It is generally considered that metabolic reactions are well described by homogeneous kinetic models in which the reaction phase is statistically uniform. In membranes, especially in photosynthetic systems where the protein complement is high, it has recently been recognized that effects of local inhomogeneity might contribute additional factors which perturb the kinetic behavior, and require more extensive treatment [1]. We show in this paper that statistical inhomogeneity in vesicular systems can also contribute to quite marked discrepancies from the behavior expected from standard kinetic and thermodynamic models, for reactions involving free diffusion in the aqueous phase.

Several recent papers from the Joliots in collaboration with Vermeglio and Lavergne have suggested that the enzymes of photosynthetic electron transfer systems might be organized as supercomplexes [1-5]. The work was based on measurements by kinetic spectrophotometry of the equilibrium poise of reactants after excitation by flashes or continuous light. On continuous illumination of cells of Rb. sphaeroides, the observed values for equilibrium constant (K_obs) for electron transfer in the high potential chain were much lower than those expected from measured redox mid-point potentials [3]. To explain their results, the authors suggested that electron transfer occurred predominantly within supercomplexes, and developed an elegant hypothesis to account for the observed behavior. Two sorts of supercomplex were propose, one with reaction center and cyt c₂ in a ratio 2:1, the other with reaction centers, bc₁-complex and cyt c₂ in a ratio of 2:1:1. Within the supercomplexes, electron transfer reactions were proposed to occur with rates in the µs to ms range, and rapidly attained the poise expected from known equilibrium constants. However, diffusion of cyt c₂ from the complex was restricted so that interaction between one supercomplex and another, or with reaction center or bc₁-complex not associated into supercomplexes, could occur only on a seconds time scale. In this condition, it was suggested that continuous illumination introduced a statistical heterogeneity into the supercomplex population, leading to a fraction of centers in which the reaction center was more oxidized than expected (because the donor pool was exhausted), accounting for the observed departure from the expected equilibrium poise.

Evidence for separate complexes, connected by diffusion of QH₂ and cyt c₂

1. There is a diffusional pathway for QH₂ between reaction center and the bc₁-complex (giving a lag before reduction of cyt b_H when the pool is initially oxidized) [6, 7].
2. Oxidation of QH₂ involves a second-order reaction [6-12].
3. Both QH₂ and cytochrome c₂ can "visit" at least 8-10 electron transfer chains, probably representing all bc₁-complexes in a chromatophore [13, 14]. In these experiments, stigmatellin or myxothiazol or antimycin were used progressively to titrate out the bc₁-complex, and the capacity of the residual active complexes to transfer electrons to the oxidized cyt c₂ produced on photoactivation with a saturating flash was tested. A full reduction of cyt (c₂ + c₁) was observed when more than 80% of bc₁-complexes were inactive.
4. The kinetics slowed in proportion to the fraction of inhibited centers, showing that the rate was determined by the same rate constant in each case, and not effected by the greater diffusional pathway. This implies that there was no impediment to diffusion of cyt c₂ in the chromatophore internal volume [13].

