INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS REFERENCES

Photosystem I (PS I) of oxygenic photosynthesis is a membrane-bound pigment-protein complex that functions as a light-dependent plastocyanin (or cytochrome c₆): ferredoxin (or flavodoxin) oxidoreductase. Light-induced electron transfer takes place in a series of reactions between neighboring cofactors that are embedded in this complex. The primary electron carriers include a symmetrical set of six chlorophyll molecules, two phylloquinones and three iron-sulfur clusters. Of these, the primary electron donor is P700, a special pair of chlorophyll a/a' molecules, and the primary electron acceptor is A₀, a monomeric chlorophyll a. A phylloquinone molecule (A₁), and three [4Fe-4S] clusters (F_X, F_A, and F_B) operate as intermediate and terminal electron acceptors, respectively. The cofactors P700, A₀, A₁, and F_X are bound to the two main polypeptides, PsaA and PsaB, whereas the terminal electron acceptors F_A and F_B are bound to the small PsaC subunit (reviewed in Brettel, 1997; Fromme, 1999; Golbeck, 1999; Manna and Chitnis, 1999; Ke, 2001; Brettel and Leibl, 2001; and Vassiliev et al., 2001a).

The x-ray structure analysis of PS I crystals at 4-Å resolution (Klukas et al., 1999a, 1999b), and more recently at 2.5-Å resolution (Jordan et al., 2001), has revealed the position of the cofactors, including the two phylloquinone molecules and the three iron-sulfur clusters F_X, F_B, and F_A (Fig. 1). The reaction center chlorophylls and the quinones in PS I have a two-fold symmetrical arrangement similar to that of purple bacteria, in which a dimer of bacteriochlorophyll molecules transfers the electron via two "monomeric" chlorin cofactors to the quinone.

View larger version (33K): [in this window] [in a new window]   FIGURE 1   Structural model of PS I. The primary electron donor, P700, is comprised of Chl a molecule eC-B1 and Chl a' molecule eC-A1. The Chl a molecule spectroscopically identified as the primary acceptor A0 is probably eC-A3, and the phylloquinone molecule spectroscopically identified as the secondary acceptor A1 is probably QK-A. The [4Fe-4S] cluster Fx is bound by two cysteines from PsaA and two cysteines from PsaB. The FA and FB [4Fe-4S] clusters are bound to the PsaC subunit.

The phylloquinone acceptor can be extracted using organic solvents, and its function can be reconstituted using artificial quinones and a variety of quinoid compounds (Itoh et al., 1987; Iwaki and Itoh, 1991a, 1991b; Iwaki and Itoh, 1994; Iwaki et al., 1996). In situ values of the quinones correlate with their E_1/2 values determined polarographically in dimethylformamide (DMF): E_m(in situ) = E_1/2(in DMF)  310 mV (Iwaki et al., 1996). The estimated energy of reorganization for electron transfer from A₀ to A₁ is ~0.3 eV (Iwaki et al. 1996), in sharp contrast with the estimated energy of reorganization for electron transfer from A₁F_X of 0.8 to 1 eV (Schlodder et al., 1998).

A number of new constructs allows genetic modification of the cofactors on the acceptor side of PS I and provides new and unique tools for the analysis of the kinetics of electron transport in PS I complexes. Johnson et al. (2000) constructed menA and menB interruption mutants in Synechocystis sp. PCC 6803, in which plastoquinone-9 is present in the A₁ site of PS I (Zybailov et al., 2000; Semenov et al., 2000). The mutants retain a photochemically active PS I complex and can grow photosynthetically even in the absence of phylloquinone. Phylloquinone can be restored into the A₁ site by adding authentic phylloquinone or its precursors, 2-carboxy-1,4-naphthoquinone or 2-methyl-1,4-naphthoquinone, to growing menB (but not menA) mutant cells (Johnson et al., 2001).

Shen et al. (2002b) constructed a rubA interruption mutant in Synechococcus sp. PCC 7002, which lacks the iron-sulfur clusters F_X, F_A, and F_B (Shen et al., 2002a). Recently a menB/rubA double mutant was constructed in Synechococcus sp. PCC 7002 (B. Zybailov, Y. Sakuragi, G. Shen, D. Bryant, and J. Golbeck, manuscript in preparation) which lacks the iron-sulfur clusters F_X, F_B, and F_A and has plastoquinone-9 in the A₁ binding site. These new biological methods constitute a useful adjunct to chemical methods to remove the iron-sulfur clusters and to incorporate novel quinones into the A₁ site of PS I.

