Simulation study of control of hepatic glycogen synthesis by glucose and insulin.

AMERICAN JOURNAL OF PHYSIOLOGY Vol. 231, No. 5, November 1976. Printed

Simulation synthesis

in U.S.A.

study of control of hepatic by glucose and insulin

MAHMOUD EL-REFAI AND RICHARD N. BERGMAN Department of Biomedical Engineering, University of Southern Los Angeles, California 90007

California,

action effect of the substrate on the anabolic pathway between glucose and glycogen (the “push” hypothesis (28)). However, a second intriguing possibility has been proposed by DeWulf and Hers and their colleagues (12, 15). That group suggests that glucose stimulates glycogen deposition by activating the enzyme glycogen synthase (UDPG-glycogen glucosyltransferase). Activation occurs when synthase 6 is dephosphorylated to the active form, synthase a. They suggest that the resulting conversion of uridine diphosphate (UDP) glucose to glycogen acts to “pull” glucose 6-phosphate to glycogen, presumably by lowering the concentration of moieties intermediate between the intracellular glucose and glycogen. The extent and manner by which insulin interacts with this proposed mechanism are unknown. Glucose has been demonstrated to increase the activity of a glycogen synthase purified from liver in vitro (12, 13). However, it remains unclear whether such an activation, even if it occurred in vivo, would result in the “pulling” of glucose carbon into glycogen. The quantitative effect of synthase activation on glucose uptake is dependent on the kinetics of the pathway of glycogen synthesis. The major purpose of this theoretical study was to compare the “push-and-pull” hypotheses, to determine which is a more suitable explanation of the effect of glucose on glucose uptake, given the known kinetics of hepatic glycogen metabolism. A second goal was to identify the manner by which insulin modulates the glucose effect. A dynamic model of glycogen metabolism is proposed which can represent the dynamic interactions between glycogen synthesis and degradation and gluconeogenesis. Kinetic parameters used in the model were obtained from literature reports. Using the model, we explored a variety of hypotheses concerning the actions of glucose and. insulin on glycogen metabolism.

EGREFAI, MAHMOUD,ANDRICHARDN.BERGMAN. Simulation study of control of hepatic glycogen synthesis by glucose and insulin. Am. J. Physiol. 231(5): 1608-1619. 1976. -The plausibility of various hypotheses concerning the effects of glucose and insulin on hepatic glycogen synthesis were tested by proposing a new dynamic model of glucose metabolism in the liver. The model consisted of six compartments representing extracellular glucose, and intracellular glucose, glucose 6phosphate, glucose l-phosphate, uridine diphosphate glucose, and glycogen. Given a set of kinetic parameters which were obtained from literature reports, the model predicted values of intermediates which were close to those reported for the liver, sampled from fasting animals. The model predicts that glucose can generate significant glycogen deposition by engendering the inhibition of glucose-6-phosphatase, but not by mass action, glycogen synthase activation, or phosphorylase deactivation. The model predicts that, although insulin can inhibit glucose production by lowering phosphorylase and gluconeogenesis, only an insulin-mediated induction of glucokinase can account for insulin’s action to potentiate the effect of glucose alone on glycogen synthesis.

hepatic carbohydrate metabolism; insulin action; biochemical kinetics; substrate cycling; metabolic control

OF GLUCOSE in the blood from exogenous sources results in rapid deposition of hepatic glycogen at a rate which can exceed 1% of liver weight per hour. Because deposition occurs at much lower rates in animals rendered diabetic (20, 28), it was believed for many years that insulin, secreted in response to the glucose load, was responsible for the glycogen synthesis. In recent years, however, attention has shifted to glucose itself as being the primary stimulus to the synthesis of hepatic glycogen. A rise in the portal glucose concentration, without any change in insulin, is a sufficient stimulus for glucose uptake (8, 19, 40). Whereas insulin is a primary inhibitor of hepatic glucose production by glycogenolysis and gluconeogenesis (5, 25), its role in glycogen synthesis seems to be limited to modulating the sensitivity of the glycogen synthetic pathway to glucose (4). Also, insulin is necessary to maintain the pathway of glycogen biosynthesis (36, 41). The recent emergence of the notion that glucose is the most significant regulator of glycogen deposition in liver has resulted in new uncertainty about the mechanism by which glycogen synthesis is controlled. The glucose effect is most easily explained by a simple mass

glycogen

THE APPEARANCE

MODEL

OF

Structure

GLYCOGEN

METABOLISM

and Assumptions

The liver was considered to be “one large hepatocyte” in the sensethat hemodynamic influences and the possibility that differing hepatic cell types make different contributions to the metabolic response of the liver vis a vis carbohydrate metabolism were ignored. Thus, it is considered that the dynamic responses of hepatic carbohydrate metabolism to variations in substrate levels in