Structural considerations

• Cogdell and colleagues have recently solved the structure of LH2 from Rhodopseudomonas acidophila by X-ray crystallography [15], and a similar structure has been computed from diffraction data for the LH2 of Rps. mollischianum by Schulten, Michel and colleagues (Prof. Klaus Schulten, personal communication). Ghosh has reported an 8.5 Å resolution structure for the LH1 complex of Rhodospirillum rubrum using electron diffraction and transmission [16], which shows a similar motif, and modelling studies have suggested the the building units for all these structures are essentially the same. However, the LH2 structures consisted of rings of 9 or 8 alpha-beta pairs, whereas the LH1 complex had 16 pairs. Ghosh [16] pointed out that there was just room for one reaction center in the LH1 ring. More recently, Kuehlbrandt, in collaboration with Cogdell, has used electron microscopic techniques to obtain low resolution structures for LH1/reaction center complexes from Rhodopseudomonas acidophila, which have confirmed Ghosh's suggestion (Dr. W. Kuehlbrandt, personal communication). It seems highly likely that the light-harvesting complex of Rb. sphaeroides is organized in a similar way, and Cogdell and colleagues, and Schulten and colleagues have constructed models of the reaction center in the palisade of the LH1 cylinder; images from both labs are shown here.
• The picture of the reaction center surrounded by a cage of LH1 molecules is supported by observations of the kinetic behavior of cells which do not make the PufX protein. The pufX gene is part of the puf operon, which codes for the subunits of LH1 and the L and M subunits of the reaction center. In pufX^- strains, the reaction center is unable to react with quinone produced by the bc₁-complex, and the bc₁-complex does not "see" the quinol produced by the reaction center [17-21], suggesting that an impediment to diffusion between reaction centers and bc₁ complex exists in the absence of PufX. The PufX gene product has a stoichiometry of ~1-2 per reaction center, and suppressor strains occur through mutations in LH1 which reduce the ratio of LH1 to reaction center, or disorder the LH1. We had previously suggested that PufX might interact with the LH1 ring to facilitate diffusion of quinone across the barrier created by the palisade of helices surrounding the reaction center. This mechanism was based on the assumption that a complete ring of LH1 surrounded the reaction center.  In the context of a such a structure, the kinetic effects seen in pufX^- strains would have been difficult to reconcile with a supercomplex model. However, a new perspective has come from recent work, initialy reported in contributions at the XIth. International Congress on Photosynthesis (27, 28), but now published (29, 30). This work has shown that in PufX containing strains, dimers of the reaction center-LH1 complex can be detected by sucrose gradient separation after mild detergent solubilization, with a substantial fraction of centers in the dimeric form. Similar treatment of a pufX^- strain showed only monomeric complexes (27). The structure of the dimers is not known, but the BChl stoichiometry suggests that there are 24 BChl per reaction centers in wild-type, compared to 29.5 in pufX^- (28). From previous data suggesting that 2 PufX subunits per reaction center participate, the loss of 4 BChl would suggest replacement of two a, b-pairs by 2 PufX. This stoichiometry is compatable with our earlier hypothesis, but could alternatively indicate that the LH1 ring might be incomplete or shared. Taken together with the experiments showing dimerization of the LH1/RC complex, the structures images by Jungas and colleagues (29) (see below) might represent such dimers.
• The bc₁-complexes are thought to be structurally (and possibly functionally [23]) dimeric. In the mitochondrial complex, this was clearly evident in low resolution electron microscopy structures [22], and has been confirmed in the X-ray structures recently reported [24, 31-33]. The complex isolated from Rb. sphaeroides runs as a dimer on sizing gels (34). Models constructed using a dimeric 3-subunit bc₁ complex abstracted from the mitochondrial bc₁ complex (31), and LH1 models from Schulten's lab (see above), show that a supercomplex incorporating such a dimer, would be large enough to be obvious in electron micrographs, but such structures have not been reported in studies in which particle sizes seen in freeze-fracture electron microscopy were carefully tabulated. Until recently, although bc₁-complex dimers, and LH1/reaction center complexes are readily isolated, there have been no reports of isolation of larger structures. The dimerization of reaction center - LH1 complexes induced by PufX (see above) is of interest in this context. The dimeric complexes isolated by Francia et al. (30) do not contain any bc₁ complex. However, Vermeglio has suggested that the dimeric structures seen in tubular structures in LH2 depleted strains of Rb. sphaeroides might include a bc₁ complex, which is found in isolated membranes in the stoichiometry expected fo the supercomplex. There is no room for a dimeric bc₁ complex in the arrays reported by Jungas et al. (29), and it is doubtful that a monomeric 3-subnit complex could fit.

In view of the apparent contradiction between results obtained using cells and chromatophores from Rb. sphaeroides, we have performed comparable experiments in both systems.

In chromatophores we could measure a low apparent equilibrium constant on continuous illumination as seen in cells and attributed to supercomplexes, yet the inhibitor titrations show that supercomplexes are absent in chromatophores.

In contrast to the chromatophore results, when inhibitor titration experiments were performed with whole cells, the electron transfer linked to cyt c₂ appeared to be restricted to a local domain of 1-2 units, and diffusion of cyt c₂ outside this domain was severely restricted, as would be expected from the supercomplex model.

