Quantitative determination of the regulation of oxidative phosphorylation by cadmium in potato tuber mitochondria

Transcription

1 Eur. J. Biochem. 225, (1994) 0 FEBS 1994 Quantitative determination of the regulation of oxidative phosphorylation by cadmium in potato tuber mitochondria Adolf KESSELER and Martin D. BRAND Department of Biochemistry, University of Cambridge, England (Received June 6iAugust 22, 1994) - EJB /6 The effects of cadmium on respiration rate, phosphorylation rate, proton leak rate, the protonmotive force and the effective P/O ratio were determined over a range of respiratory conditions and cadmium concentrations by applying top-down regulation analysis. To quantify the effects of cadmium, we determined the overall response coefficients of these variables of oxidative phosphorylation to cadmium in different respiratory states between state 4 and state 3 and at different cadmium concentrations. The overall response coefficients to cadmium showed quantitatively how cadmium stimulated substrate oxidation rate at high cadmium concentrations near state 4 but inhibited it to different extents under all other conditions, how cadmium inhibited the rate of proton leak rate at low cadmium concentrations near state 4 but stimulated it under all other conditions, and how cadmium inhibited the rate of phosphorylation and depressed the protonmotive force and the effective P/O ratio to different extents under all conditions. Cadmium is known to stimulate the proton leak and to inhibit the substrate oxidation reactions ; we calculated the elasticities of these subsystems to cadmium to quantify its effects. To describe fully how the cadmium effects on different subsystems produce the overall responses of the system to cadmium, we then calculated the partial response coefficients of the system variables to cadmium acting through each subsystem. The partial response coefficients quantify the contribution of each block to the overall effect of cadmium on each variable in any condition, and sum to the overall response coefficient in each condition. Together with the elasticity analysis and the control analysis and internal regulation analysis presented in the preceding papers [Kesseler, A. & Brand, M. D. (1994) Eur: J. Biochem. 225, pp ; Kesseler, A. & Brand, M. D. (1994) Eur: J. Biochem. 225, pp they completely describe how cadmium exerts its effects on oxidative phosphorylation at the system level. The effects of cadmium and other heavy metals on mitochondrial oxidative phosphorylation is one of the most investigated features of the impact of heavy metals on living organisms [l -41. We have chosen the effects of cadmium on oxidative phosphorylation in potato tuber mitochondria as a model system in which to demonstrate and develop the appli- Correspondence to M. D. Brand, Department of Biochemistry, University of Cambridge, Tennis Court Road, Cambridge, England, CB2 1QW Fax: Abbreviations. Ap, protonmotive force ; A y, membrane potential; ApH, ph gradient across the mitochondria1 inner membrane, all expressed in mv; Js, rate of oxygen consumption by the substrate oxidation reactions ; Jp, rate of oxygen consumption required to pump protons out at the rate equal to the rate of proton return through the phosphorylation system; J,, rate of oxygen consumption required to pump protons out at the rate equal to the rate of proton return through the proton leak; the subscripts and superscripts S, P and L refer to the three blocks of reactions: substrate oxidation, the phosphorylation system and the proton leak, respectively ; C$, overall control coefficient of subsystem S (or P or L) over J, (or J, or J, or Ap or the effective P/O ratio) ; E&, overall elasticity of subsystem S (or P or L) to cadmium; sr$d partial external response coefficient of Js (or J, or JL or Ap or the effective P/O ratio) to cadmium exerted via subsystem S (or P or L); *R&, overall external response coefficient of J, (or J, or J, or Ap or the effective PI0 ratio) to cadmium. Enzyme. Hexokinase type 111: from baker s yeast (EC ). cation of metabolic control analysis to such toxicological problems. In the preceding studies we showed how oxidative phosphorylation can be simplified to three subsystems, substrate oxidation, phosphorylation and proton leak, connected by their common intermediate protonmotive force, (dp). The sites of action of cadmium can be identified by elasticity analysis [l] ; cadmium inhibits substrate oxidation and stimulates proton leak (without causing slip in the redox proton pumps [5]), but has little effect on the phosphorylation reactions. We then showed how cadmium alters the pattern of internal regulation of oxidative phosphorylation by measuring its effect on control coefficients and partial internal response