1608

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MODEL

OF

GLYCOGEN

1609

SYNTHESIS

perfusate blood result from the movement of the substance in and out of the hepatocyte and the metabolic consequences once the substance is inside. The model is composed of six compartments (Fig. 1, GLOSSARY). They are: I ) glucose concentration in hepatic plasma, and the concentrations of the following in liver cell water: 2) glucose, 3) glucose 6=phosphate, 4) glucose l-phosphate, 5) uridine-diphosphate glucose, and 6) glycogen. Intracellular moieties were assumed to coexist in one well-mixed volume, and the rates of reaction between intermediates were therefore a function of-the activities within that volume. Gluconeogenesis was* inr eluded as a constant source of mass entering the glucose 6-phosphate pool, and the rate of appearance of glucose 6-phosphate from that source was constant except in the reprepresence of insulin. Thus, “net” gluconeogenesis sents the sum total of appearance and disappearance of glucose 6-phosphate by pathways other than glycogen synthesis or degradation, glucose phosphorylation, or glucose 6-phosphate dephosphorylation. The intracellular levels of intermediates were not predetermined. Only the plasma glucose level, the glycogen level, and the rate of gluconeogenesis were supplied to the model. The intracellular levels of ATP and UTP, as well as enzyme cofactors were not included in the model as variables, as they were assumed to be not rate limiting for glycogen synthesis and degradation. Equation

rate of G6-Gl phoglucomutase The rates of mass flux expressed by appropriate

System

WUI

rate of glucose phosphorylation via glucokinase + rate of phosphorylation via glucose-6-phosphatase + rate of G6 production via gluconeogenesis + rate of Gl to G6 conversion via phosphoglucomutase - rate of dephosphorylation via glucose-6-phosphatase -

- VlGK

WA1 ~ = VlGK

dt - VlPP + V2PR

(3%

ACTIVE

- VlPR

- [GUI)

- VZPH

+ gluconeogenesis + V2PR

- VlPR

dt

d[GLP] dt

= VlST

+ VlPR

K ss = f([GA],

[Gl]

d[cAMP] dt

- V2PR

Zx)

PART

PHORYLASE

t

t

I

I GLUCOSE 5.5

GLUCOKINASE

2

h

G L U C 0 N E 0 G E N E S : L

4 IN I IO”

(4) (5) (6) (7)

(8) 1)

y - fi[cAMPl

(9)

(lo)

Parameters

pyrophosphorylase

catalyzes

the reaction

UTP + GlP e UDPG + PPI

(6%)

It

=

p (Kssl+

(3)

The kinetic parameters (Table 1) were obtained from literature reports of in vitro measurements, except for VM2PP. VM2PP was calculated as follows UDPG

PHOSPHOR

PHOSPHATASE

= [GA]

(2)

+ VZPP

mJD1 = ViPP - V2PP - VlST

LIVER)

THASE

PLASMA m/ml

1. Model of glycogen metabolism. All intracellular moieties assumed to coexist in one well-mixed volume. Gluconeogenesis asnathwavs. sumed to be net sum of all nomzlvcoeen FIG.

+ K([GP]

+ VlPH

Zx = V2PP - VlPP

Kinetic (1)

were APPEN-

- VlPH

CW = PAI ($$)

GLYCOGEN

GLUCOSE-6-

between intermediates kinetic relations (see

Equations

= VZPH

dt

dW1

GLYCOGEN

phos-

The equations for the model are given below, with reaction velocities calculated as described in APPENDIX. The definitions of the terms are given in GLOSSARY.

Structure

=

via

DIX).

For any given intermediate, the mass balance for that compound was calculated as a function of all sources and sinks affecting its level. Flux rates were normalized per gram liver. For glucose 6-phosphate, for example ~ dt

conversion

For the purpose of these calculations, we assume PPi and UTP to be constant, making the reaction pseudofirst order in both directions. ([PP,] = 7.1 x 10e5 M (21)) Reliable measurements of intracellular UTP are not available because of the tendency of trinucleotides to be rapidly hydrolyzed (49). If the reported value of 4 x 10q4M is assumed (21), the UDPG pyrophosphorylase would greatly favor glucose l-phosphate at physiological levels of glucose l-phosphate, and net glycogen synthesis would never occur. We therefore assumed a higher concentration of UTP (7.1 x low3 M). One may write the following expression for the equivalent constant for the first-order reaction Kcequiv)

= 100.0 x K eq

wrophosphorylase

[UDPG] =

TGlPl

(11)


1610

M.

Enzyme

Glucokinase

Km1

(GK)

7.0 X low6 mol/g

Glucose-6-phosphatase

(PH)

Phosphoglucomutase

liver

1.46 x lo+

BERGMAN

synthase

(ST)

1.68 x lo+ (rat (27))

(50))

x 1o-6

(dog

2.10

(6))

1.23 x lo-” (rat (38, 39))

1.30 x lo-+ (rat (27))

1.68 x lo+ (rabbit (7))

2.92 x lo+

4.2 x lo+’ (calf (2), rabbit (50))

1.06 x lo-’

(rat (27))

x 1o-6

W, rat (27))

(dog

phosphorylase (PR) VMlPR = 1.64 x 10m5 mol/g liver VM2PR = 1.14 x lo-+ = 9.1 x 10m6 mol/gliver, K = 1.96 x lo-’ KEi KIUD = 2.1 x lo+

Glucose transport into cell K = 1.5 mol/g liver min (rat 52)) Inorganic phosphate (PJ (assumed constant)

min

3.5 x lo-” (rabbit (7))

3.92 x lo-+ (calf (2), rabbit

2.52

liver

1.00 x lo-” (rat (38, 39))

2.42 x lo-’ (rabbit (7)) (PP)

mol/g

VM2

(rat (27))

6.3 x 1O-5 (rat (38, 39))

(GM)

pyrophosphorylase

Glycogen

R. N.

Km2

VMl

(rat (51))

Glycogen

AND

1. Model parameters

TABLE

UDPG

EL-REFAI

emin K3 = 5.7 x lo-‘, K, = 2.03 x lo+,

K, = 6.5 x lo-’ K, = 9.80 x lo-”

(rabbit

(32))

l

References for described in text.

parameter Direction

2.1 x 10e6 mol/g

values are given by numbers “1,” toward glycogen; direction

liver

equiv)

=

(VMlPP)(K,ZPP) (VMZPP)(K,lPP)

(21))

in parentheses. “2,” away from

Employing the Haldane relation (11) andinserting reported value of’ K,, pyrophosphorylase (26) of 0.17 F

(rat

the

= (0.17) x (100.0)

(12)

This yields VMZPP = 1.06 x 10v7 Independent Variables in Model

Parameter glycogen.