This paradoxical behavior is open to several interpretations. One possibility is that supercomplexes are present in whole cells, but lost on preparation of chromatophores. A second possibility is that the restricted diffusion seen in cells is not due to supercomplexes, but to some structure in the periplasm, for example the murein sacculus, which is a common structural feature of Gram-negative bacteria.

In order to explore the possibilities, we have modeled the kinetic and thermodynamic behavior of the high-potential chain on illumination under three conditions:

• free diffusion and equilibration in a statistically homogeneous pool (classical model);
• free diffusion and equilibration in each vesicle of a heterogeneous population of chromatophores (Crofts model) (Fig. 1, 3);
• restricted diffusion in a population of supercomplexes with heterogeneous illumination (adapted from the Lavergne model [3])(Fig. 1, 2).

In the supercomplex model, heterogeneity is introduced by statistically random photon hits. In our alternative model, heterogeneity comes from a statistically random distribution of components within the chromatophore population. In the homogeneous system, the components remain poised at equilibrium throughout the time course of illumination. In both "heterogeneity" models, the apparent equilibrium constant was much less than that in the homogeneous model; indeed theoretical considerations show that this is a general effect of heterogeneity [3].

Predictions

• i) The observed equilibrium constants should be relatively independent of inhibitors, and (for random illumination) of fixed value (Fig. 2, but see Figs. 4, 5).
• ii) Rereduction of the oxidized reaction center, (BChl)₂⁺ (P⁺), after a saturating flash should be almost complete in all connected centers reduced before the flash, independent of inhibitor present, since no heterogeneity is introduced with a saturating, single-turnover flash, and the natural equilibrium constants are large [4,13] (but see Figs. 6, 7).

The Crofts model predicts that:

• i) The observed equilibrium constant will be variable with preparation, and dependent on the component count, and type of inhibitor (Fig. 3, 4, 5).
• ii) The extent of reduction of (BChl)₂⁺ following a saturating flash will be dependent on component count, and will depend predictably on the nature of the inhibitor (Fig. 6, 7).

Experiments with chromatophores favor the Crofts model. They show a variable equilibrium constant, perhaps depending on the amount of trapped cyt c₂, or type of inhibitor (Fig. 4, 5). In chromatophores with > 90% of reactions centers rapidly reduced in the absence of inhibitor, a substantial fraction (~20%) of (BChl)₂⁺ remained oxidized after a flash in the presence of myxothiazol, and more (~30%) with stigmatellin, the amount varying with the amount of trapped cyt c₂ (Fig. 6, 7). These are within the range predicted by the model.

Fig. 4 Kinetic traces showing the oxidation of P and cyt c on continuous illumination in the presence of myxothiazol or stigmatellin.

Fig. 5. "Magic Square" plot for experimental results on continuous illumination in the presence of myxothiazol or stigmatellin.

Figs. 6, 7. Kinetics during flash illumination in the presence of myxothiazol or stigmatellin.

Figs. 8-10 show kinetics in strains with variable stoichiometries of RC:cyt c_t:bc-complex.
In Fig. 8, the difference between the two strains is in the relative stoichiometries of the components of the chain. This can be seen from the amplitudes of the traces after four flashes in the presence of antimycin. The traces show stoichiometric ratios for RC:cyt c2:bc₁-complex close to the "normal" 2:1:1 for BC17C, but about 2:1:3 for BH6. The BH6 strain showed a substantial over expression of the bc1-complex, but the rapid reduction of cyt bH observed in the presence of antimycin following the first flash showed kinetics similar to those in a strain with normal stoichi-ometries. In the over-expressing strain, the amount of "connected" bc₁-complex was ~3-times greater than that expected from the supercomplex hypothesis, and the amount undergoing rapid reduction after the first flash corresponded to 1 cyt b_H / RC, or ~ twice that possible in a super-complex. The behavior is well explained by a diffusional mechanism in the context of the modified Q-cycle (Crofts, 1985).

