Notes on the paper by Brandt, U., Schagger, H. and von Jagow, G. (1988) Eur. J. Biochem. 173, 499-506

    Brandt et al. interpreted their data as showing that ubiquinol, and the MOA-type inhibitors (MOA-stilbene, oudemansin, or strobilurin) are bound at different sites on the bc1 complex, and bind non-competitively. However, a critical examination of their data shows that the data are not consistent with such a clear-cut interpretation, and that alternative interpretations might better explain their results. Their interpretation can be criticized on three different grounds:

  1. The application of the kinetic model from classical enzymology that they chose was inappropriate to the case of inhibitors binding tightly from the membrane phase.
  2. If it is assumed that classical enzymological methods are appropriate, then the data do not show the non-competitive inhibition claimed, but mixed inhibition with a substantial competitive component.
  3. The authors have not taken dilution effects into account in interpreting the apparent displacement of inhibitor by substrate.
These are discussed in reverse order below.

Apparent displacement of inhibitor by substrate.

In Fig. 2 of the paper, Scatchard plots for inhibitor binding in the presence and absence of nonylubihydroquinone (NBH) at 0.8 mM are shown, and the results are compiled in Table 2. The data show an intercept indicating a single binding site for inhibitor under both conditions, and a change in slope in the presence of excess substrate.

Fig. 3 shows that on addition of increasing concentrations of NBH, the Kd for oudemansin increased by a factor of about 2.

The data of Table 2 and Figs. 2 and 3 together were interpreted as showing that separate binding sites existed for NHB and inhibitor. However, under the conditions of the experiment, the addition of 0.8 mM NBH changed the apparent affinity of the enzyme for all three inhibitors by a factor of ~2 (Table 2). The experiments were done in a Triton X-100 suspension, with detergent at 0.05%. From the MW of Triton X-100, this is ~0.6 mM detergent. It seems likely that the inhibitor would partition into the available micellar phases. In the absence of NBH, the phases included Triton micelles, and mixed micelles of Triton and protein. On addition of NBH, the phases included mixed micelles of Triton and NBH, mixed micelles of Triton, NBH and protein, and possibly micelles of NBH (see Brandt and Okun, 1997). Assuming that the distribution of Triton and NBH was uniform, the inhibitor would have been diluted by addition of the NBH by approximately the mol ratio of (NBH  + Triton) to Triton, of ~ 2.3. The exact ratio of dilution cannot be readily computed from the data, because the relative partition coefficients are not known. However, it seems quite likely that the ~2-fold effect on apparent affinity could be accounted for simply by this dilution effect.

The data of Fig. 3 were taken to indicate that the substrate binding site for NBH was available in the presence of the inhibitor. The data in Table 2 show a similar increase (~2-fold) in Kd on addition of NBH for all three inhibitors, despite the fact that the KI values of strobilurin and oudemansin differed by 5- and 20-fold, respectively, from the tighter binding MOA-stilbene. The data of Fig. 3 show that the concentration of NBH required for half-maximal effect was ~100 mM,  56-fold higher than the Km (1.8 mM, Table 1) found in kinetic experiments with NBH as substrate when the complex was incorporated into liposomes. The authors ascribed this discrepancy to the different lipidic environment (Triton micelles v. phopholipid or mitochondrial membrane). However, the Kd values for the inhibitors were increased by less than this on changing from the micellar to the liposomal environment (compare Tables 1 and 2). It seems unlikely that the K50 shown in this experiement reflects the same binding site as the Km. In Fig. 1 of Brandt and Okum (1997), the authors showed titration curves under very similar conditions (complex solubilized in 0.05% Triton), with a rather different Km of 13 mM, but this value was close to the Km (10 mM) found when the complex was incorporated into liposomes. It is not clear what caused the ~5-fold discrepancy in Km values for the enzyme in liposomes between these two papers, but chosing either value, it is clear that the ~100 mM K50 value is not the same as the Km for substrate. In either case, if the K50 is a binding effect, the value is much higher than that expected from the 2-fold change in Km seen in the presence of inhibitor (se below), and would indicate a considerable degree of competition.
    The saturation effect can not be readily accounted for solely in terms of the dilution explanation above, but could possibly reflect a preferential binding of NBH to the protein micelles, and a saturation of binding sites in the protein micelles, or partition of NBH into a separate micellar phase at higher concentrations. This later explanation was suggested by Brandt and Okum (1997) for the falling-off of maximal rate above 80 mM in Michaelis-Menten plots using the Triton solubilized enzyme.
 