coefficients [6]. In the present study, we complete the control analysis by measuring the overall response coefficients of oxidative phosphorylation to cadmium and subdividing them into the partial response coefficients [7-101 to cadmium acting through each of the subsystems. The partial response coefficients quantify the contribution of each block of reactions to the overall effect of cadmium on each variable of oxidative phosphorylation and allow an evaluation of the relative importance of simultaneous cadmium effects in creating the overall effects of cadmium on oxidative phosphorylation. This regulation analysis provides a full quantitative description of the simultaneous effects of cadmium on the three blocks of reactions and how these effects interact to create

2 dy/y 924 the overall response of a particular variable to cadmium, under the full range of different conditions between state 4 and state 3 and at different cadmium concentrations. MATERIALS AND METHODS The system under consideration is shown in Fig. 1 in [l]. NADH was used as respiratory substrate in all experiments for the reasons outlined in [6]. Isolation and purification of mitochondria, protein determination, calculation of free cadmium concentrations and measurement and determination of variables of oxidative phosphorylation are described in [l]. All results were calculated from the data set making up Fig. 7 in [l], using the same respiratory conditions between state 4 and state 3 and the same cadmium concentrations as in [l, 5, 61. Note that the validity of the calculated values in the present study depends on the validity of the underlying assumptions; these assumptions are discussed in [l]. Calculation of overall response coefficients In metabolic control analysis, the responses of fluxes and steady-state concentrations to changes in effector concentrations are expressed as response coefficients. These are calculated as the fractional change in a system variable y caused by an infinitesimal fractional change in the concentration of effector x [lo]. "R", = ~ &lx dx y (1 1 At the first sight, this definition seems to be the same as the definition of the elasticity of y to changes in the concentration of an external effector x. However, the two types of coefficients differ in the conditions under which they are determined ; elasticities are determined when everything else except x is kept constant, while during the determination of response coefficients all fluxes and intermediate concentrations are allowed to find their steady-state values [ll]. In this study, the overall response coefficients of variables of oxidative phosphorylation to cadmium were derived from the same data set that was used to work out the control coefficients (Fig. 7 in [l]). In this case y in Eqn (1) represents Js, J, J,, dp or the effective PI0 ratio and x represents the free cadmium concentration. The overall response coefficients of the five variables to cadmium shown in Fig. 2 were determined from the normalised slopes when the variables were plotted against cadmium concentration as shown in Fig. 1 for Js. Alternatively (Figs 5-9), the coefficients were determined by summation of the corresponding partial response coefficients of J5, J, J,, dp and the effective PI0 ratio in any given condition, [Eqn (2)]. Calculation of partial response coefficients to cadmium The overall response coefficient *R& of a variable V to cadmium [Eqn (l)] can be broken down into three partial response coefficients (.rr&,, pred and LRgd) that describe the strength of the effect of cadmium on this variable through each of the subsystems, as shown in Eqn (2) where is Js, Jp,.I1, dp or the effective P/O ratio. Each bracket represents the partial response coefficient of a variable to cadmium through a subsystem, which is calculated as the elasticity of the subsystem to cadmium (how much a change in cadmium changes the subsystem) multiplied by the control coefficient of that subsystem over the variable (how much a change in the subsystem changes the variable), as derived in [lo, 121. The overall response coefficients to cadmium quantify how much an infinitesimal change in cadmium changes a variable of oxidative phosphorylation. They can be obtained by summation of the corresponding partial response coefficients, which quantify the fraction by which the cadmium effects on each of the three subsystems contribute to the overall effect. Partial response coefficients of J,, J, JL, dp and the effective PI0 ratio to cadmium shown in Figs 5-9 were calculated as the product of the appropriate values of and CLhryrrem and E F ~ ' using ~ " ~ ~ the data set of Fig. 7 in [l]. The control coefficients are given in Figs 1-5 in [6]. The elasticities of each subsystem to cadmium were calculated from replots