VM2

for

UDPG

pyrophosphorylase

calculated

as

The fasting rate of glucose production (glycogenolysis + gluconeogenesis) used in the model was assumed to be 3.1 mol/g liver. min, a compromise between the value of 5.32 mol/g =min of Hetenyi and Ishiwata and the value of 1.7 reported by us for the isolated crossperfused puppy liver (8). The glucose production rate was adjusted by modulating total phosphorylase activity, as the rate of gluconeogenesis and glycogen levels were predetermined.

The initial values of several variables in the model were set independently to simulate the metabolic state COMPUTATION of the in vivo liver of the fasting dog. Glycogen was set The model was simulated using the IBM Continuous at 30 mglg liver (wet wt), which was the average value Systems Modelling Program (CSMP III). In most cases we reported for the perfused liver extirpated from the 18-h fasting puppy (8). The rate of glycolysis was as- a 4th.order Runge-Kutta integration routine was utisumed to be negligible (30), and gluconeogenesis pro- lized, and the correctness of the results was checked by using alternative Adams-Moulton or rectangular intevided a flow of 1.0 x 10m7mol glucose per min g liver gration .methods. Alternative initial conditions were into the glucose 6-phosphate pool. Although accurate quantitative values for the contribution of gluconeo- shown to lead to similar final steady-state values for genesis to glucose production in the fasting dog are not intermediates. available, from balance studies in fasting man Ahlborg et al. (1) estimated that up to 25% of glucose output is RESULTS due to gluconeogenesis. Thus, if glucose output in the dog is 2.9 mg/kg min (calculated from Hetenyi and Predicted Values of Intermediates Ishiwata (ZZ)), and the liver represents 3% of body of Glycogen Metabolism weight (30 g liver/kg), then gluconeogenesis can be Because the kinetic parameters of the enzymes inestimated to .be cluded in this model were obtained in vitro by various laboratories, it was important to determine whether (25% x 2.9 mg/kg . min x 1 kg/30 g liver) the parameter estimates were consistent with meta2.4 x lo-” g glucose bolic measurements made from samples of in vivo = .024 mg/g liver emin = liver. Thus, the model was run to a quasisteady state g liver min in which the rates of change of all state variables were mol zero except for the negative rate of change of hepatic X = 1.33 X 10e7mol/g liver min glycogen. Thus, with extracellular glucose set at a 1.&X lo2 g glucose l

l

l

l


MODEL

OF GLYCOGEN

1611

SYNTHESIS

level approximating the 18-h fasting plasma glucose concentration (5.5 mM), _we expected that intermediate values would be similar to thoie measured for the liver in vivo. Reasonable agreement was found between the predicted and measured intermediate concentrations (Table 2). This agreement was consistent with the notion that in vitro kinetic measurements are compatible with reported measurements of the cellular levels of various constituents. Stimulation

of Glycogen Synthesis by Glucose

i A ijc *G

g F o-4-6 2

i 2g pi i 4 2;: w - =) 6 8 I zL

IO

In the presence of insulin, a rise in the portal glucose level alone will cause a rapid and significant stimulation of glycogen synthesis (12). In previous studies on blood-perfused livers, we have quantitated the glucose effect and have shown that a net 20% of the increased glucose presented to the liver .will be taken up by the organ (8). Two hypotheses have been advanced to explain the glucose effect: 1) glucose, by mass action, elevates the glucose 6-phosphate within the cell; glucose 6-phosphate, by virtue of its activity, induces (pushes) a flow of mass to glycogen; 2) glucose activates the hepatic glycogen synthase system, which lowers intracellular UDP-glucose and pulls glucose toward glycogen. Mass Action Effect The dynamic response of the model to an increase in extracellular glucose concentration (assuming glucose has no “parametric’! (allosteric) effects) is shown in Fig. 2 (see also Table 3). Increasing the extracellular glucose by 70 mg/lOO ml (3.85 mM) produced a rise in intracellular glucose of 47 mg/lOO g liver, but only a very small increase in hepatic glucose 6-phosphate or UDP-glucose. An abrupt, transient glucose uptake occurred (associated with glucose distribution into cell water), but net glucose production was quickly reestaTABLE

2. Initial

Plasma glucose (GP)

conditions for model 3.8 x lo-* mol/g liver (100 mg/lOO ml)

Liver glycogen (GLP) 2.42 W Gluconeogenesis

x

low4 mol glucose-eq/g

1.0 X 10V7 mol/g liver min l

Values

Predicted

By Model

Predicted

Glucose 6-phosphate

liver (3% liver

I

I .

a 1

. I

4

0

5

IO

IS

20

MINUTES

FIG. 2. Simulated effect of increasing extracellular glucose on glucose balance and intermediate concentrations in model. Only effect of glucose is due to “mass action,” due to increased extracellular activity. In each panel, 2 model variables are indicated. ,Thus, in top panel, closed circles represent net glucose balance (NHGB), and open circles, net glycogen change rate. Also, for each variable there are two curves: one for a small (70 mg/lOO ml) increase in extracellular glucose and one for a larger increase (210 mg/lOO ml).

blished. Even when an elevation in plasma glucose of 210 mg/lOO ml (final concn = 16.7 mM) was simulated, only a negligible rate of net glycogen synthesis was predicted. Thus, the model predicts that glucose must in some way alter the kinetic parameters of the pathway of glucose metabolism to influence glycogen synthesis. The primary reason for the failure of the intracellular glucose 6-phosphate to increase with increasing intracellular glucose (see below) was substrate cycling between glucose and glucose 6-phosphate (Table 3) .

