Eur. J. Biochem. 222, 1001 -1007 (1994) 0 FEBS 1994

A thermodynamic study by laser-flash photolysis of plastocyanin and cytochrome c6 oxidation by photosystem I from the green alga Monoraphidium braunii Antonio DiAZ', Manuel HERVAS', JosC A. NAVARRO', Miguel A. DE LA ROSA' and Gordon TOLLIN' ' Instituto de Bioquimica Vegetal y Fotosintesis, Universidad de Sevilla y CSIC, Sevilla, Spain * Department of Biochemistry, University of Arizona, Tucson, USA

(Received February 28/April 7, 1994) - EJB 94 0282/6

Plastocyanin and cytochrome c6 from the green alga Monoruphidium bruunii reduce the photo- oxidized algal photosystem I (PSI) reaction center chlorophyll (P700) with similar kinetics, as expected from their functional equivalence. The observed P700' reduction rate constants show a non-linear dependence on metalloprotein concentration, which indicates a (minimal) two-step kinetic mechanism involving complex formation prior to electron transfer. The dependence of the observed rate constants on NaCl concentration suggests that the electrostatic interaction forces between the negatively charged donor proteins and PSI are repulsive at neutral pH and relatively low ionic strength (I), although attractive dipole-dipole interactions may play a role at higher ionic strengths. Activation parameters for P700' reduction by cytochrome c6 and plastocyanin have been determined by studying the temperature dependence of the respective rate constants at varying ionic strength and pH. Changes in NaCl concentration and pH induce significant changes in the activation free energy of the overall reaction, even though the corresponding values for activation enthalpy and entropy undergo changes in opposite directions. Such a compensation effect between enthalpy and entropy is observed with both cytochrome cb and plastocyanin. Protein concentration dependencies of the observed rate constants at different temperatures has allowed an estimate of the free energy change during complex association, as well as the activation parameters for electron transfer, accord- ing to a two-step kinetic model

Plastocyanin and cytochrome c6 are two functionally equivalent redox proteins, which act as electron carriers be- tween the cytochrome b$complex and photosystem I (PSI) [ 11. Higher plants contain only plastocyanin, whereas green algae and cyanobacteria preferentially synthesize cytochrome c6. There are, however, a number of green algae and cyano- bacteria which can synthesize either one or other met- alloprotein depending upon the relative levels of copper and iron in the culture medium [2, 31.

We have recently reported [4] a comparative laser flash absorption spectroscopy study of the oxidation of plastocya- nin and cytochrome c6 isolated from the green alga Monoru- phidium bruunii by spinach PSI particles. It was shown that at mild acid pH, which is close to physiological conditions

Correspondence to G. Tollin, Department of Biochemistry, Uni-

Fax: +1 602 621 9288. Abbreviations. Chl, chlorophyll; AC4, AHf, A S 4 , activation free

energy, enthalpy and entropy of the overall reaction; AG,, AH,, AS,, estimated free energy, enthalpy and entropy of complex association ; AGZ, AH,:, AS,:, activation free energy, enthalpy and entropy of electron transfer; I, ionic strength; k,, second-order rate constant of complex formation; k- , , first-order rate constant of complex dissoci- ation; k,, effective second-order rate constant of the overall reaction; KA, complex association constant; k,, Boltzmann constant; k,,, esti- mated rate constant of electron transfer; koba, observed first-order rate constant; MV, methyl viologen; PSI, photosystem I; P700+, photooxidized; PSI, reaction-centre chlorophyll.

versity of Arizona, Tucson, AZ 85721, USA

inside the thylakoid lumen, plastocyanin and cytochrome c6 react with spinach PSI with approximately equal rate con- stants [4]. In the present study, PSI particles isolated from the same alga have been used.