of Js, J, and JL at the appropriate fixed value of dp against cadmium concentration (Fig. 3) and are shown in Fig. 4. The elasticities of the three subsystems to cadmium at fixed dp are given by Eqns (3-5). djlj djl Cd E", = (5) dcd1cd dcd JL The elasticities to cadmium should not be confused with the overall response coefficients of these variables to cadmium [Eqn (2)]. The elasticities to cadmium are determined when everything else but cadmium is kept constant within the system (i.e. at a clamped Ap value), whereas during the determination of the overall response coefficients all the variables and intermediate concentrations within the system (e.g. dp) may vary. (3) (4) - ~. ~ RESULTS Overall response coefficients of oxidative phosphorylation to cadmium The original data set shown in Fig. 7 in [l] was replotted to show the effect of cadmium on each of the five variables in different respiratory rates between state 4 and state 3. Fig. 1 shows the effect of cadmium on.is, similar graphs were produced for its effects on J,, JL, dp and the effective PI0 ratio (data not shown). The normalised slopes of these plots give the overall response coefficient of each of the variables to cadmium; these are shown in Fig. 2. The overall response coefficients to cadmium in Fig. 2 show how sensitive the steady-state values of the variables are to cadmium under different conditions. A negative response coefficient indicates an inhibition, while a positive coefficient indicates an activation. The three-dimensional graphs illustrate in general terms that the response coefficients vary depending on the cadmium concentration and on the flux condition. Error bars are not shown because the errors in calculating slopes from plots like those in Fig. 1 are difficult to assess. However, the overall response coefficients

3 St. 3 St.4 I [Cadmium] free (~4 Fig. 1. Effect of cadmium on substrate oxidation, J,, under different conditions. Each line represents a different respiratory condition between state 4 and state 3. Respiratory conditions are as follows : state 4 (0); endogenous hexokinase activity (0); further addition of (A), 0.11 (A), 0.22 (m) and 0.88U hexokinase to maintain state 3 (0). Data were replotted from Fig. 7 of [l]. Overall response coefficients at different respiratory conditions were calculated from the normalised slopes of each line at each cadmium concentration. Slopes at each point were estimated by averaging the slopes on each side of the point, except for 21 pm cadmium, where the slope at pm cadmium was used. shown in Fig. 2 are almost identical to the overall response coefficients calculated from the partial response coefficients shown in Figs 5-9. Since the two methods of calculation involved different assessments of slopes, from different plots, this shows that the errors introduced by the methods used to estimate slopes are not important. The overall effect of cadmium on Js (Fig. 2) is determined by its simultaneous antagonistic effects of inhibiting substrate oxidation (decreasing Js) and stimulating the proton leak (increasing Js), while the effect of cadmium on the phosphorylation system is negligible [l]. At low respiration rates and high cadmium concentrations the effect on the proton leak dominates and the overall effect of cadmium in these conditions is a stimulation of.is, indicated by a positive response coefficient. With increasing flux or decreasing cadmium concentration, the inhibition of the substrate oxidation becomes dominant and the overall response coefficients switch to negative values indicating an overall inhibitory effect. This switch in the overall response is due to the decreased contribution of the stimulated proton leak, which is maximal at state 4 but approaches zero with increasing respiration rates [l]. During the overall inhibition of J,, the sensitivity of Js to cadmium slightly increases with flux (i.e. the overall response coefficients become more negative), while the sensitivity to changes in cadmium tends to decrease with increasing cadmium concentration. The overall response coefficients of Jp to cadmium (Fig. 2) are negative for all experimental conditions indicating that cadmium inhibits Jp, though no direct effect of cadmium on the phosphorylation system could be detected [l]. Cadmium decreases Jp by inhibiting the dp producers and by stimulating proton leak [I]. No dependence of the response coefficients on respiratory state can be detected, but the response to changes in cadmium concentration is greatest around 14 pm cadmium. The overall response coefficients of JL to cadmium (Fig. 2) appear to be rather high near state 3 compared to the coefficients of Js and Jp, reflecting a higher sensitivity of 925 this branch to cadmium. The sensitivity to cadmium at low respiration