Temperature Dependence of Oxygen Evolution in the Thylakoid

Oct 26, 2009 - The temperature dependence of electron transport through photosystem II (PSII), measured as oxygen evolution, was investigated in thyla...
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J. Phys. Chem. B 2009, 113, 15392–15398

Temperature Dependence of Oxygen Evolution in the Thylakoid Membrane: Thermal Transitions above 273 K in Steady-State Conditions Ma´rio Fragata* and Venkataramanaiah Viruvuru† De´partement de Chimie-Biologie, Section de Chimie et Biochimie, et Groupe de Recherche en Biologie Ve´ge´tale, UniVersite´ du Que´bec a` Trois-RiVie`res, Trois-RiVie`res (Que´bec), G9A5H7, Canada ReceiVed: July 27, 2009; ReVised Manuscript ReceiVed: September 25, 2009

The temperature dependence of electron transport through photosystem II (PSII), measured as oxygen evolution, was investigated in thylakoid membranes irradiated with white light of 450 µmol of photons/(m2 · s). The experiments were performed in steady-state conditions at temperatures between 273 and 303 K. The results show discontinuities, or thermal transitions, in the temperature-response curves of oxygen evolution. The experimental data was examined with the Marcus theory of electron transfer modified to take into account the oxygen evolution discontinuities. For this purpose, the Gibbs free energy of activation of the electron transfer reaction, ∆G°, is replaced in the classical Marcus equation with the expression ∆H° - T∆S°, where H° and ∆S° are respectively the enthalpy and entropy of activation, and T is the temperature in kelvin. The result of the derivation is a summation of j Gaussian functions, or states, OE ) 69 250∑j{(VDA4/λT)1/2 exp[-(Tmax - T)2/2Tσo2]}j (eq 1), where OE is expressed in µmol oxygen evolution.(mg Chl · h)-1, and VDA is the electronic coupling matrix element between electron donor (D) and acceptor (A) wave functions, λ the reorganization free energy, kB the Boltzmann constant, Tmax ) (∆H° + λ)/∆S°, σo ) (2kBλ/∆So2)1/2, and σ ) T1/2σo is the standard deviation of the Gaussian band. The mathematical simulations revealed the presence of six thermal transitions, or Gaussian bands with maxima at 275.3, 281.2, 286.4, 291.4, 297.1, and 302.4 K. The resolution of the Gaussian bands is about 0.55 owing to multiple band superpositions. The theoretical analyses showed that (i) the oxygen evolution in PSII is essentially dependent on VDA2/(λT)1/2 in the preexponential term of the modified Marcus equation (eq 1), and (ii) the reorganization energy, λ, decreases exponentially with increasing temperature, and is also dependent on the electron donor-acceptor distance. It is concluded that the temperature dependence of the large enhancement of oxygen evolution observed in this work originates, at least partly, in heat-induced structural rearrangements in the photosystem II reaction center. I. Introduction The photosynthetic processes at the origin of oxygen evolution in photosystem II (PSII) start with the absorption of photons by the antenna chlorophylls and energy transfer to the PSII reaction center (PSII-RC) where takes place the formation of the excited-state chlorophyll P680*.1,2 This is followed by electron transfer from the primary electron donor chlorophyll, ChlD1, to the oxidized pheophytin (Pheo) and from Pheo- to QA, the primary quinone in the D2 protein. Then, QA · - reduces a plastoquinone, QB, transiently bound to the D1 protein at the QB site. Upon a second reduction and a protonation, the semiquinone QB · - is converted to the plastoquinol PQH2 which is rapidly exchanged for an oxidized plastoquinone from the thylakoid membrane pool. A new photosynthetic event starts with the reduction of P680 · + (or PD1 · +) by electrons from the tyrosine 161 in the D1 protein, and the transfer of an electron from the Mn4Ca cluster to the oxidized Tyr 161.3,4 In PSII-RC, sequences of four electron transfers through the S-state cycle of photosynthetic oxygen evolution, i.e., S0 f S1 f S2 f S3 f S4 f S4′, are coupled with the release of four H+ ions and the formation of dioxygen from two H2O molecules in the S4 f S4′ f S0 transition.5 The molecular structures of these electron transfer pathways have now been described in great * Corresponding author. Phone: 819-3765011. Fax: 819-3765057. E-mail: [email protected]. † Present address: D. No. 26/1079, A. K. Nagar Post, Nellore 524004, Andhra Pradesh, India.