In order to increase our understanding of the reaction mechanism of electron transfer from cytochrome c6 and plas- tocyanin to PSI, the transition state theory [5] of chemical processes has been applied. Although this is a very useful tool not only for describing the parameters that control reac- tion rates, but also for constructing models which predict the behavior and the absolute rates of reactions [6], reactions in solution are very complicated and difficult to understand because of the influence of frictional, static and dynamic solvent effects [6].

The transition-state theory has been successfully applied to biochemical fields such as enzymology [7- lo], immunol- ogy [ l l ] and redox reactions. For the latter class of reactions, applications have been made to electron transfer between small molecules, small molecules and proteins [12- 141, as well as between and through proteins, including those in- volved in the photosynthetic electron transfer chain [14-201. Most of these studies [12-191 have shown that the activation barrier is of an entropic nature (that is, entropy changes ac- count for most of the energy barrier), given that electron transfer is the rate-limiting step [13]. Moreover, the transi- tion-state theory has allowed the elaboration of theoretical models for redox reactions, such as that by Marcus [21], in

1002

which the rate constant of electron transfer is expressed as an exponential function of the standard free energy of the reaction and its reorganization energy, the latter accounting for both intramolecular and solvent reorganization occurring during the reaction.

In a previous work [4], we suggested that the ionic strength controls the rate constants for electron transfer from reduced cytochrome c, and plastocyanin, obtained from M. bruunii, to the photooxidized photosystem-I reaction-centre chlorophyll (P700+) in spinach PSI particles. This was inter- preted as indicating that an optimal orientation for electron transfer between the two oppositely charged pairs of proteins involved in these reactions is only achieved by an additional rearrangement occurring within an initially formed collision complex.

In this work, we show how the activation parameters for the overall reaction can change with various reaction condi- tions, suggesting that other factors (i.e. solvent effects, cation association to charged groups) can also control the reaction rate.

MATERIALS AND METHODS Plant material

Monoruphidium cells were grown in the culture medium described by Kessler et al. [22], and were collected by con- tinuous flow centrifugation. Spinach plants were obtained from a local market.

Purification procedures Triton-solubilized PSI particles from spinach (the so-

called TSF-1 particles) and from Monoruphidium were ob- tained following the procedure of Vernon and Shaw [23] with minor changes, and were finally suspended in 10 mM Hepes/ NaOH, pH 7.0. Algal plastocyanin and cytochrome c6 were purified as described previously [4]. The P700 content in the PSI samples was calculated either from the difference absorption spectrum (reduced minus oxidized), or by following the photobleaching at 698 nm (reference wave- length, 725 nm) using the absorption coefficient of 64 mN-' cm-' determined by Hiyama and Ke [24]. Chlorophyll con- centrations were determined according to Arnon [25]. The concentrations of plastocyanin and cytochrome c6 were cal- culated using their respective absorption coefficients of 4.5 mN-' cm-' at 597 nm (not published) and 25 mM-' cm-' at 553 nm [26].

Laser-flash kinetics

The kinetic analyses were performed using a laser flash photolysis system based on a nitrogen laser-pumped dye so- lution (excitation wavelength, 660 nm), as described pre- viously [4, 271. Unless otherwise stated, the standard reaction mixtures contained, in a final volume of 0.2m1, 1OmM Hepes, pH 7.0, an amount of Monoruphidium PSI particles equivalent to 300 pg chlorophyll ml-I, 0.1 mM methyl violo- gen (MV), 1 mM ascorbate and 10-20 pM purified protein (either plastocyanin or cytochrome c,). All experiments were carried out in a 2-mm path length-cuvette at room temper- ature (22 ? 1 "C). Transient kinetics were monitored by following the saturating flash-induced absorption changes at 697 nm; each kinetic trace was the average of 4-8 indepen- dent measurements. For most experiments, the estimated er-

30 ,

Protein (pM)

Fig.l. Kinetic traces for P700' reduction in the presence of 10 pM cytochrome cs (a) or 15 pM plastocyanin (b), and depen- dence of the observed rate constants (kobs) upon concentration of cytochrome c6 (0) and plastocyanin (a). Experimental condi- tions were as described in Materials and Methods, except that the reaction mixture was 5 mM in MgC1,.

ror in the observed rate constants was C10%, based on re- producibility and signalhoise ratios. For assays carried out at acid pH, errors could be as large as G20%.

