Phosphocreatine kinetics at the onset of contractions in skeletal muscle of MM creatine kinase knockout mice

Brian B. Roman1, Ronald A. Meyer2, and Robert W. Wiseman2

1 Department of Cardiology, University of Illinois Medical Center, Chicago, Illinois; and 2 Molecular Imaging Research Center, Departments of Physiology and Radiology, Michigan State University, East Lansing, Michigan 48824


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

Phosphocreatine (PCr) depletion during isometric twitch stimulation at 5 Hz was measured by 31P-NMR spectroscopy in gastrocnemius muscles of pentobarbital-anesthetized MM creatine kinase knockout (MMKO) vs. wild-type C57B (WT) mice. PCr depletion after 2 s of stimulation, estimated from the difference between spectra gated to times 200 ms and 140 s after 2-s bursts of contractions, was 2.2 ± 0.6% of initial PCr in MMKO muscle vs. 9.7 ± 1.6% in WT muscles (mean ± SE, n = 7, P < 0.001). Initial PCr/ATP ratio and intracellular pH were not significantly different between groups, and there was no detectable change in intracellular pH or ATP in either group after 2 s. The initial difference in net PCr depletion was maintained during the first minute of continuous 5-Hz stimulation. However, there was no significant difference in the quasi-steady-state PCr level approached after 80 s (MMKO 36.1 ± 3.5 vs. WT 35.5 ± 4.4% of initial PCr; n = 5-6). A kinetic model of ATPase, creatine kinase, and adenylate kinase fluxes during stimulation was consistent with the observed PCr depletion in MMKO muscle after 2 s only if ADP-stimulated oxidative phosphorylation was included in the model. Taken together, the results suggest that cytoplasmic ADP more rapidly increases and oxidative phosphorylation is more rapidly activated at the onset of contractions in MMKO compared with WT muscles.

skeletal muscle energetics; metabolic modeling; phosphorus nuclear magnetic resonance spectroscopy; phosphocreatine


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

CREATINE KINASE CATALYZES the reversible transfer of phosphate between creatine and ATP. Creatine kinase activity is particularly high in mammalian fast-twitch skeletal muscle, in which over 95% of the activity is due to the cytoplasmic MM isoform of the enzyme (24, 25, 29). It is generally accepted that a major functional role of the cytoplasmic creatine kinase system in normal skeletal muscle is the rapid rephosphorylation of ADP generated by actomyosin and calcium ATPases at the onset of contractions (15, 29). However, in addition to this classic ATP/ADP buffering function, it is widely believed that cytoplasmic and mitochondrial creatine kinases are important to the intracellular transport of high-energy phosphate between ATP generating and utilizing sites within muscle cells during steady-state activity (1, 8, 19, 29).

Wieringa and associates (24) have generated mouse strains lacking MM creatine kinase, as well as strains lacking the sarcomeric mitochondrial isoform (23), both muscle isoforms (22), or substituting mutated (25) or brain (18) isoforms for the normal MM isoform. The most obvious functional consequence of these manipulations in skeletal muscle has been characterized as a loss of burst activity (24). Specifically, peak twitch force decreases more rapidly during the first few seconds of repetitive stimulation in those muscles in which total creatine kinase activity was reduced by more than 90% (25). However, mitochondrial content is also increased in muscles of the MM knockout compared with wild-type mice (6, 24, 27). This adaptive change in mitochondrial content has been considered to be prima facie evidence that the creatine kinase system plays an important role in steady-state intracellular ATP transport, as well as a role in buffering adenylate changes at the onset of activity.

Surprisingly, the time course of PCr depletion in muscles of MM creatine kinase knockout (MMKO) mice during stimulation (24) or ischemia (26) was reported to be similar to that in wild-type mice, despite the loss of over 95% of the total creatine kinase activity. However, in those reports, PCr depletion was measured by phosphorous NMR spectroscopic methods with relatively poor time resolution (2 min per spectrum). This study examined PCr depletion after 2 s of twitch stimulation using gated NMR (7, 9). The results show that the initial rate of PCr depletion in creatine kinase deficient muscle is <25% of that in wild-type muscle. Furthermore, modeling of the PCr and adenine nucleotide changes at the onset of stimulation indicates that increases in ADP and oxidative phosphorylation may occur much more rapidly in the knockout compared with normal muscle. These results suggest an alternative functional interpretation for the adaptive increase in mitochondrial content in creatine kinase-deficient muscle.


    METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

Experimental methods. MM creatine kinase knockout (MMKO) (24) and control C57B (WT) mice were housed 3 per cage until the study, which was approved by the University's committee on animal use and care. Mice were anaesthetized with 50 mg/kg sodium pentobarbital (ip) and prepared for in situ stimulation via the sciatic nerve as described previously (17). 31P-NMR spectra (8,000-Hz sweep width, 1K complex data, 8 scans) were acquired at 162 MHz via a 0.5 × 0.8-cm saddle-shaped surface coil placed over the gastrocnemius muscle. Muscles were stimulated at 5 Hz, and isometric twitch force was continuously recorded on a Gould chart recorder and digitized by using a National Instruments analog-to-digital board and Labview software. After acquisition of a fully relaxed spectrum (TR = 15 s, 16 scans) of each muscle at rest, gated acquisitions were obtained 200 ms and 20, 40, 60, 80, 100, 120, and 140 s after a 2-s burst of isometric twitch contractions at 5 Hz (10-11 twitches). After a final 20-s delay, the sequence was repeated for a total of 8 scans per time point. After this gated protocol, nongated, time-averaged spectra (8 scans, TR = 2 s) were acquired from some muscles during 2 min of continuous stimulation at 5 Hz. Free-induction decays were zero-filled to 2K and multiplied by an exponential corresponding to 25-Hz line broadening before Fourier transformation. Relative changes in PCr and ATP were computed by the method of natural line widths (11). Intracellular pH was estimated from the chemical shift of the inorganic phosphate peak as described previously (17).

Modeling methods. Changes in PCr and adenine nucleotides during twitch stimulation of mouse muscle were simulated by using an iterative kinetic model similar to the creatine kinase kinetic model described previously (15, 16), with several modifications. The initial metabolite levels were set assuming the following: ATP 7.5 µmol/g muscle, total creatine 30 µmol/g, cytoplasmic fluid 0.7 ml/g, initial PCr/Cr ratio 2.75, and apparent equilibrium constants for the creatine kinase and adenylate kinase reactions 140 and 1.0, respectively (15). The unidirectional rate constants of the creatine kinase reaction (e.g., E · ADP · PCr right-arrow E · ATP · Cr; see Ref. 15) in WT muscle were set to yield resting unidirectional flux equal to the flux measured in vivo by saturation transfer NMR (7.5 µmol · g-1 · s-1; Ref. 24). For MMKO muscle, these unidirectional rate constants were reduced in proportion to the reported decrease in total creatine kinase activity measured in vitro, i.e., to 2% of that in WT (25). Adenylate kinase activity was modeled assuming a random bi-bi kinetic mechanism analogous to creatine kinase, with resting in vivo unidirectional flux of 1 µmol · -1g · s-1. Although this oversimplifies the kinetics of adenylate kinase (20), this simplification is of no consequence to the results, because the computed net adenylate kinase fluxes were never more than a few percent of unidirectional fluxes, so, in effect, the adenylate kinase reaction was assumed to always be near equilibrium. The increase in muscle ATPase during a twitch contraction was modeled by a function of the form d[ATP]/dt = A · t · exp(-k · t), where t is time after the start of the twitch. The parameter k (50 s-1) set the time at which peak ATPase occurred (20 ms), and the amplitude A set the total ATPase per twitch (integral A/k2 = 0.22 µmol ATP · g muscle-1 · twitch-1). Finally, ATP production by oxidative phosphorylation was assumed to depend instantaneously on cytoplasmic ADP with K50 = 50 µM, Hill coefficient nH = 2.3 (13), and Vmax= 1.0 µmol · g-1 · s-1. A complete description of the calculations is in the APPENDIX.


    RESULTS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

Experimental results. Initial peak twitch force was similar in MMKO vs. WT muscles (Table 1). As reported in previous studies (18, 24, 25), peak twitch force decreased rapidly during the first 2 s of 5-Hz stimulation in MMKO muscles (Fig. 1, Table 1). However, after the first minute of continuous 5-Hz stimulation, there was no significant difference in peak twitch force in MMKO vs. WT muscles (Fig. 1, Table 1). Again, this is similar to the result reported by others in the same transgenic strain (24, 25, 30).

                              
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Table 1.   Peak isometric twitch force before and during stimulation



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Fig. 1.   Time course of changes in peak twitch force (mean ± SE) in MM creatine kinase knockout (MMKO) (filled circles, n = 6) vs. wild-type C57B (WT) (n = 5) gastrocnemius muscles during a 5-Hz stimulation.

As in previous NMR studies (24, 26), there was also no significant difference in PCr/ATP ratio or intracellular pH in WT vs. MMKO muscles before stimulation (Table 2). However, in contrast to previous studies, the gated spectra show that the rate of PCr depletion at the onset of 5-Hz stimulation is dramatically decreased in MMKO vs. WT muscles (Fig. 2). Figure 3 shows the mean relative PCr changes after 2 s of stimulation computed from the gated spectra. Assuming an ATP content of 7.5 µmol/g muscle in both groups (24), these changes correspond to initial PCr hydrolysis rates of 1.08 ± 0.17 vs. 0.23 ± 0.06 (means ± SE, n = 7, P < 0.001) µmol · g-1 · s-1 for WT vs. MMKO muscle, respectively. There was no detectable change in intracellular pH or ATP after 2 s of stimulation in either group. The initial difference in PCr depletion persisted during the first minute of continuous 5-Hz stimulation (Figure 4). However, as expected from previous studies, after 60 s of continuous 5-Hz stimulation, there was no significant difference in PCr depletion (Fig. 4) or intracellular pH (e.g., mean pH during last the 48 s of stimulation was 6.34 ± 0.05 in WT vs. 6.51 ± 0.10 in MMKO).