Measured

9.2 X 10B8 mol/g liver

3.5-8.0 X 10B8 (rat (23, 33, 47), mouse

(12)) Glucose l-phosphate

7.0, x 1o-g

3.5-5.1 (33))

x 10Vg (rat

UDP-glucose

2.4 x 1O-7

1.8-3.6 x 10B7 (rat (23, 33)), mouse

(12)) Initial condition values for GP, GLP, and gluconeogenesis were supplied to the model. Simulation was run until all derivatives except dGLP/& were 0, and intermediate values predicted were those listed above.

Inhibition

of Glticose-6-Phosphatase

Figure 3 and Table 3 present simulation results for the model when cycling between glucose and glucose 6 phosphate was prevented by a direct inhibition of glucase-6-phosphatase engendered by intracellular glucose (mechanism 3). In the model, it was assumed that an increase in intracellular glucose to 2.1 mg/g liver would diminish the effective V,,, of the phosphatase (VMBPP) to 20% of its value at the basal 0.7 mglg liver. With the assumption of glucose-6-phosphatase inhibition, glucose alone was able to induce significant glycogen synthesis. The resulting glucose uptake was



action

action

hypothesized

11

10

Action liver

Inhibition of gluconeogenesis + glucokinase Inhibition of gluconeogenesis + activation of synthase Induction of synthase Inhibition of gluconeogenesis Inhibition of phosphorylase Induction of glucokinase

9

on perfused

16.7

+ +

5.55 16.7

5.55 16.7 5.55 16.7 5.55 16.7 5.55 16.7 5.55 16.7

-~

16.7

0.05 0.05 1 1 1 1 0.05 0.05

0.05

0.05

1

16.7

+

1

16.7

1

!MlPR YMlPR,

0.05 0.05 1 1 1 1 0.05 0.05

0.05

0.05

1

1

1

1

VMBPR VMZPR

Phoephorylase

1

Glucokinase, VMGK VMGK,

5.55 16.7 16.7

Extracellular glu. case mM

-

1 0.1 1 0.1 1 0.1 1 0.1

0.01

0.1

0.1

1

0.1

1

1 1 1 1 1 1 4 4 4 4

VMlST imimI

Synthase

KJST KJST,,

T

1 0.2 1 0.2 1 0.2 1 0.2 1 0.2

0.02

1

0.2

0.2

1

1

Glucose6-phosphat=e VM2PH VM2PH,

Enzyme

115.3

115.4

40.1 120.2 119.8

Glucose

Levels

39.7 115.5 38.4 116.0 38.5 110.9 39.6 89.5 36.9 112.8

116.0

118.7

I

Parameters

0.85 2.34 0.59 3.17 1.18 3.62 0.84 1.95 0.90 6.22

3.17

0.99

2.48

2.51

.92 1.25 1.19

Glc-6-P

0.07 0.18 0.05 0.25 0.09 0.27 0.07 0.15 0.07 0.52

0.25

0.08

0.19

0.19

0.07 0.10 0.09

Glc-1-P

of intermediates (mol/g) x 10’

2.21 0.75 1.3 1.0 3.22 1.12 0.68 0.24 0.68 0.29

1.0

0.30

0.80

1 7.0

2.4 3.3 0.38

UDPG

in liver

-0 0 1.0 1.0 0 0 0 0 0 0

1.0

1.0

1.0

1.0

1.0

1.0

Gluconeogenesis, mol/min . g x 10’

T 5.8 7.8 8.0

5.3 14.5 1.1 6.6 7.3 21.03 5.5 12.5 2.1 10.4

6.6

2.5

5.2

15.2

!

7.9 6.3 0.04 0.4 7.9 8.3 7.9 8.1 0.4 0.4

0.4

0.4

8.2

8.1

7.9 8.0 8.0

x 10’

5.9 10.6 5.8 10.7 10.7 19.2 5.8 9.4 10.6 19.3

10.7

10.8

10.6

10.6

5.9 10.8 10.8

mol/ min * g liver

Parameters are defined as described in the text. Steady-state was defined as I ke con .d:ltion where all derivatives except dGLP/dt were 0. Hepatic glucose balance represented in different units for comparison with earlier studies (4,8). For cases in which glucose and insulin were investigated together, glucose mechanism 4 was utilized. Glucose uptake and production and glycogen synthesis and degradation represent total flux through all available pathways. Effects of glucose and insulin on perfused liver listed for comparison (4, 8).

of insulin

of phosphorylase

Inhibition

hypothesized

of gluconeogenesis

8

action

on perfused

Inhibition

Insulin

Effect of glucose liver (8)

Activation of glycogen synthase Inhibition of glucose-6phosphatase Activation of synthase + inhibition of glucose-6phosphatase Inhibition of phosphorylase activation of synthase Phosphatase inhibition phosphorylase inhibition synthase activation

Mass

Glucose

7

Mechanism No.

