Flux control in the rat gastrocnemius glycogen
synthesis pathway by in vivo
13C/31P
NMR spectroscopy
J. R.
Chase1,
D. L.
Rothman2, and
R. G.
Shulman1
Departments of 1 Molecular Biophysics and Biochemistry and
2 Internal Medicine, Yale University School of Medicine, New
Haven, Connecticut 06510
 |
ABSTRACT |
To
determine the relative contributions of glucose transport/hexokinase,
glycogen synthase (GSase), and glycolysis to the control of
insulin-stimulated muscle glycogen synthesis, we combined 13C and 31P NMR to quantitate the glycogen
synthesis rate and glucose 6-phosphate (G-6-P) levels in rat
(Sprague-Dawley) gastrocnemius muscle during hyperinsulinemia at
euglycemic (E) and hyperglycemic (H) glucose concentrations under
thiopental anesthesia. Flux control was calculated using metabolic
control analysis. The combined control coefficient of glucose
transport/hexokinase (GT/Hk) for glycogen synthesis was 1.1 ± 0.03 (direct measure) and 1.14-1.16 (calculated for a range of
glycolytic fluxes), whereas the control coefficient for GSase was much
lower (0.011-0.448). We also observed that the increase in in vivo
[G-6-P] from E to H (0.22 ± 0.03 to 0.40 ± 0.03 mM) effects a supralinear increase in the in vitro velocity of
GSase, from 14.6 to 26.1 mU · kg
1 · min
1 (1.8-fold).
All measurements suggest that the majority of the flux control of
muscle glycogen synthesis is at the GT/Hk step.
metabolic control analysis; glucose transport; hyperglycemia; hyperinsulinemia
 |
INTRODUCTION |
THE MUSCLE
GLYCOGEN SYNTHESIS PATHWAY plays a central role in whole body
glucose homeostasis. The flux through this pathway is acutely activated
by insulin after a glucose load, allowing increased uptake of
plasma glucose. Under the conditions of a hyperinsulinemic
hyperglycemic clamp, muscle glycogen synthesis accounts for the
majority of whole body glucose uptake in humans (29).
Impaired glycogen synthesis accounts for the deficit of glucose storage
in patients with non-insulin-dependent diabetes mellitus under these
conditions (29). Glucose is
transported into the cell by facilitative diffusion mediated by
membrane glucose transporters (GT). Hexokinase (Hk)
phosphorylates the C-6 position of glucose. Glucose 6-phosphate
(G-6-P) is isomerized and activated to UDP-glucose, which is
incorporated by glycogen synthase (GSase) into the glycogen polymer.
The activities of GT (14, 20, 37), GSase (7, 8,
21), and possibly Hk (18) are regulated by insulin
levels. Both GSase and Hk are under allosteric regulation by
G-6-P.
The coordinate regulation of the activity of several enzymes in
this pathway by insulin has complicated efforts to assign a
conventional rate-limiting step for glycogen synthesis. Correlations between the rates of GT and of glycogen synthesis or muscle glucose uptake have been interpreted as supporting GT control in transgenic mice overexpressing GLUT-4 (9, 36), in previously
exercised mice overexpressing GLUT-4 (24), in
glucose-clamped rats (11), and in the human forearm
(4). However, the conclusion of transport control appears
to contradict the extensive studies establishing that the activity of
GSase correlates with the rate of muscle glycogen synthesis (3,
8, 40). The correlation between GSase activity and glycogen
synthesis and the extensive regulation of GSase activity by
phosphorylation have been the basis for the view of GSase as
controlling the glycogen synthesis flux.
A limitation of previous studies of the muscle glycogen synthesis
pathway is that they have not quantitatively assessed metabolic control. In the last 25 years, metabolic control analysis (MCA) has
provided a theoretical framework for quantitatively calculating from
experimental data the control exerted by enzymes over the flux through
a metabolic pathway (12, 16). In MCA, the control an
enzyme (E) exerts over a metabolic flux
(J) is given by the flux control coefficient,
C
, which is defined
as the fractional change in the flux through the pathway
(
J/J) when the activity of the enzyme is
changed by a fraction
E/E
|
(1)
|
Measurement of the flux control coefficient of an enzyme depends
on selectively altering the activity of the enzyme while maintaining
constant activities of other enzymes in the
pathway.1 Although these
conditions cannot always be met experimentally, MCA has been applied
successfully to determine flux control coefficients in a number of
systems (12).
Recently, we have used MCA to reanalyze a study we performed using
13C and 31P NMR to measure insulin-stimulated
muscle glycogen synthesis and G-6-P concentration in the
muscle of healthy nondiabetic humans (26, 31). The
analysis indicated that the activity of the combined steps of GT and Hk
(GT/Hk) determines the glycogen synthesis rate (31). We
proposed that the role of the insulin-dependent alteration of GSase
activity by phosphorylation was to regulate the concentration of
G-6-P rather than to determine the rate of the pathway
(31). The results of several studies of human and rat
muscle performed under hyperinsulinemic conditions were shown to be
consistent with these conclusions. However, it was necessary to combine
results from different studies to show that the conditions necessary to
apply MCA were met.
The present in vivo NMR study was designed to allow calculation of the
flux control coefficients of GT/Hk and GSase in the muscle glycogen
synthesis pathway under hyperinsulinemic conditions in the rat. The
synthesis rate of muscle glycogen was measured by 13C NMR
during a hyperinsulinemic clamp at two glucose concentrations to alter
selectively the GT activity. 31P NMR was used to verify
that phosphorylated effectors of GSase other than G-6-P
remained constant. The requirement for applying the analysis, that the
phosphorylation state of GSase remain the same at both glucose levels,
was established by direct assay. The application of MCA was extended
from previous work (31) by incorporating the muscle
glycolytic flux and using recently derived expressions that take into
account the relatively large changes in plasma glucose concentration
needed for the measurements (32, 33). The results support
the conclusion that, under euglycemic and/or hyperinsulinemic clamped
conditions, the increase in insulin-induced GT/phosphorylation activity
is the major control point for determining the rate of muscle glycogen
synthesis, whereas GSase has little control over the glycogen synthesis flux.
 |
MATERIALS AND METHODS |
Protocol.
The experimental protocol is shown schematically in Fig. 1. Combined
13C/31P NMR spectra were acquired during the
baseline period (t =
50 min to t = 0) and up to
180 min during a glucose/insulin clamp. A primed, continuous infusion
of somatostatin at 0.1 µg · kg
1 · min
1 (Bachem)
and insulin at 10 mU · kg
1 · min
1 (Novolin)
was begun at t = 0 min. A primed, variable infusion of 20%
wt/vol dextrose (100% [1-13C]dextrose) was begun at
t = 0 min and adjusted to clamp the
[glucose]plasma at ~5.5 mM (E; n = 6)
within 40 min. Euglycemic conditions were maintained for 50 min, during
which time 13C/31P NMR spectra were acquired.
At the end of this period, the infusion rate was adjusted to clamp the
[glucose]plasma at ~13.9 mM [hyperglycemia (H);
n = 6]. After a 30-min period to allow the plasma
glucose to stabilize, spectra were acquired under hyperglycemic
conditions for 50 min. In one additional animal, the clamp order was
reversed (H followed by E) as a control. At the end of the
hyperglycemic clamp, the gastrocnemius was resected and the muscle
frozen in liquid N2. The animals were euthanized by an
intravenous dose of KCl. The muscles were stored at
70°C until
assayed for [glycogen] or GSase activity.