detail using X-ray crystallographic data obtained at resolutions ranging from 3.8 to 3.0 Å,6 and at 2.9 Å in the more recent PSII model.7 The molecular structure of proteins is a makeshift arrangement which is subject to alteration as the result of temperature fluctuations (see, e.g., refs 8 and 9). Thermal agitation induces random orientations of interacting dipoles10 in the amino acid residues of protein structures with concomitant loss of hydrogenbond stability,11 the so-called “hydrogen-bond melting”.12 In this respect, Fourier transform infrared (FT-IR) spectroscopic investigations of the amide I region13,14 of photosystem II from 1700 to 1600 cm-1 revealed conformational changes of the proteins secondary structures at about 313 K.15-17 The transitions observed in the FT-IR difference spectra of PSII were correlated with the thermal denaturaturation of the PSII reaction center on the one hand,15 and a dynamic equilibrium between the PSII contents in the proteins R-helix and extended chains (β-strands) conformations observed at respectively 1657 and 1626 cm-1 on the other hand.16 What is more, these transitions are associated with changes of variable fluorescence16 and loss of oxygen-evolving activity in PSII.17 A discovery related to the above-discussed observations is the demonstration that protein flexibility and conformational changes are required to initiate electron transfer from QA · - to QB.18 Furthermore, it was shown in bacteriorhodopsin that conformational rearrangements of this kind are facilitated by the presence of cavities in the inner core of the proteins.19 A

10.1021/jp9071586 CCC: $40.75  2009 American Chemical Society Published on Web 10/26/2009

Oxygen Evolution in the Thylakoid Membrane recent important finding is the identification of protein cavities around the residues 209 and 212 in the D1 protein of PSII that may provide local flexibility to the reaction center and induce as well slowing of the QA- f QB electron transfer reaction above transition temperatures of 303 and 337 K in mesophililic and thermophilic cyanobacteria, respectively.20 Another interesting aspect of this question is the discovery of a thermo-optic mechanism in the light-harvesting proteins of the photosynthetic membranes,21 that is, the modification of the proteins molecular structure by local thermal transients which, moreover, exhibit a non-Arrhenius type of temperature dependency. We note finally that other thermal transitions related to different aspects of the photosynthetic activity were detected in various biological materials at, for example, 282, 293, 302, and 309 K,22 279 and 289 K,23 278.5-280 and 279-280 K,24 and 285 and 292 K.25 A characteristic common to most of the works referred to above is the presence of discontinuities, or thermal transitions, in the temperature-response curves of photosynthetic activity. This excludes in principle the application of mathematical functions such as, for example, the classical Arrhenius equation (see, e.g., ref 26), to the description of the thermal dependence of electron transfer or oxygen evolution in photosystem II. In the present work, we investigate this question further by performing first a detailed experimental investigation of the oxygen-evolving activity of isolated thylakoid membranes above 273 K in steady-state conditions (section III). In the second part of the work (section IV), the experimental data is examined with the Marcus theory of electron transfer27 modified to take into account the discontinuities observed in the temperature-response curves of oxygen evolution. The mathematical simulations yielded a summation of Gaussian functions revealing the presence of six thermal transitions between 270 and 310 K. The significance of this result is discussed in the last part of the work (sections IV.C and V). II. Experimental Section Chemicals. 2,6-Dichloro-p-benzoquinone was obtained from Pfaltz and Bauer (Waterbury, CT) and Sigma Chemical Co. (St. Louis, MO). All other chemicals were from Fisher Scientific Company (Fair Lawn, NJ). Isolation of Thylakoid Membranes and Oxygen Evolution Measurement. Leaves from barley seedlings were used to isolate thylakoids from chloroplasts according to procedures described elsewhere.28,29 Briefly, the leaves are first homogenized in a buffer containing 50 mM Tricine-NaOH (N-tris[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 1000 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 1000g for 5 min at 277 K. The pellet contained the thylakoid membranes which were dispersed in a buffer containing 20 mM MES-NaOH (2-[N-morpholino]ethanesulfonic acid-NaOH) (pH 6.5), 400 mM sucrose, 15 mM NaCl, and 5 mM MgCl2 (buffer C), and centrifuged at 1000g for 5 min at 277 K. The final pellet was diluted in buffer C to give a final chlorophyll (Chl) concentration of 2 mg/mL, and stored at 143 K. The chlorophyll concentration in the thylakoid preparations was measured in 80% acetone.30 The polypeptide composition of the isolated thylakoid membranes was analyzed