Thermodynamic experiments In the temperature-dependence studies, a water-thermo-

statted cell was adapted to fit a 2-mm path length cuvette and to allow the laser beam to reach the cuvette at a 45" angle. The thermoelement of a digital thermometer was at- tached to the cuvette. The outer walls of the cuvette were cleaned with ethanol before flashing the samples, in order to prevent water condensation at lower temperatures. Temper- ature was varied over 5-30°C in increments of 4°C.

RESULTS The chlorophyll pigment P700 in PSI can be photoex-

cited by a laser flash to an excited singlet state, which can in turn be oxidized to P700' in the presence of an electron acceptor such as MV. The kinetics of such redox changes can be monitored by following the absorbance changes at 697 nm, a wavelength at which P700 exhibits an absorption maximum. In the presence of eithcr plastocyanin or cyto- chrome c6, P700 is rapidly oxidized by the laser flash and re- reduced to its initial level within a few seconds in a monoex- ponential process (Fig. 1).

The rate constant of P700' reduction increases with the amount of plastocyanin or cytochrome c,, even at 200- 300 pM protein concentration. Fig. 1 shows the protein con- centration dependence of the observed first-order rate con- stant (kobr) for P700' reduction by plastocyanin and cyto- chrome c6, which appear to reduce the algal P700' with simi- lar efficiencies. For both metalloproteins, the reaction rate constants show a non-linear protein concentration depen- dence, which suggests a (minimal) two-step kinetic mecha- nism involving complex formation followed by intracomplex electron transfer as follows :

Protein,, + PSI,, + [Protein,,, ... PSI,,]

% Protein,, + PSI,,,,

where k , is the second-order rate constant of complex forma- tion, k - , is the first-order rate constant of complex dissoci-

1003

f 1 6

N

Y

G -

1 4

1 3

12

1 1

10

9

0 ' I I I 1 I I 0 0 . 2 0.4 0.6 0 . 8 1 1 .2

dI (M"2) Fig.2. Dependence of the observed rate constants (kObs) for re- duction of P700' by plastocyanin (0) and cytochrome c, (0) upon ionic strength (I). The ionic strength in the reaction cell was adjusted by varying the NaCl concentration. Solid lines are theoreti- cal curves calculated from the Watkins equation (see text for details).

ation, and k,, is the limiting first-order rate constant of intra- complex electron transfer. The data in Fig. 1 can be fitted by a non-linear least-squares analysis using the above mecha- nism [28], to obtain values for the kinetic constants and for KA, which is the complex association constant (i.e. k,/k-,) . Although this only provides a lower limit for k, and k-, , accurate values are obtained for the other parameters. From this analysis, we derive K A values of 0.9X1O4M-' and 1.5X104M-', and k,,values of 40 $- ' and 45 s-', for plasto- cyanin and cytochrome c6, respectively.

The effect of ionic strength on the observed rate constants of Monoraphidium PSI reduction by plastocyanin and cyto- chrome c6 was studied by changing the NaCl concentration in the sample. Fig. 2 shows the dependence of kobs on \h, which is a measure of charge screening by an ionic medium [29]. At ionic strengths corresponding to ,,h values of 0.15- 0.3, the reaction rate is not significantly affected. However, at NaCl concentrations higher than 0.2 M, kohc increases with increasing ionic strength, up to a value of 16 s- ' or 9 s - ' at 1 M NaCl for plastocyanin and cytochrome c6, respectively. Such a sigmoidal ionic strength dependence, as well as the high ionic-strength required to accelerate the redox reaction, is also observed under steady-state conditions (data not shown).