                              
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Table 2.   Metabolite levels in resting gastrocnemius muscles in situ



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Fig. 2.   Sample spectra acquired during gated protocol. A: WT. B: MMKO. The lowest spectrum in each series was acquired 200 ms after 2-s bursts of twitch contractions at 5 Hz. The remaining spectra were acquired at 20-s intervals during recovery between bursts. PPM, parts per million.



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Fig. 3.   Time course of change in phosphocreatine (PCr) after 2-s bursts of twitch contractions at 5 Hz in MMKO () vs. WT muscles (open circle ) (mean ± SE, n = 7).



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Fig. 4.   Time course of change in PCr during 5-Hz twitch stimulation in MMKO (, n = 6) vs. WT muscle (open circle , n = 5). The points at 2 s are from the gated experiment (Fig. 4). The other points are from ungated time averaged spectra (8 scans, TR = 2) acquired during continuous stimulation for 2.1 min. Values are means ± SE.

Previous studies of normal mammalian skeletal muscles show that PCr depletion is the major source of ATP supply during brief bursts of contractions (7, 9) and, therefore, that the initial rate of PCr depletion can be used to estimate the ATP cost of the contractions. In the WT muscles of this study, the result is 0.22 ± 0.03 µmol ATP · g-1 · twitch-1, which is similar to the ATP cost reported previously for both mouse (17) and rat mixed fast-twitch muscle (7). Peak twitch force did not significantly change in WT muscle during 2 s of stimulation but decreased to 70.9 ± 1.9% of initial (mean ± SE, n = 7) after 2 s in MMKO muscle. Despite this drop, assuming that twitch ATP cost is proportional to peak twitch force, the ATP turnover in the MMKO muscles must have been at least 0.14 µmol · g-1 · twitch-1, or 0.7 µmol ATP · g-1 · s-1, after 2 s of stimulation. Thus net PCr hydrolysis (0.23 µmol · g-1 · s-1) can account for at most one-third of the ATP used in the MMKO muscles during this period. Inasmuch as there was no difference in pH during stimulation of MMKO vs. WT muscles, it is not clear that anaerobic glycolysis can account for this extra 1.0-1.5 µmol/g of ATP production. The two other possible sources of the additional ATP produced in MMKO muscle are net ATP depletion and oxidative phosphorylation. The model described in METHODS was used to explore these possibilities.

Modeling results. Figure 5 shows modeled changes in ATPase, ADP, and AMP during a single twitch in WT vs. MMKO muscles. This calculation assumed total creatine kinase activity in MMKO muscles equal to 2% of that in WT muscles (29) and ignored any potential contribution from oxidative phosphorylation or glycolysis. As expected from the low CK activity, both computed ADP and AMP increase to much higher levels in the MMKO muscle model. Figure 6 shows the extension of this calculation through 2 s of stimulation (10 twitches), assuming the twitch ATP cost in MMKO muscles falls to 71% of that in WT muscles by the end of the 2 s. This calculation fails to match the experimental result in two major respects. First, the calculated decrease in PCr in MMKO muscle at 200 ms after the burst of twitches (7.1% of initial PCr) is over threefold greater than the decrease observed experimentally in MMKO muscle (2.2%). Second, the calculated rise in ADP (>600 µM), and therefore the corresponding decrease in ATP, is unrealistically high in view of the fact that there was no detectable change in the ATP peaks in the gated spectra of either muscle (Fig. 2). These deficiencies in the model cannot be attributed to uncertainty about the true residual creatine kinase activity in the MMKO muscles or to errors in the various binding constants assumed in the calculations. As shown in Fig. 7, if creatine kinase activity >2% of that in WT muscle is assumed, then the computed PCr depletion after 10 twitches approaches that in WT muscle. Thus the model is consistent with the observation that loss of over 50% of total creatine kinase activity had little functional effect in mouse skeletal muscle (25). On the other hand, if creatine kinase activity is reduced to <1% of that in WT so that PCr depletion after 10 twitches matches the observed result in MMKO muscle, then the calculated ADP level (>1.5 mM), and corresponding ATP depletion, become unreasonably high.


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Fig. 5.   Changes in ATPase (A), ADP (B), and AMP (C) during a single twitch in WT and MMKO muscle, ignoring oxidative phosphorylation. MMKO simulation assumes creatine kinase activity is 2% of that in WT simulation.



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Fig. 6.   Changes in ATPase (A), ADP (B), and PCr (C) during a burst of 10 twitches in 2 s, computed as in Fig. 5. MMKO simulation assumes twitch ATPase decreases to 71% of initial by the 10th twitch. Vertical dashed lines correspond to the time at which the first gated spectra were acquired in this study.



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Fig. 7.   Effect of creatine kinase activity (log scale) on cytoplasmic [ADP] (A) and net PCr depletion (B) at 200 ms after a burst of 10 twitches (ATPase decreased to 71% of initial by 10th twitch), computed by using the kinetic model described in METHODS.

