1 Department of Internal Medicine and the 2 Howard Hughes Medical Institute, Yale University School of Medicine, New Haven, Connecticut 06520-8020
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ABSTRACT |
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Metabolic control
analysis was used to calculate the distributed control of
insulin-stimulated skeletal muscle glucose disposal in awake rats.
Three separate hyperinsulinemic infusion protocols were performed:
1)
protocol I was a euglycemic (~6
mM)-hyperinsulinemic (10 mU · kg1 · min
1)
clamp, 2) protocol
II was a hyperglycemic (~11 mM)-hyperinsulinemic (10 mU · kg
1 · min
1)
clamp, and 3)
protocol III was a euglycemic (~6
mM)-hyperinsulinemic (10 mU · kg
1 · min
1)-lipid/heparin
(increased plasma free fatty acid) clamp.
[1-13C]glucose was
administered in all three protocols for a 3-h period, during which time
[1-13C]glucose label
incorporation into
[1-13C]glycogen,
[3-13C]lactate, and
[3-13C]alanine was
detected in the hindlimb of awake rats via
13C-NMR. Combined steady-state and
kinetic data were used to calculate rates of glycogen synthesis and
glycolysis. Additionally, glucose 6-phosphate
(G-6-P) was measured in the hindlimb
muscles with the use of in vivo
31P-NMR during the three infusion
protocols. The clamped glucose infusion rates were 31.6 ± 2.9, 49.7 ± 1.0, and 24.0 ± 1.5 mg · kg
1 · min
1
at 120 min in protocols
I-III,
respectively. Rates of glycolysis were 62.1 ± 10.3, 71.6 ± 11.8, and 19.5 ± 3.6 nmol · g
1 · min
1
and rates of glycogen synthesis were 125 ± 15, 224 ± 23, and 104 ± 17 nmol · g
1 · min
1
in protocols
I-III,
respectively. Insulin-stimulated G-6-P
concentrations were 217 ± 8, 265 ± 12, and 251 ± 9 nmol/g
in protocols
I-III, respectively. A top-down approach to metabolic control analysis was
used to calculate the distributed control among glucose
transport/phosphorylation [GLUT-4/hexokinase (HK)], glycogen
synthesis, and glycolysis from the metabolic flux and
G-6-P data. The calculated values for
the control coefficients (C) of
these three metabolic steps
(CJGLUT-4/HK = 0.55 ± 0.10, CJglycogen syn = 0.30 ± 0.06, and
CJglycolysis = 0.15 ± 0.02; where J is glucose
disposal flux, and glycogen syn is glycogen synthesis) indicate that
there is shared control of glucose disposal and that glucose
transport/phosphorylation is responsible for the majority of control of
insulin-stimulated glucose disposal in skeletal muscle.
nuclear magnetic resonance; flux control; glycogen synthesis; glycolysis; glucose 6-phosphate
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INTRODUCTION |
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MANY OF THE INITIAL STUDIES addressing the mechanism of metabolic control have focused on defining a rate-limiting or rate-controlling step in metabolism (20, 25, 26). It was generally thought that a rate-limiting enzyme was near the start of a metabolic pathway catalyzing a nonequilibrium reaction. As initially described by Kacser and Burns (15), the control of metabolism is often distributed over the entire system of enzymes composing the metabolic pathway. Consequently, it has been difficult to discover a single rate-limiting enzyme for metabolism by using traditional enzyme-expression or -inhibition techniques. With the use of a top-down approach to metabolic control theory, it is possible to determine a distribution of control over defined metabolic pathways and/or systems of enzymes that will vary depending on the physiological conditions present (16, 30). The top-down approach to metabolic control analysis (MCA) and its application to in vivo metabolic studies require only that flux through the applicable metabolic pathways and concentrations of associated substrates be measured. The quantitative measurements of metabolic fluxes and intermediate concentrations in vivo have been simplified in the advent of NMR spectroscopic techniques, which enables one to make simultaneous measurements of glycogen synthesis and glycolysis noninvasively in the hindlimb muscle of awake rats (12-14) by using 13C-NMR and glucose 6-phosphate (G-6-P) with the use of 31P-NMR spectroscopy (2, 3, 13).