View larger version (10K):
[in this window]
[in a new window]
|
Fig. 1.
Experimental protocol for 6 of 7 animals. Solid bar
(top): 50 min baseline and 180 min of insulin/somatostatin
infusion (insulin, 10 mU · kg 1 · min 1;
somatostatin, 0.1 mg · kg 1 · min 1); solid
bars, euglycemic (E) and hyperglycemic (H) clamps; lower solid bars,
clamp adjustment periods; upper solid bar, time of
13C/31P NMR spectroscopy. For 1 animal, E and H
clamps were performed in reverse order, with similar clamp adjustment
times.
|
|
An additional group of animals was studied outside the magnet with
unlabeled glucose under conditions identical to the E or H phases
described above (non-NMR groups: E, n = 5; H,
n = 1). The gastrocnemius was removed after the clamp
period for determination of GSase activity.
Animals.
Overnight-fasted male Sprague-Dawley rats, 260-340 g, were
anesthetized with 100 mg/kg Na+/NaCO3
thiopental. The rat was tracheotomized and ventilated on O2
supplemented with room air. Catheters were inserted into the left
jugular vein and right carotid artery for infusion and blood sampling,
respectively. The skin over the calf and the knee was removed and the
exposed muscle covered with plastic film. Brass pins were inserted
under the patella and through the Achilles tendon, and the rat was
fastened to a special Lucite holder for immobilization of the leg. For
the NMR experiments, a coil was positioned directly over the exposed
muscle. The animals were warmed throughout the experiment by means
of a circulating water bath system. The animal protocol was approved by
the Yale Animal Care and Use Committee.
Blood gases were monitored throughout on an ABL-30 analyzer
(Radiometer, Copenhagen, Denmark), and the ventilation was adjusted to
maintain O2 at 90-120 mmHg and CO2 at
35-45 mmHg. [Glucose]plasma was determined in
duplicate by the glucose oxidase method in a Glucose Analyzer II
(Beckman, Fullerton, CA). Glucose consumption was calculated from the
average steady-state glucose infusion rate. [Insulin] was measured
externally relative to human standards (VetResearch, White Plains, NY)
from blood samples taken 10 min before the end of each clamp period.
NMR spectroscopy.
NMR spectra were recorded on a 4.7 T horizontal bore Bruker Biospec
spectrometer. The radio frequency probe consisted of two concentric coils: a 5-cm 1H-coil (200.4 MHz) for C-H
decoupling and a 1.8 × 2-cm elliptical, double-turn, double-tune
coil for 13C (50.4 MHz) and 31P (81.1 MHz). The
inner coil was used for shimming on the H2O signal when
tuned by means of an external network. Water half-widths of 30-40
Hz were obtained routinely.
13C and 31P spectra were acquired
simultaneously in 11-min blocks, 13C NMR acquisitions
(TR = 100 ms) interleaved with 31P NMR acquisitions
(TR = 4 s). For 13C we used a 52-µs, 180°
hard pulse at the coil center; for 31P we used a 90° BIR4
adiabatic pulse (2.5 ms duration). Glycogen 13C-1 intensity
was measured at 100.5 parts per million (ppm) in 40-Hz line-broadened
spectra. For each block, 2,736 13C and 72 31P
scans were obtained.
The procedure for quantitating the concentration of G-6-P
and other phosphorylated metabolites from the 31P NMR
spectra (see Fig. 2) was the same as that described in Bloch et al.
(1), in which the method was validated against traditional chemical extraction. Levels of phosphorylated metabolites were determined from 31P spectra summed over 40 min during
baseline H and E periods (Fig. 2, inset). The one-half area
of the G-6-P peak (6.31 to 6.33 ppm relative to
Pi) and the Pi peak (0 to
1 ppm relative to
Pi) were measured in the 10-Hz line-broadened baseline
spectra, such as in Fig. 2. The peaks
correspond to phosphomonoesters (PME, including G-6-P)
Pi, phosphocreatine (PCr),
-ATP,
-ATP, and
-ATP.
The concentration of metabolites was determined by comparing the
spectral areas to the area of the
-ATP peak, for which the
concentration is assumed to be 7.2 mM (1). Difference
spectra were generated by subtracting the baseline from the E and H
spectra, as shown in the inset in Fig. 2. The [G-6-P] and
[Pi] for E and H were determined by integrating the
remainder of the peaks and comparing these to the ATP area. For total
concentration during H and E, the difference is added to the baseline
[G-6-P] and [Pi].