J. Phys. Chem. B, Vol. 113, No. 46, 2009 15393 by sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE).31,32 The electron transport through PSII, estimated as oxygen evolution, was measured with a Hansatech Oxygen Electrode (Hansatech Instruments Ltd., Norfolk, UK) connected to a temperature-controlled water circulator calibrated for temperatures from 273 to 303 K. The reaction medium (total volume ) 2 mL) contained a measurement buffer (pH 6.5) constituted of 20 mM MES-NaOH, 400 mM sucrose, 15 mM NaCl, and 10 mM MgCl2, and 350 µM 2,6-dichloro-p-benzoquinone, and the thylakoid membranes samples (0.0125 mg Chl/mL). Irradiation of the Preparations and Measurement of Photon Flux Density. The preparations were irradiated with white light from a Fiber-Lite high intensity illuminator, model 180, from Dolan-Jenner Industries Inc. (Lawrence, MA) equipped with a EKE lamp whose spectral range spans the ultraviolet, the visible, and the near-infrared regions.33 The photosynthetically active radiation (PAR) of the EKE lamp is from about 380 to 720 nm since, in the conditions of our experiments, the ultraviolet light is eliminated by the glass walls of the oxygen evolution chamber, and the near-infrared radiation is not used by the photosynthetic systems. Photon flux densities in µmol of photons/(m2 · s) were measured with a quantum photometer, model LI-185B, from LI-COR, Inc. (Lincoln, NE) using a LI-190SB quantum sensor. The LI-190SB sensor registers the PAR light of wavelengths from 400 to 700 nm, therefore in accord with the characteristics of the Dolan-Jenner illuminator, model 180. Temperature Measurements. The temperature inside the reaction medium compartment of the Hansatech instrument (see above) was measured directly with a VWR dual channel thermometer from VWR International Inc. (West Chester, PA). The dual channel thermometer was connected to a type-K thermocouple probe. The temperature range of the dual channel thermometer was from about -50 to 1300 °C, and its accuracy was ((0.3% + 1 °C). Data Analysis. The mathematical simulations of the temperature effects described in section IV were performed with the software Origin, version 5, from Microcal Software, Inc. (Northampton, MA), Maple V, release 5.1, from Waterloo Maple Inc. (Waterloo, ON, Canada), and QuickBASIC 4.0 from Microsoft Corp. III. Temperature-Response Curves of Oxygen Evolution in Steady-State Conditions The thylakoid membrane preparations used in this work were irradiated with white light (see Experimental Section). In all experiments reported here the light intensity was 450 µmol of photons/m2 · s. The electron transport through PSII, measured as oxygen evolution, was investigated using 2,6-dichloro-pbenzoquinone as an exogenous electron acceptor. The experimental data displayed in Figure 1 is a typical representation of the temperature dependence of oxygen evolution in the thylakoid membrane above 273 K in steady-state conditions. The error bars attached to the data points are the standard deviations (SD). It is important to note that the SD’s are small (cf. Figure 1), thereby ascertaining the quality of the experimental data. Examination of Figure 1 shows that the variation of oxygen evolution in PSII with temperature is not linear, therefore in accord with previously observed temperature effects on several other aspects of the photosynthetic activity (see, e.g., refs 22-25). Mathematical representations of these heat-induced variations were attempted often with the Arrhenius equation,26 i.e.

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k ) A exp(-Ea /RT)

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or its linear logaritmic form ln k ) ln A - Ea/RT, where k is the rate of electron transfer, A the Arrhenius coefficient, Ea the activation energy of the electron transfer reaction, R the gas constant, and T the temperature in kelvin (K). However, one sees clearly that the data in Figure 1 cannot be represented by a continuous function as eq 1. In fact, the data indicates to a first approximation the presence of several thermal transitions which are visible in the discontinuities observed at about 275, 282, 288, 293, and 303 K. Therefore, the Arrhenius plot (eq 1), at least in its present form, does not seem to be a theoretical representation consistent with the experimental data. Conclusions similar to the ones discussed above are reached if the rate of electron transfer, k, is calculated, alternatively, according to the transition-state theory of Eyring instead of the Arrhenius model (see discussions in ref 26), i.e.

k ) (kBT/hp) exp(∆Sq /R) exp(-∆Hq /RT)

k ) (2π/hp)VDA2FC

(1)

