The sum of flux control coefficients in the electron-transport chain of mitochondria

Transcription

1 Eur. J. Biochem. 226, (1994) 0 FEBS 1994 The sum of flux control coefficients in the electron-transport chain of mitochondria Martin D. BRAND, Brett P. S. VALLIS and Adolf KESSELER Department of Biochemistry, University of Cambridge, England (Received July 27, 1994) - EJB /6 The sum of the flux control coefficients for group-transfer reactions such as electron transport has been proposed to be two when the coefficients are calculated from experiments in which the concentrations of the electron carriers are changed (C,) but one when they are calculated from changes in the rates of the electron-transfer processes (C,). We tested this proposal using electron transport in uncoupled beef heart, potato tuber and rat liver mitochondria. First, with ascorbate plus N,N,N,N -tetramethyl-p-phenylenediamine as substrate, the C, flux control coefficients of ascorbate, N,N,N,N -tetramethyl-p-phenylenediamine, mitochondria and oxygen over electron-transport rate were measured by direct titration of the concentrations of these electron carriers. C, values were close to zero, one, one and zero, respectively, giving a sum of C, flux control coefficients of approximately two. At higher concentrations of N,N,N,N -tetramethyl-p-phenylenediamine, its C, control decreased and the sum decreased towards one as predicted. Secondly, the C,, control coefficients of groups of electron-transfer processes with succinate or ascorbate plus N,N,N,N -tetramethyl-p-phenylenediamine as substrate were measured. This was achieved by measuring the effects of KCN (or malonate or N,N,N,N -tetramethyl-p-phenylenediamine) on system flux when intermediates were allowed to relax and on local flux when intermediates were held constant. The C,, flux control coefficients were calculated as the ratio of the effects on system flux and on local flux. The sum of the C,, flux control coefficients was approximately one. Whether a sum of one or a sum of two was obtained depended entirely on the definition of control coefficients that was used, since either sum was obtained from the same set of data depending on the method of calculation. Both definitions are valid, but they give different information. It is important to be aware of which definition is being used when analysing control coefficients in electron-transport chains and other group-transfer systems. The control of flux through biochemical pathways is shared unequally between all of the participating steps; some steps exert little control whilst others exert more control. Flux control coefficients, CJ, quantify the control exerted by each step over pathway flux [l-31. In the original formulations of Kacser and Burns [3], the flux control coefficient of enzyme E over flux J (Ci) was conveniently defined as the fractional change in pathway flux caused by an infinitesimal fractional change.in the concentration of E as follows: Ci = (dj/d[i). ([E]/J), (1) although from the start it was recognised that a definition in terms of control by enzyme activity rather than concentration was in some ways preferable [2, 41. Correspondence to M. D. Brand, Department of Biochemistry, University of Cambridge, Tennis Court Road, Cambridge, England CB2 1QW Fax: Abbreviations. C, control coefficient (parameters are given as subscripts and have control over variables, given as superscripts) ; J, flux; E, enzyme; u, enzyme local rate under defined conditions; C,, control coefficient with respect to enzyme concentration; C,, control coefficient with respect to enzyme local rate (also known as process control coefficient); P, parameter; E, elasticity coefficient; Ph(NMe,),, N,N,N,N -tetramethyl-p-phenylenediamine ; FCCP, carbonylcyanide p-trifluoromethoxyphenylhydrazone. In straightforward cases, where the activity of an enzyme is proportional to its concentration, all the flux control coefficients in a pathway defined in this way sum to one. This is readily proved and is known as the summation theorem [3]. Theoretically, the theorem is important because it makes explicit the existence of a limit to the total control that can be exerted, regardless of how that control may be distributed amongst the steps in the pathway. Experimentally, summation of flux control coefficients to one is important because it allows us to assess the importance of the experimental value of a control coefficient (in simple cases a step with a CJ value of 0.2 has 20% of the total control). Also, if the sum of control by the steps investigated so far is less than one, then there is probably more control yet to be discovered, and if the sum is more than one then there is an experimental error, or other steps with negative control exist, or there are other subtleties in the system. However, several cases have been discussed where the sum of the flux control coefficients as defined by Eqn (1) differs from one. This occurs if there are kinetic consequences of enzyme/enzyme interactions [3] between molecules of the same [4] or different enzymes [5], or if there is covalent modification of enzymes [6]. This difference from unity also occurs if there is a moiety-conserved metabolite (such as NAD plus NADH, where the total NAD is con-

2 820 stant) and high enzyme concentrations that can bind this metabolite and change the total concentration of the free moiety [ Each of these cases can be satisfactorily dealt with by introducing appropriate correction terms to quantify the non-proportionality between enzyme concentration and enzyme rate (u) at fixed concentrations of all metabolites. Another way to deal with these non-ideal cases is to employ a slightly different definition of the coefficients, so that they refer to flux changes caused not by changes in enzyme concentration (which gives C,) but by changes in enzyme activity or velocity at fixed values of all other parameters and variables (which gives C,) [2, 4-14]. Thus for enzyme E', C;, = (6 J/6 0,). ( u,/j). A more general definition of C, recognises that u is changed by a primary change in some other parameter, P, for example by adding an enzyme inhibitor [12, 131. Thus, In simple cases where u is proportional to [El, the change