Figure 8 shows results of the same model as in Fig. 6 but with the addition of ADP-stimulated oxidative phosphorylation as described in METHODS. This addition has little impact on the computed PCr depletion in the model of WT muscle, because the high creatine kinase activity limits the rise in ADP during this short period. On the other hand, in the model of MMKO muscle, the rise in ADP is instead limited by oxidative phosphorylation, resulting in less drive on the creatine kinase reaction and net PCr depletion 200 ms after the burst comparable to that observed experimentally (2.2%). The use of alternative respiratory control models, for example, with simple Michaelis-Menton dependence of respiration rate on ADP concentration, changed the computed peak ADP in the MMKO model but had no substantive effect on the basic result.


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Fig. 8.   Changes in ATPase (A), ADP (B), and PCr (C) during a burst of 10 twitches in 2 s, computed as in Fig. 6, but with the addition of oxidative phosphorylation as described in METHODS.


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

The main experimental result of this study is that the initial rate of PCr depletion at the onset of stimulation is dramatically decreased in skeletal muscle of MM creatine kinase knockout compared with WT mice. In contrast, previous phosphorus NMR studies found no difference in PCr depletion between MMKO vs. WT muscle during stimulation (24) or ischemia (26). However, in those studies the spectra were the average of scans acquired over 2-min periods. If our results during continuous stimulation (Fig. 4) are averaged over 2 min, there is also no significant difference between PCr depletion in the MMKO vs. WT muscle. Clearly, the residual mitochondrial creatine kinase in the MM knockout muscle is sufficient to support the required net flux after the first minute of 5-Hz stimulation, when ATP is supplied predominantly by glycolysis and oxidative phosphorylation (15), or during ischemia, when the ATPase rate is relatively low (2, 26). On the other hand, PCr is the main source of ATP supply in normal mammalian skeletal muscle during transitions from rest to activity. Therefore, it is during these transitions that the loss of total creatine kinase activity might be expected to have the greatest effect.

The immediate metabolic consequence of muscle activity is hydrolysis of ATP to ADP. Thus the expected effect of creatine kinase deficiency at the onset of contractions is a faster rise in cytoplasmic ADP compared with normal muscle. Unfortunately, free cytoplasmic ADP is low in muscle at rest and cannot be directly measured. Instead, muscle ADP is typically calculated from the assumed equilibrium of the creatine kinase reaction. Of course, this assumption cannot be made in the MMKO muscles. Therefore, we resorted to a kinetic model to estimate the change in ADP at the onset of stimulation. The model includes many assumptions, several of which are open to question. Nonetheless, quantitative comparison of the model with the experimental results leads to the conclusion that an additional source of ATP must be rapidly activated at the onset of contraction in MMKO muscle.

The key assumption of the model calculations is that the ATP cost of twitch contractions scales linearly with peak twitch force in both muscle types. This assumption is based on many previous studies of normal mammalian muscles. For example, both steady-state oxygen consumption and PCr depletion are linearly correlated with twitch rate times peak twitch force within various skeletal muscle types (10, 12, 14). The only chronic adaptation likely to significantly alter the intrinsic ATP cost of contractions is a change in muscle fiber type. However, the fiber type distribution in gastrocnemius muscle of MMKO mice is not significantly different than that in WT mice (24, 28).

The modeling also assumes that the kinetics of creatine kinase in vivo are adequately described by the random bi-bi model of Morrison and Cleland (16). This model includes several enzyme-substrate binding constants, each of which might vary with creatine kinase isoform, species, temperature, pH, or ionic strength. However, any errors introduced by these assumptions are unlikely to alter our basic conclusion for the following reasons. First, in the WT muscle simulation, the computed unidirectional creatine kinase flux always greatly exceeded the net flux so that the reaction was never far from equilibrium. Thus, as shown in Fig. 7, there was no change in predicted PCr depletion after 2 s of stimulation, even if total creatine kinase activity was reduced to <10% of that assumed for WT muscle. Second, no variation in creatine kinase activity alone could reproduce the small PCr depletion observed in the MMKO muscles after 2 s of stimulation. Assuming lower creatine kinase activity necessarily resulted in impossibly high ADP levels and assuming greater activity necessarily resulted in greater net PCr depletion than was actually observed. Therefore, the modeling leads to the inescapable conclusion that another mechanism for ATP generation must have been rapidly activated in the MMKO, but not in the WT, muscle.

In principle, this additional 1.0-1.5 µmol/g of ATP could have been supplied both by anaerobic glycolysis and by oxidative phosphorylation. If supplied entirely by anaerobic glycolysis, this would be accompanied by production of about 1 µmol/g of lactic acid. Assuming an intracellular buffer capacity of 30 Slykes, this should decrease the cytoplasmic pH of the muscle by 0.03 pH units, which is below the limit of detectability at the resolution and signal-to-noise of our gated spectra. Therefore, a contribution of glycolysis to this extra ATP production cannot be ruled out. On the other hand, there is no evidence that acid production is increased in MMKO muscle during longer stimulation protocols. Furthermore, inasmuch as the inorganic phosphate liberated from PCr hydrolysis may play a role in muscle glycogenolysis (4, 5), it could be argued that activation of glycogenolysis is likely to be delayed in MMKO muscle. In any case, it is difficult to model glycolytic flux because there is no satisfactory mathematical model of glycogenolytic and glycolytic control in skeletal muscle (4). In contrast, many studies have examined the relationship between changes in cytoplasmic ADP and muscle oxidative phosphorylation. The higher order control model suggested by Jeneson et al. (13) provides a good operational description of muscle oxidative phosphorylation, independent of its mechanistic interpretation.

