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MITOCHONDRIAL MODELING AND FUNCTION
Faculty of Biotechnology, Jagiellonian University, Crakow, Poland
Submitted 17 February 2006 ; accepted in final form 2 June 2006
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ABSTRACT |
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 TOP ABSTRACT THEORETICAL PROCEDURESTHEORETICAL RESULTSDISCUSSIONREFERENCES |
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respiration rate; parallel activation; oxidative phosphorylation; metabolic control analysis; flux control coefficient; muscle contraction
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With the first mechanism, which will be called the output-activation mechanism, only ATP usage (output of the system) is directly activated by calcium ions during muscle work, whereas oxidative phosphorylation is activated only indirectly, through negative feedback involving increase in [ADP] (and [Pi]). It was originally postulated by Chance and Williams (4, 5) that the dependence of the respiration rate (
O2) on ADP concentration is hyperbolic (first order at low ADP concentrations). Jeneson et al. (19) modified this proposal and postulated that the mechanistic O2/[ADP] dependence is much steeper, at least second order. The output-activation mechanism is presented in Fig. 2A.
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Theoretical studies by means of the computer model of oxidative phosphorylation in skeletal muscle mitochondria and intact skeletal muscle developed previously (35, 36) led to the conclusion that only a direct activation by some cytosolic factor of all oxidative phosphorylation enzymes is able to account for large changes in O2 and ATP turnover accompanied by only very moderate increase in ADP concentration during rest-to-work transition in skeletal muscle (26–29). This mechanism, called the each-step-activation mechanism or parallel-activation mechanism is presented in Fig. 2C. Within this mechanism the feedback regulation via [ADP] and [Pi] plays only a minor, fine-tuning role in intact skeletal muscle in vivo (26, 29) and essentially no role in intact cardiac muscle (33).
It has been shown that the each-step-activation mechanism is able to explain many, apparently unrelated, kinetic properties of oxidative phosphorylation in skeletal muscle (26–29, 37). These properties comprise the relative stability of [ADP], [Pi], phosphocreatine/creatine (PCr/Cr), NADH/NAD+, and protonmotive force (
p) during rest-to-work transition (26, 27), the much steeper phenomenological O2/[ADP] relationship in intact skeletal muscle than in isolated muscle mitochondria (26, 27), the two to five (to seven) times greater maximum oxygen consumption in intact human skeletal muscle than in isolated mitochondria, skinned fibers, or muscle homogenate when scaled for the amount of mitochondrial proteins (36, 44, 52), the increase in the relative slope of the phenomenological O2/[ADP] relationship as a result of muscle training (37), the greater O2 at a given [ADP] and amount of mitochondrial protein in trained muscle than in untrained muscle and in untrained muscle than in hypothyroid muscle (29), the asymmetry of the half-transition time for [PCr] between the on transient (rest-to-work transition) and off transient (work-to-rest transition) (29), and the PCr recovery overshoot (29, 39). In addition, there is a great variability of the kinetic properties of oxidative phosphorylation in different muscles and various experimental conditions (29). To explain this variability, it was proposed that the intensity of the each-step activation is highest in oxidative skeletal muscle, medium in glycolytic skeletal muscle under physiological conditions, and low or absent in perfused glycolytic muscle stimulated electrically (29) (therefore, in the last case, the output-activation mechanism predominates). Recently, it was also postulated (33) that the each-step-activation mechanism is responsible for the almost perfect stability of several oxidative phosphorylation metabolites (ADP, PCr, Pi, NADH) between steady-states with very different work intensities and oxygen consumption rates (2, 14, 21, 50). The differences in the regulation of oxidative phosphorylation between skeletal muscle and heart are discussed in Ref. 33. Generally, the idea of the each-step activation in both skeletal muscle and heart seems to be well founded.
As to glycolysis, it also has been postulated that the regulation of this process by intermediate metabolites ADP, AMP, ATP, Pi, NADH, and NAD+ (plus activation of glycogen phosphatase by calcium ions) is not sufficient to account for the kinetic behavior of this pathway in vivo (7) (for instance, ATP supply by anaerobic glycolysis is not significantly activated during anoxia and muscle recovery, when [ADP], [AMP] and [Pi] are elevated). In particular, it has been demonstrated that a direct activation of glycolysis by some external cytosolic factor is necessary to explain the large increase in the glycolytic flux taking place during transition from rest to heavy exercise in skeletal muscle (32).