In an effort to determine the control of glucose disposal in skeletal muscle during conditions of hyperinsulinemia, we used 13C- and 31P-NMR spectroscopy to measure noninvasively the partitioning of glucose disposal via glycogen synthesis and glycolysis, and G-6-P concentrations in the hindlimb skeletal muscles of rats during three separate infusion protocols, which were used to differentially modulate both the fluxes and intramuscular G-6-P concentrations. With the use of a top-down approach to MCA, elasticities (a relationship between enzyme velocity and substrate concentration) for glucose transport/phosphorylation, glycogen synthesis, and glycolysis to G-6-P were measured, and corresponding control coefficients were calculated. This study illustrates the utility of combining MCA with in vivo NMR to measure the distributed control of insulin-stimulated glucose disposal through associated transport and metabolic steps in rat skeletal muscle; it may be useful in characterizing the control of these pathways in different insulin-resistant states.
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EXPERIMENTAL PROCEDURES |
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Animals. Sprague-Dawley rats (Charles River, Raleigh, NC) were housed in an environmentally controlled room with a 12:12-h light-dark cycle. At a weight of 300-350 g, rats were chronically catheterized as described elsewhere (33) and allowed to recuperate for another 5-10 days.
In vivo experiments.
All rats were fasted 24 h before the infusion experiment. Rats were
placed in a customized restraining tube that allowed their left
hindlimb to be secured to the outside of the tube in a manner to limit
free movement of the leg for NMR measurements. The rats were
transiently anesthetized (<30 s) with a low dose (2.5-5.0 mg) of
thiopental (Sigma) to place them in the restraining tube. One of three
infusion protocols was started: protocol
I was a euglycemic (~6 mM)-hyperinsulinemic (10 mU · kg1 · min
1;
Humulin Regular, Eli Lilly) clamp, with 20% dextrose administered at
2.5 min after the commencement of the primed-continuous insulin infusion (n = 10 rats for
13C-NMR and
n = 6 for
31P-NMR);
protocol II was a hyperglycemic (~11
mM)-hyperinsulinemic (10 mU · kg
1 · min
1)
clamp with somatostatin (1 µg · kg
1 · min
1;
n = 10 for
13C-NMR and
n = 6 for
31P-NMR); and
protocol III was a euglycemic (~6
mM)-hyperinsulinemic (10 mU · kg
1 · min
1)-lipid/heparin
(Liposyn II, Abbott; 1:3 vol/vol saline at 39 µl/min with heparin at
0.0975 IU/min) clamp (n = 9 for
13C-NMR and
n = 5 for
31P-NMR).
[1-13C]glucose (99%
enriched, 20% wt/vol; Cambridge Isotope Laboratories, Cambridge, MA)
was used during the 13C-NMR
experiments. The glycolytic and glycogen synthesis flux measurements in
protocols I-III originated from
our previously published work (12-14). All clamps lasted for
180-240 min. Blood samples were drawn during the baseline NMR
measurement, at 7.5 min, at 15 min, and every 15 min thereafter for
immediate assessment of plasma glucose and lactate concentrations. At
the end of the in vivo NMR experiment, rats were anesthetized with
thiopental (50 mg/kg). Superficial skin was rapidly removed from the
left hindquarter, followed by in situ freeze clamping of the
gastrocnemius and biceps femoris muscles. Rats were euthanized with a
lethal dose of thiopental. The protocol was reviewed and approved by the Yale University Animal Care Committee.
In vivo NMR spectroscopy.