After inclusion of oxidative phosphorylation, the kinetic model accurately reproduces the extent of PCr depletion in both WT and MMKO muscle after 2 s of stimulation. This result leads to the clear and testable prediction that the kinetics of oxygen consumption at the onset of contractions will be dramatically faster in MMKO compared with WT. Furthermore, this result suggests an alternative teleological explanation for the adaptive increase in mitochondrial content in muscle of MMKO compared with WT mice: this increase can more effectively substitute for creatine kinase in buffering ATP/ADP changes at the onset of contractions. Therefore, the adaptive increase in mitochondrial content in MMKO muscle provides no prima facie evidence that creatine kinase is also required for intracellular ATP transport during steady-state activity. On the contrary, the fact that there is no deficit in mechanical (Fig. 1) or metabolic (Fig. 4) performance in MMKO muscle after the first minute of stimulation argues that cytoplasmic creatine kinase is not important for steady-state ATP turnover.

The increase in mitochondrial content in MMKO muscle, and also in muscle depleted of total creatine content by chronic feeding of creatine analogs (21), is reminiscent of the well-known increase which occurs during chronic activity, suggesting a common regulatory mechanism. The molecular mechanism(s) which regulates muscle mitochondrial biogenesis and fiber-type plasticity is not fully understood. However, recent evidence indicates that calcium-sensitive regulatory pathways play an important role (3, 31). In this context, it is worth noting that the energetic deficiency reported in this study at the onset of contractions is accompanied by a rapid drop in peak twitch force, consistent with a change in calcium handling. In fact, Steeghs et al. (22) have reported that calcium transients are altered in mice lacking both MM and sarcomeric mitochondrial creatine kinase isoforms. Whether these alterations in calcium handling, and/or some other signal modulated by cellular energetics, regulate the adaptations in creatine kinase-deficient muscle remains to be determined.

In summary, this study shows that loss of MM creatine kinase profoundly alters the kinetics of PCr depletion at the onset of contractions but not later during more prolonged series of contractions. The results suggest that the kinetics of oxygen consumption are faster in MMKO muscle and that increased mitochondrial capacity is an adaptive response to the loss of ATP/ADP buffering by creatine kinase at the onset of contractions.


    APPENDIX
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

Both the creatine kinase and adenylate kinase reactions were modeled by a random bi-bi mechanism. Assumed enzyme-substrate dissociation constants for creatine kinase were, in molar concentrations
E · ADP ↔ E + ADP   <IT>K</IT><SUB>id</SUB> = 1e − 4

E · PCr ↔ E + PCr   <IT>K</IT><SUB>ip</SUB> = 4e − 3

E · ATP ↔ E + ATP   <IT>K</IT><SUB>ia</SUB> = 1.2e − 3

E · Cr ↔ E + Cr   <IT>K</IT><SUB>ic</SUB> = 15e − 3

E · ADP · PCr ↔ E · ADP+ Cr <IT>K</IT><SUB>p</SUB> = 2e − 3

E · ATP · Cr ↔ E · ATP + Cr  <IT>K</IT><SUB>c</SUB> = 10e − 3

E · ADP · Cr ↔ E · ADP + Cr  <IT>K</IT><SUB>y</SUB> = 10e − 3 (dead

end complex)
The instantaneous forward and reverse fluxes through creatine kinase were computed from
<IT>J</IT><SUP>f</SUP><SUB>CK</SUB> = <IT>J</IT><SUP>f</SUP><SUB>CK max</SUB>·[ADP] · [PCr]/(<IT>K</IT><SUB>id</SUB> · <IT>K</IT><SUB>p</SUB> · <IT>D</IT><SUB>CK</SUB>) (A1)

<IT>J</IT><SUP>r</SUP><SUB>CK</SUB> = <IT>J</IT><SUP>r</SUP><SUB>CK max</SUB> · [ATP] · [Cr]/(<IT>K</IT><SUB>ia</SUB> · <IT>K</IT><SUB>C</SUB> · <IT>D</IT><SUB>CK</SUB>) (A2)
where
<IT>D</IT><SUB>CK</SUB> = 1 + [ADP]/<IT>K</IT><SUB>id</SUB> + [PCr]/<IT>K</IT><SUB>ip</SUB> + [ATP]/<IT>K</IT><SUB>ia</SUB> + [Cr]/<IT>K</IT><SUB>ic</SUB> (A3)

+ ([ADP] · [PCr])/(<IT>K</IT><SUB>id</SUB> · <IT>K</IT><SUB>p</SUB>) + ([ATP] · [Cr])/(<IT>K</IT><SUB>ia</SUB> · <IT>K</IT><SUB>c</SUB>)