View larger version (25K):
[in this window]
[in a new window]
|
Fig. 2.
Sample 31P spectra, with the characteristic
phosphomonoester peaks (left to right): inorganic
phosphate (Pi), phosphocreatine (PCr), -ATP, -ATP,
and -ATP. Inset: ×10 magnification of the glucose
6-phosphate (G-6-P) peak (crosshatched) from difference
spectra for H [H to baseline (B)] and E (E to baseline). ppm, Parts
per million.
|
|
In vitro assays.
Total [glycogen] was determined by amyloglucosidase digestion of
precipitated glycogen. The [13C]glucose enrichments of
glucose in extracted glycogen and plasma were determined by gas
chromatography-mass spectrometry, as described previously
(2). The fraction of GSase in the
G-6-P-independent form (GSase%I) was assayed from the
incorporation of [14C]glucose into glycogen by a
modification of the method of Thomas (34) at 0 and 6.7 mM
G-6-P, as described previously (2). The GSase
velocity in muscle homogenates was assayed enzymatically in a
"physiological" mixture containing 8.4% glycogen, 0.1 mM UDP-glucose (UDPG), 7.2 mM ATP, and 0, 0.2, 0.4, 0.8, and 1.2 mM
G-6-P, corresponding to the in vivo range of
[G-6-P].
Calculations.
The [glycogen] at each time point was calculated as in Bloch et al.
(2) from the increment in the 13C spectra and
the [1-13C]glucose enrichment. The synthesis rates
reported for E and H were calculated from the slope of the linear
regression of the glycogen concentrations over the 50 min of the clamp periods.
MCA.
The MCA description of the glycogen synthesis pathway used to calculate
the flux control coefficients is described in the APPENDIX.
The responsivity coefficient at euglycemia was calculated from the
change in glycogen synthesis rate in going from E to H by use of the
following expression (32), which takes into account the
noninfinitesimal change in plasma glucose concentration
|
(2)
|
where J is the in vivo or in vitro glycogen synthesis
flux, and G is the concentration of plasma glucose. The in vitro and in
vivo elasticities of GSase to G-6-P were calculated using
|
(3)
|
where G-6-P is the concentration of glucose
6-phosphate. The elasticity of GT/Hk to G-6-P was calculated
from the expression
|
(4)
|
The term JGT/Hk is total muscle glucose
uptake, which is the sum of muscle glycogen synthesis and glycolysis.
For calculations, whole body glucose uptake was used to approximate
muscle glucose uptake. Under the experimental conditions of
hyperinsulinemia, studies have shown that the muscle is the major
pathway of disposal of infused glucose. All elasticity values were
calculated with the group averages.
A minimum estimate of the glycogen synthesis flux control coefficient
for GT/Hk at euglycemia was calculated from the responsivity (30)
|
(5)
|
The relative glycogen synthesis flux control coefficients of
GSase, GT/Hk, and glycolysis were calculated using the following expressions that are derived in the APPENDIX. The in vivo
value for 
was used in these calculations. Elasticities and control coefficient values were calculated for
Jglycolysis/JGT/Hk
ranging from 0.14 to 0.50. This will maximize the estimate of
C
and minimize the estimate
of C
.
|
(6)
|
|
(7)
|
|
(8)
|
All results are presented as means ± SE. Statistical
significance was calculated using a two-tailed Student's
t-test for the paired data.
 |
RESULTS |
Glucose clamps.
The concentrations of plasma glucose for individual animals during the
E and H periods are shown in Table 1.
Plasma glucose concentration increased 2.5 ± 0.03-fold, averaging
5.45 ± 0.05 and 13.8 ± 0.14 mM during the E and H clamps,
respectively. The whole body glucose consumption increased to the same
degree (2.8 ± 0.3-fold) as the plasma glucose consumption,
averaging 123 ± 19 and 315 ± 17 µmol · kg
1 min
1 during
the E and H periods, respectively. The concentrations of plasma insulin
were similar during the H and E periods [308 ± 55 vs. 216 ± 32 mU/ml, not significant (NS) P < 0.3].
View this table:
[in this window]
[in a new window]
|
Table 1.
Glycogen synthesis rates and glucose plasma concentration values
for individual animals during clamp periods
|
|
Glycogen synthesis.
The animals varied in the starting [glycogen], ranging from 13.5 to
31.8 mmol/kg wet wt, with the average 21.0 ± 2.5 mmol/kg wet wt.
The total amount of glycogen synthesized during the experiment ranged
from 15 to 41 mmol/kg wet wt. Individual curves of the increments in
[glycogen] during the hyperinsulinemic clamp are shown in Fig.
3. The synthesis rate averaged 0.087 ± 0.012 and 0.24 ± 0.03 mmol · kg
1 · min
1
(P < 0.01) during E and H, respectively. The rates of
glycogen synthesis for individual animals are listed in Table 1.
Although the rates of glycogen synthesis varied between animals, the
relative rates during the E and H periods were similar in all animals
(Table 1). The average glycogen synthesis rate increased in proportion with the [glucose]plasma (Fig.
4).

View larger version (33K):
[in this window]
[in a new window]
|
Fig. 3.
Glycogen increments over
starting [glycogen] for 6 animals clamped at E followed by H. [Glycogen] for the 7th animal, for which the clamp order was
reversed, is not shown. Values in text are averages of all 7 animals.
Time 0 is start of glucose/insulin/somatostatin
infusion.
|
|

View larger version (20K):
[in this window]
[in a new window]
|
Fig. 4.
Relative glycogen synthesis rates (means ± SE, gray
bars) vs. [glucose]plasma (means ± SE, open bars).
Rates increased 2.7-fold, whereas [glucose]plasma
increased 2.5-fold, from E to H.
|
|
Concentrations of phosphorylated effectors.
To verify the constancy of phosphorylated effectors of GSase, the
concentrations of ATP and Pi were measured from different spectra under H and E conditions. The concentration of Pi
did not change with plasma glucose level (1.4 ± 0.09 mM at E vs.
1.5 ± 0.1 at H, NS, P < 0.4). The concentration
of ATP, which was assumed to be 7.2 mM, remained constant throughout
the study.
To assess the relative elasticities of GSase and GT/Hk to
G-6-P, we measured the in vivo G-6-P
concentration (Table 2). The baseline
G-6-P concentration was 0.18 ± 0.02 mM. The
G-6-P concentration did not increase significantly over
baseline during the E portion of the clamp (0.22 ± 0.03 mM, NS,
P < 0.3). During the H portion of the clamp, the
concentration of G-6-P increased by
= 0.22 ± 0.03 mM over baseline (P < 0.001). The increase in
[G-6-P] was smaller than the increase in glycogen
synthesis rate between E and H, as shown in Fig.
5.