Frequently the term "regulation of some biochemical pathway" is referred to the mechanism by which the metabolite flux through the pathway is changed in response to some external signal/disturbance. On the other hand, the term "control of the flux" may be attributed to the potential strength with which a given enzyme concentration/activity determines the flux through the entire system (28). The best means of describing the extent to which a given enzyme (or process or metabolic block) controls the metabolite flux through a given metabolic pathway is Metabolic Control Analysis (MCA) (9, 15, 20). According to this theoretical approach, no enzyme determines the flux uniquely (there are no so-called "rate-limiting" steps). The contribution of particular enzymes to the control over the metabolite flux is quantified by a parameter called the flux control coefficient. It is defined as the ratio of the relative change in a given flux caused by a small relative change in the enzyme concentration/activity to this change itself. For enzyme i and flux J we have the following expression:
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Jeneson et al. (18) calculated, based on their experimental data, the flux control coefficients for ATP usage (by actomyosin-ATPase and calcium-ATPase) and ATP production (by oxidative phosphorylation) in an electrically stimulated glycolytic muscle. They concluded that, as in isolated mitochondria in state 3, at higher ATP turnovers (stimulation frequencies >3 Hz) the control over the ATP turnover flux is shifted from ATP consumption to ATP production, and therefore the latter becomes limiting for the flux. However, as discussed above and in Ref. 29, in electrically stimulated glycolytic skeletal muscle there is probably no each-step activation, and therefore only the output-activation mechanism (that is present in isolated mitochondria) is responsible for adjusting the rate of ATP production to the current energy demand in this case.
The aim of the present theoretical study is to analyze the effect of the each-step-activation (parallel activation) mechanism that was postulated to take place in oxidative and glycolytic skeletal muscle under physiological conditions (neurally stimulated muscle in vivo) (29) on the distribution of control over the oxygen consumption flux among ATP usage, substrate dehydrogenation, and particular oxidative phosphorylation complexes at different work intensities. It is demonstrated that each-step activation allows maintenance of more or less constant values of the flux control coefficients of particular steps over a very broad range of energy demand, and therefore ATP usage may remain the main controlling step even at very high ATP turnovers. It is also shown that at low oxygen concentrations, the oxidative phosphorylation system (in particular, cytochrome oxidase) takes over most of the control and becomes limiting for the ATP turnover and oxygen consumption flux. Overall, the present in silico study strongly suggests that under physiological conditions, the availability of oxygen, and not potential capacity of oxidative phosphorylation for ATP synthesis, may determine the maximal respiration rate, ATP turnover, and mechanical work intensity in oxidative skeletal muscle.
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THEORETICAL PROCEDURES |
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TOPABSTRACTTHEORETICAL PROCEDURESTHEORETICAL RESULTSDISCUSSIONREFERENCES |
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-oxidation, fatty acid transport), complex I, complex III, complex IV (cytochrome c oxidase), proton leak, ATP synthase, ATP/ADP carrier, phosphate carrier, adenylate kinase, creatine kinase, and ATP usage. The dependences of the rates of particular reactions, processes, and/or metabolic blocks on different metabolite concentrations are described by appropriate kinetic equations. For instance, the rate of the reaction catalyzed by cytochrome oxidase (complex IV) vC4 is expressed as follows:
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benio/. The model has been validated for a broad range of different parameter values and system properties in both isolated mitochondria and intact skeletal muscle and heart (24, 26, 28, 29, 33, 36). In the context of the present study, particularly important is the fact that the model reproduces correctly the inhibitor titration curves and flux control coefficients for particular oxidative phosphorylation complexes in state 3 in isolated mitochondria, where oxidative phosphorylated is saturated, and the metabolic control is distributed more or less uniformly between different enzymes (35).
In the first part of the study, the dependence of fluxes, metabolite concentrations, and flux control coefficients on energy demand for constant saturating oxygen concentration (240 µM) were investigated. In computer simulations, the energy demand (rate constant of ATP usage) was increased n times in relation to the resting state; in subsequent simulations, n increased by 1, from 1 (no activation) to 100. In the case of the output-activation mechanism, only ATP usage was directly activated. In the case of the each-step-activation mechanism, all oxidative phosphorylation complexes and substrate dehydrogenation were directly activated in parallel with the activation of ATP usage. The direct activation of particular oxidative phosphorylation complexes was equivalent to an increase in the rate constants (or maximal velocities) of these steps. High intensity of the each-step activation was used; this means that all steps in the ATP-producing block were activated n0.4 times when ATP usage was activated n times. The power coefficient equal to 0.4 was chosen to ensure that a large relative increase in O2 during rest-to-work transition is accompanied by only a moderate relative increase in [ADP]; if this coefficient equals zero, then the phenomenological O2/[ADP] relationship becomes near hyperbolic (first order at low ADP concentrations), and if it is much higher than 0.4, then the relative increase in [ADP] becomes very small. In each simulation, the system stabilized at a new, active steady state that was verified using an appropriate numerical procedure, checking that the rates of changes in variable values were below some assigned, very low rate. The fluxes and metabolite concentrations in the active steady state were recorded, and the values of flux control coefficients were calculated according to Eq. 1. Rate constants/maximal velocities of particular steps were increased by 0.01%, and the resultant relative changes in the oxygen consumption and ATP turnover flux between the original and the new steady state were recorded. The summation theorem of MCA was used to validate the calculated flux control coefficients. The maximal error for the sum of flux control coefficients was <0.001.