+ ([ADP] · [Cr])/(<IT>K</IT><SUB>id</SUB> · <IT>K</IT><SUB>y</SUB>)
Assumed initial concentrations of ATP, PCr, and creatine in muscle at rest were 7.5, 22, and 8 µmol/g, or 10.7, 31.4, and 11.4 mM, respectively. Initial ADP and AMP concentrations were computed assuming equilibrium of the creatine kinase and adenylate kinase reactions at rest and ignoring any effects of pH
 [ADP] = ([ATP] · [Cr])/([PCr]·<IT>K</IT><SUB>CK</SUB>), where <IT>K</IT><SUB>CK</SUB> = 140 (A4)

[AMP] = (<IT>K</IT><SUB>AK</SUB>·[ADP]<SUP>2</SUP>)/[ATP], where <IT>K</IT><SUB>AK</SUB> = 1.0 (A5)
J<UP><SUB>CK:max</SUB><SUP>f</SUP></UP> and J<UP><SUB>CK:max</SUB><SUP>r</SUP></UP> of creatine kinase in WT muscle were computed from Eqs. A1-A3 by using these initial, resting metabolite levels and assuming J<UP><SUB>CK</SUB><SUP>f</SUP></UP> and J<UP><SUB>CK</SUB><SUP>r</SUP></UP> in resting WT muscle of 7.5 µmol · g-1 · s-1 (10.7 mM/s). Maximum fluxes in MMKO muscle were assumed to be 2% of that in WT muscle.

Assumed dissociation constants for adenylate kinase, where site 1 and 2 are the ATP and AMP binding sites, respectively, were, in molar concentrations
<AR><R><C>E·ADP<SUB>1</SUB> ↔ E + ADP (site 1)</C><C><IT>aK</IT><SUB>i1</SUB></C><C>=</C><C>3.3e − 4</C></R><R><C>E·ADP<SUB>2</SUB> ↔ E + ADP (site 2)</C><C><IT>aK</IT><SUB>i2</SUB></C><C>=</C><C>1e − 3</C></R><R><C>E·ATP ↔ E + ATP</C><C><IT>aK</IT><SUB>ia</SUB></C><C>=</C><C>3e − 4</C></R><R><C>E·AMP ↔ E·  + AMP</C><C><IT>aK</IT><SUB>a</SUB></C><C>=</C><C> 2.5e − 4</C></R><R><C>E·AMP · ATP ↔ E·  AMP + ATP </C><C><IT>aK</IT><SUB>a</SUB></C><C>=</C><C> 2.5e − 4</C></R><R><C>E·ADP1 · ADP<SUB>2</SUB> ↔ E·ADP<SUB>1</SUB> + ADP  </C><C><IT>aK</IT><SUB>d</SUB></C><C>=</C><C>3.3e − 4</C></R></AR>
Instantaneous forward and reverse fluxes through adenylate kinase (J<UP><SUB><IT>aK</IT></SUB><SUP>f</SUP></UP>, J<UP><SUB><IT>aK</IT></SUB><SUP>r</SUP></UP>) were computed from equations analogous to Eqs. A1-A3 (but with no dead-end complex). The maximum adenylate kinase flux was computed assuming unidirectional fluxes of 1.0 µmol · g-1 · s-1 (1.43 mM/s) in both WT and MMKO muscle at rest. As noted above, this assumption proved to be equivalent to assuming equilibrium of the adenylate kinase reaction in both muscle types, because the net adenylate kinase flux was never more than a few percent of the unidirectional fluxes.

The time dependence of ATP hydrolysis during a twitch contraction (JC, mM/s) was modeled by a function which approximates the time course of twitch force
J<SUB>C</SUB> = A·<IT>t</IT>·exp(−<IT>k</IT>·<IT>t</IT>), (A6)
where t is time after the start of the twitch, k is the time at which the peak ATPase occurs (set to 20 ms), and the integral A/k2 is the total ATP hydrolysis per twitch (set to 0.22 µmol/g or 0.31 mM for WT muscle).

Finally, when included, ATP production by oxidative phosphorylation (JO) was assumed to depended on ADP concentration according to
<IT>J</IT><SUB>O</SUB> = <IT>J</IT><SUB>O max</SUB>·([ADP]/<IT>K</IT><SUB>50</SUB>)<SUP><IT>n</IT><SUB>H</SUB></SUP>/[1 + ([ADP]/<IT>K</IT><SUB>50</SUB>)<SUP><IT>n</IT><SUB>H</SUB></SUP>] (A7)
where the Hill coefficient nH = 2.3, K50 = 5 × 10-5 M and JO max = 1 µmol · g-1 · s-1 (1.43 mM/s).