In Fig. 9, the kinetics of turn-over of cytochrome c₁ and isocyt c₂ are shown in strain CYCA65R7 (pVWF1R) (Witthun et al., 1996). In this strain, the gene for cyt c₂ was deleted, but expression of the gene for isocyt c₂ allowed photosynthetic growth. The isocyt c₂ showed some degree of over expression compared to the very low levels normally observed. The stoichiometric ratios of RC:isocyt c₂:bc₁-complex were 2:<0.3:1, as assayed from kinetic traces using this strain in experiments similar to those in A above. It is clear from the results that the photosynthetic chain in this strain is not organized as a supercomplex. Both in chromatophores, and in cells (not shown), the small amplitude of the fast phase indicates that most of the isocyt c₂ does not bind to the reaction center. Such a binding can be observed at higher concentrations in vitro, and gives rise to a rapid (< 2 ms) phase of oxidation (Witthun et al., 1996). The stoichiometry is also incompatible with that expected for a supercomplex; the amount of bc1-complex undergoing redox change is >3-fold greater than the estimated concentration of isocyt c2, but the components of the complex nevertheless undergo rapid electron transfer with a stoichiometry and kinetics similar to the wild type. This clearly indicates that rapid diffusion of isocyt c₂ must occur to connect bc₁-complexes to RCs. In order to give the kinetics observed, each isocyt c2 molecule must visit ~3 RCs and bc1-complexes during the rise kinetics (t_1/2 ~300 ms), and ~6 of each during the reduction phase of the RC (t_1/2 ~1.5 ms in the absence of inhibitor).

Fig. 10 shows the kinetics of oxidation of cyt c in strains in which either the bc₁ complex or cyt c₂ is overproduced. Note that the stoichiometry of the overproduced component is several fold in excess of that in the wild-type. For the cytochrome c₂ overproducer, the stoichiometry is ~2.5 per reaction center, and the oxidation is complete in ~50 ms. This shows that reaction centers must have a ready access to cytochrome c₂ in stoichiometry about 5 x that expected from the supercomplex model. The traces at higher time resolution show that cyt c oxidation occurs with greater amplitude than in wild-type. With the rate constant used in these experiments, the kinetics are much more rapid than in wild-type, suggesting that most of the phase in excess of the "normal" complement of 1 cyt c₂ / RC is due to oxidation of additional cyt c₂. The increased rate could be due to increased binding, or to a second-order dependence on concnetration. In either case, the results are not compatible with a supercomplex with a fixed stoichiometry of cyt c₂, and a restricted dissociation from the complex.

Additional sources of heterogeneity

In distributing components at random, the program assumed that both reaction center and bc₁-complex were monomeric (left in Fig. 3), or that both were dimeric (right in Fig. 2). In both cases, chrompatophores were assumed to be of uniforn size, and "illumination" was assumed to by uniform. The left model represents the least heterogeneity possible with random distribution. Any additional heterogeneity tends to decrease the K_obs; thus smaller values would be obtained in both situations if "illumination" was random, if the size of chromatophores was non-uniform, and if the number of components per chromatophore was smaller. The results of inhibitor titrations suggested that the reaction domain seen by cyt c₂ included about 8-10 bc-complexes (rather than the 15 used in the simulation)(11), and that the bc-complex may be dimeric. We have recently developed a new isolation proceedure for the bc-complex with a (His)₆-tagged cyt b. This complex appears to be structurally dimeric. We would therefore expect the value for K_obs to be towards the low end of the range shown in Fig.3. The simulation shown in Fig. 11 has a mean distribution ratio of 16:8:8 for RC:cyt c₂:bc-complex per chromatophore, and the bc-complex is dimeric.