(2)

where kB, hp, and R are respectively the Boltzmann, Planck, and gas constants, ∆H‡ and ∆S‡ are the activation enthalpy and entropy, and T is the temperature in K. IV. Theoretical Description of the Temperature Dependence of Oxygen Evolution A. Marcus Theory Applied to j Temperature-Dependent States. We undertake here the mathematical simulation of the experimental data taking into account that electron transfer in photosystem II is nonadiabatic and occurs over donor-acceptor distances of about 10-13 Å (see structural data in refs 6 and 7). To this end, we expressed the electron transfer rate, k, with Marcus equation27

(3)

where k is given in s-1 (or per hour, h-1, as is usual in oxygen evolution studies of photosystem II), and hp is the Planck constant; VDA2 is the square of the electronic coupling matrix element between electron donor (D) and acceptor (A) wave functions, and FC the Franck-Condon weighted density of states. Among several possibilities (see discussions in ref 27), FC is expressed as

FC ) (π/λkBT)1/2 exp[-(∆G◦ + λ)2 /4λkBT]

(4)

where λ is the reorganization free energy, kB the Boltzmann constant, and ∆G° the Gibbs free energy of activation of the electron transfer reaction. An important characteristic of eqs 3 and 4 is the Gaussian dependence of k on ∆G°, meaning that the maximum value of the exponential term in eq 4 is equal to 1 for -∆G° ) λ. It is interesting to note that a similar Gaussian property of the rate of biological electron transfer was also described by Redi and Hopfield34 in their study of thermal and photoassisted electron tunneling. Theoretical Analysis. The Gausian property of eq 4 is applied to model the effect of temperature on the rate of electron transfer or oxygen evolution in PSII. For this purpose, we use the standard Gibbs free energy expression

∆G° ) ∆H° - T∆S°

(5)

where ∆H° and ∆S° are respectively the activation enthalpy and entropy. The master equations (eqs 6-8) for the examination of the discontinuities in the temperature-response curves of oxygen evolution in photosystem II (Figure 1) are obtained by modifying first eq 4 to replace ∆G° with the expression ∆H° - T∆S°. Second, the calculations are done for j temperature dependent states to simulate the discontinuities in the temperature-response curves of oxygen evolution (OE). This yields a summation of j Marcus expressions

OE ) f1

∑ f2kj

(6)

j

for

kj ) {(2π/hp)VDA2(π/λkBT)1/2 × exp[-(∆H◦ + λ - T∆S◦)2/4λkBT]}j

(7)

or

kj ) {(2π/hp)VDA2(π/λkBT)1/2 × Figure 1. Theoretical simulation, according to the Arrhenius model, of the effect of temperature on the oxygen evolution in isolated thylakoid membranes. The error bars attached to the experimental data points are the standard deviations (SD). The theoretical curve was obtained from mathematical simulations performed with Origin 5.0 and Maple V (see Experimental Section). The activation energy of the electron transfer reaction, Ea, is obtained from the equation k ) A exp(-Ea/RT), where k is the rate of electron transfer, A the Arrhenius coefficient, R the gas constant, and T the temperature in kelvin.

exp{-[(∆H◦ + λ)/∆S◦ - T]2 /(4λkBT/∆S◦2)}}j

(8)

where f1 ) 3600/N[Chl] and f2 ) 1/3600 are scale factors to express OE in “µmol oxygen evolution (mg Chl · h)-1 units” instead of s-1. In short, the multiplication of kj with 1/3600 converts s-1 into h-1 (i.e., “per hour units”). In f1, N is Avogadro’s number, [Chl] the amount of chlorophyll (in mg) contained in the reaction medium used for oxygen evolution

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measurement, and 3600 takes into account the correction of kj with the factor f2 ) 1/3600. We note that either eq 7 or eq 8 give Gaussian representations of the experimental data. However, in the mathematical simulations performed in section IV.B, it is easier to use eq 8 instead of eq 7. In fact, in eq 8 the term (∆H° + λ)/∆S° ()Tmax) is the temperature that gives the maximum amplitude of the Gaussian curve, i.e., exp[-(Tmax - T)2/2σ2] ) 1, where 4λkBT/∆S°2 equals 2σ2. Hence

σ)T1/2[(2kBλ)1/2 /∆S°]