rates (state 4) is similar to the sensitivity of Js and J, At high and even at intermediate respiration rates, JL. is very small compared to Js and Jp [l]. Therefore, the cadmium effects on the proton leak will not contribute much to the effects of cadmium on oxidative phosphorylation at high respiration rates, though the proton leak has the highest sensitivity of all variables at high flux conditions. All response coefficients of JL are positive indicating that this rate is stimulated by cadmium, except at low cadmium concentrations near state 4, where JL is inhibited due to the inhibition of substrate oxidation and the reduction in dp despite the stimulation of the proton leak pathway [l]. The response coefficients of dp to cadmium (Fig. 2) become more negative with increasing flux and might be greater at lower cadmium concentrations. However, the values of the overall response coefficients are very small over the full range of experimental conditions indicating that dp is rather insensitive to cadmium. The same is found for the control coefficients over dp, which change very little with respiratory conditions [13] or in presence of increasing cadmium concentrations [6]. This reflects the way the system keeps dp fairly constant over the range of respiratory conditions or rates of ATP synthesis [14]. However, it is evident from [l] that the absolute value of dp is successively decreased by increasing cadmium concentrations due to the inhibition of the dp producers and the simultaneous stimulation of the dp-consuming proton leak. Both effects decrease the rate of ATP synthesis under all respiratory conditions [l]. The overall response coefficients of the effective P/O ratio to cadmium (Fig. 2) are negative because cadmium decreases the coupling ratio. The effect is strongest at high cadmium concentrations and nearer state 4 because cadmium mainly lowers the PI0 ratio by increasing the fraction of Js used for J,, and JL is largest near state 4 and most responsive to cadmium at higher cadmium concentrations (Fig. 4). Elasticities of the three subsystems to cadmium The elasticity of a block of reactions to cadmium [Eqns (3-5)] must be measured under conditions in which all other relevant effectors are held constant. The value of dp is the other important effector in our system, so the elasticities to cadmium must be measured under conditions in which dp is constant. Thus the elasticity of substrate oxidation to cadmium cannot be determined from Fig. 1, where dp varies. To determine the value of J, as a function of cadmium concentration at fixed dp, Fig. 3 was constructed by interpolation from the data in Fig. 7 in [l]. Similar plots were produced for the effects of cadmium on Jp and J, at fixed dp (data not shown). The normalised slopes of these replots then gave the values of the elasticities to cadmium shown in Fig. 4. These plots of the elasticities of each of the three subsystems to cadmium (Fig. 4) describe how sensitive they are to cadmium over a range of respiratory states and cadmium concentrations. Together with the kinetic responses of the subsystem to dp in the presence of different cadmium concentrations shown in Figs 4-7 of [l] (from which they are derived), they fully describe how cadmium affects oxidative phosphorylation in potato tuber mitochondria at the level of individual subsystems. The elasticity of substrate oxidation to cadmium is negative, showing how it inhibits this subsystem. Substrate oxidation is particularly sensitive to cadmium at low respiration

4 926 Fig. 2. Overall response coefficients of J,, J,, J,, Ap and the effective P/O ratio to cadmium as a function of respiratory condition and cadmium concentration. Values were determined from Fig. 1 (for Js) and from similar plots of Jp, JL, dp and the P/O ratio (data not shown). Note that some of the scales are inverted for clarity; the lower three panels have the respiratory state scale and the right hand two panels have the [cadmium] scale inverted. Note also that the vertical scales differ. HK, hexolunase. rates near state 4. The phosphorylation system is almost unaffected by cadmium [l]; the slight inhibition shown in Fig. 4 is within the noise of the measurements. The elasticity of the proton leak to cadmium is large and positive under all conditions, showing how cadmium stimulates this subsystem strongly under all conditions (1, 51. Proton leak is particularly sensitive to cadmium at higher cadmium concentrations. Partial response coefficients of oxidative phosphorylation to cadmium The partial response coefficients of the variables of oxidative phosphorylation to cadmium through substrate oxidation, the phosphorylation system and the proton leak were calculated from the elasticities of these subsystems to cadmium (Fig. 4) and