1

TABLE 3. Predicted steady-state concentrations of intermediates and rates of flux ofglucose into liver and glycogen for six glucose. and five insulin mechanisms

8.4 4.3 6.0 5.5 11.4 6.4 8.3 5.1 8.8 9.3

5.5

9.7

4.5

4.6

9.0 12.0 11.8

+0.4 -23.58

+4.7 -11.3 +0.5 -9.4 +l.l -22.8f +4.4 -7.9 -2.9 - 18.0

+3.4 - 13.6

-9.4

-2.0

-11.0

- 10.9

+5.6 +2.1 +1.8

mg/min lm3

+0.2 -13.1

+2.6 -6.3 +0.3 -5.2 +0.7 -12.7 +2.4 -4.4 -1.6 - 10.0

+1.9 -7.6

-5.2

-1.1

-6.1

-6.1

+3.1 +1.2 +l.O

mol/min . g liver x 10’

Net hepatic glucose balance, mg/min - 100 g (production = posi-

MODEL

OF

GLYCOGEN

1613

SYNTHESIS

It is not necessary to assume that the glucose-6phosphatase inhibition which occurs concomitant with elevated intracellular glucose is a direct effect of glucose itself. If the inhibition occurs, it may be mediated by intracellular nucleotides or pyrophosphate levels, which rise as a secondary result of the increased glucose (see DIscussIoN). Activation

IO

5

I

1 1

* 1

I I

I

0

5

IO

I5

20

MINUTES

FIG.

decrease 2.

3. Effect of glucose on model V,,, for glucose-6-phosphatase.

when glucose is postulated to Symbols defined as in Fig.

correlated with a rise in the hepatic levels of glucose 6phosphate and UDP-glucose. It can be seen from the figure that a low simulated increase in extracellular glucose of 70 mg/lOO ml (3.85 mM) increased glucose 6 phosphate by only 75%, yet there was a net increase in glycogen accumulation of 3.3 X 10B7 mol/min l g liver. At the higher glucose dose shown (final value = 16.7 mM>, net glycogen accumulation was 7.1 x 10s7 mol/ min g liver (glycogen synthesis - breakdown in Table 3). Thus, by proper adjustment of the effect of intracellular glucose on VM2PH, it was possible to enhance glycogen deposition in the liver to yield a rate of glucose uptake of 6.1 x 10~~ mol/min . g liver with an extracellular glucose concentration of 16.7 mM. This rate is similar to the uptake we reported for the dog liver, cross-perfused with blood, with a similar plasma glucose concentration (8). The dynamics of glycogen deposition predicted by the model with glucose-6-phosphatase inhibition are similar to those reported for the in vivo mouse liver. It has been reported that the intravenous administration of glucose to the mouse results in an abrupt onset of glycogen deposition, detectable in 2 min, which reaches a steady rate at 5 min (12). As Fig. 3 shows, glycogen deposition predicted by the model follows a similar time course. It is to be emphasized that significant glycogen synthesis was predicted without glucosemediated conversion of the inactive form of glycogen synthase (svnthase b) to svnthase a (active). I Y

of Glycogen

Synthase

The pull hypothesis is not confirmed by the model of glycogen metabolism. Figure 4 shows that in the model when glucose reduces the effective& for UDP-glucose of the synthase system from 2.52 x low6 to 2.52 x 10m7 mol/g liver (14), it generates a 67% reduction in UDPG, but only a transient period of net glycogen synthesis (Table 3). Th us, after 4 min, the large depletion in UDPG is reflected in only a 60% reduction in net glycogen breakdown. Including the inhibition of glucose-6phosphatase (as described above) results in net glycogen synthesis, but net synthesis which is quantitatively similar to that predicted without synthase activation (Table 3). The major effect of the glucose-mediated decrease in the effective K, for synthase (K,lST) was that intracellular UDP-glucose, rather than increasing, decreased with increasing glucose. Thus, the model predicts that glucose may decrease K,lST, decrease UDP-glucose, but that the decrease in UDP-glucose does not increase the glycogen synthesis that would have occurred if glucose had no effect at all on the synthase system. In a recent study on perfused liver, Jakob and Diem (24) have shown glucose to simultaneously raise glucose 6-phosphate and lower UDP-glucose. The reason for the failure of the UDP-

l

w 2

I

I I

.

0

5

IO

L ,

IS

I

20

MINUTES

FIG.

4. Activation

of glycogen

synthase

by glucose.