(9)

expressed in kelvin (K) is the standard deviation of the Gaussian curve and, therefore, a measure of the kj bandwidth. Another interesting aspect of eq 9 is the magnitude of σ which, for a given T, is entirely determined by the λ1/2/∆S° ratio. That is to say, σ is actually a function of the relative variations of the square root of the reorganization energy, λ1/2, and the activation entropy, ∆S°. B. Details of the Mathematical Simulations. To perform the oxygen evolution simulations, eqs 6 and 8 are rearranged to

OE ) {7200π3/2 /([Chl]NhpkB1/2)}

∑ kj(o)

(10)

j

Figure 2. Theoretical simulation, according to the Marcus model, of the effect of temperature on the oxygen evolution in isolated thylakoid membranes. The error bars attached to the experimental data points are the standard deviations (SD). The theoretical curves were obtained from mathematical simulations using eq 12, and performed with Origin 5.0 and Maple V (see Experimental Section).

TABLE 1: Theoretical Data Obtained from the Mathematical Simulations Performed According to Eq 12 (see Section IV.B)a

and

temperature, K

kj(o) ) {(VDA4 /λT)1/2 × ◦

◦

◦2

exp{-[(∆H + λ)/∆S - T] /(4λkBT/∆S )}}j 2

(11)

where VDA and λ are expressed in eV, T in kelvin, and OE in µmol oxygen evolution (mg Chl · h)-1. The final expression of OE is obtained by using in eqs 10 and 11 the numerical values of the constants and other numerical data, VDA2 ) 0.012 eV2, and [Chl] ) 0.025 mg to take into account the conditions of our experiments (see Experimental Section). The result of the derivation is

OE ) 831

∑ {(λT)-1/2 exp[-(Tmax - T)2/2Tσo2]}j j

Tmax

∆Tmax

275.3 281.2 286.4 291.4 297.1 302.4

5.9 5.2 5.0 5.7 5.3

OEmax λ (eV) VDA2 (eV2) σ (K) (µmol O2/(mg Chl · h)) 1.66 0.63 0.41 0.22 0.094 0.041

0.012 0.012 0.012 0.012 0.012 0.012

1.99 2.10 2.20 2.39 2.59 2.78

38.9 62.4 76.7 103.8 157.2 236.0

a Abbreviations: eV, electronvolt; K, degrees kelvin; λ, reorganization energy; OEmax, oxygen evolution at Tmax; σ, standard deviation of the j Gaussian functions in eq 12; Tmax, temperature at which OE is maximal (i.e., OEmax) in each j Gaussian curve; ∆Tmax, Tmax variation; VDA2, square of the electronic coupling matrix element between electron donor (D) and acceptor (A) wave functions.

(12) where Tmax ) (∆H° + λ)/∆S°, σo ) (2kBλ/∆S°2)1/2 and therefore σ ) T1/2σo (see section IV.A). The graphical representation of eq 12 is displayed in Figure 2 (see, however, ref 35). The result of the calculations yielded a summation of Gaussian functions revealing the presence of six transitions (or j states) with band maxima at 275.3, 281.2, 286.4, 291.4, 297.1, and 302.4 K, and an average bandwidth (fwhm)36 of about 6 K. It is important to note that these Tmax are the temperature at which the oxygen evolution is maximal in each Gaussian curve. These data and other details are collected in Table 1. First, we note that an interpretation of the Gaussian representations of oxygen evolution in Figure 2 is to take the kj’s as the probability density distributions of j states (cf. Figure 2), or the probability distribution of populations of j structural states. This is plausible if the Gaussian functions predicted by the mathematical simulations depicted in Figure 2 result from the effect of thermal fluctuations on the structural organization and function of the PSII proteins (see Introduction): for example,

the heat-induced variations observed in the PSII reaction center,15 or the fluctuations of the dynamic equilibrium between the PSII contents in the proteins R-helix and extended chains (β-strands) conformations16 which were associated with changes of variable fluorescence16 and loss of oxygen-evolving activity in PSII.17 Second, recent discoveries show the influence of temperature on protein flexibility and conformational changes required to initiate electron transfer from QA · - to QB,18 and on conformational rearrangements of molecular cavities in the inner core of the proteins.19,20 In this respect, it is interesting to note that Figure 2 shows multiple superpositions of the Gaussian bands, meaning therefore that their resolution (Br) might be small. In fact, Br was found to be about 0.55, thus indicating the coexistence of multiple temperature-dependent structural arrangements that are likely at the origin of strong interactions between j states components. C. Thermal Transitions Comparison to Other Works. The analysis of the data in Figure 2 in comparison to works performed elsewhere discloses several similarities. In brief,