View larger version (19K):
[in this window]
[in a new window]
|
Fig. 5.
Relative glycogen synthesis rates (gray bars) vs.
[G-6-P], (means ± SE, open bars).
[G-6-P] increased 1.7-fold, whereas the synthesis rate
increased 2.7-fold.
|
|
In vitro GSase%I and velocity as a function
of [G-6-P].
To verify that the activity of GSase was not altered by the change in
glucose concentration, the GSase%I was measured in vitro under
standard conditions. No difference was found in GSase%I between E and
H conditions (38 ± 3 vs. 44 ± 3%, NS, P < 0.2).
To assess the regulation of GSase velocity by G-6-P, we
measured the velocity of GSase extracted under E and H conditions as a
function of [G-6-P] under physiological concentrations of Pi and ATP. The curve for the velocity of the enzyme
extracted under E and H as a function of [G-6-P] is shown
in Fig. 6. The velocity in the in vivo
range of [G-6-P] was determined from a linear regression.
When the in vivo concentrations of G-6-P were used, the
velocity for E at 0.22 mM G-6-P was found to be 14.6 mU · kg
1 min
1 and that for H at
0.40 mM G-6-P to be 26.1 mU · kg
1
min
1. The 1.8-fold change in in vitro velocity is
significantly lower (P < 0.001, Z-test)
than the 2.8 ± 0.2-fold change in glycogen synthesis flux.

View larger version (16K):
[in this window]
[in a new window]
|
Fig. 6.
In vitro glycogen synthase (GSase) velocity
(mU · kg wet wt
muscle · min 1) in a physiological
assay buffer [5.5 mM ATP inhibitor, 8.4% glycogen, 0.1 mM uridine
diphosphate glucose (UDPG)] as a function of [G-6-P] for
Gsase%I = 41 ± 2%, ± SE. The formula of the dotted
regression line is V (velocity) = 64 · [G-6-P] + 0.50 (r = 0.997).
|
|
Calculation of responsivity.
The responsivity of glycogen synthesis flux (J) to plasma
glucose was calculated from Eq. 2 and the measured
fractional change in glycogen synthesis and
[glucose]plasma for each animal (Table 1). The values of
R
for individual animals
ranged from 0.88 to 1.13, with an average
R
= 1.1 ± 0.03 (Table
1). From this value and Eq. 6, the
C
= 1.1 ± 0.03 for
the GT/Hk step.
Calculation of elasticities to [G-6-P].
The elasticity of GSase to [G-6-P] was calculated from the
measured changes in the velocity of GSase in the in vitro assay and
Eq. A9 to be 
= 0.79. The in vivo elasticity of GSase to [G-6-P]
was higher; 
= 1.9. The 
values were determined using Eq. 5 for a range of ratios of glycolysis
to GT/Hk. For the range of ratios of 0.15 to 0.4, the

ranged from
0.185 to
0.556. Ratios <0.15 yielded values of

>0, which would correspond to
activation of GT/Hk by product G-6-P.
Calculation of flux control coefficients from elasticities.
From the calculated 
values and
the in vivo 
at each ratio of
glycolytic and GT/Hk flux, the control coefficients for GT/Hk, GSase,
and glycolysis were calculated (Table 3.)
The values were calculated for a glycolytic flux ranging from 0.15 to
0.4 times the flux through the GT/phosphorylation step. Throughout the
range of glycolytic flux ratios, GT/Hk has the largest control coefficient for the glycogen synthesis flux, with a constant
C
~1.1 compared with
C
<0.5. The highest ratios
of C
to C
were found at a
glycolytic flux equal to 0.15 of the GT/Hk step. The absolute
value of the C
was smaller
than C
at all
ratios of
Jglycolysis/JGT/Hk.
View this table:
[in this window]
[in a new window]
|
Table 3.
Calculated values of control coefficients for GT/Hk, GSase, and
glycolysis for the flux for glucose through glycogen synthesis
|
|
 |
DISCUSSION |
Because of the coordinate increases in the activity of GT, Hk, and
GSase with insulin, it has long been difficult to assess the
flux-controlling step(s) in the muscle glycogen synthesis pathway. In
this study, we applied MCA to determine quantitatively the
contributions of GT/Hk, GSase, and glycolysis to the control of this
pathway. The synthesis rate of muscle glycogen was measured at two
glucose concentrations during a hyperinsulinemic clamp to alter GT
activity. A flux control coefficient of
C
= 1.1 ± 0.03 was
calculated for the GT/Hk step from the responsivity to glucose
and Eq. 6, which indicates that the rate of glycogen synthesis is approximately proportional to the total activity of this
step. An independent measure of
C
based on the elasticities
and the Branch Point Theorem yielded values comparable to the direct
measure (Table 3). The measured in vitro and in vivo elasticity of
GSase to G-6-P was high relative to the elasticity of GT/Hk
measured in vivo, also indicative of minimal control by GSase over the
muscle glycogen synthesis flux. Although glycolysis was not measured
directly, it was shown not to affect the conclusion that GT/Hk is the
major flux control point, whereas GSase exerts less control over the
glycogen synthesis flux than does glycolysis. In the sections to
follow, we discuss evidence supporting the validity of the MCA approach
used here and additional applications for the control of glycogen synthesis.
Validation of the MCA model of muscle glycogen
synthesis.
The primary assumption in applying MCA to calculate flux control is
that the activity of GT/Hk may be altered (through plasma glucose
concentration) without affecting the activity of GSase other than
through a change in the concentration of G-6-P. A change in
G-6-P concentration is allowable, because it is internal to the portion of the glycogen synthesis pathway being modeled (13, 31). The primary external effectors of GSase activity are ATP and Pi, which were measured by 31P NMR and
found not to change between the E and H stages of the clamp. The
constancy of ATP agrees with the findings in 31P NMR
studies of human muscle during hyperinsulinemia (26, 27). In human studies, a small increase in [Pi] was measured
during H relative to E under hyperinsulinemic conditions that was not observed in the rat muscle. The GSase activity may also be altered by
phosphorylation. To assess whether this occurred, the GSase%I was
measured and found to be the same under E and H conditions at the
insulin level used in this study. This finding is in agreement with a
previous study of human muscle (39), which found that, under high plasma insulin, GSase%I is independent of plasma glucose concentration.
Effects of muscle glycolysis on the calculated control
coefficients.
To calculate a flux control coefficient for GSase, it was assumed that
the muscle glycolytic flux is independent of plasma glucose
concentration under hyperinsulinemic conditions. If this is the case,
then the elasticity of glycolysis to G-6-P is negligible, and the control coefficient of GSase may be directly calculated from
the relative elasticities of GT/Hk and glycolysis to G-6-P. The independence of muscle glycolysis to glucose concentration is
supported by several studies that estimated the constancy of muscle
glycolysis either from measurements of whole body glucose oxidation
(27, 40), for which muscle is the primary disposal pathway
under hyperinsulinemic conditions, or from arteriovenous difference
measurements across limbs (22). Under almost identical conditions of plasma insulin and glucose as used in the present study,
Farrace and Rossetti (11) measured no change in glycolysis with glucose concentration.
Because glycolysis was not directly measured, the flux control
coefficients were calculated for a range of glycolytic fluxes from 0.15 to 0.4, the rate of the flux through the GT/Hk combined reactions. The
minimal value of 0.15 was used because