Starting from the initial conditions described above, metabolite changes during twitch stimulation were then computed by using finite difference methods with a time step of 1 µs, according to the following equations
d[PCr]/d<IT>t</IT> =<IT>J</IT><SUP>r</SUP><SUB>CK</SUB> − <IT>J</IT><SUP>f</SUP><SUB>CK</SUB> (A8)

d[Cr]d<IT>t</IT> = −d[PCr]/d<IT>t</IT> (A9)

d[ATP]/d<IT>t</IT> = <IT>J</IT><SUP>f</SUP><SUB>CK</SUB> − <IT>J</IT><SUP>r</SUP><SUB>CK</SUB> + <IT>J</IT><SUP>f</SUP><SUB>AK</SUB> − <IT>J</IT><SUP>r</SUP><SUB>AK</SUB> − <IT>J</IT><SUB>C</SUB> + <IT>J</IT><SUB>O</SUB> (A10)

d[AMP]/d<IT>t</IT> = <IT>J</IT><SUP>f</SUP><SUB>AK</SUB> − <IT>J</IT><SUP>r</SUP><SUB>AK</SUB> (A11)

d[ADP]/d<IT>t</IT> = −(d[ATP]/d<IT>t</IT> + d[AMP]/d<IT>t</IT>). (A12)


    ACKNOWLEDGEMENTS

This work was supported by National Institutes of Health Grants AR-043903 and NSBRI MA-00210.


    FOOTNOTES

Address for reprint requests and other correspondence: R. W. Wiseman, Dept. of Physiology, 2201 Biomedical Physical Sciences Bldg., Michigan State Univ., East Lansing, MI 48824 (E-mail: rwiseman{at}msu.edu).

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

10.1152/ajpcell.00210.2002

Received 10 May 2002; accepted in final form 19 August 2002.


    REFERENCES
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

1.   Bessman, SP, and Geiger PJ. Transport of energy in muscle: the phosphorylcreatine shuttle. Science 211: 448-452, 1981[ISI][Medline].

2.   Blum, H, Schnall MD, Chance B, and Buzby GP. Intracellular sodium flux and high-energy phosphorus metabolites in ischemic skeletal muscle. Am J Physiol Cell Physiol 255: C377-C384, 1988[Abstract/Free Full Text].

3.   Chin, ER, Olsen EN, Richardson JA, Yang Q, Humphries C, Shelton JM, Wu H, Zhu W, Bassel-Duby R, and Williams RS. A calcineurin-dependent transcriptional pathway controls skeletal muscle fiber type. Genes Dev 12: 2499-2509, 1998[Abstract/Free Full Text].

4.   Connett, RJ, and Sahlin K. Control of glycolysis and glycogen metabolism. In: Handbook of Physiology. Exercise: Regulation and Integration of Multiple Systems. Bethesda, MD: Am. Physiol. Soc, 1996, sect. 12, chapt. 19, p. 870-919.

5.   Crowther, GJ, Carey MF, Kemper WF, and Conley KE. Control of glycolysis in contracting skeletal muscle. I. Turning it on. Am J Physiol Endocrinol Metab 282: E67-E72, 2002[Abstract/Free Full Text].

6.   De Groof, AJ, Smeets B, Groot Koerkamp MJ, Mul AN, Janssen EE, Tabak HF, and Wieringa B. Changes in mRNA expression profile underlie phenotypic adaptations in creatine kinase-deficient muscles. FEBS Lett 506: 73-78, 2001[ISI][Medline].

7.   Foley, JM, and Meyer RA. Energy cost of twitch and tetanic contractions of rat muscle estimated in situ by gated 31P NMR. NMR Biomed 5: 32-38, 1993.

8.   Greenhaff, PL. The creatine-phosphocreatine system: there's more than one song in its repertoire. J Physiol (Lond) 537: 657, 2001[Abstract/Free Full Text].

9.   Harkema, SJ, Adams GR, and Meyer RA. Acidosis has no effect on the ATP cost of contraction in cat fast- and slow-twitch skeletal muscles. Am J Physiol Cell Physiol 272: C485-C490, 1997[Abstract/Free Full Text].

10.   Harkema, SJ, and Meyer RA. Effect of acidosis on control of respiration in skeletal muscle. Am J Physiol Cell Physiol 272: C491-C500, 1997[Abstract/Free Full Text].

11.   Heineman, FW, Eng J, Berkowitz BA, and Balaban RS. NMR spectral analysis of kinetic data using natural lineshapes. Magn Reson Med 13: 490-497, 1990[ISI][Medline].

12.   Hood, DA, Gorski J, and Terjung RL. Oxygen cost of twitch and tetanic isometric contractions in rat skeletal muscle. Am J Physiol Endocrinol Metab 250: E449-E456, 1986[Abstract/Free Full Text].

13.   Jeneson, JAL, Wiseman RW, Westerhoff HV, and Kushmerick MJ. The signal transduction function for oxidative phosphorylation is at least second order in ADP. J Biol Chem 271: 27995-27998, 1996[Abstract/Free Full Text].

14.   Meyer, RA. A linear model of muscle respiration explains monoexponential phosphocreatine changes. Am J Physiol Cell Physiol 254: C548-C553, 1988[Abstract/Free Full Text].