The results of Fig. 2 cannot be easily explained by a sim- ple electrostatic (monopole-monopole) kinetic model, as in the Debye-Huckel theory [29]. A possible alternative is that dipolar forces play an important role in the interaction. The solid lines in Fig. 2 are theoretical curves obtained by a non- linear least-5quares fit of the experimental data to the com- plete version of the Watkins equation [30, 311 (although the theoretical model due to Van Leeuwen [32] also yielded simi- lar results). Both of these models include terms which corre- spond to monopole-monopole, dipole-dipole and monopole- dipole interactions ; the Watkins equation also takes into ac- count some exclusion of water molecules at the interaction site [31]. It is clear that the fits to the data are quite satisfac- tory, providing some support for an interpretation based on a contribution due to dipole interactions. It should be noted that the fits to the Watkins model without including the dipo- lar terms are significantly poorer, especially in the low-ionic- strength region.

3 8 4 0 4 2 4 4 4 6 4 8 50 5 2

AG' (kJ rnol I)

Fig. 3. Dependence of the effective second-order rate constant (k,) on the apparent activation free energy (AG') for P700' re- duction by plastocyanin (0) and cytochrome c, (0). Experimental data were obtained at 20 pM donor protein concentration and pH 7, but at different NaCl or MgCl, concentrations. Inset, typical Eyring plot for cytochrome c6, in the presence of 50mM MgCl,, from which the activation parameters were obtained. Units for second- order rate constants are M-'s- ' .

The effect of temperature on P700' reduction by cyto- chrome c6 and plastocyanin was first determined at an inter- mediate ionic strength, as little or no temperature dependence was observed in the absence of added salt. Fig. 3 shows the temperature dependence of the second-order reaction rate constant (k2) at 50 mM MgCl,, which corresponds to a linear Eyring plot with no breakpoints. From the slope of this line and the intercept at 1/T = 0, the apparent enthalpy (AH') and entropy (ASf) can be determined, which in turn allows calculation of the corresponding activation free energy (AG') for the formation of the intermediate complex, according to the two-step kinetic model described above. Fig. 3 shows that there is an exponential relation between k, for both cyto- chrome ch and plastocyanin under different experimental conditions and the apparent activation free energy (AG'), as would be expected from the Eyring equation :

k, = (k,T/h)e-AG"RT

where k , is the Boltzmann constant, T is the absolute temper- ature, h is Planck's constant, and R is the gas constant. The plot of In k, versus AG' at 25°C yields a line with a slope of -0.398 kJ-' mol and a value of 29.23 for In k, at AG' = 0. These values are in close agreement with those expected from the theory, which are -0.404 k.-' mol and 29.45, re- spectively.

Fig. 4A shows the ionic-strength dependence of the ob- served rate constants (kobJ for PSI reduction by cytochrome ch at different temperatures. As is evident, the reaction-rate constant is virtually independent of temperature at low salt concentrations, but has a considerable dependence at high ionic strength. The ionic-strength dependencies of the activa- tion parameters obtained from these data are presented in Fig. 4B, in which the apparent activation energy (dGf) at 298 K decreases by 3.5 kJ mol-' over 0-0.9 M NaCI. This would explain the increase in the rate constant observed at increasing ionic strengths (see Figs 2 and 4A). It is interest- ing to note that computer simulation of the activation param- eters according to the Watkins and Van Leewen models yields similar results, i.e. a decrease in AG of 3 kJ mol-'.

1004

294 K

u

01 I

h

40

30

20

10

0 0.2 0.4 0.6 0.8 1

Jl (M"L)

Fig.4. Effect of the ionic strength on k,,,, AH', AS' and AG' for electron transfer from cytochrome c, to P700'. (A) Ionic- strength dependence of the observed rate constant (kohs) for electron transfer from cytochrome c, to P700 ' at varying temperatures. Ionic strength was determined by adding NaCI. (B) Effect of ionic strength on the apparent activation enthalpy (AHf), entropy (AS') and free energy (AG') of cytochrome c6 oxidation by P700' as calculated from experimental data in (A) at 294 K.