0 at ratios <0.145, which
would indicate the improbable activation of Hk by product
G-6-P. The maximum ratio of 0.5 was determined from the
ratio of whole body glucose oxidation to whole body glucose uptake
measured by Farrace and Rossetti (11), providing a maximum estimate of muscle glycolysis under these conditions of
hyperinsulinemia because it neglects other tissues oxidizing glucose,
such as the brain. More recently, Jucker et al. (15)
measured directly the rates of rat muscle glycolysis and glycogen
synthesis under conditions of euglycemic and hyperglycemic
hyperinsulinemia using 13C NMR. They found that the muscle
glycolysis flux did not change with plasma glucose level, which
supports our assumption that the elasticity of glycolysis to
G-6-P is close to 0. They measured a ratio for glycolysis of
0.3 to the total flux through GT/Hk under euglycemic conditions
(15). Over the entire range of ratios (see Table 3), it
was found that the flux control coefficient of GT/Hk is the highest for
the pathway, whereas control by GSase remains much smaller. At higher
values of the ratio of glycolysis to total GT/Hk flux, the glycolytic
pathway exerts significant flux control for glycogen synthesis. The
physiological significance of a high negative control coefficient of
glycolysis may be to allow the muscle to rapidly shunt glucose away
from storage as glycogen when an increase in energy is needed. Because
of the low elasticity of glycolysis and GT/Hk to G-6-P, an
increase in the glycolytic rate to meet the energy requirements of the
muscle would shunt glucose away from storage as glycogen in a near 1:1 ratio. In contrast to the situation in the rat muscle, the relative rate of muscle glycolysis to muscle glycogen synthesis under
hyperinsulinemic conditions in the human is low (27, 31),
and this pathway will have a small flux control coefficient.
Comparison with other work.
Several recent studies of muscle glycogen synthesis measured its rate
at different plasma glucose concentrations under hyperinsulinemic conditions. We have calculated the flux control coefficient for GT/Hk
from the results presented in these studies. The results of this
calculation are shown in Table 4
(11, 21, 22, 26). The values, ranging from 0.99 to 1.74, are consistent with the conclusion that GT/Hk exerts the majority of
flux control in the muscle glycogen synthesis pathway. The values are
generally greater than 1, which reflects the negative control
coefficient of glycolysis. In the study of Jucker et al.
(15), the change in glycogen synthesis rate and
G-6-P with glucose level was similar to the change in the
present study, which implies that the majority of control is exerted at
GT/Hk. The elasticities to G-6-P were estimated by
inhibiting glycolysis with a free fatty acid (FFA) infusion, which led
to a substantial decrease in total glucose uptake with only a small
increase in G-6-P. From this result they concluded that the
in vivo elasticity of GT/Hk is high (
2.18), and they reported that
the C
= 0.55 ± 0.1 compared with a C
= 0.30 ± 0.06. The discrepancy from our finding of a low
elasticity of GT/Hk may be reconciled by the subsequent finding that
the activity of glucose transport is reduced during FFA infusion
(10). In light of these findings, the reduction in total
glucose uptake during FFA infusion was more likely due to a reduction
in GT/Hk activity than a high elasticity of Hk, as proposed by the
authors.
GT may exert the majority of flux control for the
GT/Hk step.
In the present analysis, the GT- and Hk-catalyzed reactions are treated
as a single equivalent reaction, because the intracellular glucose
concentration was not measured. The relative control exerted by the
individual GT and Hk reactions may be determined from the intracellular
glucose concentration. Several studies, including two recent
13C NMR studies (5, 28), have found that,
under hyperinsulinemic conditions, intracellular muscle glucose is <1
mM, which is the precision of the measurement. The low concentration of
intracellular glucose relative to plasma glucose and the high
Michaelis-Menten constant of the transporters (~20 mM glucose)
(19) suggest that the glucose transport flux at euglycemia
is insensitive to changes in intracellular glucose concentration. From
this it may be concluded that transport is responsible for the major
part of flux control. Studies that have found a correlation between
unidirectional GT measured using nonmetabolizable glucose analogs and
muscle glucose uptake (3, 6) are consistent with GT having
a higher flux control coefficient than Hk.
Compartmentation.
A complication in the calculation of the in vivo elasticities is the
possibility of compartmentation of G-6-P leading to a different concentration in the environment of GSase than the whole tissue concentration measured by 31P NMR. This
compartmentation may be between different fiber types or within the
microenvironment of individual muscle cells. There is no effect of
compartmentation on the calculated flux control coefficient of GT/Hk
from the measured responsivity. The elasticity used in this calculation
(31) is a minimum value that is assumed on the basis of
the enzymatic properties of the isolated GT and Hk (31)
enzymes. Furthermore, the concentration of the modulated effector
(extracellular glucose) is not effected by compartmentation. For GSase
to have a high control coefficient, its elasticity to G-6-P
would have to be at least an order of magnitude lower than the values
measured in vivo and in vitro. On the basis of in vitro kinetics of the
enzyme, such a low elasticity would only occur at saturating
concentrations of G-6-P, which at the GSase%I ratio measured in vitro would only occur at G-6-P concentrations
well over 1 mM (25). This high local concentration is
unlikely, because it defeats the ability to regulate the enzyme by
phosphorylation, which alters the kinetics of GSase by shifting the
G-6-P association constant of the enzyme.
The role of GSase in maintaining G-6-P homeostasis.
The low flux control coefficient of GSase seems paradoxical, given the
known increase in GSase activity with insulin concentration (7,
35, 39). The GSase%I measured in the present study is
consistent with previous measurements under similar conditions and well
above the activity measured under basal insulin (21, 25).
An explanation we have proposed for the function of the insulin-dependent regulation of GSase phosphorylation state is that it
reduces the changes in G-6-P concentration required for the
velocity of the enzyme to match the rate set by the GT/Hk steps. As
shown by Roach and Larner (25) and others
(23), under in vivo concentrations of ATP, the velocity of
GSase has a sigmoidal relationship to %I at fixed G-6-P
concentrations. The region of maximum sensitivity to %I at the in vivo