in definition from C, to C,, makes no difference because the two definitions are equivalent. In the non-ideal cases mentioned above, the correction terms nearly always become unnecessary if C, is used, but the meaning and values of the control coefficients are slightly changed. It is very important to be clear about this difference in definitions. It constrains the mixtures of experimental approaches for the determination of flux control coefficients that can be used in any one case; determinations of C, cannot successfully be mixed with determinations of C, unless the system is simple. The choice of which definition to use depends on the question to be asked; if the effect on flux of changing the concentration of an enzyme, for example by genetic means, is of interest, then C, is appropriate; if it is necessary to discover how control is distributed in a pathway in which there is no interest in physically altering the enzyme concentrations, then it is more appropriate and simpler to use C,. The simplest and most general analysis will employ C,, whilst C, can be seen as a special case. Indeed, Schuster and Heinrich [12] recommend that C, should be regarded not as a control coefficient (Ci) but as a response coefficient (R;). If this sensible suggestion was more widely adopted then many of the complications discussed in the literature could be readily avoided. Two interesting theoretical cases have been described recently, in which the sum of the flux control coefficients is expected to be considerably greater than one if they are defined as C, but to be exactly one if they are defined as C, (or as C in terms of elemental rate constants) [13, 141. The first case concerns channelled pathways, in which each enzyme passes its product directly to the next enzyme as its substrate. In such pathways, the sum of the values of C, can be as high as the number of enzymes in the pathway if there is complete static channelling (enzymes effectively permanently associated). For complete dynamic channelling (enzymes collide but never release free metabolite), the sum should be two [13, 141. Partial channelling gives intermediate sums. However, if the C, coefficients are used, in this case considering changes in elemental rate constants within the whole pathway, then the sum should normally be one 114, 151. The second case concerns group-transfer pathways, in which a chemical group is passed along a series of carriers. Note that a series of group-transfer reactions can also be thought of as an example of dynamic channelling. Van Dam et al. [13] have presented a theoretical analysis of the sugar phosphotransferase system of Escherichia coli, which involves transfer of a phosphate group from one protein to the next. These authors were primarily concerned with this specific system, but they based their analysis on the general case and indicated that it should also apply to electron-transport chains, in which the transferred chemical group is an electron. In both of these group-transfer pathways the sum of the C, values should be two, as long as every carrier (including the pathway substrate and pathway product) is included. The sum is two because each carrier is involved in two processes, one transfer from the donor and one transfer to the acceptor. Changing the concentration of the carrier changes both these processes, so if each carrier is varied in turn, each process is changed twice and the sum of the C, values is twice the sum of the underlying C,, values that refer to the individual processes of group transfer. The sum of the C,, flux control coefficients for the processes is one as usual. Sums of C, values intermediate between one and two will be found if non-transfer reactions, such as enzyme complex dissociation, become kinetically significant [ 131. None of these theoretical predictions has yet been demonstrated experimentally either for electron-transport chains or for any other group-transfer system. The control over oxidative phosphorylation and electrontransport has been analysed extensively over the last ten years using metabolic control analysis [ In these studies, the distinction between C, and C,. flux control coefficients has not usually been made explicit, and the description of the electron-transport chain as a group-transfer system and the possibility of the sum of the control coefficients being different from one have not been considered. Part of the confusion arises from the convention of calling some of the electron carriers 'enzymes'. This seems natural for carriers such as cytochrome oxidase, but it disguises the fact that other carriers, such as coenzyme Q, have exactly the same status. The convention incorrectly implies particular formulations of the electron-transport chain in which coenzyme Q and cytochrome c are substrates and products, while the large protein complexes are enzymes ; the formal description could be reversed, with coenzyme Q and cytochrome c as enzymes and the protein complexes as substrates. To avoid this pitfall, we will regard all of the carriers as enzymes when we discuss control in terms of C,, but as moiety-conserved substrate cycles (oxidised carrier converted to reduced carrier or vice versa with conservation of total carrier concentration) when we discuss control in terms of C,. Indeed, in this view, electron-transport chains are simply chains of electrontransfer processes connected by moiety-conserved cycles, and they obey the rules that have been worked out for such systems [32]. In the present study, we test the theoretical predictions of van Dam and colleagues [13] as applied to electron-transport chains. We show that in simplified electron-transport chains, the sum of the C, flux control coefficients is indeed approximately two, but it decreases below two if electron-transport components become saturating. The sum of the C,, flux control coefficients in both simplified and normal mitochondria1 electron-transport chains is approximately one as predicted. The difference in the values obtained for the sum of the flux control coefficients depends entirely on the type of control coefficient chosen and thus on the methods of calculation, since the same experimental data can yield either sum.

