns,30-32 and between 200 ps34 and 400 ps30,31 for the reaction -
Phe + QA f Phe + QA
-•
(9)
In other words, the Phe reduction is much slower than the electron transfer from Phe- to QA. Thus, Phe- never attains a significant concentration as it reacts rapidly with the primary quinone QA to form QA-•. Consequently, the function of the electron-transfer chain in the thylakoid membrane is not limited by the formation of reduced pheophytin. The Langmuir Adsorption Isotherm Equations. In the chain of reactions displayed in eq 8, the evolution of the transient electron-transfer complex P680+‚Phe- in the course of time is
[P680+‚Phe-] ) [P680‚Phe]T{I/(L1/2 + I)}
(18) (19)
Upon multiplication of each term of eq 19 by k3, we get
k3[P680+‚Phe-] ) k3[P680‚Phe]T{I/(L1/2 + I)}
(20)
V ) VmaxI/(L1/2 + I)
(21)
and
since V ) k3[P680+‚Phe-] (cf. eq 11 above) and Vmax ) k3[P680‚Phe]T. It is worth noting that the term I/(L1/2 + I) in eq 21 is a useful measure of the fraction of the total number of open PSII centers available for photochemistry as it equals about 0 in low light intensity conditions and is close to 1 at high irradiance. Application of V ) VmaxI/(L1/2 + I) to Oxygen EVolution in PSII. To apply eq 21, i.e., V ) VmaxI/(L1/2 + I), to electron transfer through PSII, estimated as oxygen evolution, V and Vmax are correlated to OEth and OEth(max) (cf. eq 3) by appropriate scale factors, say R1 and R2, respectively. These corrections yield V ) R1OEth and Vmax ) R2OEth(max), and eq
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J. Phys. Chem. B, Vol. 111, No. 12, 2007 3319
21 becomes
R1OEth ) R2OEth(max)I/(L1/2 + I)
(22)
If the molecular mechanisms that affect R1 at V < Vmax are similar to those influencing R2 at Vmax or at electron-transfer velocities close to Vmax, a conjecture that is reasonable, one may conclude that R1 and R2 are about identical. Then, eq 22 becomes OEth ) OEth(max)I/(L1/2 + I), which is eq 3 (see sections I and III). The above conjecture is justified for an ensemble of PSII photochemical centers presenting small or no differences, that is, the steady-state approximation conditions of the experiments discussed here. At the molecular and structural levels this means that in the ensemble of PSII particles and thylakoid membranes used in the work reported here the electron-transfer velocity V might not change substantially in the electron sequence from the Mn4Ca cluster to the reduction of QA: first, in the transfer of electrons from P680* to the oxidized Phe in the D1 protein with formation of P680+, second, in the electron transfer from Phe- to QA in the protein D2, and finally, in the reduction of P680+ by electrons from Tyr161 in the D1 protein, followed by the Tyr161 reduction by electrons originating in the Mn4Ca cluster (see refs 1-3, and structural details in ref 7). Therefore, it is reasonable to assume that the rate of oxygen evolution and the electron-transfer velocity in the ensemble of PSII photochemical centers present in the PSII particles and thylakoid membranes might have comparable values. What is more, this conclusion gives further support to the use of the Langmuir adsorption isotherm (eq 3) to represent the variation of oxygen evolution with the light intensity as is seen in Figure 1 and elsewhere (see, e.g., refs 16, 18, and 19). B. On the Phenomenological Significance of the Langmuir Equation. In eq 3, OEth(max) and L1/2 are assumed to contain functional and structural information if the OEth(max) magnitude is interpreted as the maximal number of PSII reaction centers open for photochemistry, and L1/2 as 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 by electrons in provenance from P680*. As a consequence, it is predictable that at least some molecular perturbations in the D1 and D2 proteins, or in their vicinity, where are localized the major components of the electron transport chain, namely, Tyr161, P680 Chl’s, Phe, QA, and QB, might affect the PSII function and thereby the oxygen evolution in the Mn4Ca cluster, and this might be reflected in the Langmuir equation if it is to keep its phenomenological significance. A demonstration of this view was developed in ref 18 to explain the effect of β-cyclodextrin (β-CD) on oxygen evolution in isolated thylakoid membranes. For this purpose, eq 3 was rewritten to correct the values of OEmax and L1/2 observed in thylakoid membranes incubated in the absence of β-CD, i.e., OEmax(0) and L1/2(0). To achieve this physiological control, OEmax(0) and L1/2(0) are multiplied by scale functions dependent on the β-CD concentration (C), i.e., G1(C) and G2(C), to transform eq 3 into eq 23