G-6-P concentration of 200-400 µmol/kg is in the
30-40%I range achieved by insulin.
The high in vivo elasticity of GSase to G-6-P (Fig. 6) would
further act to reduce the changes in G-6-P concentration
needed to accommodate changes in GT/Hk velocity due to plasma glucose. A high elasticity to G-6-P was also measured in human muscle
by use of 31P NMR to measure G-6-P
concentrations (26). The high elasticity may be explained
by the sigmoidal relationship between GSase velocity and
G-6-P concentration under simulated in vivo conditions when GSase%I is <60% (25). We found the slope of the in
vitro GSase velocity vs. G-6-P curve to be greater than
unity in the in vivo G-6-P range (Fig. 6), which supports
this explanation. However, within the accuracy of the in vivo measure
of G-6-P concentration, other mechanisms cannot be ruled out.
Conclusions.
Under hyperinsulinemic conditions, the combined reactions of GT and Hk
primarily determine the rate of muscle glycogen synthesis in the rat.
The use of different plasma glucose levels to modulate GT/Hk activity
allows MCA to be applied to the pathway, because effectors external to
the glycogen synthesis pathway, such as ATP and the activity of
GSase%I, were not affected by the glucose level. The low
control coefficient of GSase is consistent with our previous proposal
that the role of insulin stimulation of GSase dephosphorylation is for
maintaining G-6-P homeostasis rather than controlling the
flux (31). Because of the enhanced rate of glycolysis in
rat muscle relative to human muscle, there may be a significant role
for glycolysis in the control of the rate of glycogen synthesis.
However, the primary control of the rate of muscle glycogen synthesis
is exerted by the combined reactions of GT and Hk.
 |
APPENDIX |
In the MCA model of the glycogen synthesis pathway
(30), the pathway is simplified into a two-step reaction.
The combined reactions of GT and Hk convert extracellular glucose to
G-6-P. Subsequently, G-6-P is converted by the
combined reactions of glucose phosphate isomerase, UDP-glucose
transferase, and glycogen synthase to glycogen. Because GSase is the
only enzyme in the proximal reactions that changes activity with
insulin, this series of reactions is referred to as GSase. The
combination of sequential reaction steps into a single equivalent
reaction has been shown to be valid, provided that substrates within a
grouped series of reactions do not act as effectors outside of the
group (13). For the muscle glycogen synthesis pathway,
G-6-P is the only substrate that effects the activity of
both the GT/Hk and GSase group of enzymes (38) and is
therefore treated explicitly in the model.
The most direct method for determining the flux control coefficients of
the enzymes in the glycogen synthesis pathway would be to vary the
activity of each enzyme individually and to measure the resultant
change in glycogen synthesis flux. For the case of muscle glycogen
synthesis, it is not possible to directly alter the activity of GT/Hk
without affecting the activity of GSase because of the coordinated
regulation of these enzymes. In MCA, several methods have been
developed to calculate flux control coefficients by modulating the in
vivo velocity of an enzyme through variation of the concentration of
either substrates or allosteric effectors. In this APPENDIX
we describe the application of MCA to determine
C
,
C
, and
C
from the
experimental data.
The glycogen synthesis flux control coefficient for the combined GT and
Hk reactions is defined as
|
(A1)
|
where EGT/Hk is the total activity of the GT/Hk
step, and J is the glycogen synthesis flux. The combined
activity of GT/Hk is used in the analysis because the concentration of
intracellular glucose cannot be directly measured. The sum of all the
control coefficients is equal to 1 for an arbitrary metabolic pathway. The flux control coefficients of GT/Hk and GSase are related by the
summation theorem of MCA (16)
|
(A2)
|
The additional control coefficient is for glycolysis, which
shunts G-6-P away from glycogen synthesis.
Determination of CGT/Hk
from the Measured Responsivity
In the present study, we modulated the activity of the combined
GT/Hk step through changing the level of the substrate, plasma glucose
(Go). The measured change in the glycogen synthesis flux was used to quantitate the responsivity
(R
) of the pathway
flux, where
|
(A3)
|
The responsivity yields an estimate for
C
at euglycemia from the
relationship (17)
|
(A4)
|
It has been shown for the combined reactions of GT and Hk that
1 (31), so that a minimum estimate of the flux
control coefficient of GT/Hk is given by
|
(A5)
|
Equation A5 was used to calculate
C
from the experimental
measurement of the responsivity (Eq. 3).
Determination of C
and
C
from the Measured Elasticities
to G-6-P and the Branch Point Theorem
The relative control of GT/Hk and GSase was determined from the
sensitivity of the velocity of these reactions to the change in
G-6-P concentration. This sensitivity, termed
"elasticity" (
), is
defined as the fractional change in enzyme velocity (V) for
a fractional change in the level of an effector, Z
|
(A6)
|
This relationship is valid at the in vivo substrate and effector
levels. The value may be quantitated in vivo, or in vitro if assayed in
the presence of all effectors at their in vivo levels. On the basis of
the connectivity theorem of MCA (16), the control coefficients for GT/Hk and GSase and glycolysis are related by the
elasticities of these pathways to G-6-P:
|
(A7)
|
The reaction that is more sensitive to changes in
G-6-P has lower flux control for glycogen synthesis. Because
of the low elasticity of glycolysis to G-6-P, the above
relationship holds, even though the pathway branches at
G-6-P, as will be shown.
A third relationship among the control coefficients of GT/Hk, GSase,
and glycolysis is provided by the branch point theorem of Fell and
Sauro (13)
|
(A8)
|
The terms JGT/Hk and
Jglycolysis are the fluxes through the
GT/phosphorylation-combined reactions and glycolysis, respectively. Equations A2, A7, and A8 were solved for expressions for
C
, C
, and
C
in terms of the
elasticities and the fluxes JGT/Hk and
Jglycolysis
|
(A9)
|
|
(A10)
|
|
(A11)
|
In Vivo Elasticities of GT/Hk,
GSase, and Glycolysis to G-6-P
Relative flux control was determined from the ratio of the in
vivo elasticity of GSase to the in vivo elasticity of GT/Hk to
G-6-P changes (Eq. A7). The in vivo elasticity of
GSase was calculated using Eq. 4 in the text. Calculation of
the elasticity of GT/Hk is complicated by the change in the external
substrate, plasma glucose. Writing the velocity of the GT/Hk
step as a total differential in Go and G-6-P
gives
|
(A12)
|
Because the GT/Hk reaction feeds both glycogen synthesis and
glycolysis, the flux J' is the sum of these pathways.
Equation A12 may be solved for