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thermal transitions were detected at (i) 282, 293, 302, and 309 K in a study of the effect of temperature on electron transfer in isolated barley chloroplasts;22 (ii) 279 and 289 K in the oxidation of the S2 state to S3 in, respectively, PSII membrane fragments from spinach23a and thermophilic cyanobacteria;23b (iii) 278.5-280 K and 279-280 K in the investigation of the oxygen evolution in, respectively, isolated thylakoids and intact cells of Euglena gracilis;24 and (iv) 285 and 292 K in energy-transducing reactions in spinach chloroplasts.25 In spite of the diversity of biological materials and methodologies used in the various works, these transitions are quite close to the discontinuities observed in the temperature-response curves of oxygen evolution seen in Figure 2, thereby corroborating the mathematical simulations performed in the present study. A question remaining is the exact number of thermal transitions in either the PSII reaction center or the whole thylakoid membrane. We saw above that the available data is only partly consistent, meaning that more detailed experimental work is required. The matter is still more stringent on comparing Figure 2 with the thermal transitions (or bands) observed in thermoluminescence37 (TL) studies. The TL technique uses a rapid cooling of a sample (e.g., a plant leaf) followed by the progressive warming of the preilluminated sample. This reveals several emission bands related to different types of charge pairs. The major TL band maxima observed after preillumination are at 258 K (A-band),37c 278-298 K (Q-band),37c,d 295-313 K (B-band),37c,d 308-318 K (AG-band),37c and 323-328 K (C-band).37c,d The charge pairs at the origin of these transitions are described in ref 37. The TL experiments contributed significantly to the interpretation of the electron transfer mechanisms in photosystem II. Therefore, it would be an advantage to demonstrate a correlation between the TL data and the thermal transitions described in Figure 2. However, a reliable comparison does not seem feasible at this stage, at first, because the data obtained in this study, contrarily to the TL, result from experiments performed in steady-state conditions. The other point is the bandwidth size in TL which, in general, is large compared to the values reported here. For example, fwhm ) 25-30 K in refs 37c and d which contrasts with the much smaller average fwhm ) 6 K in the thermal spectra of Figure 2. To explain these apparent discrepancies, an interesting conjecture is to assume that the large TL bands are a composite of sub-bands not yet resolved. V. Oxygen Evolution Dependence on VDA2/(λT)1/2 The Electronic Coupling Matrix Element, VDA. The conclusion that the maximum OE amplitude for each j state depends on (λT)-1/2 in the pre-exponential term is implicit in the present configuration of eq 12 with VDA2 ) 0.012 eV2. Although this is a reliable approximation in the mathematical simulations performed in section IV, it is important to note that the definition of the electronic coupling matrix element in the context of Hopfield’s square-barrier tunneling model38 may elucidate further this question. In brief, Hopfield theory predicts that VDA decreases exponentially with the distance r between the donor (D) and acceptor (A) redox centers according to the expression

VDA(r)2 ) VoDA(ro)2 exp[-β(r - ro)]

(13)

where VoDA(ro)2 is the value of VDA(r)2 when D and A are at the van der Waals contact distance ro, and β accounts for the

Figure 3. Variation of the reorganization energy, λ, with temperature. The λ’s were obtained from eq 12 (see text) for VDA2 ) 0.012 eV2. The equation λ ) 1.6 exp[-(T - 275.3)/7.1] is an empirical exponential function. Abbreviations: T, temperature in kelvin; VDA, electronic coupling matrix element between electron donor (D) and acceptor (A) wave functions.

effect of the molecular environment on the propagation of the wave function. This has been the object of many comprehensive discussions (see, e.g., ref 27e). In the theoretical analyses performed in section IV, the value VDA(r)2 ) 0.012 eV2 used in eq 12 was chosen to take into account the most probable range of λ values, that is, from 0.7 to 1.5 eV as was determined in ref 39 on the one hand, and the λ’s yielded by the mathematical simulations of OE shown in Figure 2, that is, from 0.041 to 1.66 eV, on the other hand. In this perspective, we acknowledge that the exact solution of eq 13 for the conditions of the experiments reported in this study is a matter that requires a more detailed examination. This is not, however, a simple matter since the paradigm of a square tunneling barrier means that, in the present theory, one is confronted with the question of a homogeneous medium separating the electron donor from the electron acceptor. But, this requirement does not conform exactly to the complex structural conditions of the PSII reaction center (see refs 6 and 7), a matter that points to the need for modification of the theory. Temperature Dependence of the Reorganization Energy, λ. A major issue in the present work is the demonstration that the maximum amplitude of OE for each j state depends on λ-1/2 in the pre-exponential term of OE in eq 12. This is quite clear in Table 1 where one sees a decrease of the reorganization energy accompanied by a large augmentation of oxygen evolution, that is from OEmax ) 38.9 µmol O2/(mg Chl · h) at λ ) 1.66 to OEmax ) 236.0 µmol O2/(mg Chl · h) at λ ) 0.041. Table 1 displays also the temperature dependence of λ which is depicted in Figure 3 with an empirical mathematical representation of λ vs T expressed as