Here, we analyze the kinetics of P700⁺ dark reduction in PS I complexes that contain either an intact set or a subset of the iron-sulfur clusters F_X, F_B, and F_A, with A₁ site occupied by phylloquinone or plastoquinone-9. Our analysis shows that, in wild-type PS I complexes that contain phylloquinone in the A₁ site, the free energy gap between A₁ and iron-sulfur clusters F_A/F_B is ~205 mV. In mutant PS I complexes that contain plastoquinone-9 in the A₁ site, the free energy gap between A₁ and iron-sulfur clusters F_A/F_B is ~70 mV. The acceleration in the rate of P700⁺ dark reduction in plastoquinone-containing PS I and the absence of a contribution from F_X to the reduction of P700⁺ in the absence of iron-sulfur clusters F_A and F_B can be explained by the +135-mV change in the midpoint potential of A₁.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS REFERENCES

Construction and growth of mutant cells

The menA mutant was constructed in Synechocystis sp. PCC 6803 as described in Johnson et al. (2001) and grown phototoautotrophically under low levels of illumination. The phenotype of this mutant is that PS I contains plastoquinone-9 in the A₁ site. The rubA mutant was constructed in Synechococcus sp. PCC 7002 (Shen et al., 2002b) and grown photoheterotrophically using glycerol as a carbon source. The phenotype of this mutant is that PS I lacks the iron-sulfur clusters F_X, F_B, and F_A (Shen et al., 2002a). The menB/rubA double mutant was constructed in Synechococcus sp. PCC 7002 (B. Zybailov, Y. Sakuragi, G. Shen, D. Bryant, and J. Golbeck, manuscript in preparation) and grown photoheterotrophically using glycerol as a carbon source. The phenotype of this mutant is that PS I contains plastoquinone-9 in the A₁ site, and additionally lacks the iron-sulfur clusters F_X, F_B, and F_A.

Isolation of PS I complexes

PS I complexes from the wild-type, and the menA and menB/rubA mutants were isolated from membranes using n-dodecyl--D-maltoside and purified by sucrose gradient ultracentrifugation as described in Golbeck (1995). The PS I complexes were resuspended in Tris buffer (0.05 M Tris, pH 8.3) with 15% glycerol, frozen as small aliquots in liquid nitrogen, and stored at 95°C. PS I complexes were stripped of the F_A and F_B iron-sulfur clusters by removal of the PsaC protein using 6.8 M urea as described in Golbeck (1995). The presence of the F_X cluster was verified in the PsaC-stripped preparations by slow freezing to 77 K in the light to photoaccumulate P700 F followed by EPR spectroscopy at 8 K.

Time-resolved absorbance spectroscopy

Samples for optical experiments were in quartz cuvettes with air-tight stoppers. The reaction medium contained 25 mM Tris buffer (pH 8.3), 4 µM 2,6-dichlorophenol-indophenol (DCPIP), 10 mM sodium ascorbate, and 0.04% n-dodecyl--D-maltoside. The chlorophyll concentration was 50 µg/ml. Methyl viologen was added where indicated. The solutions were prepared in an anaerobic chamber using oxygen-free distilled water, air being substituted in a Thunberg tube by high-purity nitrogen. All chemicals were obtained from Sigma (St. Louis, MO).

The kinetics of absorbance changes at 832 nm (A₈₃₂) were measured in 10 × 4 mm cuvette using a spectrophotometer described in Vassiliev et al. (2001a). In experiments with wild-type samples, the measuring beam (power, 30 mW; , 832 nm) was provided by a PMT-25 laser diode assembly (Power Technology Inc., Little Rock, AR). In experiments with mutant samples that require faster time resolution, the measuring beam was provided by a titanium-sapphire laser (model TI-SPB, Schwartz Electro-Optics, Orlando, FL) tuned to 832 nm (power, ~200 mW) pumped with a diode-pumped, frequency-doubled CW Nd:YVO4 laser (Millenia, Spectra Physics, Mountain View, CA) at 5.4-W output power. Single turnover flashes were provided by a frequency-doubled (, 532 nm), Q-switched (FWHM, 10 ns) Nd-YAG laser model DCR-11 (Spectra Physics). A flash energy of 3.6 mJ was sufficient for saturation of P700 photochemistry without producing significant antenna chlorophyll triplets. The intervals between the actinic flashes were 50 s.

