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 |
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 |
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 |
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
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 |
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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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.
|
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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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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 ( ) (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 ( , 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.
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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.
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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.
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 |
DISCUSSION |
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 |
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
The instantaneous forward and reverse fluxes through creatine
kinase were computed from
|
(A1)
|
|
(A2)
|
where
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(A3)
|
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
|
(A4)
|
|
(A5)
|
J
and J
of creatine kinase in WT muscle were computed from
Eqs. A1-A3 by using these initial, resting
metabolite levels and assuming J
and J
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
Instantaneous forward and reverse fluxes through adenylate
kinase (J
,
J
) 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
|
(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
|
(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
|
(A8)
|
|
(A9)
|
|
(A10)
|
|
(A11)
|
|
(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.
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