, yielding
|
(A13)
|
We have shown previously that, as a result of the kinetic
properties of GT and Hk, the maximum value for

= 1 (31). Because

0 because of product
inhibition of the Hk reaction, and both the fractional increase of
G-6-P concentration
(
G-6-P/G-6-PE) and total glucose
uptake (
JGo/JGo) were
positive at the higher plasma glucose concentration, then the maximum
negative value of 
is
given when 
is set to
its maximum value of 1
|
(A14)
|
The value 
was
calculated for a range of
Jglycolysis/JGT/Hk values
(0.5-0.15) and used in Eq. A4.
Effect of Glycolysis
Previously, glycolysis was not included in the MCA of the
glycogen synthesis pathway, because in nondiabetic human subjects it is
a small fraction of total glucose uptake under hyperglycemic hyperinsulinemic conditions (31). Under the experimental
conditions in the rat muscle, glycolysis may account for up to one-half
of the glucose uptake at euglycemic conditions and is therefore
included in the control analysis.
According to measurements by Farrace and Rossetti (11),
the rate of muscle glycolysis does not change with plasma glucose during hyperinsulinemia. Therefore,

was set to 0 in Eq. A9 for calculation of the flux control coefficient of GSase.
If this assumption is not correct, and the

> 0, the effect would be
that our assumption leads to an overestimation of the control
coefficient of GSase, because