3 821 MATERIALS AND METHODS Preparation of mitochondria Beef heart mitochondria were prepared as in [33]. Aliquots were frozen in liquid N, and stored at -70 C; samples were thawed at room temperature then kept on ice on the day of use. Potato tuber mitochondria were prepared as in [27]. In this case, mitochondria were kept on ice and were used on the day of preparation. Rat liver mitochondria were prepared by standard methods [34]. Aliquots were frozen at -2O"C, thawed at room temperature, and kept on ice on the day of use. Mitochondria1 protein was measured by a biuret method [35] or by a modified Lowry method (potato tuber mitochondria) [ 361. Experimental measurements The oxygen consumption rate was measured with a Clark oxygen electrode (Rank Bros., Bottisham, Cambridge). Electrode non-linearity was checked and corrected for if present. The endogenous cytochrome c redox state was measured using a dual-wavelength spectrophotometer at SSO- 540 nm. The incubation was maintained at 37 C and was stirred vigorously with an air-driven overhead paddle. The signal in the presence of rotenone and absence of succinate or ascorbate was taken to represent complete oxidation; the signal in the presence of substrate and excess KCN was taken to represent complete reduction of cytochrome c. 8 mm KCN was found to be a sufficient excess. Titrations with different effectors were carried out by making a small addition and waiting for 2min until a new steady state was established before making the next addition. Statistical treatment of results Experiments were repeated at least three times unless otherwise stated. The experimental data points are presented as means 2 SEM. The derived values of control coefficients are presented as the mean -+ SEM of the values obtained on individual days. RESULTS The systems to be analysed The electron-transport chain can be thought of either as a chain of electron carriers (enzymes) connected by electrontransfer processes, or as a chain of electron-transfer processes connected by moiety-conserved redox couples. It is important to be clear about which definition we are using at any particular time, since the first definition leads naturally to enzyme flux control coefficients, C,, and the second definition leads naturally to process flux control coefficients, C,. Fig. 1 shows the two different systems and the different views of these systems that are used in this study. Fig. 1A shows the four different redox processes (labelled 1-4) that take place during ascorbate oxidation by mitochondria mediated by the artificial electron carrier, N,N,N',N'-tetramethylp-phenylenediamine [Ph(NMe,),]. Fig. 1 B shows how these reactions can conveniently be divided into four blocks of carriers [ascorbate, Ph(NMe,),, mitochondria and oxygen] connected by three processes of electron-transport, 1, 2 and 4. The grouping is performed this way for experimental convenience; analogous division into any set of 1-5 blocks would be equally valid. Fig. 1 C shows the conceptually very different way of grouping the reactions into two blocks of processes; the reducers of cytochrome c (processes 1 and 2) and the oxidisers of cytochrome c (processes 3 and 4), connected by the moiety-conserved reduced and oxidised cytochrome c pool. The choice of cytochrome c as intermediate is again a matter of convenience. In principle, the division could be made around any of the three central redox carriers in this system [Ph(NMe,),, cytochrome c or complex IV]. Uncoupled oxidation of ascorbate plus Ph(NMe,), by mitochondria gives us a very convenient model system in which we can investigate the control coefficients during the group-transfer reactions of electron-transport. However, this model system is clearly artificial, so we also investigated the control coefficients using the more physiological system of electron-transport from succinate to oxygen. Fig. 1 D shows this system divided into two blocks of processes; the reducers of cytochrome c (processes S - 8) and the oxidisers of cytochrome c (processes 3 and 4). C, flux control coefficients with ascorbate plus Ph(NMe,), as substrate In the first set of experiments, we tested the prediction [13] that the C, flux control coefficients in an electron-transport chain divided according to Fig. 1 B should sum to two and not to one. We used ascorbate plus Ph(NMe,), as substrate so that no substrate transport reactions across membranes would be included in the system, and we used uncoupled, frozen-thawed beef heart mitochondria in the absence of ADP to ensure that all the reactions within the system were group-transfer reactions, with no rate limitation imposed by ATP synthesis or by proton leak reactions across the membrane. Thus every relevant process in the system was a group-transfer reaction passing electrons from one carrier to the next, and the sum of the C, flux control coefficients should approach the theoretical value of two. To change the concentrations of the 'enzymes' (blocks of carriers) involved, we simply carried out separate titrations of the concentrations of each of the four blocks shown in Fig. 1 B and observed the effect on oxygen consumption rate. Fig. 2 shows the result of this experiment. As intuitively expected, the rate was a linear function of the amount of mitochondria1 protein added (Fig. 2A). The C, flux control coefficient was calculated as the normalised slope of the line at the standard point (0.5 mg protein/ml) and had a value of (n = 4) (values are presented as means? SEM with the number of independent determinations in parentheses). The rate was also a linear function of the concentration of Ph(NMe,), at these low Ph(NMe,), concentrations (Fig. 2B); the C, flux control coefficient of Ph(NMe,), over respiration rate was (n = 4) at SO pm Ph(NMe,),. In both cases, estimates of the slope at the standard point without any assumption of linearity did not change the calculated slopes and flux control coefficients substantially. We also determined the dependence of the rate on oxygen concentration and ascorbate concentration (data not shown) and found little or no dependence (C, flux control coefficients of 0.06 and -0.08, respectively). The sum of all these values was (n = 4), exactly as predicted by van Dam et al. [13]. The same analysis was carried out using potato tuber mitochondria (Fig. 3 A and B). The same result was obtained, namely the sum of the C, flux control coefficients was two. The enzyme control coefficients in group-transfer chains are the sum of the flanking process control coefficients [13].