Data analysis using a stretched exponential

The A₈₃₂ kinetics shown in Figs. 2 and 3 reflect the dark reduction of P700⁺, and are presented on a logarithmic time scale so that the charge recombination from different electron acceptors can be easily visualized. The distribution of time constants can be described as , where F(, 0) is the distribution function of amplitudes over the continuum of time constants. An alternative method of fitting the kinetics with fewer numbers of components is provided by the Kohlrausch law (Kohlrausch, 1854, 1863), or stretched-multiexponential, in which each component is represented as A(t) = A₀exp((t/)) and in which the stretch parameter  varies between 0 and 1 (for discussion, see Vassiliev et al., 2001a, 2001b). This equation represents a robust solution of a general equation for kinetics with a distributed time constant. In the case when  = 1, the equation turns into a simple exponential. It is particularly useful for PS I kinetics, in which nonexponential kinetics may reflect different conformational states of the reaction center (Vassiliev et al., 1997). The stretched exponential is used in this study to simplify the analysis of the kinetic components that are ascribed to a particular electron acceptor.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS REFERENCES

Measurement of the kinetics of P700⁺ dark reduction

The relationship of a lifetime of P700⁺ dark reduction and a particular electron acceptor can be established using preparations lacking some or all of the iron-sulfur clusters, F_X, F_B, and F_A. Ideally, the monomolecular back reaction between a particular reduced acceptor and P700⁺ should follow monoexponential kinetics, but, in many instances, the experimental data are best fitted by two or more closely-spaced kinetic components (Vassiliev et al., 1997) that are folded here into a single stretched exponential without losing the quality of the fit (see Figs. 2 and 3). The value of the stretch factor  varies between 0 and 1 (with 1 being a simple exponential), and it provides a measure of the heterogeneity of the kinetics. The nature of this heterogeneity in the dark reduction of P700⁺ is not fully understood, but it may be related to existence of different conformational (sub)states in the PS I complex (Vassiliev et al., 1997). Such a heterogeneity has been reported in PS I (Schlodder et al., 1998) and in reaction clusters from purple bacteria (McMahon et al., 1998). Additional phases in purified PS I complexes can also arise from differential damage to the iron-sulfur clusters during isolation, but these are usually identifiable by their distinctive lifetimes. The decay of the triplet state of chlorophyll (Brettel and Golbeck, 1995; Vassiliev et al., 1997) can further contribute to a microsecond kinetic phase, but this assignment can be readily verified by studying the flash-saturation profile and wavelength dependence in the near-IR. The proposed participation of two different branches of cofactors in electron transport in PS I has been recently suggested as an additional source of heterogeneity of the measured kinetics (Guergova-Kuras et al., 2001). Even though several decay rates may exist for a particular forward or backward reaction, we will use only one rate constant to simplify the analysis in this paper. Usually this chosen rate constant is the weighted average of the two rate constants. A more comprehensive analysis, which takes into account multiple rate constants and the possibility of multiple pathways, will be forthcoming in a separate work.

Kinetics of P700⁺ dark reduction in PS I complexes with phylloquinone in the A₁ site

Figure 2 A shows typical kinetics of flash-induced absorbance changes at 832 nm in wild-type (phylloquinone-containing) PS I complexes from Synechocystis sp. PCC 6803 in the presence of DCPIP and ascorbate. The stretched multiexponential fit of the kinetics shows three different components with characteristic lifetimes of 2.2 ms (0.94), 107 ms (0.93), and 2.0 s (0.76) with relative amplitudes of ~5%, 68%, and 28%, respectively (the stretch factor is in parenthesis). The minor, 2.2-ms kinetic phase may be due to a subset of PS I complexes in which PsaC has been lost during isolation (see Fig. 2 B). The 2.0-s kinetic phase is due to forward electron donation by DCPIP in PS I complexes in which the electron has been lost from the iron-sulfur clusters, presumably by donation to dioxygen (Vassiliev et al., 1997).