is positive, whereas

is negative. The calculations
of flux control coefficients (Eqs. A9, A10, and
A11) were performed for a range of
Jglycolysis from 0 to 0.5 JGT/Hk.
 |
FOOTNOTES |
Address for reprint requests and other correspondence: J. R. Chase, Dept. of Chemistry, Northwest Nazarene Univ., 623 Holly St.,
Nampa, ID 83686 (E-mail: jrchase{at}nnu.edu).
1
We define activity as the velocity of the enzyme
under fixed conditions of substrate and allosteric effector
concentration. In some cases this is proportional to enzyme concentration.
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.
Received 31 January 2000; accepted in final form 11 December 2000.
 |
REFERENCES |
1.
Bloch, G,
Chase JR,
Avison MJ,
and
Shulman RG.
In vivo 31P NMR measurement of glucose-6-phosphate in the rat muscle after exercise.
Magn Reson Med
30:
347-350,
1993[ISI][Medline].
2.
Bloch, G,
Chase JR,
Meyer DB,
Avison MJ,
Shulman GI,
and
Shulman RG.
In vivo regulation of rat muscle glycogen resynthesis after intense exercise.
Am J Physiol Endocrinol Metab
266:
E85-E91,
1994[Abstract/Free Full Text].
3.
Bogardus, C,
Lillioja S,
Stone K,
and
Mott D.
Correlation between muscle glycogen synthase activity and in vivo insulin action in man.
J Clin Invest
73:
1185-1190,
1984[ISI][Medline].
4.
Bonadonna, RC,
Saccomani MP,
Seely L,
Zych KS,
Ferrannini E,
Cobelli C,
and
DeFronzo RA.
Glucose transport in human skeletal muscle: the in vivo response to insulin.
Diabetes
42:
191-198,
1993[Abstract].
5.
Cline, GW,
Petersen KF,
Krssak M,
Shen J,
Hundal RS,
Trajanoski Z,
Inzucchi S,
Dresner A,
Rothman DL,
and
Shulman GI.
Impaired glucose transport as a cause of decreased insulin-stimulated muscle glycogen synthesis in type 2 diabetes.
N Engl J Med
341:
240-246,
1999[Abstract/Free Full Text].
6.
Cobelli, C,
Saccomani MP,
Ferrannini E,
DeFronzo RA,
Gelfand R,
and
Bonadonna R.
A compartmental model to quantitate in vivo glucose transport in the human forearm.
Am J Physiol Endocrinol Metab
257:
E943-E958,
1989[Abstract/Free Full Text].
7.
Craig, JW,
and
Larner J.
Influence of epinephrine and insulin on uridine diphosphate glucose-
-glucan transferase and phosphorylase in muscle.
Nature
202:
971-973,
1964[ISI].
8.
Danforth, WH.
Glycogen synthetase activity in skeletal muscle: interconversion of two forms and control of glycogen synthesis.
J Biol Chem
240:
588-593,
1965[Free Full Text].
9.
Deems, RO,
Evans RW,
Deacon CM,
Honer DT,
Chu K,
Bürki WS,
Fillers DK,
Cohen DK,
and
Young DA.
Expression of human GLUT4 in mice results in increased insulin action.
Diabetologia
37:
1097-1104,
1994[ISI][Medline].
10.
Dresner, A,
Laurent D,
Marcucci M,
Peterson K,
Cline GW,
Rothman DL,
and
Shulman GI.
Effect of free fatty acids on glucose transport and IRS 1 associated phosphatidylinositol 3-kinase activity.
J Clin Invest
103:
253-259,
1999[Abstract/Free Full Text].
11.
Farrace, S,
and
Rossetti L.
Hyperglycemia markedly enhances skeletal muscle glycogen synthase activity in diabetic, but not in normal conscious rats.
Diabetes
41:
1453-1463,
1992[Abstract].
12.
Fell, DA.
Metabolic control analysis: a survey of its theoretical and experimental development.
Biochem J
286:
313-330,
1992[ISI][Medline].
13.
Fell, DA,
and
Sauro HM.
Metabolic control and its analysis. Additional relationships between elasticities and control coefficients.
Eur J Biochem
148:
555-561,
1985[Abstract].
14.
Goodyear, LJ,
Hirshman MF,
Smith RJ,
and
Horton ES.
Glucose transporter number, activity, and isoform content in plasma membranes of red and white skeletal muscle.
Am J Physiol Endocrinol Metab
261:
E556-E561,
1991[Abstract/Free Full Text].
15.
Jucker, BJ,
Barucci N,
and
Shulman GI.
Metabolic control analysis of insulin-stimulated glucose disposal in rat skeletal muscle.
Am J Physiol Endocrinol Metab
277:
E505-E512,
1999[Abstract/Free Full Text].
16.
Kacser, H,
and
Burns JA.
The control of flux.
Soc Exp Biol
27:
65-104,
1973.
17.
Kacser, H,
and
Porteous JW.
Control of metabolism: what do we have to measure?
Trends Biochem Sci
12:
5-14,
1987[ISI].
18.
Katzen, HM.
The multiple forms of mammalian hexokinase and their significance to the action of insulin.
Adv Enzyme Regul
5:
335-356,
1967[Medline].
19.
King, PA,
Hirshman MF,
Horton ED,
and
Horton ES.
Glucose transport in skeletal muscle membrane vesicles from control and exercised rats.
Am J Physiol Cell Physiol
257:
C1128-C1134,
1989[Abstract/Free Full Text].
20.
Klip, A,
Ramlal T,
Young DA,
and
Holloszy JO.
Insulin-induce translocation of glucose transporters in rat hindlimb muscles.
FEBS Lett
224:
224-230,
1987[ISI][Medline].
21.
Kruzynska, YT,
Home PD,
and
Alberti KGMM
In vivo regulation of liver and skeletal muscle glycogen synthase activity by glucose and insulin.
Diabetes
35:
662-667,
1986[Abstract].
22.
Mandarino, LJ,
Consoli A,
Jain A,
and
Kelly DE.
Differential regulation of intracellular glucose metabolism by glucose and insulin in human muscle.
Am J Physiol Endocrinol Metab
265:
E898-E905,
1993[Abstract/Free Full Text].
23.
Piras, R,
Rothman LB,
and
Cabib E.
Regulation of muscle glycogen synthetase by metabolites. Differential effects on the D and I forms.
Biochemistry
7:
56-66,
1968[ISI][Medline].
24.
Ren, JM,
Semenkovich CF,
Gulve EA,
Gao J,
and
Holloszy JO.
Exercise induces rapid increased in GLUT4 expression, glucose transport capacity, and insulin stimulated glycogen storage in muscle.
J Biol Chem
269:
14396-14401,
1994[Abstract/Free Full Text].
25.
Roach, RJ,
and
Larner J.
Covalent phosphorylation in the regulation of glycogen synthase activity.
Mol Cell Biochem
15:
179-200,
1977[ISI][Medline].
26.
Rothman, DL,
Magnusson I,
Cline G,
Gerard D,
Kahn CR,
Shulman RG,
and
Shulman GI.
Decreased muscle glucose transport/phosphorylation is an early defect in the pathogenesis of non-insulin-dependent diabetes mellitus.
Proc Natl Acad Sci USA
92:
983-987,
1995[Abstract].
27.
Rothman, DL,
Shulman RG,
and
Shulman GI.
31P nuclear magnetic resonance measurements of muscle glucose-6-phosphate. Evidence for reduced insulin-dependent muscle glucose transport or phosphorylation activity in noninsulin-dependent diabetes mellitus.
J Clin Invest
89:
1069-1075,
1992[ISI][Medline].
28.
Roussel, R,
Velho G,
Carlier PG,
Jouvensal L,
and
Bloch G.
In vivo NMR evidence for moderate glucose accumulation in human skeletal muscle during hyperglycemia.
Am J Physiol Endocrinol Metab
271:
E434-E438,
1996[Abstract/Free Full Text].
29.
Shulman, GI,
Rothman DL,
Jue T,
Stein P,
DeFronzo RA,
and
Shulman RG.
Quantitation of muscle glycogen synthesis in normal subjects and subjects with non-insulin-dependent diabetes by 13C nuclear magnetic resonance spectroscopy.
N Engl J Med
322:
223-228,
1990[Abstract].
30.
Shulman, RG,
Bloch G,
and
Rothman DL.
In vivo regulation of muscle glycogen synthase and the control of glycogen synthesis.
Proc Natl Acad Sci USA
92:
8535-8542,
1995[Abstract].
31.
Shulman, RG,
and
Rothman DL.
Enzymatic phosphorylation of muscle glycogen synthase: a mechanism for maintenance of metabolic homeostasis.
Proc Natl Acad Sci USA
93:
7491-7495,
1996[Abstract/Free Full Text].
32.
Small, JR,
and
Kacser H.
Responses of metabolic systems to large changes in enzyme activities and effectors. 1. The linear treatment of unbranched chains.
Eur J Biochem
213:
613-624,
1993[Abstract].
33.
Small, JR,
and
Kacser H.
Responses of metabolic systems to large changes in enzyme activities and effectors. 2. The linear treatment of branched pathways and metabolite concentrations. Assessment of the general non-linear case.
Eur J Biochem
213:
625-640,
1993[Abstract].
34.
Thomas, JA,
Schlender KK,
and
Larner J.
A rapid filter paper assay for UDPglucose-glycogen glucosyltransferase, including an improved biosynthesis of UDP-14C-glucose.
Anal Biochem
25:
486-499,
1968[ISI][Medline].
35.
Thornburn, AW,
Gumbiner B,
Bulacan F,
Brechtel G,
and
Henry RR.
Multiple defects in muscle glycogen synthase activity contribute to reduced glycogen synthesis in non-insulin dependent diabetes mellitus.
J Clin Invest
87:
489-495,
1991[ISI][Medline].
36.
Tsao, TS,
Burcelin R,
Katz EB,
Huang L,
and
Charron MJ.
Enhanced insulin action due to targeted GLUT4 overexpression exclusively in muscle.
Diabetes
45:
28-36,
1996[Abstract].
37.
Wilson, CM,
and
Cushman SW.
Insulin stimulation of glucose transport activity in rat skeletal muscle: increase in cell surface GLUT-4 as assessed by photolabelling.
Biochem J
299:
755-759,
1994[ISI][Medline].
38.
Wilson, JE.
Regulation of Carbohydrate Metabolism. Boca Raton, FL: CRC, 1985, vol. I, p. 45-85.
39.
Yki-Järvinen, H,
Mott D,
Young AA,
Stone K,
and
Bogardus C.
Regulation of glycogen synthase and phosphorylase activities by glucose and insulin in human skeletal muscle.
J Clin Invest
80:
95-100,
1987[ISI][Medline].
40.
Yki-Järvinen, H,
Young AA,
Lamkin C,
and
Foley JE.
Kinetics of glucose disposal in whole body and across the forearm in man.
J Clin Invest
79:
1713-1719,
1987[ISI][Medline].
Am J Physiol Endocrinol Metab 280(4):E598-E607
0193-1849/01 $5.00
Copyright © 2001 the American Physiological Society