4 822 ascorbate dehydroascorbate [Ph(NMe,),l,, cyt cred y cyt cox Complex IVox /+ H Complex Iv,,d-/ 02 D. Electron transport chain from succinate to oxygen divided into blocks of processes f \ 1 succinate x x Q r e d x Cvcred Complex IVox fumarate Y 11 red Q ox - cytcox 4Lx c-reducers Complex Ivred H20 02 c-oxidisers Fig. 1. Conceptual division of electron-transport chains into blocks of different types. Processes of electron transfer are numbered 1-8. The redox state of the electron carriers is indicated by ox for oxidised or red for reduced. (A) The sequence of carriers and processes during oxidation of ascorbate by mitochondria. Note that two forms of each electron carrier constitute a moiety-conserved cycle in which the sum of the carrier molecules is constant. (B) The same sequence grouped into blocks of electron carriers, with cytochrome c and complex IV grouped together as a single block corresponding to the mitochondrial electron transfer reactions. (C) The same sequence conveniently grouped into processes 1 and 2 that together reduce cytochrome c (the c-reducers) and processes 3 and 4 that together oxidise cytochrome c (the c-oxidisers). (D) Electron-transport from succinate divided in the same way as in C. 11, complex 11; Q, coenzyme Q; 111, complex o Mitochondria1 protein (mg/ml) Fig. 2. Determination of the C, flux control coefficients of mitochondria and Ph(NMe,), over respiration rate in uncoupled, frozenthawed beef heart mitochondria at 50 pm Ph(NMe,),. Beef heart mitochondria were incubated at 37 C in 2 ml 120 mm KCI, 20 mm sucrose, 3 mm Hepes, 2 mm EGTA, 100 pm magnesium acetate, 5 pm rotenone, 0.5 pm myxothiazol, 2 mm ascorbate and 6 pm FCCP, ph 7.2. The respiration rate was measured with an oxygen electrode. In A, 50 pm Ph(NMe,), was present and mitochondrial protein was added at the concentrations shown; in B, 0.5 mg mitochondrial proteirdml was present and Ph(NMe,), was added as shown. The oxygen consumption rates in the absence of mitochondria were subtracted. The values are means? SEM from four independent experiments. The lines are least squares fits to all points. The standard conditions being investigated are indicated (*).

5 Mitochondrial protein (mg/ml) Fig. 3. Determination of the C, flux control coefficients of mitochondria and Ph(NMe,), over respiration rate in uncoupled potato tuber mitochondria. Potato tuber mitochondria were incubated at 25 C in 4 ml 30 mm KCI, 400 mm mannitol, 30 mm Hepes, 5 mm magnesium chloride, 2 mm potassium dihydrogen phosphate, 1 mg/ml bovine serum albumin, 10 mm ascorbate and 25 nm valinomycin (uncoupler [27]), ph 7.1. The respiration rate was measured with an oxygen electrode. In A, 125 pm Ph(NMe,), was present and mitochondrial protein was added as shown; in B, 0.15 mg mitochondrial protedml was present and Ph(NMe,), was added as shown. The values are means +range from two independent experiments. The lines are least squares fits to all points. The standard conditions being investigated are indicated (*). a- a Mitochondrial protein (mglml) Fig. 4. Determination of the C, flux control coefficients of mitochondria and Ph(NMe,), over respiration rate in uncoupled, frozenthawed beef heart mitochondria at 200 pm Ph(NMe,),. Beef heart mitochondria were incubated at 37 C in 2 ml 120 mm KC1, 20 mm sucrose, 3 mm Hepes, 2 mm EGTA, 100 pm magnesium acetate, 5 pm rotenone, 0.5 WM myxothiazol, 2 mm ascorbate and 6 pm FCCP, ph 7.2. The respiration rate was measured with an oxygen electrode. In A, 200 pm Ph(NMe,), was present and mitochondrial protein was added as shown; in B, 0.5 mg mitochondrial protein/ml was present and Ph(NMe,), was titrated in as shown. The oxygen consumption rates in the absence of mitochondria were subtracted. The values are means 2 SEM from four independent experiments. The line in A is a least-squares fit to all points; the line in B is drawn to pass through most of the points. The standard conditions being investigated are indicated (*). Since the C, flux control coefficients of Ph(NMe,), and mitochondria were each approximately one, with negligible control elsewhere (Figs 2 and 3), we can conclude that process 2 in Fig. t B [that mediates electron transfer from Ph(NMe,), to mitochondria] had a C, flux control coefficient of approximately t.o under our conditions, with near-zero C, flux control by processes 1 and 4. As indicated by van Dam et al. [13], if the concentrations of the carriers are high so that association is very rapid, their interactions will become pseudo-first order, and the sum of the C, flux control coefficients will tend to decrease towards one. To see if this effect could be observed with mitochondrial electron-transport, the experiment of Fig. 2 was repeated at a higher concentration of Ph(NMe,),, where [Ph(NMe,),] starts to become saturating. Fig. 4A shows that the respiration rate was still a linear function of mitochondrial concentration at 200 pm Ph(NMe,),; the C, flux control coefficient of the mitochondrial block of carriers was (n = 4). Fig. 4B shows that the Ph(NMe,), concentration was becoming limiting at 200 pm Ph(NMe,),, the C, flux control coefficient calculated from the tangent at 200 pm Ph(NMe,), was (n = 4). The apparent control exerted by oxygen and ascorbate concentrations was small; C, flux control coefficients of and -0.13, respectively, were obtained (data not shown). The sum of all these values was (n = 4), showing that the sum does decrease below two at high concentrations of carriers, as predicted [ 131.