All in vivo 13C- and
31P-NMR experiments were performed
on a Bruker Biospec 7.0-T system (horizontal/22-cm-diameter bore
magnet) as previously described (11).
13C-NMR spectra were processed
with the use of a Gaussian filter, followed by Fourier transformation
and peak integration with the use of Bruker DISNMR processing software;
31P-NMR spectra were processed
with the use of a Gaussian resolution enhancement and 100% Gaussian
weighted peak fitting algorithm (Nuts NMR processing software; Acorn
NMR, Fremont, CA). Concentrations of
G-6-P,
Pi, and phosphocreatine (PCr) were
extrapolated from the in vivo spectra after correction for differential
saturation with respect to the -ATP peak and measured
ATP concentrations. The concentration of
G-6-P was calculated as the average of
three spectra taken between 105 and 135 min to increase the sensitivity of the measurement. Free intracellular
Mg2+ was calculated with the use
of the chemical shift difference between
- and
-ATP resonances,
with a dissociation constant of 50 µM (at pH 7.2, 37°C) for
Mg-ATP (1, 8). The ADP concentration was calculated with the use of the
creatine kinase equilibrium equation, and the creatine concentration
was calculated from the measured total creatine and PCr concentrations
(with an equilibrium constant of 1.66 × 109) (22). The intracellular pH
was calculated with the use of the chemical shift difference of
intracellular Pi and PCr as
previously described (35).
Tissue extract analysis. Muscle tissue extracts (13C-NMR experiments) were prepared for high-field NMR analysis by homogenization of ~1 g of combined gastrocnemius and biceps femoris muscle with a variable high-speed electric homogenizer after the sample was placed in a vortex tube filled with 0.9% perchloric acid (3 vol/wt). After homogenization over ice, the sample was centrifuged at 4°C for 10 min (4,000 rpm). The supernatant was extracted, and the pellet was saved for glycogen enrichment measurements. KOH (4 N, 0.675 vol/wt) was added to the supernatant to precipitate excess perchlorate ions. The sample was centrifuged once more at 4°C for 15 min (4,000 rpm). The supernatant was extracted, and 0.5 M phosphate buffer (pH 7) was added to neutralize the sample. The sample was dried in a speed-vac (Savant, Farmingdale, NY) overnight, and 0.5 ml 2H2O was added to the dried powder before it was placed in a 5-mm NMR tube for NMR analysis at 8.4 T (Bruker WB-360 NMR spectrometer). Proton-observed carbon-enhanced spectroscopy was performed on tissue extract samples for fractional enrichment calculations. The broadband 13C inversion pulse was turned on during alternate transients, with raw data separated into two data sets, providing spectra with heteronuclear-coupled spins, inverted (spectrum B) and noninverted (spectrum A). The fractional enrichments [atom percent excess (APE)] of lactate and alanine were calculated from their respective resonances in spectrum A (A) and spectrum B (B) as follows
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Analytic procedures. Plasma glucose concentrations were measured by the glucose oxidase method (Glucose Analyzer II; Beckman Instruments, Fullerton, CA). Plasma immunoreactive free insulin was measured with a double-antibody RIA technique (Linco Research, St. Charles, MO). 13C enrichment of plasma glucose was determined with the use of a Hewlett-Packard 5890 gas chromatograph (HP-1 capillary column, 12-m × 0.2-mm × 0.33-mm film thickness) interfaced to a Hewlett-Packard 5971A mass-selective detector, operating in the positive chemical ionization mode with methane as a reagent gas (6).