1614 glucose level to influence glucose uptake is the value of K,2PP. This parameter has been measured by several laboratories, and estimated values range from 3.5 x lo+ to 4.6 x lo+ mol]g liver (2, 26, 50). Since UDPglucose levels in the liver are at least 10 times the value of the K, (Table 2), the UDP-glucose-to-glucose l-phosphate conversion reaction is always saturated, and the velocity of conversion of UDP-glucose does not vary with the UDP-glucose level. Thus, a fall in UDPglucose generated by synthase activation does not induce glucose l-phosphate and glucose 6-phosphate to fall, events that would be necessary to induce greater hepatic glucose uptake. Inhibition of Glycogen Phosphorylase and Synthase Activation Because phosphorylase and synthase are coupled; in that cyclic 3’,5’-AMP is believed to activate phosphorylase and deactivate synthase (9, 45), Stalmans et al. (45) have examined the time course of the effects of glucose on these two enzyme systems in mouse liver. They have presented good evidence that glucose activation of synthase occurs in vivo only after the deactivation of phosphorylase, and indirect evidence that the phosphorylase deactivation was mediated directly by glucose, and not by increasing insulin or decreasing glucagon. It can be seen in Table 3 that deactivation of phosphorylase along with synthase activation (mechanism 5 compared with 2) is less effective in promoting glycogen synthesis than synthase activation alone. However, because of the decrease in glycogen breakdown, net glucose balance is somewhat more negative with the dual mechanism than with the activation of synthase alone. Nevertheless, even with portal plasma glucose equal to 16.7 mM, net glucose balance equals 1.1 x 10m7mol/min . g liver, which is only 18% of the net uptake observed with glucose-6-phosphatase inhibition (Table 3, mechanism 3). Therefore, according to these simulation studies, glucose inhibition of glucose-6-phosphatase and the related push of glucose carbon to glycogen remains the most plausible mechanism of glucose action on glycogen synthesis. The addition of synthase activation, with or without phosphorylase inhibition, may affect the intracellular concentrations of intermediates (e.g., uridine diphosphate glucose) but does not materially affect net glycogen synthesis predicted in response to glucose. Effect of Insulin Diminution of hepatic glucose production. As previously discussed, insulin is now generally regarded as playing a somewhat secondary role to glucose in the stimulation of glycogen synthesis in liver. In previous studies from our laboratory done on canine blood-perfused liver, insulin was shown to have two effects on the hepatic glucose balance (4). First, confirming earlier studies (46), insulin slowly decreased the net glucose production of fasting liver, bringing it from a normally positive value to near zero within 60 min. Second. preinfusion of insulin for an hour at a concen-

M.

EL-REFAI

AND

R. N. BERGMAN

tration within the physiological (portal vein) range (200 $J/ml) enhanced the net glucose uptake which occurred at any portal vein glucose concentration. Thus, whereas glucose itself engendered a net 20% uptake of the administered hexose (8), preinfusion of insulin increased the percentage uptake to almost 30% of the administered load. The inhibition of glucose production by insulin has been comfirmed in vivo (18) and in perfused liver systems (37). It is generally believed to represent a combination of diminished glycogen phosphorylase activity (possibly due to diminished hepatic cyclic AMP (16)) and a lowered rate of gluconeogenesis. In this study, the effect of insulin was modeled as a slow process in accord with the concept of insulin’s action requiring protein synthesis secondary to RNA synthesis (Fig. 5) (48). In the model, insulin-mediated inhibition of either glycogenolysis or gluconeogenesis caused a significant decline in glucose output (Fig. 6). It is interesting to note, however (Table 3, mechanism 7), that diminishing gluconeogenesis by 1 x 10e7 mol/g min caused a decrease in net glucose production of only 0.5 x lo-’ min. A simulated fall in gluconeogenesis lowered glucose 6=phosphate, which, besides diminishing glucose output increased the net breakdown of glycogen. A fall in phosphorylase activity, however, had no influence on the rate of gluconeogenesis in our model. Insulin inhibition of glucose production via glycogenolysis and gluconeogenesis, however, did not accentuate the effect of glucose on glycogen synthesis (Table 3, mechanisms 7 and 8). Thus, it was necessary to postulate an alternative mechanism of insulin action to explain its enhancement of glycogen deposition. Enhancement of glucose-stimulated glycogen synthesis. Table 3 lists the predicted steady-state rates of glycogen synthesis, with and without insulin, for two values of extracellular glucose. We examined this relationship for 1) insulin-mediated induction of the glycogen synthase system, (mechanism 10) and 2) insulin induction of glucokinase (Fig. 7, mechanism S0 (41). As was the case with glucose activation, increi ssing the synthase activity had only a negligible effect on glycogen synthesis. Insulin induction of glucokinase, however, had a large effect, and when the hormone doubled VMlGK, the insulin potentiation of the glucose effect observed in perfused-liver was predicted by the model. Thus, by inducing synthesis of the glucokinase enzyme, insulin increased the potential of glucose to elevate glucose 6-phosphate, and to push glucose carbon toward glycogen. l

mol/g

l

0 FIG.

terase,

5. Postulated phosphorylase,

IO

20

30 MINUTES

40

time course of effect of insulin or glycogen synthase.

50

60

on phosphodies-


MODEL

OF

GLYCOGEN

1615

SYNTHESIS

A 09990 GulCOSE PRODUCTION

2

(Moler/g~min.)x107

(Molar/g)

G-6-P

x I07

2 ---=omg t

-99-

---9

INSULIN t 0

INFUSION,

:

:

x IO’

:

:

:

1

:

I2

:

:

:

20

:

4

m--o

1

---0--9~,9,~--~

010 t

1 x IO’

i

2

0

(Molar/g

200pUIml

: 40 MINUTES

C -99=99mom99-,,q,

UDPG

2

-0-99-99-O-99

4

G-6-P (MOlO8/Q)

:

--9-

:

60

:

(Molar

UDPG /g 1 x IO’

I

80

MI ZTES

FIG. 6. Simulated diminution in glucose production and changes in intermediate concentrations for insulin inhibition of a) glycogen phosphorylase, or b) gluconeogenesis. To determine effect of glucose (not shown in figure), insulin effect was allowed to proceed to its maximum after which simulated increase in glucose occurred.