View larger version (29K): [in this window] [in a new window]   FIGURE 2   Kinetics of absorbance changes at 832 nm in wild-type PS I complexes with phylloquinone in the A1 site. (A) Intact PS I complex with FX, FB, and FA present (wild-type). (B) PS I core lacking FA and FB, (prepared by chemically removing PsaC from the wild-type with urea). (C) PS I core lacking FX, FA, and FB (prepared from the rubA mutant). Reaction medium: (top) 25 mM Tris buffer (pH 8.3), 0.04% n-dodecyl--D-maltoside, 4 µM DCPIP, and 10 mM sodium ascorbate. Each individual component of the stretched multiexponential fit is plotted with a vertical offset relative to the next component (with a longer lifetime) or the baseline, the offset being equal to the amplitude of the latter component. The values indicate the (1/e) lifetime and the stretch parameter.

Figure 2 B shows the kinetics of flash-induced absorbance changes in a wild-type PS I core stripped of PsaC, and hence devoid of the F_A and F_B iron-sulfur clusters. The stretched multiexponential fit of the kinetics shows four different components with characteristics lifetimes of 11.6 µs (0.73), 192 µs (0.73), 971 µs (0.85), and 426 ms (0.49), and amplitudes ~20%, 20%, 48%, and 5%, respectively. The kinetic phase with an ~1.0-ms lifetime has been shown by optical and EPR spectroscopy to represent the backreaction of P700⁺ with F (Golbeck, 1995), and agrees with the lifetime of P700⁺ measured in a psaC interruption mutant in Synechocystis sp. PCC 6803 (Yu et al., 1995). The kinetic phases of ~12 and 200 µs in a 1:1 ratio represents the backreaction of P700⁺ with A (Vassiliev et al., 1997; also, see Fig. 1 C) in PS I complexes in which F_X has inadvertently been destroyed. The kinetic phase with a 426-ms lifetime probably represents a population of PS I complexes in which PsaC has not been removed.

Figure 2 C shows the kinetics of flash-induced absorbance changes in a PS I core isolated from the rubA mutant that contains phylloquinone in the A₁ site, but no F_X, F_A, or F_B iron-sulfur clusters. The stretched multiexponential fit of the kinetics shows three different components with characteristic lifetimes of 12.6 µs (0.96), 80.7 µs (0.95), and 1.1 ms (0.78) with relative amplitudes of 49.7%, 43.1%, and 4.1%, respectively. The two microsecond components have been shown by optical and EPR spectroscopy to represent the backreaction of P700⁺ with A (Shen et al., 2000a). These lifetimes are similar to the ~10- and 110-µs lifetimes measured in a chemically prepared P700-A₁ core that also lacks F_X, F_A, and F_B. Both kinetic phases show spectral signatures in the near-UV characteristic of the semiquinone anion radical (Brettel and Golbeck, 1995).

Kinetics of P700⁺ dark reduction in PS I complexes with plastoquinone in the A₁ site

Figure 3 A shows typical kinetics of flash-induced absorbance changes at 832 nm in menA (plastoquinone-containing) PS I complexes from Synechocystis sp. PCC 6803 in the presence of DCPIP and ascorbate. The stretched multiexponential fit of the kinetics shows two different components with characteristic lifetimes of 4.1 µs (1.00) and 2.9 ms (1.00) with relative amplitudes of 9% and 80%, respectively. Optical and EPR studies (Semenov et al., 2000) have shown that the ~3-ms component represents the backreaction of P700⁺ with a reduced iron-sulfur cluster, most probably [F_A/F_B].

View larger version (28K): [in this window] [in a new window]   FIGURE 3   Kinetics of absorbance changes at 832 nm in menA PS I complexes with plastoquinone in the A1 site. (A) Intact PS I complex with FX, FB, and FA present (menB mutant). (B) PS I core lacking FA and FB (prepared by chemically removing PsaC from the menB mutant with urea). (C) PS I core lacking FX, FA, and FB (prepared from the rubA/menB double mutant). Note that the relatively low A is due to the inadvertent loss of a population of plastoquinone-9 from the A1 binding site during detergent isolation (B. Zyabilov, Y. Sakuragi, G. Shen, D. Bryant, and J. Golbeck, manuscript in preparation). Reaction medium: 25 mM Tris buffer (pH 8.3), 0.04% n-dodecyl--D-maltoside, 4 µM DCPIP, and 10 mM sodium ascorbate. Each individual component of the stretched multiexponential fit is plotted with a vertical offset relative to the next component (with a longer lifetime) or the baseline, the offset being equal to the amplitude of the latter component. The values indicate the (1/e) lifetime and the stretch parameter.