In the second part of the study, the dependence of fluxes, metabolite concentrations, and flux control coefficients on oxygen concentration for relative energy demand of 100 was investigated. Simulations were performed, assuming the each-step-activation mechanism (parallel activation of all oxidative phosphorylation complexes 1000.4 times in the active state). [O2] ranged from 240 to 0.01 µM; in each subsequent simulation, [O2] was lower by 3% in relation to the previous simulation. For each oxygen concentration, a new steady state was achieved; fluxes and metabolite concentrations were recorded, and flux control coefficients were calculated as discussed above.
Some other models of oxidative phosphorylation in skeletal muscle have been proposed. The model developed by Meyer (42), involving a simple linear dependence of ATP production by oxidative phosphorylation on [Cr], represents the output-activation mechanism and therefore is applicable only to perfused glycolytic muscle stimulated electrically (see text above and below, as well as Ref. 29). In addition, the linear phenomenological dependence on [Cr] can be derived from the more mechanistic near-hyperbolic dependence of oxidative phosphorylation on [ADP] (23, 36). The model developed by Connett and colleagues (6, 7) is also very phenomenological (it simply relates [ATP], [ADP], [AMP], [Pi], [PCr], and [Cr] to each other at different energy demands via the creatine kinase and adenylate kinase equilibrium) and implicitly assumes the output-activation mechanism. Both models treat oxidative phosphorylation as a black box, and therefore they do not analyze the internal properties of the system and, in particular, do not calculate the flux control coefficients of particular enzymes. They ignore the proton leak through the inner mitochondrial membrane and therefore do not distinguish between the oxygen consumption flux and ATP turnover flux. For all these reasons, although the discussed models provided a better understanding of several quantitative properties of oxidative phosphorylation in skeletal muscle, they could be used for only a limited set of theoretical studies.
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THEORETICAL RESULTS |
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TOPABSTRACTTHEORETICAL PROCEDURESTHEORETICAL RESULTSDISCUSSIONREFERENCES |
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O2 and metabolite concentrations at different energy demands (rate constants of ATP usage) for the output-activation mechanism (A) and the each-step-activation mechanism (B). The energy demand is expressed as a multiplicity of the rate constant of ATP usage at rest (the resting ATP usage equals 0.73 mM/min; its contribution to the respiration rate at rest is 40%, with the remaining 60% being due to proton leak). One can see that in the case of output activation, the oxygen consumption increases linearly with ATP demand up to the relative energy demand of about 30 and then remains constant (ATP production by oxidative phosphorylation becomes saturated). The maximal O2 reaches 3.7 mM/min. This value corresponds well with the maximal oxygen consumption in isolated mitochondria, skinned fibers, and muscle homogenate (when recalculated for the amount of mitochondrial proteins) but is much smaller than the maximal O2 in intact skeletal muscle, amounting to 7–16 (to 26) mM/min (1, 3, 36, 44, 52). On the other hand, each-step activation allows a linear increase in O2 in the whole simulated range of ATP demand. The O2 reaches >12 mM/min at a relative energy demand of 100 (the maximum value shown in Fig. 3) and can increase much more (up to 30 mM/min for [PCr] = 1 mM or up to 38 mM/min for very low [PCr]) at higher energy demands (not shown).
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When the energy demand (rate constant of ATP usage) increases, the metabolite concentrations are much more constant in the case of the each-step-activation mechanism than in the case of the output-activation mechanism. In the latter case (Fig. 3A), metabolite concentrations change significantly up to the "critical" relative energy demand of 30: [PCr] drops to zero, whereas [Cr] and [Pi] rise to the maximal values (35 mM and 38 mM, respectively). [ATP] is relatively constant up to the relative energy demand of 27 because of a high ATP/ADP ratio and then begins to fall to zero. [ADP] increases to 1.6 mM and then decreases, whereas [AMP] starts to increase; this is caused by the reaction catalyzed by adenylate kinase. [ATP] decreases below the Km constant of ATP usage for ATP, and therefore a further increase in the rate constant of ATP usage does not cause a further acceleration of ATP hydrolysis.