The data show mixed inhibition with a substantial competitive component.

In Fig. 4 of the paper, Eadie-Hofstee plots of kinetic data are shown, in which the substrate was NBH, and experiments were performed with a control, and with two concentrations of each inhibitor. The authors interpreted the data as showing non-competitive inhibition of NBH oxidation by all three inhibitors, using the following scheme:

If we accept that the experimental conditions are appropriate for this application of classical enzymological techniques, a brief examination of the data indicates that, for all three inhibitors, the effect is not simple non-competitive inhibition, but mixed inhibition. Perhaps some of the confusion arises because the term "non-competitive inhibition" is sometimes used to cover both cases, when a similar kinetic scheme is used. However, in more recent papers, Brandt and colleagues have implied that the results showed a non-competitive binding, with separate non-competing sites for quinol and inhibitor.

For non-competitive inhibition, the slopes of Eadie-Hofstee plots (Km values) with and without inhibitor would be parallel, and the intercepts showing Vmax would reflect this, since the same degree of inhibition is found at all concentrations of substrate. In mixed inhibition, the slopes are not parallel, and the intercepts occur closer to the uninhibited value because Vmax reflects the competition by substrate. A number of different mechanistic situations can give rise to mixed inhibition, but in general, "..an inhibitor affects the slope of a Lineweaver-Burke plot ... if it and the substrate  ... compete directly for the same form of the enzyme or for different forms that are in reversible equilibrium ..." (Creighton, T., in "Proteins", p. 390.).

The data in Fig. 4 show:

1. The slopes (Km values for substrate) changed by a factor of 2 in the presence of inhibitor, showing some competition.
2. The intercepts (Vmax values) changed by much less than expected from the Ki values. For example, with MOA-stilbene, Vmax changed from 262 to 204 on addition of MOA-stilbene at 25 nM; Ki and I50 were both 14 nM. For non-competitive inhibition, Vmax at I50 would be half Vmax with no inhibitor.
    In non-competitive inhibition, because the binding of I and S are to separate sites, the presence of I does not effect the binding constant for S, so that KS = K'S, and KI = K'I. In mixed inhibition, the binding of I does affect the binding of S, because of competition, and vice versa; from the thermodynamic cycle, KS/K'S  =  KI/K'I. The data of the paper clearly show the latter mixed effect, since the values for binding constants, Km and Vmax values, changed. Indeed, this was recognized at the time, and discussed at length, by the authors. The data of Figs. 2 and 3, and Tables 1 and 2 provide some of the values for the binding parameters. Because the changes in Km in the presence of inhibitor indicated by the Eadie-Hofstee plots were in line with the changes in KI in the presence of substrate, and satisfied the requirements of the thermodynamic cycle (KS/K'S  =  KI/K'I), the authors concluded that their use of classical inhibitor kinetics was justified. However,  if we choose to regard the K50 value of Fig. 3 as equivalent to K'S, we could say that the 8-56 fold change from the KS value (assuming this is close to Km) reflects the competition with I. In this case, the values given for KI and K'I do not satisfy the requirements of the thermodynamic cycle, since KI appears to change only by a factor of 2 at saturating substrate. The authors explain the discrepancy between the K50 value and the Km by invoking differences in the hydrophobic component of the reaction mixture, but, as noted above, the more recent results of Brandt and Okun (1997, see Fig. 1) show that the Km values were the same for the Triton X-100 solubilized complex, and the liposome embedded complex. The validity of this kinetic treatment is therefore open to question.

Was the kinetic mechanism chosen by Brandt et al. from classical enzymology appropriate?