60

50

-- 40 - 0 E 30 c,

s. 20

2 10

H

I

0 50 100

AS ' (J mol-' K-') Fig. 5. Correlation between the apparent activation enthalpy (AH') and entropy (AS') of P700' reduction by either cyto- chrome c, (0) or plastocyanin (0).

Such a change in AG' is the result of opposite changes in enthalpy and entropy (Fig. 4B), an effect which is not pre- dicted by the aforementioned models. Thus, upon increasing NaCl concentration from 0 M to 0.9 M at 298 K (Fig. 4B), A S z increases by 104 J mol-' K-' (i.e. the term - T A S f decreases by approximately 31 kJ mol-' and thus lowers the activation barrier), but this is compensated by a parallel increase of 27.5 kJ mol-' in AHf. As can be seen in Fig. 5, the apparent activation enthalpies and entropies for the over- all reaction are directly related by a straight line.

The dependence of the rate constant on metalloprotein concentration, over the range 20-250 pM, was studied in the absence of added salt at a variety of temperatures (data not shown). By applying the two-step kinetic model de- scribed here, the association (KA) and electron-transfer (keJ

constants were calculated at different temperatures, which al- lowed us to estimate the changes in free energy for complex association (AG,) and electron transfer (AGZ). The results obtained are summarized in Table 1. Noteworthy, the associa- tion of the reaction partners seems to be an exergonic process (AG, for cytochrome ch is -25.60 kJ mol-' and is mostly enthalpic) but the electron-transfer step shows a high energy barrier (approximately 70 kJ mol-' for cytochrome c, and plastocyanin) in which the entropy term accounts for most of the energy required.

It is also interesting to note that the estimated k,, for cyto- chrome c6 and plastocyanin oxidation by PSI in the absence of added salts is 1.9 s-' and 2.1 s-', respectively, but it is 45 s-' and 40 s-I, respectively, at 5 mM MgCI, (see above). However, k, is only 10-times higher with cytochrome c6 and 2.5-times higher with plastocyanin when 5 mM MgCl, is added (data not shown).

The effect of MgCl, on the apparent activation parame- ters for the overall reaction (i.e. without separating complex formation and electron transfer) was compared to that of NaCl at two different pH values. As can be seen from Table 2, addition of either Mg" or Na' cations at neutral pH results in a parallel increase in both the activation enthalpy and entropy, with the effect of Mg" being larger than that of Na'. Table 2 also shows the activation enthalpy and en- tropy at pH 4, which, consistent with the above-mentioned enthalpy-entropy compensation, are similarly increased with respect to the values obtained at neutral pH.

DISCUSSION

The first purpose of this work was to determine'the rela- tive efficiencies of Monoraphidium plastocyanin and cyto- chrome c6 for electron transfer to PSI particles isolated from the same alga, and to compare these with our previous data for spinach PSI particles [4]. The kobs values (as well as the derived values for k , and ket) reported here for oxidation of these proteins by algal PSI particles are indeed similar to one another, as predicted by their physiological interchangeabil- ity. However, both proteins react with the algal photosystem about 100 times more slowly than they do with spinach PSI [4]. In agreement with these results, Nechustai and Nelson [33] have observed a low interaction efficiency between PSI components for the green alga Chlamydomonas and its phys- iological donor proteins, as a consequence of which the redox reaction only takes place at high NaCl concentrations. Such low rates have also been shown for cytochrome ch photooxi- dation by PSI particles isolated from the cyanobacterium Sy- nechococcus elongatus [34]. The biochemical basis for these results is not known. However, the interaction specificity for donor proteins appears to remain unaffected in Monoraphi- dium PSI, i.e. plastocyanin and cytochrome ch behave simi- larly and neither spinach nor algal P700' is able to oxidize tuna cytochrome c.