15.   Meyer, RA, and Foley JM. Cellular processes integrating the metabolic response to exercise. In: Handbook of Physiology. Exercise: Regulation and Integration of Multiple Systems. Bethesda, MD: Am. Physiol. Soc, 1996, sect. 12, chapt. 18, p. 841-869.

16.   Morrison, JF, and Cleland WW. Isotope exchange studies of the mechanism of the reaction catalyzed by adenosine triphosphate: creatine phosphotransferase. J Biol Chem 241: 673-683, 1966[Abstract/Free Full Text].

17.   Roman, BB, Foley JM, Meyer RA, and Koretsky AP. The effect of increased creatine kinase activity on contractile function and metabolism in mouse skeletal muscle. Am J Physiol Cell Physiol 270: C1236-C1245, 1996[Abstract/Free Full Text].

18.   Roman, BB, Wieringa B, and Koretsky AP. Functional equivalence of creatine kinase isoforms in mouse skeletal muscle. J Biol Chem 272: 17790-17794, 1997[Abstract/Free Full Text].

19.   Saks, VA, Ventura-Clapier R, Leverve X, Rossi A, and Rigoulet M. What do we know of cellular energetics?-a general view on the state of the art. Mol Cell Biochem 184: 3-9, 1998[ISI][Medline].

20.   Sheng, XR, Li X, and Pan XM. An iso-random Bi Bi mechanism for adenylate kinase. J Biol Chem 274: 22238-22242, 1999[Abstract/Free Full Text].

21.   Shoubridge, EA, Challiss RAJ, Hayes DJ, and Radda GK. Biochemical adaptation in the skeletal muscle of rats depleted of creatine with the substrate analog B-guanidinopropionic acid. Biochem J 232: 125-131, 1985[ISI][Medline].

22.   Steeghs, K, Benders A, Oerlemans F, de Hann A, Heerschap A, Ruitenbeck W, Jost C, van Deursen J, Perryman B, Pette D, Bruckwilder M, Koudijs J, Jap P, Veerkamp J, and Wieringa B. Altered Ca2+ responses in muscles with combined mitochondrial and cytosolic creatine kinase deficiencies. Cell 89: 93-103, 1997[ISI][Medline].

23.   Steeghs, K, Heerschap A, de Haan A, Ruitenbeek W, Oerlemans F, van Deursen J, Perrryman B, Pette D, Bruckwilder M, Koudijs J, Jap P, and Wieringa B. Use of gene targeting for compromising energy homeostasis in neuro-muscular tissues: the role of sarcomeric mitochondrial creatine kinase. J Neurosci Methods 71: 29-41, 1997[ISI][Medline].

24.   Van Deursen, J, Heerschap A, Oerlemans F, Ruitenbeek W, Jap P, ter Laak H, and Wieringa B. Skeletal muscles of mice deficient in muscle creatine kinase lack burst activity. Cell 74: 621-631, 1993[ISI][Medline].

25.   Van Deursen, J, Ruitenbeek W, Heerschap A, Jap P, ter Laak H, and Wieringa B. Creatine kinase (CK) in skeletal muscle energy metabolism: a study of mouse mutants with graded reduction in muscle CK expression. Proc Natl Acad Sci USA 91: 9091-9095, 1994[Abstract].

26.   Van Zandt, JHA, Oerlemans F, Wieringa B, and Heerschap A. Effects of ischemia on skeletal muscle energy metabolism in mice lacking creatine kinase monitored by in vivo 31P nuclear magnetic resonance spectroscopy. NMR Biomed 12: 327-334, 1999[ISI][Medline].

27.   Veksler, VI, Kuznetsov AV, Anflous K, Mateo P, van- Duersen J, Wieringa B, and Ventura-Clapier R. Muscle creatine-kinase-deficient mice. II. Cardiac and skeletal muscles exhibit tissue-specific adaptation of the mitochondrial function. J Biol Chem 270: 19921-19929, 1995[Abstract/Free Full Text].

28.   Ventura-Clapier, R, Kuznetsov AV, Albis A, van Deursen J, Wieringa B, and Veksler VI. Muscle creatine kinase-deficient mice. I. Alterations in myofibrillar function. J Biol Chem 270: 19914-19920, 1995[Abstract/Free Full Text].

29.   Wallimann, T, Wyss M, Brdiczka D, Nicolay K, and Eppenberger HM. Intracellular compartmentation, structure and function of creatine kinase isoenzymes in tissues with high and fluctuating energy demands: the phosphocreatine circuit for cellular energy homeostasis. Biochem J 281: 21-40, 1992[ISI][Medline].

30.   Watchko, JF, Daood MJ, Wieringa B, and Koretsky AP. Myofibrillar or mitochondrial creatine kinase deficiency alone does not impair mouse diaphragm isotonic function. J Appl Physiol 88: 973-980, 2000[Abstract/Free Full Text].

31.   Wu, H, Kanatous SB, Thurmond FA, Gallardo T, Isotani E, Bassel-Duby R, and Williams RS. Regulation of mitochondrial biogenesis in skeletal muscle by CaMK. Science 296: 349-352, 2002[Abstract/Free Full Text].


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