In the case of the each-step-activation mechanism, much more moderate changes in metabolite concentrations with an increased energy demand take place. There is no critical point at which concentrations achieve zero or maximal values (in fact, this critical point is present at much higher values of ATP demand than 100; see above and DISCUSSION). [ATP] is essentially constant in the whole range of energy demand analyzed. [AMP] remains at very low values, whereas [ADP] increases 10-fold between an energy demand of 1 (rest) and an energy demand of 100, from 7 to 68 µM. [Cr] and [Pi] increase to 24 and 18 mM, respectively, whereas [PCr] decreases to 11 mM. At an energy demand of 100 there is still some "reserve" of ATP and PCr, and [ADP] also does not reach the maximal value encountered in intact skeletal muscle (over 100 µM). Therefore, a further increase in energy demand (above 100) can still cause a further increase in O2 and ATP turnover, as discussed above. It is worthwhile to emphasize that the each-step-activation mechanism allows a much better ADP homeostasis at varying energy demand than the output-activation mechanism.
It seems to be interesting to compare what factors cause the increase in O2 brought about by an increase in ATP demand in the output-activation mechanism and the each-step-activation mechanism. There are four potential signals transducing this stimulation of O2: increase in [ADP], increase in [Pi], decrease in [ATP], and direct each-step-activation. Figure 4 presents the simulated contribution of these signals for both mechanisms at different energy demands. The increase in O2 accompanying an increase in relative ATP demand by 0.01 is shown. The increase in O2 caused by a given signal (S) is a product of two things: relative change in this signal intensity when relative ATP demand increases (dS for an increase in relative ATP demand by 0.01) and the sensitivity of O2 to this signal intensity (dO2/dS). In computer simulations, the values of dS for particular signals and the total dO2 when the system passed from an old to a new steady state because of an increase in relative energy demand by 0.01 were recorded first. Next, the old steady state was restored and the "new" value of one signal S was set, while "old" values of the remaining signals were kept. The increase in O2 (dO2) caused by a change in S was recorded. This procedure was repeated for all signals. Of course, the total increase in O2 is the sum of the increases caused by particular signals.
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O2 is slightly lower than at higher (but before saturation) work intensities because of a significant contribution (up to 60% in rest) of proton leak to O2 at low work intensities. Namely, an increase in relative energy demand decreases p and thus decreases proton leak, which leads to a partial compensation of the increase in O2 caused by an elevated energy demand.
On the other hand, in the each-step-activation mechanism, almost half of the O2 stimulation is transduced by direct parallel activation of particular oxidative phosphorylation steps, the contribution of an increase in [ADP] to the O2 stimulation is very similar to the contribution of direct activation, and the contribution of an increase in [Pi] is below 10%, whereas a decrease in [ATP] plays essentially no role. Therefore, in the each-step-activation mechanism, about half of the stimulation of O2 is due to the increase in [ADP] and [Pi], whereas the remaining half is due to the direct activation of oxidative phosphorylation.
Figure 5 presents the simulated pattern of metabolic control of particular components of the oxidative phosphorylation system over the oxygen consumption flux (A) and ATP turnover flux (B) at different energy demands (between 1 and 100) in the case of the output-activation mechanism. It can be seen (Fig. 5A) that at rest (relative energy demand 1), the proton leak through the inner mitochondrial membrane has the highest control over O2 (flux control coefficient equal to 0.48); this is due to the fact that 60% of oxygen consumption in skeletal muscle at rest is due to proton leak (45, 46). ATP usage keeps 35% of the control, and the remaining 17% is shared among particular oxidative phosphorylation complexes and substrate dehydrogenation. As the energy demand increases, most of the control (over 90%) is taken over by ATP usage. However, when oxidative phosphorylation becomes saturated at an energy demand of 30, the flux control coefficient of ATP usage over oxygen consumption falls to zero and the control becomes distributed more or less uniformly (flux control coefficients are of the same order of magnitude) between oxidative phosphorylation complexes and substrate dehydrogenation.
The distribution of control over ATP turnover (Fig. 5B) is rather similar to that over O2. The main difference is that near the resting state, essentially all the control over ATP production/consumption is kept by ATP usage, whereas proton leak, oxidative phosphorylation, and substrate dehydrogenation possess almost no control.
Figure 6 presents the simulated pattern of control over oxygen consumption (A) and ATP turnover (B) in the case of the each-step-activation mechanism. In the vicinity of the resting state, the distribution of control is essentially the same as for the output-activation mechanism. However, when the relative energy demand progressively increases up to 100, ATP usage continues to keep almost 100% of the control over both O2 and ATP production/consumption, whereas the control exerted by other steps is essentially 0%. Therefore, the control is not taken over by ATP-producing processes even at high values of energy demand.