[13C]glycogen fractional enrichments were determined with the use of the precipitated glycogen from the initial muscle perchloric acid extraction (99% recovery) (13), and absolute glycogen concentrations were measured on a separate portion of muscle (17). Skeletal muscle ATP concentrations (31P-NMR experiments) were determined enzymatically with the use of a diagnostic ATP assay kit (no. 366; Sigma Chemical, St. Louis, MO) modified for tissue analysis. Total creatine concentrations in muscle were measured by 13C-NMR analysis performed on a Bruker AM 500 NMR spectrometer system, for which the total [2-13C]creatine peak intensity [54.4 parts per million (ppm)] was referenced to the [2-13C]acetate peak (24.2 ppm), which was added as an internal concentration standard. Spectra were acquired with a repetition time of 1.4 s, number of scans of 10,000, 16 kilobytes of data, and Waltz-16 broadband proton decoupling. Peak intensities were corrected for saturation and nuclear Overhauser effect contributions. Plasma free fatty acids (FFAs) were determined with the use of an acyl-CoA oxidase-based colorimetric kit (Wako NEFA-C; Wako Pure Chemical Industries, Osaka, Japan). Plasma lactate concentrations were measured with the use of a 2300 Stat Plus lactate analyzer.Glycogen synthesis rate calculation. The incremental change in C-1 glycogen peak intensity from [1-13C]glucose incorporation was measured at 100.5 ppm. Incremental plasma [13C]glucose fractional enrichment as well as final [13C]glycogen enrichment and concentrations were used to back extrapolate the glycogen concentration (in µmol/g, which represents µmol glucosyl units/g muscle wet wt) at each measured time point to baseline, as described by Bloch et al. (3). Glycogen synthesis rates were determined with the use of a linear regression analysis over the individual-time-point glycogen concentrations.
Glycolytic flux calculations. Metabolic steady-state conditions were assumed for the calculation of carbon flux through the glycolytic pathway into the intermediate triose pool of lactate, pyruvate, and alanine. We have previously shown (12, 13) that these intermediates are at steady-state concentrations before and after a euglycemic- or hyperglycemic-hyperinsulinemic clamp. The 13C label incorporation from [1-13C]glucose into [3-13C]lactate and [3-13C]alanine in the hindlimb muscles was observed by 13C-NMR as an indirect marker of pyruvate labeling. Label incorporation into lactate and alanine is a qualitative indicator of glycolytic flux. Differential equations were developed from steady-state rate equations and solved for glycolytic flux (12).
MCA.
A brief introduction to MCA theory is described in the
APPENDIX. A top-down approach to MCA
was used. In doing so, numerous enzymes associated with a particular
metabolic step or pathway can be lumped together so that control
coefficients for those groups of enzymes can be determined. In this
manner, we determined the control of glucose disposal distributed
between glucose transport through insulin-stimulated GLUT-4 and
phosphorylation via hexokinase (GLUT-4/HK); glycogen synthesis,
consisting of phosphoglucomutase, UDP-glucose pyrophosphorylase, and
glycogen synthase enzymes; and glycolysis, consisting of numerous
enzymes including phosphofructokinase and pyruvate kinase in skeletal
muscle (Fig. 1).
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Statistical analysis. All data are reported as means ± SE. Single-factor ANOVA was performed on data to determine significance at a minimum P < 0.05 threshold among the three protocols. A multiple-comparison Fisher's protected least significant difference post hoc test was used when necessary to determine significance among protocols. Error analysis of control coefficients was calculated with the use of the SE in the flux and [G-6-P] measurements.
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RESULTS |
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Basal measurements.
Basal plasma concentrations of glucose, insulin, and FFA were similar
in all three protocols (Table 1).
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Protocol I.
During the euglycemic-hyperinsulinemic clamp experiment, the plasma
glucose concentration was maintained at ~6 mM throughout the study,
and the plasma insulin concentration increased to 206 ± 43 µU/ml,
whereas plasma FFA decreased to 0.4 ± 0.1 mM (Table 1). The glucose
infusion rate was stable throughout the clamp period (31.6 ± 2.9 mg · kg1 · min
1
at 120 min; Table 2). The ATP and total
creatine concentrations were 5.1 ± 0.3 and 31.1 ± 7.1 µmol/g,
respectively.
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Protocol II.