their control coefficients over the variables (Figs 1-5 of [61). The partial response coefficients show the origin of the overall response coefficients shown in Fig. 2. The overall response coefficients can also be calculated from the sum of the partial response coefficients. The partial response coefficients of Js to cadmium through substrate oxidation, the phosphorylation system and the proton leak are shown in Fig. 5. The overall effect on J, is determined by the antagonistic effects of cadmium inhibiting the respiratory chain (negative partial response coefficient, "R$J and the simultaneous stimulation of the proton leak (positive partial response coefficient, "A'-&).The effects through the proton leak dominate at low fluxes (when JL

5 T- h.- t 9) c 2 a c.- E 0-8 St I 1. 1 I. n pm cadmium 7 pm cadmium St. 4 n I I I I St I \ 14pM cadmium I pm cadmium \ \ \ ----_ St. 3 ) I St is high) and high cadmium concentrations (stimulating JL), resulting in an overall stimulation of Js. With increasing flux and lower cadmium concentrations, the inhibition of substrate oxidation dominates resulting in an overall inhibition of Js. The effects through substrate oxidation and the proton leak are always antagonistic to the overall cadmium effect on Js, but at low respiration rates this antagonism is much more pronounced (higher absolute values), than at high respiration rates. The partial and overall response coefficients of Jp to cadmium are shown in Fig. 6. Though the phosphorylation system itself is negligibly affected by cadmium, the overall response coefficients of J, to cadmium are negative for all experimental conditions. As the phosphorylation branch is almost insensitive to cadmium, this block has a very small contribution to the overall effect of cadmium on Jp and the partial response coefficients are close to zero. The overall response is composed of the cadmium effects exerted through the substrate oxidation and the proton leak. The partial response coefficients of these two blocks both contribute to the overall response of J,, as all values are negative. The inhibition of substrate oxidation by cadmium decreases Ap and consequently decreases the rate of Ap consumption by the phosphorylation system. The stimulation of the proton leak by cadmium also decreases Ap, and so also decreases Jp. Fig. 7 shows the response coefficients of JL to cadmium. Cadmium stimulates JL and the overall response coefficients are positive under most conditions. The effects of cadmium on JL exerted through substrate oxidation are negative, because cadmium inhibits substrate oxidation and lowers the production of dp, the driving force for the proton leak. The overall response coefficient of JL to cadmium is dominated by the partial response coefficients exerted through the proton leak except at low cadmium concentrations near state 4, when the effect on substrate oxidation are large enough to cause a net inhibition of JL. The contribution of the phosphorylation system to the overall effect of cadmium on J, is negligible. The partial and overall response coefficients of Ap to cadmium (Fig. 8) are close to zero over the full range of experimental conditions, illustrating how the system keeps Ap fairly constant over the range of respiration rates [13, 141. Fig. 8 shows that there is only a very small negative overall response coefficient indicating that Ap is decreased due to Fig. 3. Effect of cadmium on the rate of substrate oxidation, J,, in different respiratory states at the same value of dp. The lines of Fig. 7 in [I] describing the kinetic response of Js to Ap at different cadmium concentrations were plotted together as in Fig. 5B in [l] (data not shown). For each data point, the interpolated values of Js for the other cadmium concentrations at the same Ap were read from the graph. These values of J, were then plotted against cadmium concentration and joined by dashed lines, thus each dashed line represents the response of J, to cadmium at a particular value of Ap, defined by the original cadmium concentration and respiratory state. The vertical lines join the definitive points for the six respiratory states at each cadmium concentration. The elasticities of J, to cadmium were calculated as the average of the normalised slopes on each side of the data point; where the dashed lines terminate at the point, the missing slopes were estimated by eye. Respiratory conditions were as follows: state 4 (0); increasing intermediate respiration rates due to endogenous hexokinase (0); further addition of (A), 0.11 (A), or 0.22 U hexokinase (m) and state 3 in the presence of 0.88 U (saturating) hexokinase (0). The elasticities of the phosphorylation system and the proton leak to cadmium were determined by the same procedure (data not shown).