Figure 7 presents the simulated dependence of O2 and metabolite concentrations on (extracellular) oxygen concentration at high relative energy demand equal to 100 (the rightmost point in Figs. 3–6) in the case of the each-step-activation mechanism. As shown, O2 is essentially insensitive to oxygen concentration over a very broad range and begins to fall when [O2] decreases below 3 µM. Under the simulated conditions, the half-saturating extracellular [O2] for the respiration rate is slightly greater than 1 µM. However, several metabolite concentrations, including [ADP], [Pi], [PCr], and [Cr] (and also NADH/NAD+, reduction level of cytochrome c, and p; not shown, see Ref. 25) start to change at much higher oxygen concentrations. These changes represent the response of the system to low [O2]; they lead to an activation of particular components of the system that counteracts the inhibition of the system caused by a decrease in oxygen concentration. As a result, the respiration rate decreases much less than it would in the absence of changes in intermediate metabolite concentrations, and the phenomenological (apparent) half-saturation constant of oxidative phosphorylation for oxygen is much smaller than the mechanistic Michaelis-Menten constant of cytochrome oxidase for oxygen (see below) (25, 55). At [O2] equal to 3 µM, the capacity of oxidative phosphorylation for ATP production becomes exhausted and a critical point (analogous to the critical point in energy demand at the output-activation mechanism) appears, below which [PCr] and [ATP] fall to zero, [Cr] and [Pi] rise to the maximal values, and [ADP] first rises and then decreases, being progressively converted to AMP by adenylate kinase (as a consequence, essentially all adenine nucleotides are in the form of AMP).
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p and reduction level of cytochrome c; reduction level of cytochrome a3 is a function of these variables) Michaelis-Menten constant of cytochrome oxidase for oxygen (compare Eq. 2) is much greater (120 µM) than the phenomenological half-saturation constant of oxidative phosphorylation for oxygen. The difference is due to the compensation of the decrease in oxygen concentration by an increase in the reduction level of cytochrome c and decrease in p (25, 28). It should be also stressed that the value of the apparent (phenomenological) half-saturation constant depends on the relative energy demand; it is slightly greater than 1 µM for a relative energy demand of 100 (see Fig. 7) but drops to 0.8 µM at a relative energy demand of 50. At relative energy demands lower than 100, the simulated changes in metabolite concentrations (for instance, in the reduction level of cytochrome c and in p) between normoxic and anoxic conditions are higher, because at high oxygen concentrations they are more different from their "final" values for saturated (because of high ATP usage and/or low [O2]) oxidative phosphorylation (simulations not shown).
Figure 8 shows the simulated dependence of the distribution of metabolic control over O2 on oxygen concentration for relative energy usage of 100 in the case of the each-step-activation mechanism. One can see that above the critical oxygen concentration of 3 µM ATP usage keeps almost all the control, whereas below this oxygen concentration the entire control is quickly taken over by cytochrome oxidase (complex IV of the respiratory chain), the enzyme for which O2 is a substrate. Therefore, at low oxygen concentrations, an increase in energy demand (rate constant of ATP usage) cannot further elevate the oxygen consumption (and ATP turnover) flux.
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DISCUSSION |
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TOPABSTRACTTHEORETICAL PROCEDURESTHEORETICAL RESULTSDISCUSSIONREFERENCES |
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O2 and ATP production/consumption flux. In addition, the question was addressed as to how evenly the metabolic control over the flux is distributed between particular oxidative phosphorylation complexes when ATP production by oxidative phosphorylation becomes saturated, and therefore how many complexes must be directly activated to cause a great increase in the flux. Finally, we analyzed how low oxygen concentration affects the pattern of metabolic control and therefore how it can determine the maximal respiration rate and ATP turnover in skeletal muscle. First of all, computer simulations demonstrated (Fig. 3) that the each-step-activation mechanism helps to maintain much more constant metabolite concentrations in a much wider range of energy demand than the output-activation mechanism does. This is very important for the distribution of the metabolic control, because as long as ATP concentration is much higher than the Km constant of ATP usage for ATP (equal to 150 µM within the model) and therefore ATP usage is essentially saturated with ATP, this process will keep most of the control (within Metabolic Control Theory, flux control coefficients are inversely proportional to elasticity coefficients quantifying the sensitivity of the reaction rate to metabolite concentrations). When [ATP] drops to values similar to or lower than the Km constant of ATP usage for ATP, the rate of ATP usage becomes strongly dependent on [ATP] and other processes take control over the flux. Of course, [ATP] is related to [ADP], [AMP], [Pi], [PCr], [Cr], and other metabolite concentrations, and therefore a possibly high constancy of these concentrations in relation to low-work concentrations is crucial for maintaining a high value of the flux control coefficient of ATP usage. This in turn enables a further increase in the oxygen consumption and ATP turnover flux when the rate constant of ATP usage (energy demand) is increased.