References

1. Lavergne, J., Joliot, P. and Vermeglio, A. (1989) Partial equilibration of photosynthetic carriers under weak illumination: a theoretical and experimental study. Biochim. Biophys. Acta 975, 347-355.
2. Joliot, P., Vermeglio, A. and Joliot, A. (1989) Evidence for supercomplexes between reaction centers, cytochrome c₂ and cytochrome bc1 complex. Biochim. Biophys. Acta 975, 336-345.
3. Lavergne, J. and Joliot, P. (1991) Restricted diffusion in photosynthetic membranes. TIBS 16, 129-134
4. Sabaty, M. Jappe, J. Olive, J. Vermeglio, A. (1994) Organization of electron transfer components in Rb. sphaeroides forma SP denitrificans whole cells. Biochim. Biophys. Acta 1187, 313-323
5. Vermgeglio, A., Joliot, P. and Joliot, A. (1993) The rate of cytochrome c₂ photo-oxidation reflects the subcellular distribution of reaction centers in Rb. sphaeroides Ga Cells. Biochim, Biophys. Acta 1183, 352-360.
6. Crofts, A. R. and Wraight, C. A. (1983). The Electrochemical Domain of Photosynthesis. Biochim. Biophys. Acta, 726, 149-186.
7. Crofts, A. R., Meinhardt, S. W., Jones, K. R. and Snozzi, M. (1983). The Role of the Quinone Pool in the Cyclic Electron Transfer Chain of Rps. sphaeroides: A Modified Q-cycle Mechanism. Biochim. Biophys. Acta, 723, 202-218.
8. Crofts, A. R. (1985) The Mechanism of the Ubiquinol:cytochrome c Oxidoreductases of Mitochondria and of Rhodopseudomonas sphaeroides. In The Enzymes of Biological Membranes, (Martonosi, A.N., ed.), Vol. 4, pp. 347-382, Plenum Publ. Corp., New York.
9. Glaser, E.G. and Crofts, A.R. (1984). A New Electrogenic Step in the Ubiquinol-cytochrome c₂ oxidoreductase complex of Rhodopseudomonas sphaeroides. Biochim. Biophys. Acta, 766, 322-333.
10. Meinhardt, S. W. and Crofts, A. R. (1983). The Role of Cytochrome b566 in the Electron Transfer Chain of Rps. sphaeroides. Biochim. Biophys. Acta, 723, 219-230.
11. Crofts, A.R. (1986) Reaction center and UQH₂:cyt c₂ oxidoreductase act as independent enzymes in Rps. sphaeroides. J. Bioenerg. Biomemb. 18, 437-445.
12. Crofts, A.R. and Wang, Z. (1989) How rapid are the internal reactions of the UQH₂:cyt c₂ oxidoreductase? Photosynth. Res. 22, 69-87.
13. Fernandez-Velasco, J. and Crofts, A.R. (1991) Complexes or super complexes: Inhibitor titrations show that electron transfer in chromatophores from Rb. sphaeroides involves a dimeric ubiquinol: cytochrome c₂ oxidoreductase , and is delocalized. Biochem. Soc. Trans. 19, 588-593
14. Fernandez-Velasco, J. and Crofts, A.R. (1992) The diffusion domain for mobile redox carriers in the photosynthetic electron transfer chain of Rhodobacter sphaeroides explored through inhibitor titrations.
15. McDermott, G., Prince, S.M., Freer, A.A., Isaacs, N.W. Papiz, M.Z., Hawthornthwaitelawless, A.M. and Cogdell, R.J. (1995) The 3-dimensional structure of the light harvesting antenna complex (LHII) from Rps. acidophila, strain 10050, at 2.5 A resolution. Protein Engineering 8, 43-43.
16. Karrasch, S., Bullough, P.A. and Ghosh, R. (1995) The 8.5-Angstrom projection map of the light-harvesting complex I from Rhodospirillun rubrum reveals a ring composed of 16 subunits. EMBO J. 14, 631-638.
17. Barz, W.P., Vermeglio, A., Francia, F., Venturoli, G., Melandri, B.A. and Oesterheldt, D. (1995) Role of the PufX protein in photosynthetic growth of Rb. sphaeroides. 2. PufX is required for efficient ubiquinone ubiquinol exchange between the reaction center Q_B site and the cytochrome bc₁-complex. Biochemistry 34, 15248-15258.