   Interpretation of kinetic data for inhibition through classical enzymological procedures is not unambiguous. Two different models can be used to account for non-competitive inhibition. The simpler mechanism is through tight binding of inhibitor to the enzyme at the substrate binding site, so as to remove the active enzyme from reaction. If the binding is irreversible, the classical non-competitive effects are observed. To the extent that unbinding can occur on the time scale of turnover, competitive effects will be observed; this will give the behavior described as mixed inhibition. The second type of scheme is that shown above. In order to quantify non-competitive inhibition in the context of a mechanism such  as that above, substrate and inhibitor would both have to bind reversibly, with on and off constants rapid compared to the turn-over of the enzyme. This is because the overall rate is determined by the concentration of E.S. If the reactions preceding formation of E.S are not in equilibrium, the steady-state rate will not reflect the values for the binding constants. This is intuitively obvious in the case of irreversible binding of an inhibitor at the same site as the substrate, which will give classical "non-competitive" plots because E is effectively removed from the reaction mixture on binding I.
    In the experiments of Brandt et al (1988), the enzyme was incubated with saturating cytochrome c, and with inhibitor at various concentrations, and then the rate assayed on addition of quinol substrate. If the dissociation of inhibitor was slow compared to the turnover of the enzyme, the kinetics observed would have reflected predominantly the free enzyme, rather than the equilibrium mixture. It is therefore pertinent to ask what value for off-rate constant might be expected.

    Taoka and Crofts (1986, and see also Taoka, S., Ph.D. thesis, U. of Illinois) studied the kinetics of binding and unbinding of inhibitors at the QB-site of photosystem II. They measured the kinetics of binding as a function of concentration, and the partition coefficients into the membrane phase, in order to arrive at second-order rate constants for binding. They showed that values for on-rate constants for all five inhibitors studied were in the range 0.4-6.1 x 104 M-1.s-1 with respect to membrane concentration. These were within a factor of 16-250 of the expected diffusion limit (~106 M-1.s-1), suggesting that stochastic exploration of the binding site was the limiting factor. Since the on-rate constants were similar for all inhibitors, but the KI values differed by a factor of 100 or more, the strength of binding was clearly determined predominantly by the off-rate. For inhibitors such as DCMU, with an apparent KI value in the 200 nM range with respect to membrane concentration (or ~1 nM from the aqueous phase), the off-rate constant was <0.02 s-1. The octanol-water partition coefficient for MOA-stilbene is ~1000 (Sauter et al., 1994), so if the partition into the membrane were similar, and the on-rate constant were in the same range as that for the QB-site inhibitors, the off-rate constant, on the basis of the KIaq value of 14 mM given in the Brandt et al. (1988) study, would have a value  <1 s-1. Since the Vmax values shown were in the range 270-700 mol.(mol enzyme)-1.s-1, it is unlikely that the concentration of E.S, and hence the rate, reflected equilibration of the inhibitor-bound states. Sauter et al. (1994) concluded that, for a series with a similar pharmacophoric group, lipophilicity was the major determinant of activity, so it seems likely that the differences between the three inhibitors used reflected predominantly the partition coefficient. Clearly, from the structures, binding must occur from the membrane or lipid phase, so the treatment above is appropriate. However, a similar conclusion follows if we take the KI values, and assume that binding from the aqueous phase occurred. It is unlikely that this would be faster than 1% of that implied by the diffusion limited rate constant (~1010 M-1s-1).

    Given these values, if measurement of initial rate was made over the first few seconds after addition of substrate, the enzyme would have turned over several hundred times before half the centers had a chance to exchange the inhibitor.

Fig. 1. Titration of the Qo-site with myxothiazol. Oxidation of quinol at the Qo-site was followed in chromatophores from Rb. sphaeroides by measuring the reduction of cyt bH following flash activation in the presence of antimycin. The reaction was followed by measuring the difference kinetics at 561 and 569 nm. Myxothiazol was added at the concentrations indicated in the Fig. Chromatophores from strain B17C (bc1 complex from wild-type expressed in plasmid) were suspended in 100 mM KCl, 50 mM Mops buffer, pH 7.0, to give a concentration of bc1 complex of ~150 nM. The Eh was adjusted to 100 mV. Kinetic traces shown are the average of 4. Experimental protocols were essentially as described in Crofts and Wang (1989).