The effect of ionic strength was then studied in order to analyze the electrostatic interaction3 between the negatively charged PSI and its correspondingly negative donor proteins. As expected from simple electrostatic considerations based on the Debye-Huckel theory [29], the P700' reduction rate increased with increasing ionic strength at neutral pH, but this only became apparent at NaCl concentrations higher than 0.2 M. Such unusual ionic-strength behavior cannot be ex- plained solely in terms of repulsive ion-ion forces between electrostatic charges. Our analysis showed that a significant

1005

Table 1. Estimated thermodynamic parameters for protein association and transition-state energies for the electron-transfer step. The reaction mixture was as described under Materials and Methods. n.d., not determined.

Protein AH,

kJ mol-' J mol-' K-' kJ mol-' J mol-' K-' kJ mol-'

Cytochrome c6 -24.72 3.34 -25.60 28.40 -142.10 70.45 Plastocyanin n.d. n.d. n.d. 6.23 -218.70 71.15

Table 2. Apparent activation parameters for the overall reaction at varying pH and ionic strength. The buffers used were either 10 mM Hepes, pH 7 or 10 mM sodium succinate.

Protein AH' AS' AG'

Cytochrome c, pH 7, no salt pH 7, 150 mM NaCl pH 4, no salt pH 4, 150 mM NaCl

pH 7, no salt pH 7, 150 mM NaCl pH 7 ,50 mM MgCl, pH 4, no salt

Plas tocyanin

kJ mol-'

2.27 9.61

61.90 35.26

7.47 19.43 34.24 29.16

J mol-' K-

-145.90 -118.50

79.25 - 12.17

-128.27 - 81.74 - 22.20 - 47.95

-' kJ mol-'

45.75 44.93 38.26 38.89

45.72 43.79 40.85 43.45

contribution of the opposite sign from the protein dipole mo- ments, as described in the theories of Watkins [30, 311 and Van Leeuwen [32], can account for this. According to this interpretation, the attractive dipole interactions presumably affect the mutual orientation of the proteins during complex formation and, consequently, modify the efficiency of electron transfer. Electrostatic treatments, including dipole terms, have successfully been applied to several other sys- tems as well [35, 361.

The results presented here also indicate that P700' reduc- tion by cytochrome c6 and plastocyanin proceeds according to a simple transition-state theory, i.e. Eyring plots are linear and the effective rate constant k, is an exponential function of AG'. It should be noted that biphasic Eyring plots have been observed previously [16] and were interpreted in terms of changes in the lipid bilayer, but such breakpoints have never been observed in Triton-solubilized PSI complexes. The values for the activation energy reported here are in the range 40-50 kJ mol-', which are higher than those obtained by Wood (30.3 kJ mol-') for the reduction of plastocyanin by cytochrome f [17], but are lower than those reported by Itoh (approximately 60 kJ mol-') for the reduction of P700' by ascorbate and ferrocyanide [18]. This fact is indicative of the lower efficiency of such small molecules when transfer- ring electrons to P700' as compared to the physiological do- nor proteins. The AG" values reported here are in the same range as those obtained by Takabe et al. [19] for the reduc- tion of spinach P700' by plastocyanin at pH 4.8 in the ab- sence of salts (43 kJ mol-') and at neutral pH when Mg" is added (44 kJ mol-I). Cox [15] has estimated the activation energy for cytochrome f oxidation by P700' in thylakoids to be 80 kJ mol-' and 76 kJ mol-' in the presence and in the absence of NH,CI, respectively.