6 824 In theory, we should have been able to obtain a similar result of C, l-lux control coefficients summing to less than two at low [Ph(NMe,),] and very high concentrations of mitochondria. In practice, sufficiently high mitochondria1 concentrations were not reached or sought (Figs 2A and 3A). C, flux control coefficients with succinate as substrate Having shown that the sum of the C, flux control coefficients for an electron-transport chain can be two, we tested whether the sum of the C, flux control coefficients was one. To measure the C, values we used the relationship described by Eqn (2), which states that C, is the ratio of the effects of a parameter change on the system flux (when system variables relax to new values) and on the local rate (when system variables do not relax to new values). For a specific parameter change (such as the addition of a certain inhibitor concentration) in a linear system where the initial values of J and v are the same, Eqn (2) reduces to C;, = 6Jl6 v,. Thus C, can be calculated from the measured effects of an inhibitor on J and 11. This is a particularly good way to measure C, flux control coefficients since, unlike the normal inhibitor titration methods, it does not require any quantitative informafion about the kinetics of the inhibitor that is used. Experimentally the approach is simple; it is only necessary to measure the effect of a small concentration of a specific inhibitor on the system flux under two conditions, the first when the system relaxes after inhibition (to obtain the change in system flux, 6 4 and the second when it does not (to obtain the effect on local enzyme rate 6 u). C, is then 6 Jl6 u. We used succinate as substrate and conceptually divided the system into blocks of processes around cytochrome c as shown in Fig. 1 D. Frozen-thawed rat liver mitochondria uncoupled by excess carbonylcyanide p-trifluoromethoxyphenylhydrazone (FCCP; 5 pm) were used so that proton cycling (and substrate transport) would have no control over flux. The succinatelfumarate and oxygedwater couples are effectively infinite and constant, so there is only one intermediate to be considered (the cytochrome c pool) in the system defined in this way. Thus 6 J is obtained from the effect of an inhibitor on rate when the cytochrome c redox state is allowed to alter, and 60 is obtained from the effect of the same concentration of inhibitor on rate when cytochrome c redox state is returned to the original value. We first measured the C,, flux control coefficient of complex IV over respiration rate by inhibiting it specifically with cyanide. 6J is the effect on flux when the cytochrome c- oxidisers are inhibited with cyanide and the system is allowed to relax to a new steady state. 6 u is the effect on flux when the cytochrome c-oxidisers are inhibited with cyanide and the flux is measured when the cytochrome c redox state is brought back to its original value. This reversion of the redox state can be achieved by titration with malonate, an inhibitor of the cytochrome c-reducers. Fig. 5 shows the result of this experiment. Under the condition to be analysed (point a at 100% oxygen consumption rate and 0% change in cytochrome c reduced) the respiration rate was (n = 3) nmol 0. min-'. (mg protein)-' and cytochrome c was (n = 3)% reduced. These values suggest that freezing and thawing had damaged the mitochondria significantly, perhaps with partial loss of cytochrome c. However, such damage is not important for the purposes of the present experiments, although it makes it difficult to extrapolate our conclusions to intact mitochondria to predict the sum of flux control coefficients in situ. The addition of a small amount c (I) m m S s v U (I) 3 p I" I I I I I I I Rate of oxygen consumption ('?A of control) Fig. 5. Determination of the C, flux control coefficients of cytochrome c-reducers and cytochrome c-oxidisers over respiration rate in uncoupled, frozen-thawed rat liver mitochondria with succinate as substrate. Rat liver mitochondria (2 mg proteidml) were incubated at 37 "C in 3 ml 120 mm KC1, 5 mm Hepes. 1 mm EGTA, and 5 pm rotenone, ph pm FCCP was added, followed by 10 mm succinate for 2 min (point a). Respiration was partially inhibited by addition of 0.5 mm KCN for 2 min (point b) followed by three successive additions of 1 mm malonate at 2-min intervals in the indicated experiment (-). Respiration was partially inhibited by addition of 1 mm malonate for 2 min (point c) followed by three successive additions of 0.33 mm KCN at 2-min intervals in the other experiment (---). In each case, the fully reduced cytochrome c signal was obtained at the end of the experiment by addition of excess KCN (8 mm). The respiration rate was measured with an oxygen electrode. In parallel experiments, the cytochrome c redox state was measured with a double-beam dual-wavelength spectrophotometer. The control oxygen consumption rate and cytochrome c redox state at point a are given in the text. The values are means 2 SEM from three independent experiments, each camed out in duplicate. The C, flux control coefficient of the cytochrome c-oxidisers was calculated as ab/ae; the C, flux control coefficient of the cytochrome c-reducers was calculated as ac/ad and the ratio of these coefficients was calculated as gf/gh as described in the text. The standard conditions being investigated are indicated (*). of KCN decreased respiration by 6.3% to point b (giving the value of 6J as the difference between a and b, ab) and caused the reduction of cytochrome c. Subsequent titration of the cytochrome c-reducers with malonate progressively caused oxidation of cytochrome c and decreased the respiration rate. When the cytochrome c redox state was back to its original value at point e, the respiration rate was found to be inhibited 49.5% by the original cyanide addition (giving the value of 6u as ae). Thus the C, flux control coefficient of complex IV under the original conditions was ablae ( or 0.127). The SEM from three independent determinations was To determine the C, flux control coefficient of the cytochrome c-reducers over respiration rate, the reverse titration with malonate to inhibit the cytochrome c-reducers (point c) and with KCN to inhibit the cytochrome c-oxidisers bringing the redox state of cytochrome c back to its original value at point d was also performed (Fig. 5). This titration gave a value for 6Jl6u of aclad ( or 0.946, with SEM of? 0.04) for three independent experiments. Thus, the sum of the C, flux control coefficients over the respiration rate was 1.07 _f 0.06 (n = 3). Similar titrations were carried out on one occasion using myxothiazol instead of malonate (i.e. myxothiazol followed by KCN addition and KCN followed