OEth ) [OEmax(0)G1(C)]I/[L1/2(0)G2(C) + I]
(23)
where, in the conditions of the experiments reported in ref 18, one has
G1(C) ) 1 + 3.3C4.8/(13.14.8 + C4.8)
(24)
G2(C) ) 1 + 5.2C7.8/(14.87.8 + C7.8)
(25)
The comparison of theory and experiment performed in ref 18 showed clearly that the theoretical result yielded by eq 23 is a reliable approximation of the combined effect of light intensity and β-CD concentration on oxygen evolution in isolated thylakoid membranes. This indicates therefore that the modified Langmuir equation (eq 23) has a significant predictive value in structure-function studies. Finally, it is worth noting that the afore discussed interpretations are corroborated by earlier studies examined by Adamson in ref 25 showing that the formulation of the temperature effect on the adsorption of a gas in a solid surface is well justified with a Langmuir equation provided that one undertakes its correction with appropriate scale factors. What is more, the corrections proposed by Adamson25 were performed in much the same way as we did above in eq 23 (see discussions in ref 18). V. Concluding Remarks First, we showed that in steady-state conditions the effect of light intensity on oxygen evolution in isolated PSII particles and thylakoid membranes irradiated with white light is well described by a hyperbolic function (eq 3). A major issue in this work is the demonstration that the Langmuir adsorption isotherm for heterogeneous catalysis is a reliable explanation of the photon-chlorophyll (P680) interaction in the PSII reaction center and the subsequent electron transfer from P680* to the oxidized Phe, then from Phe- to the primary quinone QA. In the approximation represented by eq 3 (Langmuir equation), the P680 molecules are the adsorption surfaces (or heterogeneous catalysts) and the incident (or exciting) photons the substrate. This notion has emerged from an argumentation initiated by Turro26 on the nature of the photon as a reagent in chemical reactions in which light is represented as a stream of particles instead of an electromagnetic wave. Second, we note that the phenomenological significance of eq 3 is apparent in the interpretation of OEth(max) and L1/2 which contain specific functional and structural information (see discussion in ref 18). In short, OEth(max) is a measure of the maximal number of PSII reaction centers open for photochemistry, and L1/2 is the equilibrium between the electron transfer from Phe- to QA and the formation of the reduced Phe molecule in the PSII reaction center. In addition, the function of a physiological control inherent to eq 3 is demonstrated by the finding that the magnitude of OEth(max) and L1/2 is affected differently by exogenous stimulators of oxygen evolution in photosystem II.18 From the above considerations, we conclude that the Langmuir equation (eq 3) is a novel mathematical formulation of energy and electron transfer in photosystem II. Acknowledgment. This work was supported by grants to M.F. from the Natural Sciences and Engineering Research Council of Canada. We thank Prof. N. J. Turro for helpful comments on the “photon as a reagent” concept. We are grateful to the reviewers for several remarks that clarified some aspects of the paper. References and Notes (1) Hankamer, B.; Barber, J.; Boekema, E. J. Annu. ReV. Plant Physiol. Plant Mol. Biol. 1997, 48, 641. (2) Nelson, N.; Ben-Shem, A. Nat. ReV. Mol. Cell Biol. 2004, 5, 971. (3) Renger, G.; Holzwarth, A. R. In Photosystem II: The Water/ Plastoquinone Oxido-Reductase in Photosynthesis; Wydrzynski, T., Satoh, K., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2005; p 139. (4) Garbers, A.; Reifarth, F.; Kurreck, J.; Renger, G.; Parak, F. Biochemistry 1998, 37, 11399.
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