6 928 Fig. 4. Elasticities of substrate oxidation, the phosphorylation system arid the proton leak to cadmium under different conditions. Elasticities were calculated from the data in Fig. 3 and from similar plots of Jp and 1, against cadmium concentration. HK, hexokinase. the cadmium effects on the system. The partial response coefficients of dp through substrate oxidation are negative, because cadmium inhibits substrate oxidation and decreases Ap production. The partial response coefficients of Ap through the proton leak are negative, because cadmium stimulates the proton leak and increases dp consumption through that subsystem. The contribution of the cadmium effects on the phosphorylation system is negligible. The inhibitory effect of cadmium on the effective PI0 ratio (Fig. 9) is dominated by the effects exerted through the proton leak. The partial response coefficient through the proton leak is negative, because cadmium stimulates proton leak and so decreases J,, due to the competition of the two Ap consumers for their common substrate dp. The more JL contributes to the flux through the system, the more cadmium may exert its effects through this block of reactions. So the higher JL and the higher the cadmium concentration (and consequently the cadmium induced increase in JL), the higher are the negative overall response coefficients of the P/O ratio to cadmium. DISCUSSION The top-down analysis described in this study and the two preceding ones [l, 61 is a simple yet powerful general method that can be used to produce a complete description at the system level of the action of any external effector (in this case cadmium) on a complex steady-state biological system (in this case oxidative phosphorylation in potato tuber mitochondria). We have chosen to investigate the effect of a toxic agent, but in principle the approach is equally applicable to the description of the action of physiological effectors such as hormones or second messengers. The method is particularly useful if, like cadmium, the effector has multiple sites of action on the system; the relative importance of each site for different variables can be readily established. It provides the context within which a more detailed mechanistic study could be performed if required, to establish the exact sites and modes of action of the effector. For example, we have determined whether the effect of cadmium on J, is caused by increased proton leak through the membrane or by increased slip reactions in the redox proton pumps [S]. The steps involved in conducting the analysis are as follows. First, the system is divided into a small number of subsystems connected by a single intermediate and not other- wise in significant contact [15] (it may be possible to relax this constraint, see [16]). For oxidative phosphorylation we choose dp as the intermediate and divide the system into a block of reactions that produces dp (substrate oxidation), and two blocks that consume dp (the phosphorylation system and the proton leak) [l]. A top-down elasticity analysis is then carried out to discover the sites of action of the effector [l]. This involves measuring the kinetic response of each subsystem to dp. If the effector alters the kinetic response of a subsystem to dp, then it will change the fluxes and concentrations in the whole system. The absolute magnitude of the effect on a block can be assessed, as (for example) a twofold activation at a designated value of dp. However, if the effector does not change the kinetic response of the subsystem to Ap, then it cannot change the system fluxes and concentrations by this route. Thus, even if we know from the literature that the effector has an action on a particular block of reactions, this action can be dismissed as unimportant for the system behaviour