During the hyperglycemic-hyperinsulinemic clamp experiment, the plasma
glucose concentration increased and was maintained at ~11 mM
throughout the study, and the plasma insulin concentration increased to
279 ± 88 µU/ml, whereas plasma FFA decreased to 0.2 ± 0.1 mM
(Table 1). The glucose infusion rate was stable throughout the clamp
period (49.7 ± 1.0 mg · kg1 · min
1
at 120 min; Table 2). The ATP and total creatine concentrations were
4.9 ± 0.1 and 27.6 ± 2.2 µmol/g, respectively.
Protocol III.
During the euglycemic-hyperinsulinemic-lipid/heparin clamp experiment,
the plasma glucose concentration was maintained at ~6 mM throughout
the study, and the plasma insulin concentration increased to 229 ± 12 µU/ml, whereas the plasma FFA increased to 2.3 ± 0.4 mM as a
result of the lipid/heparin infusion (Table 1). The glucose infusion
rate decreased throughout the duration of the clamp period and was 24.0 ± 1.5 mg · kg1 · min
1
at 120 min (Table 2). The ATP and total creatine concentrations were
5.2 ± 0.1 and 27.8 ± 2.2 µmol/g, respectively.
In vivo
13C-NMR.
Figure 2A
illustrates a 15-min acquired baseline spectrum
(bottom) and a spectrum taken at 120 min (top), when significant 13C label incorporation into
metabolite intermediates was achieved. The - and
-anomer peaks of
[1-13C]glucose appear
at 96.8 and 93.0 ppm, respectively, and the large peak slightly
downfield at 100.5 ppm corresponds to the C-1 glucosyl unit of the
glycogen polymer.
[3-13C]lactate and
[3-13C]alanine can
also be observed at 21.0 and 16.9 ppm, respectively.
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In vivo
31P-NMR.
Figure 2B illustrates a
31P-NMR baseline spectrum with
G-6-P,
Pi (both extracellular and
intracellular), PCr (assigned to 0 ppm), and -,
-, and
-ATP
indicated. The basal
[G-6-P] values were the
same in all groups before the three clamp protocols, as indicated in
Table 3. The incremental change in
G-6-P during the
hyperglycemic-hyperinsulinemic clamp can be seen in Fig.
2B (inset).
[G-6-P] in all three
protocol groups increased at 105-135 min, as presented in Table 3,
with [G-6-P] higher in the
hyperglycemic-hyperinsulinemic and
euglycemic-hyperinsulinemic-lipid/heparin clamps vs.
euglycemic-hyperinsulinemic clamp (265 ± 12 and 251 ± 9 vs. 217 ± 8 nmol/g; P < 0.005 and P < 0.05, respectively).
Concentrations of Pi, PCr, ADP,
Mg2+, and pH were not
significantly different at baseline or at 120 min in all three clamp
protocols (Table 3).
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Metabolic flux control analysis.
With the use of the top-down approach to calculate the elasticities
associated with glucose disposal, the resulting elasticities for
glucose transport/phosphorylation, glycogen synthesis, and glycolysis
with respect to G-6-P were as follows:
GLUT-4/HKG-6-P =
2.18,
glycogen synG-6-P = 3.56, and
glycolysisG-6-P = 0.69, respectively (see APPENDIX).
From these elasticity measurements, we were able to calculate the
control coefficients by solving the three equations described
above simultaneously. The majority of control of glucose disposal
during hyperinsulinemia was determined to be at the glucose transport/phosphorylation step
(CJGLUT-4/HK = 0.55 ± 0.10), with approximately one-half of the
control distributed between glycogen synthesis
(CJglycogensyn = 0.30 ± 0.06) and glycolysis
(CJglycolysis = 0.15 ± 0.02).
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DISCUSSION |
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MCA theory was developed as an amalgamation of independent work in the
early 1970s by Kacser and Burns (15) and Heinrich and Rapoport (10).