Increasing the ionic strength and lowering the pH, as well as Mg2+ addition, result in a drastic increase in the apparent

activation entropy of Monoraphidium P700' reduction by cytochrome c, and plastocyanin. However, this effect is ac- companied by a parallel increase in the apparent activation enthalpy, although not so much as to totally compensate the increase in entropy. The final result is a significant increase in the reaction rates because of a decrease in the activation free energy. The effect of ionic strength, divalent cations and pH on the activation parameters are quite similar, thus allow- ing us to conclude that these factors control the overall reac- tion rate by similar mechanisms. It is interesting to note that comparable trends have been described for the reaction of the copper proteins plastocyanin and azurin with inorganic complexes [ 141.

These findings cannot be explained on the basis of changes in the electrostatic interaction energy, since this only accounts for small modifications in the activation energy as deduced from the values of electrostatic energy obtained by applying the Van Leeuwen and Watkins equations. According to our computer simulations at 298 K, AS' in the range 0- 0.9 M NaCl should decrease by less than 10 J mol-' K-' and show a minimum at moderate ionic strength, whereas AHf should decrease by approximately 5 kJ mol-'. However, the largest changes in activation parameters predicted by these models are at low ionic strength, which are contrary to the changes observed, i.e. an increase in AS" of 104 J mol-' K-' and an increase in AH" of 27.5 kJ mol-' (see above). This is probably a consequence of the fact that such estimations consider neither the activation parameters of the electron transfer nor possible solvent effects. In small organic mole- cules, the solvent effect on the reaction rates is mediated by an entropy-enthalpy compensation effect [37, 381 in such a way that solvent changes induce large and parallel changes in AH' and A S z , thus yielding small changes in AGf. Sim- ilar effects have been observed in the hydrolysis of acetyl phosphate and are attributed to differential cation association to the reactant and to the transition-state complex [39]. In spite of this, the role of electrostatic forces cannot be ex- cluded, since solvent effects can be induced both by the in- teraction between reaction partners and by the electron transfer itself. However, the contribution of the solvent re- arrangement to AG' should be rather small because of the enthalpy-entropy compensation.

It should be noted that although addition of 5 mM Mg" cations is enough to increase the electron transfer rate by approximately 20 times, it does not affect the estimated K,. This indicates that the main influence in making the reaction faster involves the electron-transfer step. It has been sug- gested [I91 that Mg" cations, even at low concentrations, allow the proteins to approach one another in the right orien- tation, by acting as a bridge between negative charges. The same effect should ultimately bc obtained by addition of Na', which increases the ionic strength so as to make the electrostatic interactions between charges negligible. Mea- surements of the ionic-strength dependence (using NaCl) of

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the observed rate constants as a function of pH showed an inversion of sign from repulsive to attractive as the solution changed from neutral to mildly acidic (data not shown). Thus, at the physiological pH inside the thylakoid lumen, the electrostatic interaction forces between PSI and its electron donors are attractive, which presumably allows them to ap- proach each other in a more favorable manner.

The activation parameters of the electron-transfer step for redox reactions between inorganic complexes and proteins have been extensively reviewed [13, 141. In general, highly negative activation entropies were found for the electron- transfer step. Even though this entropic barrier could be partly explained in terms of changes in protein conformation [13], the authors attribute this effect to the low probability of electron transfer between the reaction partners because of ‘the absence of an efficient conducting pathway between them’ [ 141. In consequence, AS’,, should be controlled by any factor affecting the probability of electron transfer, e.g. the relative orientation of the donor and acceptor proteins in the complex or the distance between them. In this regard, Takabe et al. [19] have suggested that the changes in transi- tion-state entropy for electron transfer from plastocyanin to spinach PSI are due to different distances between the reac- tion partners.

Work has been supported by the Direccidn General de Investiga- cidn CientljFca y Tlcnica, grant No. PB90-99 (to MAR), the NIH, grant NO. DK150.57 (to GT), and NATO, Collaborative Research grant No. CRG 900065. Thanks also due to Z. Salamon and J. Sou- lages for helpful discussions.

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