DISCUSSION

The purpose of the modelling studies presented here was to test the feasibility of several mechanisms which have been proposed to explain the effects of glucose and insulin on the deposition of glycogen in the mammalian liver. We have concluded that, given the structure and kinetic parameters of glycogen metabolism, glucose acts by raising the intracellular concentration of glucose 6-phosphate, thus pushing glucose carbon into glycogen. The alternative hypothesis, that glucose-mediated activation of glycogen synthase results in a sufficient lowering of the concentration of UDP-glucase, glucose l-phosphate, glucose 6=phosphate, and glucose in the hepatocyte to increase net flux of the hexose into the liver cell (15) is not supported by the simulation results. Thus, it does not follow necessarily that if glucose can motivate conversion of glycogen synthase from the b, or inactive form, to the a, or active form, such a conversion will result in increased glycogen synthesis. In fact, glucose activation of synthase is not denied by these studies; an effect of such an activation onglycogen deposition was not supported. One possible rationale for the glucose activation of synthase is that this interaction preyents the sequestration of uridine in the UDP-glucose form during glucose uptake.. If synthase is not activated, the model predicts that UDP-glucose levels will increase fourfold. Under those conditions, the lack of availability of UTP

might limit unnecessarily the rate of glycogen deposition. This model predicts that concomitant with elevated intrahepatic glucose the phosphohydrolase activity of glucose-6-phosphatase is inhibited. No statement can be made from the model as to the mechanism of that inhibition. Glucose is a known noncompetitive inhibitor of this function of the enzyme (42), but is relatively ineffective at concentrations within the physiological range (3). On the other hand, inorganic pyrophosphate (PPi) is a competitive inhibitor for dephosphorylation at PPi concentrations which occur within the cell. Stadtman (44) has suggested that a feedback loop exists whereby elevated intracellular glucose results in higher PPi because of increased UDP-glucose-to-glycogen conversion. The PPi could “feed back” and inhibit dephosphorylation, thus further increasing intracellular glucose 6-phosphate. More PPi would thus be produced due to a further increase in flux of glucose 6phosphate to glycogen. This “vicious cycle” could be expected to quickly result in a marked inhibition of the glucose-6-phosphatase phosphohydrolase activity, and a large increase in glycogen synthesis would result. The Stadtman hypothesis is particularly appealing because it could explain the absence of inhibition of glucase-6-phosphatase phosphohydrolase in diabetic liver, despite a greatly elevated intrahepatic glucose concentration. In diabetes, total synthase activity would be so low (20,48) that significant UDP-glucose-glycogen conversion would not occur, and PPi would not be high despite the greatly elevated glucose concentration in the cytosol. In a previous study, we were able to confirm that A m--o GLUCOSE PRODUCTION (Molrr/g.min.)x IO’

4

4

09-90

-9.4

G-6-P (Molor/g)x

IO’

2

-44 ----I-

I 0

:

: 20

:

: 40 MINUTES

:

: 60

:

4 80

9 r

B

3

GLUCOSE PRODUCTION

-0.

J4

gg-ll~-----

c--

rr~*-9dJo---+ x IO’

2

2

t

0

FIG.

’

-% 2 t

4

-

activation

7

-----a-

099-o

G-6-P (Moles/g)

UDPG (Molar/g) x IO’

2

:

:

20

:

:

40 MINUTES

:

:

60

:

NET GLVC~GEN BREAKDOWN

Ol-rO U DPG (Molos/aI x IO7

k

80

7. Effect on net glucose production of a simulated of (A) pllvcogen svnthase. or (23) Prlucokinase.

insulin


1616 insulin not only slowly diminished the rate of glucose production by the liver, but also increased the sensitivity of hepatic glucose uptake to glucose (4). This model allowed for us to test whether any single action of insulin on the glycogen metabolic pathway could explain these two effects or whether separate mechanisms were required. Either insulin inhibition of glycogen breakdown or inhibition of gluconeogenesis could, of course, explain a decrease in glucose production. (It was interesting to note that diminishing gluconeogenesis was proportionately less effective because, due to a resultant diminution in glucose 6phosphate, there was a reflexive increase in glycogenolysis which partially compensated for the lowered flux of carbon into glucose 6-phosphate.) Neither of these two postulated insulin mechanisms, however, could explain the enhancement of the sensitivity of glucose uptake to glucose, when it was assumed that glucose both inhibited glucose-6-phosphatase and activated glycogen synthase. Of the two alternative mechanisms tested for the effect of insulin on glucose uptake, insulin induction of synthase was ineffective, whereas insulin regulation of glucokinase activity (41) was extremely effective in controlling the amount of hepatic glucose uptake (mechanism 9, Table 3). Thus, we are able to explain insulin’s two separate actions on the liver by no less than two separate mechanisms: inhibition of glycogenolysis (probably by interaction with the cyclic 3’,5’-AMP system) and induction of glucokin .ase. It is presumably by control of glucokinase (and not synthase) that insulin exerts its “modulating” effect on hepatic glycogen synthesis (4). The limitations of the glycogen model are readily apparent. We have limited the extent of the kinetic analysis to include only a small portion of the possible paths of glucose metabolism. However, it can be assumed that 1) other routes of glucose metabolism in the liver besides the path to glycogen are insignificant when the availability of glucose is high (30), and 2 > the rate of glycogen deposition is not limited by products or cofactors (such as UTP or ATP, for example) which may be produced or utilized in other metabolic pathways within the cell. With these assumptions in mind, it seems reasonable to propose a limited model which includes only those pathways (e.g., gluconeogenesis) the fluxes through which will clearly affect the intracellular concentrations of intermediates of glycogen metabolism. A second limitation of the model-is that kinetic parameters for the enzymes were obtained from in vitro on liver of vario us species (Table 1>, and mea surements the parameters were assumed to aPPlY in vivo. However, using the kinetic parameters in the model equations, values for the intermediates glucose 6-phosphate and UDP-glucose were’ pr.edicted which were similar to those measured in the in vivo liver. Thus, it seems likely that the parameters used represent reasonable estimates of the kinetic parameters of the enzymes as they exist within the liver cell. Despite its limitations, this formulation has several distinct advantages over previous attempts to model hepatic glvcogen metabolism. The model is dynamic, .