7 by myxothiazol addition) with relatively similar results (data not shown). There will be some error in these values caused by the use of relatively large finite changes 6JI6v instead of the infinitesimal changes 6 Jl6 v demanded by theory, and the associated assumption of perfect linearity between the cytochrome c redox state and the respiration rate over the range examined. This was inevitable because of the requirement for reasonably accurate determinations of changes in cytochrome c redox state. For greater accuracy, the experiments could have been carried out at different concentrations of primary inhibitor and the C, flux control coefficients at zero inhibitor concentration obtained by extrapolation, but this did not seem necessary for the present purpose. Note that we assume that the free concentration of cytochrome c (reduced plus oxidised) did not change during our titrations with inhibitors. If the free concentration of cytochrome c did change significantly (for example because of inhibitor-induced changes in its binding to the cytochrome c- reducers or the cytochrome c-oxidisers), then the parameter change would affect more than one local rate and the analysis would yield control coefficients that differ from the uninhibited C, values [lo-12, 14, 151. Since KCN and malonate should be non-competitive with respect to cytochrome c, the assumption that the free concentration of cytochrome c was constant should be valid in all of our experiments and this complication should not arise, although we cannot be certain about this. There is an alternative way to measure the sum of the C,, flux control coefficients over respiration rate from Fig. 5, using one of the absolute values obtained above and deriving the second value from the relative elasticities of the two blocks of processes to cytochrome c redox state. From the connectivity property, it is known that the ratio of the control coefficients of adjacent blocks of enzymes is the inverse of the ratio of their elasticities to the common intermediate [I, 31. This is the basis of the top-down approach to control analysis [37, 38-47] that we have applied to oxidative phosphorylation around the protonmotive force and the NADHI NAD ratio in mitochondria and intact cells [20, 21, 23, 30, 31, 48, 491. The relative elasticities in Fig. 5 to the cytochrome c redox state are given by the slopes of the two lines extending from the original point at a. The ratio - c: rrduc, VIE; rlrrdrzen (and therefore the ratio C: oxrdzzprjc;i.redur erj is given by gf/gh [20] and had the value 0.14; thus, the C, flux control coefficient of the cytochrome c-reducers over respiration rate based on the KCN titration of the cytochrome c-ouictisers was (0.91; SEM 0.12 for three independent experiments) and the C, flux control coefficient of the cytochrome c-oxidisers over respiration rate based on the malonate titration of the cytochrome c-reducers was 0.946X0.14 (0.13; SEM 0.12 for three independent experiments). The sums of the C, flux control coefficients over respiration rate calculated this way were using the elasticity ratio and the value of C, for the cytochrome c- oxidisers and using the elasticity ratio and the C, value for the cytochrome c-reducers, agreeing closely with the sum determined above from different but overlapping subsets of the data in Fig. 5. C, and C, flux control coefficients from the same data set with ascorbate plus Ph(NMe,), as substrate Up to this point, we have shown that the sum of the C, flux control coefficients over respiration rate in this group Rate of oxygen consumption (% of control) 825 Fig. 4. Determination of the C, flux control coefficients of cytochrome c-reducers and cytochrome c-oxidisers over respiration rate in uncoupled, frozen-thawed rat liver mitochondria with ascorbate as substrate. Rat liver mitochondria (2 mg proteidml) were incubated at 37 C in 3 ml 120 mm KC1, 5 mm Hepes, 1 mm EGTA, 5 pm rotenone and 20 pm myxothiazol, ph pm FCCP was added, followed by 10 mm ascorbate for 2 min (lowest points). Respiration was progressively stimulated in the first experiment by bringing the Ph(NMe,), concentration successively to 5, 15 (point b) and 25 pm (point a), then progressively inhibited by bringing the KCN concentration successively to 667 nm (point c), 1.33 pm and 2 pm, all at 2 min intervals (-). 667 nm KCN was added in the second experiment, and respiration was progressively stimulated by bringing the Ph(NMe,), concentration successively to 5, 15, 25 (point c) and 35 pm at 2-min intervals (---). In each case, the fully reduced cytochrome c signal was obtained at the end of the experiment by addition of excess KCN (8 mm). The respiration rate was measured with an oxygen electrode; the small oxygen consumption rate without mitochondria was subtracted. In parallel experiments, the cytochrome c redox state was measured with a doublebeam dual-wavelength spectrophotometer. The control oxygen consumption rate and cytochrome c redox state at point a are given in the text; the values in the second experiment (---)were normalised to those of the first experiment (-) by small correction factors needed to make point c on the two curves superimpose in each case. Values are means 2 SEM from three independent experiments. The C, flux control coefficient of the cytochrome c-oxidisers was calculated as adad; the C, flux control coefficient of the cytochrome c- reducers was calculated as ab/ae and the ratio of these coefficients was calculated as gf/gh as described in the text. The standard conditions being investigated are indicated (*). transfer system was two using ascorbate plus Ph(NMe,), as substrate and the sum of the C, flux control coefficients over respiration rate was one using succinate as substrate. The final set of experiments was designed to examine whether both sums could be obtained with a single substrate in a single set of experiments depending only on the method of calculation. The respiration of uncoupled frozen-thawed rat liver mitochondria with ascorbate plus Ph(NMe,), as substrate was measured as shown in Figs 6 and 7. The system was conceptually divided into blocks of processes (Fig. 1 C) for analysis of the C,, flux control coefficients and into blocks of carriers (Fig. 1 B) for analysis of the C, flux control coefficients. Fig. 6 shows the central part of the experiment, analogous to the experiment shown in Fig. 5, but using ascorbate plus Ph(NMe,), as substrate instead of succinate. The C,, flux control coefficient of complex IV over respiration rate was again measured by inhibiting it specifically with cyanide. The res-