Figure 3 B shows the kinetics of flash-induced absorbance changes in a menA PS I core stripped of PsaC, and hence devoid of the F_A and F_B iron-sulfur clusters. The stretched multiexponential fit of these kinetics shows four different components with characteristic lifetimes of 3 µs (0.81), 26 µs (0.59), 584 µs (0.82), and 1.7 ms (0.28), and amplitudes of 13%, 21%, 66%, and 20%, respectively. Optical studies in the near-UV at 315 nm show kinetics components with lifetimes of ~25 and 700 µs ascribed to a semiquinone anion radical (J. Golbeck, A. Semenov, and B. Diner, unpublished results). Thus, the 26- and 584-µs kinetic components in the stripped menA PS I core are assigned to the P700⁺ A backreaction.

Figure 3 C shows the kinetics of flash-induced absorbance changes in a PS I core isolated from the rubA/menB double mutant that contains plastoquinone in the A₁ site, but no F_X, F_A, or F_B iron-sulfur clusters. The stretched multiexponential fit of the kinetics shows four different components with characteristic lifetimes of 2.5 µs (0.60), 26 µs (0.75), 362 µs (0.96), and 5.9 ms (0.93), with relative amplitudes of 17%, 14%, 54%, and 7%, respectively. The spectra of the 26- and 362-µs components have derivative-like absorbance changes between 400 and 600 nm ascribed to electrochromic bandshifts of pigments in the vicinity of A, i.e., -carotene and chlorophyll (B. Zybailov, Y. Sakuragi, G. Shen, D. Bryant, and J. Golbeck, manuscript in preparation). Optical studies in the near-UV show kinetic components with lifetimes of ~15 and 400 µs with a spectrum between 250 and 340 nm, characteristic of a semiquinone anion radical (J. Golbeck, B. Zybailov, and B. Diner, unpublished results). Thus, the 26- and 362-µs kinetic components in the rubA/menB double mutant are assigned to the P700⁺ A backreaction.

The similarity of the lifetimes and spectral characteristics of the 584- and 362-µs components in menA PS I cores with PsaC and F_X removed, compared to the lifetimes and spectral characteristics of the 1-ms and 10-100-µs components in similar wild-type PS I cores indicates significant changes in the energetics of the acceptor side of the menA PS I complexes. This phenomenon, and the acceleration in the backreaction in fully-intact menA PS I, can be explained by shift of the midpoint potential of A₁ in such a way that equilibrium between A₁ and F_X is shifted in favor of A₁ (see Discussion).

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS REFERENCES

General expression for the rate constant of the flash-induced dark reduction of P700⁺

To understand the kinetics of P700⁺ dark reduction in wild-type and menA PS I complexes, we need to consider baseline information concerning the kinetics of electron transfer. Figure 4 shows the generally accepted scheme of flash-induced electron transfer in PS I. The rate constants and respective midpoint potentials are taken from the current literature and provide general guidance rather than exact values. They can be adjusted to fit the kinetics in a particular sample or strain, if needed. What is important here is that forward electron transfer at each successive step is faster than the back reaction to P700⁺. Hence, we can assume the (quasi)equilibrium between different states of the PS I complex during dark reduction. The assumption of the (quasi)equilibrium between different states of the PS I complex is frequently used for the analysis of the electron transfer in PS I (see e.g., Iwaki and Itoh, 1994; Brettel, 1997). Using such assumption, the observed rate constant of P⁺ dark reduction can be described by the general expression (Shinkarev and Wraight 1993),

(1)

Here k_pp is the rate constant for P* deexcitation; k_A0P is the rate constant of direct electron transfer from A to P700⁺; k_A1P is the rate constant of direct electron transfer from A to P700⁺; k_FXP is the rate constant of direct electron transfer from F to P700⁺; k_FAP is the rate constant of direct electron transfer from F to P700⁺; and k_FBP is the rate constant of direct electron transfer from F to P700⁺.

View larger version (16K): [in this window] [in a new window]   FIGURE 4   (A) Scheme of electron transport in PS I (reviewed in Brettel, (1997) and Ke, (2001)). Note that we depict the rate constant of direct electron transfer for reactions A0P, A1P. The indicated time for the reaction FA/FBP corresponds to the indirect electron transfer via FX. (B) Notations used for the rate and equilibrium constants. The values depicted for the redox potentials and backreaction times are taken from the literature, and are either experimentally determined or deduced from thermodynamic or kinetic arguments (i.e., the Em of A0 and A1).