under the conditions of interest if the effector does not alter the kinetic response of the block as a whole to dp. Finally, the values of the elasticities of each subsystem to dp at each concentration of the effector [l] and to the effector at each value of dp that is of interest (as in the present study) can be worked out under a range of different conditions. The internal control of the system can then be worked out under different conditions using the elasticities to dp and the measured fluxes [6]. These control coefficients show how much control each block of reactions exerts over the system variables, which are the fluxes through each subsystem (i.e. Js, J, and JJ, the concentration of the intermediate (is. dp), and the ratio of fluxes through different branches (e.g. Jp/ Js, the relative effective P/O ratio). Partial internal response coefficients of the variables to the intermediate also can be calculated, to show how the value of dp determines the value taken by each variable under different conditions. The way that the internal control and regulation shifts as the effector concentration is altered can give useful insights into the way the system behaves under different conditions. The most revealing way of quantitatively assessing the action of an external effector is to conduct a top-down regulation analysis, as in the present study. Overall response coefficients are calculated to show how sensitive the variables are to changes in the effector under a range of different conditions. The elasticities of the subsystems to the effector can be used to show how the subsystems respond to changes in

7 Fig. 5. Partial response coefficients of substrate oxidation rate, J,, to cadmium exerted through substrate oxidation, the phosphorylation system and the proton leak and their summation to the overall effect of cadmium on J,. The partial response coefficients shown on the left hand panels are summed to give the overall response coefficients on the right hand panel. They were calculated in each condition from the elasticities (& $.d and E&) shown in Fig. 4 and the control coefficients (C?, C$ and C2) shown in Fig. 1 of [6]. HK, hexokinase. 929

8 930 Fig. 6. Partial response coefficients of phosphorylation rate, J,, to cadmium exerted through substrate oxidation, the phosphorylation system and the proton leak and their summation to the overall effect of cadmium on J,. The partial response coefficients shown on the left hand panels are summed to give the overall response coefficients on the right hand panel. They were calculated in each condition from the elasticities (& E:., and E&) shown in Fig. 4 and the control coefficients (C?, C$ and C:!) shown in Fig. 2 of [6]. HK, hexokinase.

9 93 1 Fig. 7. Partial response coefficients of proton leak rate, J,, to cadmium exerted through substrate oxidation, the phosphorylation system and the proton leak and their summation to the overall effect of cadmium on J,. The partial response coefficients shown on the left hand panels are summed to give the overall response coefficients on the right hand panel. They were calculated in each condition from the elasticities (gd, egd, and &,) shown in Fig. 4 and the control coefficients (C$, C$ and CP) shown in Fig. 3 of [6]. HK, hexokinase.

10 932 Fig. 8. Partial response coefficients dp to cadmium exerted through substrate oxidation, the phosphorylation system and the proton leak and their summation to the overall effect of cadmium on dp. The partial response coefficients shown on the left hand panels are summed to give the overall response coefficients on the right hand panel. They were calculated in each condition from the elasticities (Ed, &, and &,) shown in Fig. 4 and the control coefficients (C?, CgP and C,".) shown in Fig. 4 of [6]. HK, hexokinase.