8 ' O L 25 Mitochondria1 protein (mghl) [Ph(NMe,),I (PM) Fig. 7. Determination of the C, flux control coefficients of mitochondria and Ph(NMe,), over respiration rate in uncoupled, frozenthawed rat liver mitochondria at 25 pm Ph(NMe,),. The data are from the experiment shown in Fig. 6 and supplementary titrations with mitochondria were carried out at the same time. In A, 25 pm Ph(NMe,), was present and mitochondrial protein was added as shown; in B, the titration with Ph(NMe,), from the first experiment in Fig. 6 (-) is shown. Values are means -+ SEM from three independent experiments. The standard conditions being investigated are indicated (*). piration rate at the original cytochrome c redox state was not determined by inhibiting the cytochrome c-reducers as it was for the data in Fig. 5, but was measured in a separate titration in which the cytochrome c-reducers were progressively stimulated in the presence of the same concentration of KCN by addition of Ph(NMe,),. Under the condition to be analysed in Fig. 6 (point a at 100% oxygen consumption rate and 0% change in cytochrome c reduced) the respiration rate was 14.0 t 4.1 (n = 3) nmol 0. min-'. (mg protein)-' and cytochrome c was (n = 3)% reduced, again suggesting damage that was of no importance to the purpose of the experiment. The addition of a small amount of KCN (point c) decreased respiration by 23.8% (giving the value of SJ as ac) and caused the reduction of cytochrome c. Parallel titration of the cytochrome c-reducers with Ph(NMe,), in the presence of the same KCN concentration progressively caused reduction of cytochrome c and increased the respiration rate. When the cytochrome c redox state was back to its original value at point d, the respiration rate was found to be inhibited 38.8% by the original cyanide addition (giving the value of So as ad). Thus, the C, flux control coefficient of complex IV under the original conditions was aclad ( or 0.613). The SEM from three independent determinations was To determine the C, flux control coefficient of the cytochrome c-reducers over respiration rate, the opposite calculation was performed. The decrease in respiration rate from point a to point b with the next lower Ph(NMe,), concentration is equivalent to inhibition of the cytochrome c-reducers with associated oxidation of cytochrome c. The decrease in J was 20.5%, giving the value of SJ as ab. By extending a line from point b through the point with the same Ph(NMe,), concentration on the titration shown by the dashed line, the respiration rate at the original cytochrome c redox state at point e could be determined. Respiration was found to be inhibited 40.5 % by the original cyanide addition (giving the value of 6 u as ae) Thus the C, flux control coefficient of the cytochrome c-reducers under the original conditions was abl ae ( or 0.506), with SEM for three independent experiments. The sum of the C, flux control coefficients over respiration rate was 1.I2 t 0.20 (n = 3). As with the experiment in Fig. 5, the values of the C, coefficients could also be calculated from the data in Fig. 6 using the elasticities to the cytochrome c redox state. The ratio -E: reducer$lg onrdrzers (and therefore the ratio C,' oarrlr J C: rpdurrrr) is given by gflgh and had the value 2.36; thus, the C, flux control coefficient of the cytochrome c-reducers over respiration rate based on the KCN titration of the cytochrome c-oxidisers was (0.26; SEM 0.20 for three independent experiments) and the C, flux control coefficient of the cytochrome c-oxidisers over respiration rate based on the Ph(NMe,), titration of the cytochrome c-reducers was X 2.36 (1.19 ; SEM 0.21 for three independent experiments). The sums of the C, flux control coefficients over respiration rate calculated this way were (0.87 f 0.24) and ( ), agreeing fairly well with the sum determined above from different but overlapping subsets of the data in Fig. 6. The errors introduced by making relatively large finite changes and assuming perfect linearity between cytochrome c redox state and respiration rate are clearly apparent in this experiment, particularly for the direct measurement of the C, flux control coefficient of the cytochrome c-reducers, which seems to be too high. Crude extrapolation to very low KCN additions reduces its value from to approximately 0.3 and changes the calculated sums to 0.9 using the first method and to 0.87 and l using the second method. Thus, the sum of the C, flux control coefficients with ascorbate as substrate is approximately one, as it is with succinate as substrate. Data from the same set of experiments could also be used to obtain a value for the sum of the C, flux control coefficients over respiration rate, with the system redefined in terms of blocks of carriers as described in Fig. 1 B. Fig. 7B shows the dependence of respiration rate on Ph(NMe,), concentration replotted from Fig. 6. Calculation of the C, flux control coefficient for Ph(NMe,), as described for Fig. 2 yielded a value of (n = 3). In supplementary experiments carried out at the same time, the mitochondrial concentration was varied under the standard conditions [25 pm Ph(NMe,),, no KCN] as shown in Fig. 7A. The C, flux control coefficient for mitochondria was (n = 3). Thus the sum of the C, flux control coefficients was 1.76 t Least squares fits to the lines in Fig. 7A and B yielded C, flux control coefficients of 1.09 and respectively, with a sum of Either method of calculation gave sums of the CF flux control coefficients approaching two and