This theory was formulated to determine how the intermediate steps of a
pathway react to a variable that might affect it (i.e., a change in
substrate and/or external effector amount or change in enzyme
expression). In this manner, a system of intermediary steps can be
analyzed as a whole to determine fractional contribution of any one
step to the overall control of flux through a metabolic pathway.
Because we cannot obtain relative information with regard to the way in
which each individual enzyme in a metabolic pathway reacts to variables
affecting it (bottom-up approach) from NMR metabolic flux measurements,
we used a top-down approach to MCA, in which we can define control over
only a few metabolic components, each consisting of a number of enzymes
(e.g., glucose transport/phosphorylation, glycogen synthesis, and
glycolysis). In our studies, three separate infusion protocols were
necessary to indirectly modulate
[G-6-P] to measure the
elasticities of these three metabolic components to
G-6-P (i.e.,
GLUT-4/HKG-6-P,
glycogen synG-6-P, and
glycolysisG-6-P).
It was necessary to maintain concentrations of known allosteric effectors and covalent modulation of enzymes that make up these pathways. Because the 13C-NMR measurement of glycolytic flux at euinsulinemia might not be possible (12), we maintained hyperinsulinemic conditions in all three groups, and no significant differences among groups with respect to concentrations of ADP, Mg2+, Pi, or pH were measured (Table 3). Although it has been shown that an acute elevation of plasma FFA can directly regulate insulin signaling or glucose transporter function, these events generally occur only after 3-5 h (9, 23). Additionally, we (13) and others (9) have shown that [G-6-P] values remained elevated during the initial 3-4 h of clamp before elevated plasma FFA could affect insulin signaling or glucose transporter function and result in a decrease in [G-6-P]. Therefore, with proper control of the physiological effectors of these metabolic pathways, one can couple MCA to in vivo metabolic studies in skeletal muscle.
MCA is a logical extension of traditional studies that attempted to define a rate-limiting enzyme in the pathway but were unsuccessful. For example, in heart, when intracellular glucose was not detected as extracellular concentrations varied from 2 to 16 mM, this led to the belief that glucose transport was rate limiting for glucose disposal (24). In recent heart work, MCA was used to illustrate that the control of glucose uptake is distributed among glucose transport and phosphorylation, glycogen synthesis, and glycolysis (16). Additionally, the distribution of control was shown to change, depending on substrate availability or hormonal environment.
In skeletal muscle, it has been suggested that the glycogen synthase enzyme controls the rate of glycogen synthesis (4, 21). On the other hand, insulin stimulation has been shown to increase glucose transport via an increase in GLUT-4 translocation to the cell membrane (19). The glycogen synthase enzyme is additionally regulated by insulin by reduction of its degree of phosphorylation. With the unique capability to measure net glycogen synthesis flux and intermediate substrate (G-6-P) by NMR and with the use of a top-down approach, it was shown that glucose transport/phosphorylation could indeed account for almost the entire control of insulin-stimulated glycogen synthesis in normal or diabetic humans (27, 31). In these analyses, control of glycogen synthesis was distributed over glucose transport/phosphorylation and glycogen synthesis only while glycolysis was neglected. This was thought reasonable in light of whole body extrapolation of skeletal muscle glycogen synthesis rates determined by NMR that suggested that glycogen synthesis in skeletal muscle accounts for ~90% of the whole body glucose metabolism under hyperglycemic-hyperinsulinemic conditions (32).
However, through MCA, it has been theoretically shown that glycolytic enzymes do indeed contribute to the control of [G-6-P] (30). Additionally, in rat, glycolysis accounts for a significant portion of the glucose disposal in muscle under euglycemic-hyperinsulinemic conditions (18, 28). Therefore, the potential for glycogen synthesis and glycolysis to account for a significant fraction of control in glucose disposal is evident.