Figure 3 demonstrates that the each-step-activation mechanism causes a much greater maximal increase in the flux than the output-activation mechanism and, at the same time, only moderate changes in [ADP]. As a result, the phenomenological O2/ADP relationship is much steeper here, and the maximal O2 (when recalculated for the amount of mitochondrial proteins) is much larger than in isolated mitochondria (8, 16, 19, 36, 52).
Comparison of Fig. 6B with Fig. 5B shows that in the case of the each-step-activation mechanism, ATP usage keeps almost 100% of control over ATP turnover in the whole range of energy demand, whereas in the case of the output-activation mechanism, the control is taken over by oxidative phosphorylation complexes and substrate dehydrogenation above the critical energy demand of 30. The situation is similar for the control over the oxygen consumption flux (Figs. 5A and 6A), except that the proton leak exerts substantial control in the near vicinity of the resting state, as found in experimental studies by Rolfe and Brand (45). The critical energy demand is also the point where [ATP] falls very close to zero and other metabolite concentrations quickly change and reach their final (high energy demand) values.
When oxidative phosphorylation becomes saturated above the energy demand of 30 in the case of the output-activation mechanism, the control is shared more or less evenly (flux control coefficients are of the same order of magnitude) by particular oxidative phosphorylation complexes, and the flux cannot be further increased by elevating energy demand (rate constant of ATP usage) (Fig. 5). Figure 6 demonstrates that the flux can be easily further increased (above the critical energy demand for output activation) if all oxidative phosphorylation complexes and substrate dehydrogenation are directly activated by some cytosolic factor in parallel with the activation of ATP usage, and therefore the flux control coefficient for ATP usage continues to be close to unity. However, the question arises as to whether it is necessary to activate directly all oxidative phosphorylation complexes or whether it would be enough to activate only some of them, or even only the substrate dehydrogenation system. The answer to this question lies in the pattern of control in the "saturated state" (an equivalent of state 3 in isolated mitochondria). Namely, if most of the control were kept by a few (or maybe only one) step(s) of the ATP-producing system, it would suffice to activate directly just those few (or one) step(s). On the other hand, if, as in the case presented in Fig. 5, the control is distributed more or less uniformly among all steps (for no step, its flux control coefficient is very close to zero), all these steps must be directly activated to account for the increase in O2 and [ADP] during rest-to-work transition in skeletal muscle encountered in experimental studies (if even one step is not directly activated, the activation of other steps would increase its flux control coefficient to near 1). The model used in the present study was extensively tested for the values of flux control coefficients of particular oxidative phosphorylation complexes in state 3 in isolated skeletal muscle mitochondria (35). It has been demonstrated that only the activation of all steps (each-step activation) can account for the behavior of the system in intact skeletal muscle during rest-to-work transition (26). A similar situation prevails in intact heart in vivo, where only a well-balanced parallel activation of ATP usage, substrate dehydrogenation, and all oxidative phosphorylation complexes is able to explain (33) the perfect stability of [ADP], [Pi], PCr/ATP, and NADH/NAD+ during low-to-high work transition (2, 14, 21, 50). Fell and Thomas (10) demonstrated in a more abstract and general way (within the frame of their "multisite modulation" concept) the necessity of the direct activation of many steps to increase significantly the flux when the control is distributed. Generally, in some important sense, the idea of each-step activation or multisite modulation can be regarded as a direct consequence of the theoretical and experimental development of MCA (9, 15, 20).
Figures 7 and 8 show that at low extracellular oxygen concentration (<3 µM), [ATP] falls to zero and the control over the flux is shifted from ATP usage to oxidative phosphorylation (in particular, cytochrome oxidase) [such an effect of low oxygen concentration was first predicted theoretically (34) and then confirmed experimentally (54)]. The effect of low oxygen concentration is in a sense opposite to the effect of each-step activation (see Figs. 3A and 5).