Square brackets in Eq. 1 indicate the relative (per PS I complex) concentrations of the different states of PS I. Assuming (quasi)equilibrium between different states during dark reduction, the relative concentrations of the components can be found as functions of an equilibrium constant of electron transfer between the components,

(2)

Here, L_PA0 is the equilibrium constant for electron transfer from P* to A₀, L_A0A₁ is the equilibrium constant for electron transfer from A₀ to A₁, etc.



(see Fig. 4 B for a notation of the equilibrium constants between electron carriers).

The distance between F_A (F_B) and P700 provided by the x-ray crystal structure is so large (>30 Å (Jordan et al., 2001) that, based on the dependence of the logarithm of the rate constant on distance (Moser et al., 1995), we can ignore direct electron transfer between them and P700⁺ on a millisecond time scale. Thus, electron transfer from F and F to P700⁺ occurs indirectly via thermal repopulation of F_X, F_A, etc. Similarly, the edge-to-edge distance of 26-27 Å between F_X and P700 also indicates that the time of electron transfer from F to P700⁺ should be seconds.

Assuming k_FAP = 0, k_FBP = 0, and k_FXP = 0, Eq. 1 for the observed rate constant of P700⁺ dark decay can be rewritten in the simplified form,

(3)

Inserting the values of the relative concentrations of the different states from Eq. 2 into Eq. 3 gives the expression for the apparent rate constant of P700⁺ dark reduction after a flash,

(4)

This equation can be rewritten via the relevant free energy differences, G_XY = RT ln(L_XY),

(5)

Both Eqs. 4 and 5 can be used as the starting point for the analysis of the changes of P700⁺ dark reduction introduced by plastoquinone-9. We assume on the first iteration of this model that the absence of PsaC does not influence the thermodynamic or kinetic properties of F_X, and that the absence of F_X does not influence the thermodynamic kinetic properties of A₁.

Phylloquinone-containing PS I complexes

Flash-induced reactions of wild-type PS I in the absence of the FA/FB iron-sulfur clusters

View larger version (17K): [in this window] [in a new window]   FIGURE 5   Scheme of electron transport in wild-type PS I in the absence of PsaC.

(6)

(7)

(8)

Flash-induced reactions of wild-type PS I in the absence of all iron-sulfur clusters

Flash-induced reactions of wild-type PS I in the absence of A₁

Expression for the ratio of two different pathways

(9)

Flash-induced reactions of wild-type PS I in the presence of iron-sulfur clusters

(10)

(11)

(12)

Plastoquinone-9-containing PS I complexes

When phylloquinone is replaced by plastoquinone-9 in the A₁ binding site, we should expect, as a first approximation, that all rate and equilibrium constants not connected with A₁ are the same in wild-type and menA PS I complexes, and only the reactions of A₁ with other electron carriers are modified.

Flash-induced reactions of plastoquinone-9-containing PS I in the absence of iron-sulfur clusters

Flash-induced reactions of menA PS I in the absence of F_A and F_B

Flash-induced reactions of menA PS I in the presence of iron-sulfur clusters

(13)

(14)

(15)

View larger version (11K): [in this window] [in a new window]   FIGURE 6   Schemes of electron transport in (A) phylloquinone and (B) plastoquinone containing PS I complexes. Shaded box in (B) indicates uncertainty in the value of estimated midpoint redox potential of A1 due to the heterogeneity of the rate constant kA1P. The values depicted for the redox potentials and backreaction times are taken from the literature, and are either experimentally determined or deduced from thermodynamic or kinetic arguments (i.e., the Em of A0 and A1).

Mathematical modeling of electron transfer in PS I

The consistency of the above description of electron transport in mutant and wild-type PS I complexes with an intact set or a subset of iron-sulfur clusters F_X, F_B, and F_A and with the A₁ binding site occupied by phylloquinone or by plastoquinone can be checked further using mathematical modeling of respective processes with a system of differential equations. Figure 7 shows a series of theoretical curves calculated by solving a respective system of linear differential equations that describe the flash-induced transitions between different states in PS I (see Fig. 4),

where [A], [A], [F] are the relative (per PS I complex) concentrations of the PS I states with reduced A₀, A₁, and F_X, respectively. This system of stiff differential equations was solved by using Matlab software. As initial conditions for this system, we assumed that A₀ is completely reduced after the short flash of light, i.e., [A (0)] = 1. The following values of rate constants and free energy differences (summarized in Table 1) were assumed to be the sa