The control of glucose transport/phosphorylation when partitioned into individual flux components of glucose transport and HK activity can be determined if elasticities of these flux components to intracellular glucose are known. We have previously determined that intramuscular glucose is negligible in rat during a hyperglycemic-hyperinsulinemic clamp by using an NMR spectroscopic assay (5), and, therefore, it would most likely be negligible during a euglycemic-hyperinsulinemic clamp. Consequently, we would not have the NMR sensitivity to detect the required modulation of intracellular glucose necessary for calculating elasticities in our experiments. Hypothetically, if intracellular glucose were negligible during both euglycemic- and hyperglycemic-hyperinsulinemic clamps, then, with the use of a bottom-up approach to MCA in which known enzyme kinetic parameters are used, the control of HK would be negligible as well (29).
Insulin sensitivity varies with skeletal muscle fiber composition (11); thus there is the potential for differences in the distribution of control in slow- vs. fast-twitch muscle fibers. For example, it has been shown that the regulation of glycogen synthase is different in fast- vs. slow-twitch muscle after a glucose load (34). Because of the intrinsic sensitivity of the in vivo NMR measurement, it is not possible to make glycolytic and glycogen synthesis flux measurements in small muscles such as soleus and extensor digitorum longus. Therefore, the hindlimb placement over the NMR-sensitive volume of the radio frequency (RF) coil was such that the NMR signal obtained was predominantly from the larger mixed fiber tissue composing the gastrocnemius and biceps femoris muscles. Additionally, it must be noted that the distribution of control might vary depending on the physiological conditions (16, 30).
In conclusion, we have presented a study that takes unique advantage of the in vivo NMR measurements of glycogen synthesis and glycolytic flux and [G-6-P] to apply a top-down analysis of MCA to determine the control of insulin-stimulated glucose disposal in skeletal muscle distributed among glucose transport/phosphorylation, glycogen synthesis, and glycolysis. It was determined that during insulin stimulation, the majority of control resides at glucose transport/phosphorylation, although glycogen synthesis and glycolysis do share in the control of glucose disposal as well. This approach might be useful in characterizing the control of these pathways under conditions of insulin resistance and/or diabetes.
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APPENDIX |
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MCA Theory
The following is a brief description of MCA theory (15). The flux control coefficient is defined by the ratio of fractional change of the flux through an enzyme in the pathway to fractional change in enzyme concentration (E)
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All of the enzymes or metabolic pathways that can affect the flux
through a metabolic system share control of that flux; thus, via the
summation theorem, the sum of all of the coefficients equals one, i.e.,
CJi = 1. If a metabolite is both a substrate and product to separate enzymes in a two-enzyme system, then the use of the connectivity theorem to relate the flux control coefficients to the kinetic properties of the enzyme gives us
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ACKNOWLEDGEMENTS |
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We are indebted to Veronika Walton, Laura Burdon, and Kevin Cadman for expert technical assistance. We are grateful to electrical engineers Terry Nixon and Scott Mcyntire for NMR technical improvements and Peter Brown for radio frequency antenna design and construction. We also thank Dr. Douglas L. Rothman for helpful discussions on MCA.
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FOOTNOTES |
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This study was supported by grants from the National Institute of Diabetes and Digestive and Kidney Diseases (RO1-DK-40936 and P30-DK-45735), the American Diabetes Association (Mentor-Based Postdoctoral Fellowship to B. M. Jucker), and an unrestricted grant from Bristol-Myers Squibb.
G. I. Shulman is an investigator for the Howard Hughes Medical Institute.
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. §1734 solely to indicate this fact.
Address for reprint requests and other correspondence: B. M. Jucker, Dept. of Internal Medicine, Yale Univ. School of Medicine, PO Box 208020, Fitkin 1, 333 Cedar St., New Haven, CT 06520-8020 (E-mail: Jucker{at}mrclin1.med.yale.edu).
Received 9 November 1998; accepted in final form 21 April 1999.
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