It has been postulated that the intensity of the each-step-activation (parallel activation) is high in oxidative skeletal muscle under physiological conditions, moderate in glycolytic (but mitochondria rich, containing type IIA fibers) muscle under physiological conditions, and low or nonexistent in electrically stimulated perfused glycolytic muscle (29). The simulations performed in the present study concern mostly the first case, high each-step activation in oxidative skeletal muscle in vivo stimulated neurally (voluntary exercise). As shown in Fig. 3B, this mechanism offers a possibility of a very high increase in the oxygen consumption (and ATP turnover) flux up to very high values. In fact, computer simulations show that for a relative energy demand of 200, O2 increases to 24 mM/min (and [PCr] decreases to 3.4 mM), and for a relative energy demand of 250, O2 increases to 30 mM/min (and [PCr] decreases to 1 mM), whereas for the saturating (in the case of high each-step activation) relative energy demand equal to 370, O2 reaches 38 mM/min (and [PCr] drops to near zero). The maximal O2 in human skeletal muscle equals 16 mM/min in single muscle exercise (1, 3, 36, 48) [in one experiment, the value of 26 mM/min was obtained (44)] and is about twice as low in whole body exercise (e.g., cycling) (36, 48, 52). One possible explanation of this difference in humans can be a limitation of oxygen transport by blood (48), leading to a decrease in muscle oxygen concentration and thus to limitation of the respiration rate (compare Figs. 7 and 8). On the other hand, it has been postulated that in quadrupeds, this limitation of the cardiovascular system does not exist (47, 49). Therefore, the maximal O2 during single muscle exercise in humans and during whole body exercise in quadrupeds may be simply determined by the maximal rate of ATP usage during sustained exercise by muscles.
It also has been postulated that in quadrupeds, the whole animal maximal sustained oxygen uptake is similar, when recalculated for the mitochondria volume, to the maximal oxygen uptake in isolated mitochondria (17, 49). However, a detailed analysis of the presented experimental data demonstrates that this conclusion is not so straightforward. First, O2 per mitochondria volume during whole body spontaneous exercise in quadrupeds is almost twice that in isolated mitochondria incubated with the "physiological" substrate (product of glycolysis) pyruvate (17, 49) (succinate and, especially, cytochrome c are not physiological substrates of oxidative phosphorylation in skeletal muscle; with both substrates the maximal O2 is overestimated because succinate is an FAD-related substrate that "omits" complex I and the "key," rate-controlling TCA cycle dehydrogenases, whereas reduced cytochrome c is a substrate of cytochrome oxidase, the activity of which is much greater than the activity of entire oxidative phosphorylation; under physiological conditions, cytochrome c is reduced 20–30% and not 100%). If it is taken into account that isolated mitochondria are incubated with saturating [ADP], [O2], and respiratory substrate concentrations, one can estimate that the "true" capacity of oxidative phosphorylation in quadrupeds during whole body exercise is at least twice greater than in isolated mitochondria. Second, maximal O2 per mitochondria volume in quadrupeds is at least three times greater during spontaneous whole body exercise than during single muscle electrically stimulated exercise (Table 1 in Ref. 17). Both results agree well with our proposal that the presence of each-step activation results in much greater maximal O2 in neurally stimulated muscles than in electrically stimulated muscles or in isolated mitochondria.
The distribution of metabolic control over the ATP turnover flux between ATP supply and ATP usage at different energy demands simulated for the output-activation mechanism, presented in Fig. 5B, is similar to that calculated on the basis of experimental data and their extrapolation by Jeneson et al. (18). The authors demonstrated that in glycolytic skeletal muscle stimulated electrically, ATP usage (actomyosin-ATPase and Ca2+-ATPase) has almost entire control over ATP turnover at low (0.3–2 Hz) stimulation frequency; at moderate (3 Hz) stimulation frequency, half of the control is taken over by ATP supply that becomes an almost fully controlling step (flux control coefficient 0.9) at high (10 Hz) stimulation frequency. In fact, the experimental data obtained covered the range of stimulation frequency between 0.3 and 1.8 Hz, whereas the flux control coefficients for higher frequencies were calculated using a simple kinetic model developed by the authors. It can be estimated on the basis of the experimental data presented in Tables 1–3 in Ref. 18 that ATP turnover increases 20 times between rest (extrapolation to 0-Hz stimulation frequency) and the maximal stimulation frequency (1.8 Hz), which caused a sustained muscle work in the discussed experimental system (at higher frequencies, muscle work ceased quickly because of fatigue). This finding agrees well with the computer simulations presented in Fig. 3A if it is assumed that muscle becomes fatigued when the ATP/ADP ratio falls below 50. Therefore, in real conditions, muscle ceases to work (because of fatigue) before ATP production takes control over the ATP turnover flux. Generally, it seems that, as has been discussed above and elsewhere (29), there is no each-step activation (parallel activation) in electrically stimulated glycolytic muscle.