For similar inhibitors acting on the photosynthetic chain in chromatophores of Rhodobacter sphaeroides, it is possible to show these characteristics directly (Fig. 1). The turnover of the Qo-site can be assayed by following the reduction of cyt bH by the absorbance change difference at 561 - 569 nm, following flash activation in the presence of antimycin. With the suspension poised at Eh ~100 mV, the quinone pool is ~30% reduced, and the rate of quinol oxidation is rapid, and close to maximal. Fig. 1 shows traces for cyt bH reduction at several points in a titration with myxothiazol. The following points should be noted:

  1. The shape of the kinetic curve is similar at all concentrations.
  2. The kinetics of the remaining active enzyme reflect a single turnover of the Qo-site, and show a half-time of ~650 ms, increasing slighlty at higher concentration. .

    From these characteristics, it can be concluded that:

  1. The inhibitor did not exchange from its binding site (so as to allow entry of substrate), or between complexes (so as to open previously inhibited sites), in the 45 ms time range shown. For a loosely binding inhibitor such as diphenylamine, the kinetic characteristics are completely different, - the rate of reaction is slowed by increasing concentration, but the amplitude remains the same.
  2. Since, at sub-stoichiometric concentrations, the initial rate of the uninhibited complexes was unchanged, the concentration of free inhibitor in the membrane was negligible. This shows that the binding constant from the membrane phase was high enough to sequester virtually all inhibitor at a binding site.
It seems clear that myxothiazol binds tightly, and that the off-time constant was several orders of magnitude greater than the turnover time of the enzyme. Essentially the same results have been demonstrated with mucidin, a MOA-type inhibitor similar to those used by Brandt et al. (1988). The effects shown in Fig. 4 of Brandt et al. (1988) are consistent with involvement of an inhibitor for which the off rate constant was small compared to the turnover time of the enzyme, and both inhibitor and substrate bound at a common site. This interpretation provides an alternative to the claims by the authors that the inhibition is non-competitive, and that NBH and the inhibitors bind at separate sites. The data are consistent with an overlapping of binding sites, and a relatively long residence time for the inhibitor compared to the turnover time. This latter interpretation removes the apparent contradiction between the results of Brandt et al. (1988), and those of Ding et al. (1992, 1995, 1995a).

Brandt, U. (1996) Energy conservation by bifurcated electron-transfer in the cytochrome-bc1 complex. Biochim. Biophys. Acta 1275, 41-46.

Brandt, U. (1998) The chemistry and mechanics of ubihydroquinone oxidation at center P (Qo) of the cytochrome bc1 complex. Biochim. Biophys. Acta 1365, 261-268.

Brandt, U. and Okun, J.G. (1997) Role of deprotonation events in ubihydroquinone: cytochrome c oxidoreductase from bovine heart and yeast mitochondria. Biochemistry 36, 11234-11240

Brandt, U., Schagger, H. and von Jagow, G. (1988) Eur. J. Biochem. 173, 499-506

Crofts,  A.R. and Wang, Z. (1989) How rapid are the internal reactions of the UQH2:cyt  c2 oxidoreductase? Photosynth. Res. 22, 69-87.

Ding, H., Robertson, D.E., Daldal, F. and Dutton, P.L. (1992) Cytochrome bc1 complex [2Fe-2S] cluster and its interaction with ubiquinone and ubihydroquinone at the Qo site: a double-occupancy Qo site model. Biochemistry 31, 3144-3158.

Ding, H., Daldal, F. and Dutton, P.L. (1995) Ion pair formation between basic residues at 144 of the Cyt b polypeptide and the ubiquinones at the Qo site of the Cyt bc1 complex. Biochemistry 34, 15997-16003.

Ding, H., Moser, C.C., Robertson, D.E., Tokito, M.K., Daldal, F. and Dutton, P.L. (1995) Ubiquinone pair in the Qo site central to the primary energy conversion reactions of cytochrome bc1 complex. Biochemistry 34, 15979-15996.

Sauter, H., Ammermann, E., and Roehl, F.(1996) In: "Crop Protection Agents from Nature" (Leonard G. Copping, ed.) pp. 50 - 81.  The Royal Society of Chemistry, Thomas Graham House, Cambridge, UK.

Taoka,  S.  and  Crofts, A.R. (1986) Competition of Inhibitors with the  secondary  quinone  in dark-adapted  thylakoid membranes. Proc. VII Internatl. Cong. Photosynthesis (Biggin, J.,  ed.), Vol 2, pp. 425-428.