λ ) 1.6 exp[-(T - 275.3)/7.1]

(14)

where λ is given in eV, T is the temperature in kelvin at the OE maxima of the thermal transitions (cf. Figure 2), and 1.6 and 7.1 are scale factors in eV and K, respectively. Figure 3 shows that λ is quite large at low temperatures, e.g., 1.67 at 275 K, and decreases steadily to much lower values at higher

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temperatures, e.g., 0.037 at 302 K. An explanation of this effect is attempted with Marcus’ equation for the outer sphere reorganization energy (λo), that is27f

λo ) ∆q2(1/εop - 1/εS)(1/2rD + 1/2rA - 1/RDA)

(15) where ∆q is the charged transferred, εop and εs are the optical and static dielectric constants of the medium, respectively, rD and rA are the cavity radii of the electron donor and acceptor, and RDA is the donor-acceptor distance. Note, in addition, that experimental values of εop were determined to be between 1.5 and 2.5 (see ref 27f). Equation 15 shows that, all parameters being constant except εs, the decrease of λo results from the decrease of the static dielectric constant, or a loss of polarity. From this, a simple conclusion is the decrease of the electron-transfer rate with the decrease of polarity of the reaction medium. But this contradicts well-known data showing that the redox activity is enhanced by the augmentation of the dielectric constant. For example, the reaction of ferrocytochrome c with ferricyanide (see discussions in ref 40). In principle, one might exclude the static dielectric constant as a factor capable of explaining the temperature dependence of electron transfer through photosystem II. An alternative interpretation of eq 15 is to assume that the λo variation is dependent on RDA. In this context, a decrease of λo is accompanied by a decrease of the donor-acceptor distance of the redox couple, meaning that the strength of its interactions might change. The quantitative expression of this conclusion can be obtained with Keesom equation10 for the average potential energy of interaction of two dipoles; that is

∆G(µ,µ)av ) -2µ4 /3kBTr6

(16)

where µ is the dipole moment, kB the Boltzmann constant, T the temperature in kelvin, and r the dipoles separation distance. In this framework, a calculation requiring a decrease of r, on account of the conditions put forward above (i.e., a RDA decrease), yields a stronger dipole-dipole interaction energy, ∆G(µ,µ)av. The obvious effect is the induction of more stringent, or less random, orientations of the dipoles which, in macromolecular structures, affect the stability of the hydrogen-bond network. We note finally that the variation of ∆G(µ,µ)av with (kBTr6)-1 in eq 16 points to a relationship between the variations of thermal agitation (kBT) and dipole-dipole distance (r6) which may induce opposite effects on ∆G(µ,µ)av. VI. Concluding Remarks First, we showed that the temperature-response curves of oxygen evolution in photosystem II above 273 K in steadystate conditions display several discontinuities, or thermal transitions, that cannot be fitted with mathematical functions such as, for example, the classical Arrhenius equation26 (Figure 1). Second, the examination of the experimental data with the Marcus theory of electron transfer27 modified to take into account the heat-induced discontinuities of oxygen evolution yielded a summation of Gaussian functions revealing the presence of six thermal transitions at 275.3, 281.2, 286.4, 291.4, 297.1, and 302.4 K (Figure 2). The resolution of Gaussian bands is about 0.55 owing to multiple superpositions, suggesting the