Of course, the main criticism that may be addressed to the each-step-activation mechanism is that the physical nature of the factor/mechanism X that activates in parallel all oxidative phosphorylation complexes is somewhat unclear. From among the known factors, some mechanism involving calcium ions remains the most attractive candidate. Because high constant [Ca2+] only moderately activates isolated mitochondria (22, 43), it has been postulated (27) that the relevant factor may be the frequency of calcium oscillations. This frequency could be integrated over time by some protein, analogous to calmodulin, that is lost or inactivated during isolation of mitochondria. Recent studies have shown that calcium ions are tunneled from sarcoplasmic reticulum to mitochondria in skeletal muscle (51). Nevertheless, the oxidative phosphorylation complexes, being transmembrane proteins located in the inner mitochondrial membrane, could be potentially activated by cytosolic calcium and therefore would not need the calcium transport to the matrix for their activation. Nevertheless, the postulated activation by some calcium-related mechanism of particular oxidative phosphorylation complexes has not been confirmed yet experimentally and therefore remains only a hypothesis. It also has been proposed (29) that some hormones could play an important role in the each-step activation.
Several targets of parallel activation in the substrate dehydrogenation block are known. It is widely recognized that calcium ions activate TCA cycle dehydrogenases and glycogen phosphorylase. There is also strong evidence that skeletal muscle contraction causes a AMP- and PKA-mediated activation of fatty acid oxidation and glucose uptake (56).
Rolfe et al. (46) demonstrated that during rest-to-work transition in skeletal muscle, the p-producing subsystem and p-consuming subsystem are directly activated to a very similar extent. Generally, a well-balanced parallel activation of the production and consumption of some metabolite M (where M can be ATP/ADP, p, NADH/NAD+, or reduction level of cytochrome c) was demonstrated for neural and hormonal stimulation of hepatocytes, skeletal muscle, and heart within the so-called Proportional Activation Approach (31).
Nevertheless, the factor/mechanism that directly activates all oxidative phosphorylation complexes during muscle contraction still awaits to be discovered experimentally. Therefore, computer modeling and the each-step-activation idea offer a unique opportunity to predict the existence of some new, still undiscovered phenomena. It is common in physics that some objects/phenomena are first predicted theoretically and then discovered experimentally; positon (antiparticle of electron), gravitational lens, and quark t may serve as just a few examples. On the other hand, such a prediction would be an exciting and novel achievement in biology.
The limitation of the present study is that it does not take into account several processes and phenomena that can affect to some extent the pattern of metabolic control, especially at high skeletal muscle work intensities. These processes/phenomena comprise anaerobic glycolysis, downregulation of ATP usage, AMP deamination, slow component of the oxygen uptake kinetics, cytosol acidification, and so on. On the other hand, the present study is focused on the control of oxidative phosphorylation and concerns mostly the oxidative skeletal muscle, whereas most of the mentioned processes and phenomena occur primarily in the glycolytic skeletal muscle. Nevertheless, it would be interesting to analyze in the future the control of the mentioned processes and phenomena over the oxygen consumption and ATP turnover flux.
The present study does not take into account the diffusion limitations and displacement of creatine kinase from thermodynamic equilibrium postulated by the Saks group [see e.g., Ref. 53]. In our opinion, the magnitude of these phenomena in the muscle in vivo is not great, as discussed elsewhere (33), and our model is able to reproduce correctly the behavior of the system without involving them (29, 38).
Of course, in skeletal muscle (especially glycolytic skeletal muscle), the maximal rate of ATP supply is determined not only by the rate of ATP production by oxidative phosphorylation but first of all by the rate of ATP synthesis by anaerobic glycolysis and (in the initial stage of exercise) by creatine kinase. Therefore, the theoretical results presented in the present article concern only the rate of oxygen consumption and oxidative ATP production.
In summary, the present theoretical study demonstrates that the each-step-activation mechanism of the regulation of oxidative phosphorylation during muscle contraction has a great impact on the control exerted by particular elements of the ATP supply-demand system over the oxygen consumption and ATP turnover flux in skeletal muscle. Namely, this mechanism prevents the shifting of metabolic control from ATP usage to oxidative phosphorylation complexes when the energy demand (rate constant of ATP usage) increases. As a consequence, O2 and oxidative ATP production may potentially increase to very high values, even higher than those observed under physiological conditions in skeletal muscle. It is also shown that at low oxygen concentrations, the control over the flux is shifted from ATP usage to cytochrome oxidase, which prevents a further increase in O2 and ATP turnover caused by an increase in energy demand. Therefore, it is concluded that in skeletal muscle, especially in oxidative skeletal muscle where the each-step-activation is highest, it is not the potential capacity of oxidative phosphorylation but oxygen delivery by blood that determines the maximal oxygen consumption, oxidative ATP production, and sustained work intensity.
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