9 827 clearly greater than the sum of the C,, flux control coefficients of approximately one derived from the same data set. DISCUSSION It is clear from the results presented in this study that the sum of the C, flux control coefficients over oxygen consumption rate for electron-transport chains in mitochondria can be two, as predicted by van Dam et al. [13], and is not necessarily one as has previously been implicitly assumed. This is true for electron-transport from ascorbate through Ph(NMe,),, cytochrome c and complex IV to oxygen (Figs 2, 3 and 7) when the Ph(NMe,), concentration is not too high. Under appropriate conditions (high ascorbate and high oxygen, Figs 2 and 3) all of the flux control by electrontransport processes is at the point of interaction of Ph(NMe,), with mitochondria, and there is C, flux control of approximately one by the concentrations of two electron carriers, namely mitochondria and Ph(NMe,),. At higher Ph(NMe,), concentrations, the control by Ph(NMe,), decreases as the reduction of mitochondria becomes more pseudo-first order, and the sum of the C, flux control coefficients over oxygen consumption rate decreases towards one as predicted [ 131 (Fig. 4). In contrast to this result, the sum of the C, flux control coefficients over oxygen consumption rate is approximately one in a more physiological electron-transport chain from succinate through complex 11, coenzyme Q, complex 111, cytochrome c and complex IV to oxygen (Fig. 5). The sum of the C, flux control coefficients is also approximately one for oxidation of ascorbate plus Ph(NMe,), (Fig. 6), as predicted ~131. This difference in the sum depends completely on the choice that is made over the definition of the flux control coefficients. The same data set (Figs 6 and 7) yields either sum depending on which definition is used. Neither definition is incorrect; C, flux control coefficients describe control by processes, which in other systems often corresponds to control by enzyme activities, whereas C, flux control coefficients describe control by group-transfer carriers or moietyconserved metabolite cycles, which in other systems often corresponds to control by enzyme concentrations. Confusion can arise if group-transfer carriers such as redox carriers in electron- transport chains, phosphotransferases or aminotransferases are thought of uncritically as enzymes; in the context of flow of the group that is transferred, then these carriers are more analogous to substrates and products of the interconversion processes. In particular, it is inappropriate in the present context to consider the large protein complexes of the mitochondria1 electron-transport chain (complexes I- IV) as enzymes and the small, more abundant electron carriers (coenzyme Q and cytochrome c) as substrates or products, since they have identical formal status in electron-transport. It follows that great care has to be taken when considering the distribution of control in complex systems like oxidative phosphorylation that contain group-transfer reactions within them. It is very important to be clear about which definition of control coefficients is being used, since the C, flux control coefficients in the system should sum to one but the C, flux control coefficients will not. Methods based on the measurement or calculation of elasticities give C, flux control coefficients, thus most of the work on oxidative phosphorylation, including the top-down approach [20, 211, is not affected by the higher sum obtained using C, flux control coefficients. However, it is important not to mix definitions as the values for the coefficients that are obtained will not be comparable. In an earlier study, we concluded that complex IV had no control over respiration in mitochondria respiring on ascorbate plus Ph(NMe,), because the Ph(NMe,), concentration had a (C,) flux control coefficient of approximately one, leaving no residual control for complex IV [24]. This conclusion is wrong using the results of this study; a C, flux control coefficient for Ph(NMe,), of one does not rule out a finite C, or C,] flux control coefficient for complex IV. In their classic study of the control of oxidative phosphorylation, Groen et al. [16] discussed the control coefficients that they calculated as if they were C, flux control coefficients. The authors measured the control exerted by the adenine nucleotide carrier using the (effectively) irreversible inhibitor carboxyatractyloside and calculated the concentration of enzyme that was inhibited by a given addition of inhibitor (I) from Z/Imax (where I,,, is the minimum inhibitor concentration needed for maximum inhibition). Also, control by added hexokinase was calculated from experimental changes in hexokinase concentrations. Both of these methods give the C, flux control coefficient; since the enzymes involved were not part of the group-transfer system, the values are probably not different from the C,, values. However, the values for control by the dicarboxylate carrier, complex I11 and complex IV measured by Groen et al. [16] were in fact C, flux control coefficients since they were worked out from calculated activity changes caused by the addition of reversible inhibitors [12]. The calculated control by the proton leak would have been a C, value had the method used been valid, but it was not [20]; the correct control coefficients for the proton leak calculated from elasticities [20,21] are C, values. Thus, it is important to realise that the calculation of flux control coefficients for group-transfer reactions such as electron-transport using irreversible inhibitors and the Z/ZmaX method will give C, flux control coefficients, and such values cannot be directly compared with values from other methods that give C, flux control coefficients. However, the conclusions of Groen et al. [16] appear to be essentially unaffected by the present distinction between C, and C, control coefficients ; the conclusions remain valid if their calculated control coefficients are equivalent to C, control coefficients and the erroneous method for estimating control by the proton leak is ignored. Use of irreversible inhibitors tends to give C, flux control coefficients and use of reversible inhibitors tends to give C, flux control coefficients [5, 101. However, this is not necessarily the case; it depends on the method of calculation. The method that we have used (Figs 5 and 6) will always give C, flux control coefficients, since it compares the effect of an inhibitor (whether reversible or irreversible) on the global flux J and the local flux o under identical conditions [12]. Note that previous attempts to measure C, flux control coefficients in this way [19, 291 have not ensured that all other effectors are held constant and so will be subject to errors. Similarly, if the inhibitor that is used changes the total concentration of a moiety-conserved intermediate, the meaning of the control coefficients obtained will be changed [lo, 141; to avoid confusion, such inhibitors should normally not be used. Due to its experimental simplicity and because it does not require knowledge of the exact values of the parameters associated with inhibition (K,,,, K,, V,,,,,, [S], [PI, I,,,, extent of sequestration of inhibitor by other proteins, etc.), we rec-

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