11 Fig. 9. Partial response coefficients of the effective P/O ratio to cadmium exerted through substrate oxidation, the phosphorylation system and the proton leak and their summation to the overall effect of cadmium on the P/O ratio. The partial response coefficients shown on the left hand panels are summed to give the overall response coefficients on the right hand panel. They were calculated in each condition from the elasticities (E&, E:~, and &) shown in Fig. 4 and the control coefficients (Cyo, C;'" and CC'O) shown in Fig. 5 of [6]. HK, hexokinase. 933

12 934 the effector, and can also be combined with control coefficients to allow calculation of partial response coefficients to the effector. These describe how the effector exerts its overall effect on the system through its interactions with each of the subsystems. Since the partial response coefficients sum to give the overall response coefficients, they can be used to explain why the system as a whole responds in the way it does to the effector under different conditions. Thus metabolic control analysis can provide an accurate quantitative description at the system level of how external effectors work based on a very simple set of titrations with any of a number of experimental effectors. This description is useful because it gives us a clearer understanding of the system response without the lack of overview that more traditional piecemeal approaches engender. It also allows us to assess the significance of particular effects in any condition that is examined, so that we can know whether one recognised effect plays a dominant role in the system response or whether it is only important for the effect on particular variables under a limited range of conditions. The corresponding disadvantage of top-down metabolic control analysis is that it produces a rather coarse picture of system behaviour, with no fine detail about the effects occurring within each of the subsystems. However, if such detail is required then it can be obtained by repeating top-down analysis around different intermediates or by established methods of enzymology, with the benefit of an appreciation from the start of how the detail fits into the overall system behaviour. Our results show quantitatively how cadmium affects the system of oxidative phosphorylation in potato tuber mitochondria through its primary effects (inhibition of substrate oxidation reactions and stimulation of the proton leak reactions) and its secondary effects (lowering of dp and consequent decrease in the rate of ATP synthesis). These results provide a context within which previous studies can be assessed. Cadmium is known to inhibit respiration [2-4, 171 and particular enzymes such as the cytochrome bc, complex that are part of our substrate oxidation subsystem [ 181. It also inhibits substrate transport [19], NADH-dependent enzymes [20] and succinate dehydrogenase [21] that were not part of this subsystem under our conditions, but could become so if different substrates were used. Other heavy metals such as mercury and lead are also known to inhibit different enzymes of this subsystem [2, 22-25]. Cadmium is also known to uncouple mitochondria, in other words to increase the proton leak reactions [2-4, 26,271, particularly at higher concentrations [18]. Both of these effects are compatible with our observations of inhibited substrate oxidation and stimulated proton leak, although the results cannot be compared directly because previous workers did not buffer the free cadmium concentration to known values as we have done. If cadmium inhibits reactions within the phosphorylation subsystem as mercury does [22], our work shows that such inhibition would be of no consequence for system behaviour under our conditions. It is important to note that our specific conclusions about the effects of cadmium apply only to the system that we have investigated ; namely isolated mitochondria respiring on an excess of NADH. The effects of cadmium on mitochondria might differ in vivo. First, it is not clear for any plant tissue how strongly mitochondria control the overall oxygen consumption rate and other fluxes, or the ATP/ADP ratio. Secondly, we have not analysed conditions where substrate availability is limiting, as it may be in vivo, and we have used NADH as substrate rather than the more physiological pyruvate and malate. We conclude that top-down regulation analysis is easy to apply and is extremely powerful for the investigation of the effects not only of cadmium or heavy metals, but of any environmental pollutant or toxic compound on oxidative phosphorylation. It therefore has potential as a standard method for toxicological or ecological research. Further, the method can be extended to more physiological conditions such as the action of external effectors on cells or cellular respiration, where the external effectors might be toxic compounds or effectors of physiological relevance, such as hormones or calcium. This work was supported by the European Science Foundation (ESF Research Fellowship in Toxicology (Ref. no. RF/93/7/E) to A. K.). This investigation was initiated as an integrated part of a research project on the impact of heavy metals on plants in the laboratory of Prof. K. Brinkmann (Abteilung fur Experimentelle Okologie, Universitat Bonn, Germany) and was partially supported by the Deutsche Forschungsgemeinschaft (Br ). REFERENCES 1. Kesseler, A. & Brand, M. D. (1994) Localisation of the sites of action of cadmium on oxidative phosphorylation in potato tuber mitochondria using top-down elasticity analysis, Eur J. Biochem. 225, Brierley, G. P. (1977) Effects of heavy metals on isolated mitochondria, in Biochemical effects of environmental pollutants (Lee, S. D., ed.) pp , Ann Arbor Science Publications, Ann Arbor. 3. Byczkowski, J. Z. & Sorenson, J. R. J. (1984) Effects of metal compounds on mitochondria1 function: a review, Sci. Total Environ. 37, Miller, R. J., Bittell, J. 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