coexistence of multiple temperature-dependent structural arrangements (or j states). Third, we found that the oxygen evolution in PSII is essentially dependent on VDA2/(λT)1/2 in the pre-exponential term of the modified Marcus equation (eq 12). Moreover, the calculations performed with VDA2 ) 0.012 eV2 showed that the reorganization energy, λ, decreases with increasing temperature according to an exponential function (see Figure 3), and is also dependent on the electron donor-acceptor distance. Finally, theoretical analyses of the data indicate that the large enhancement of oxygen evolution in photosystem II observed with increasing temperatures from 273 to 302 K has its origin, at least partly, in heat-induced structural rearrangements in the PSII reaction center. These conclusions are in accord with recent observations demonstrating that local thermal transients and protein flexibility are essential for photosynthetic function.18-21 Acknowledgment. This work was supported by the Natural Sciences and Engineering Research Council of Canada. We thank the reviewers for their comments, and specially for the remarks on “hydrophobicity and the temperature effect” which helped to clarify the paper. References and Notes (1) 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. (2) Burda, K. Cell Biochem. Biophys. 2007, 47, 271. (3) Kern, J.; Renger, G. Photosynth. Res. 2007, 94, 183. (4) Brudvig, G. W. Philos. Trans. R. Soc. London B 2008, 363, 1211. (5) Buchta, J.; Grabolle, M.; Dau, H. Biochim. Biophys. Acta 2007, 1767, 565. (6) (a) Zouni, A.; Witt, H.-T.; Kern, J.; Fromme, P.; Krauss, N.; Saenger, W.; Orth, P. Nature 2001, 409, 739. (b) Kamiya, N.; Shen, J. R. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 98. (c) Ferreira, K. N.; Iverson, T. M.; Maghlaoui, K.; Barber, J.; Iwata, S. Science 2004, 303, 1831. (d) Biesiadka, J.; Loll, B.; Kern, J.; Irrgang, K.-D.; Zouni, A. Phys. Chem. Chem. Phys. 2004, 6, 4733. (e) Loll, B.; Kern, K.; Saenger, W.; Zouni, A.; Biesiadka, J. Nature 2005, 438, 1040. (7) Guskov, A.; Kern, J.; Gabdulkhakov, A.; Broser, M.; Zouni, A.; Saenger, W. Nat. Struct. Mol. Biol. 2009, 16, 334. (8) Tanford, C. The Hydrophobic Effect. Formation of Micelles and Biological Membranes; John Wiley & Sons: New York, 1973. (9) Schellman, J. A. Biophys. J. 1997, 73, 2960. (10) A straightforward demonstration of the thermal agitation effect on dipole orientation is the Keesom equation (see discussion in ref 11) for the average potential energy of interaction of two dipoles; that is, ∆G(µ,µ)av )-2µ4/3kBTr6, where µ is the dipole moment, kB the Boltzmann constant, T the temperature in kelvin, and r the dipoles separation distance. The equation shows that transient changes of temperature cause intermittent variations of the dipole-dipole interaction energy, thereby inducing random orientations of the dipoles which, in macromolecular structures, affect concomitantly the stability of the hydrogen-bond network. (11) Adamson, A. W. Physical Chemistry of Surfaces, 4th ed.; John Wiley & Sons: New York, 1982; p 234. (12) Ross, P. D.; Rekharsky, M. V. Biophys. J. 1996, 71, 2144. (13) The amide I band in the infrared spectra of proteins extends from 1700 to 1600 cm-1. This spectral region contain a set of vibrational modes which are related to several periodic structures found in many proteins. The amide I band is associated with in-plane CdO stretching vibrations (νCO, ∼80%) weakly coupled with some contributions from CN stretching and CCN deformation. In other words, this band originates mainly in νCO vibrations of the peptide bond (1700-1620 cm-1) mixed with vibrational modes between 1620 and 1600 cm-1 from aromatic side chains, e.g., tyrosine at about 1608 cm-1, and chlorophylls around 1693-1692 cm-1 (see details in refs 14-17). (14) (a) Krimm, S.; Bandekar, J. AdV. Protein Chem. 1986, 38, 181. (b) Arrondo, J. L. R.; Muga, A.; Castresana, J.; Gon˜i, F. M. Prog. Biophys. Mol. Biol. 1993, 59, 23. (c) Arrondo, J. L. R.; Castresana, J.; Valpuesta, J. M.; Gon˜i, F. M. Biochemistry 1994, 33, 11650. (d) Fragata, M. In Methods in Molecular Biology: Photosynthesis Research.Protocols; Carpentier, R., Ed.; Humana Press Inc.: Totowa, NJ, 2004; p 183. (15) De Las Rivas, J.; Barber, J. Biochemistry 1997, 36, 8897. (16) Joshi, M.; Fragata, M. Z. Naturforsch. 1999, 54c, 35.

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