18. Barz, W.P., Francia, F., Venturoli, G., Melandri, B.A., Vermeglio, A. and Oesterheldt, D. (1995) Role of PufX protein in photosynthetic growth of Rb. sphaeroides 1. PufX is required for efficient light-driven electron transfer and photophosphorylation under anaerobic conditions. Biochemistry 34, 15235-15247.
19. Lilburn, T.G., Prince, R.J. and Beatty, J.T. (1995) Mutation of Ser2 codon of the light-harvesting B870 alpha polypeptide of Rb. capsulatus partially suppresses the PufX phenotype. J. Bact. 177, 4593-4600.
20. Barz, W.P. and Oesterheldt, D. (1994) Photosynthetic deficiency of a pufX deletion mutant is suppressed by point mutations in the light-harvesting genes pufB or pufA.Biochemistry 33, 9741-9752.
21. McGlynn, P., Hunter, C.N. and Jones, M.R. (1994) The Rb. sphaeroides PufX protein is not required for photosynthetic competence in the absence of light harvesting system. FEBS Lett. 349, 349-353.
22. Karlsson, B., Hovmöller, S., Weiss, H. and Leonard, K. (1983) Structural studies of cytochrome reductase. Subunit topology determined by electron microscopy of membrane crystals of c subcomplex. J. Mol. Biol. 165, 287-302.
23. Nieber, P. and Berden, J.A. (1992) Triple inhibitor titrations support the functionality of the dimeric character of mitochondrial ubiquinol:cytochrome c oxidoreductase. Biochim. Biophys. Acta 1101, 90-96.
24. Xia, D., Yu, C.-A., Deisenhofer, J., Xia, J.-Z.. and Yu, L. (1996) Abstracts. Biophys. Soc. Meeting, Baltimore, Feb. 1996.
25. Dutton, P.L. and Prince, R.C. (1978) Reaction-center-driven cytochrome interactions in electron and proton translocation and energy coupling. In The Photosynthetic Bacteria (Clayton, R.K. and Sistrom, W.R., eds.), pp. 525-570. Plenum Press, New York
26. Witthuhn, V.C., Gao, J., Hong, S., Halls, S., Rott, M., Wraight, C.A., Crofts, A.R. and Donohue, T. (1997) The reactions of isocytochrome c₂ in the photosynthetic chain of Rb. sphaeroides. Biochemistry 36, 903-911.
27. Francia, F., Wang, J., Barz, W.P., Venturoli. G., Melandri, B.A. and Oesterheldt, D. (1998) The PufX protein influences the oligomerization state of the RC-LH1 core cmplex in Rb. sphaeroides. Abstracts, X1th Internatl. Cong. Photosynth. # SY1-2-P24.
28. Kramer, H., Francke, C., Hunter, C.N., and Amesz, J. (1998) The size of the LH1 antenna of purple bacteria. Abstracts, X1th Internatl. Cong. Photosynth. # SY1-2-P3.
29. Jungas C., Ranck, J.-L., Joliot, P. and Verméglio, A. (1999) Supramolecular organization of the photosynthetic apparatus of Rhodobacter sphaeroides. EMBO J. 18, 534-542
30. Francia, F., Wang, J., Venturoli, G., Melandri, B.A., Barz, W. and Oesterhelt, D. (1999) The Reaction Center-LH1 Antenna Complex of Rhodobacter sphaeroides Contains One PufX Molecule Which Is Involved in Dimerization of This Complex. Biochemistry 38, 6834-6845
31. Zhang, Z., Huang, L.-S., Shulmeister, V.M., Chi, Y.-I., Kim, K.-K., Hung, L.-W., Crofts, A.R., Berry, E.A., and Kim, S-H. (1998) Electron transfer by domain movement in cytochrome bc₁. Nature (Lond.) 392, 677-684.
32. Iwata, S., Lee, J.W., Okada, K., Lee, J.K., Iwata, M., Rasmussen, B., Link, T.A., Ramaswamy, S. and Jap, B.K. (1998) Science 281, 64-71.
33. Crofts, A.R., Guergova-Kuras, M., Huang, L.-S., Kuras, R., Zhang, Z. and Berry, E.A.(1999) The mechanism of ubiquinol oxidation by the bc₁ complex: the role of the iron sulfur protein, and its mobility. Biochemistry, in press.