M.

EL-REFAI

AND

R. N.

BERGMAN

unlike, for example, the earlier model of London (31), and the results can be compared with dynamic measurements obtained on in vitro or in vivo systems. Also, we believe the model to be sufficiently simple, i.e., only relevant aspects of glucose metabolism were included, and factors which are not known to influence the processes of interest were ignored. It is believed that the model structure captures the essence of the control of glycogen metabolism within the cell. This simulation effort supports the notion that demonstrating the modulation by a proposed regulator of the activity of a given enzyme does not necessarily imply that that particular modulation is the mechanism by which the modulator works. In fact, more to the point in the case .of glycogen metabolism would be to predict, by means of a model, the time-dependent changes in metabolic i .nter Imediates which occur with competing hypotheses and perform specific experiments to examine the time courses to choose between hypothetical mechanisms. For example, it is clear that the pull hypothesis requires that glucose 6-phosphate and glucose l-phosphate fall rather than rise when extracellular glucose appears; the push hypothesis which is supported by these studies predicts a rise in these intermediates. A fall in UDPG, however, is consistent with both. Evidence on this point is conflicting. Glucose causes a rise in glucose 6-phosphate and a fall in UDP-glucose (concomitant with synthase activation) in perfused liver (9, 24), but in mouse liver samples in vivo, glucose 6-phosphate has been observed to fall (12). Glucose is known to inactivate glycogen phosphorylase (9,45); it may be th at phosphory lase in samples taken from living ani .mals 1s artifactually elevated, and the fall in glu .cose 6-phosphate may result from phosphorylase inactivation rather than synthase activation. New measurements of dynamic changes in metabolic intermediates under controlled conditions are needed to clarify the conclusions reached by these studies. APPENDIX The kinetic formulations for the various fluxes between compartments in the model are described in this APPENDIX. Three classes of en zyme mechanisms were used in formulating the system equations. CZass I Enzymes For the enzymes glucose-6-phosphatase, glucokinase, UDPG PY-rophosphorylase, and glycogen synthase, the class I mechanism shown in Fig. 8 was utilized. Thus, the rate of conversion of substrate S to product P in the “1” direction was given by

and the conversion

d[Sl -=-

Iwcnax

dt

[S] + K:l

of P to S via route

WI -=dt

(13)

2 by

EWIX3,, PI + Kn2

(14)

in which d[S]/& is the rate of unidirectional S-to-P conversion, and d[P]/dt is the unidirectional P-to-S conversion. In order for the reaction velocities (equations 13,L4 ) to be proportional to substrate concentration, one must assume that for each infinitesimal change in substrate level, a new steady-state enzyme-substrate complex concentration is reached almost immediately (34). Thus, it is assumed that the dynamics of formation and breakdown of enzyme-


MODEL

OF

GLYCOGEN

1617

SYNTHESIS

s+

StE

P

kinetics observed in vitro were for glycogen in solution, whereas in liver only a small portion of stored glycogen is available for reaction due to the geometry of the glycogen particle. Nevertheless, the fraction of stored glycogen which is chemically active is approximately constant for widely ranging amounts of stored glycogen (43). We therefore adjusted the parameters VM2PR to yield a rate of glycogenolysis for fasting liver similar to that observed in vivo, assuming that the adjustment compensates for the geometry of the hepatic glycogen particle. Class

\\\ 8. Assumed E, enzyme.

FIG.

product;

mechanism

for class I enzymes.

S, substrate;

P,

substrate complex are so fast that they do not contribute to overall dynamics of hepatic glucose uptake and production, which are dominated by the much slower velocity of transfer of mass between compartments. Thus, for example, for the simple system of Fig. 8, it is possible to write

e-z-dW3

WI

dt

dt

=----mcnax, [Sl + K,l

uwnax2 [PI + Km2

Reactions catalyzed by glucokinase and glycogen synthase are essentially irreversible (29, 4l), and therefore only one fractional term would appear on the right-hand side of equation 15. The specific formulations for the six conversions involving the four class I enzymes are presented below (see GLOSSARY). Glucose-6-phosphatase (PH) (EC 3 .1.3.9)

UDPG

=

[GU]VMlPH KJPH + [GU]

(164

V2PH

=

[GGJVMBPH K,2PH + [G6]

U6b)

Glucokinase

(GK)

(PP)

synthase

[Gl]VMlPP KJPP + [Gl]

(17a)

V2PP

=

[ UD]VMBPP K,lPP + [UD]

U7b)

(ST) VlST

Class

2.7.1.2) [GUJVMlGK = K,lGK + [GUI (EC =

The distribution given as shown

of GA below

dt

is, in steady zx

= Zx + GNEO between

the

Gl

= Zx + VlGM

(21)

+ Zy and

G6 compartments

is

- V2GM

state +

VMlGM[G6] K,lGM + [G6]

VM2GM[Gl] - K,2GM + [Gl]

o =

(23)

2.7.7.9)

=

(EC

WA1 dt

That

VlPP

‘lGK Glycogen

(EC

The enzyme phosphoglucomutase (EC 2.7.5.1) presents a particular problem, because the Gl-G6 interconversion velocities are at least lo-fold higher than any other. This difference resulted in computational difficulties when equation 15 was used for this enzyme in the model. The alternative approach we used was as follows: we assumed that the bidirectional phosphoglucomutase reactions were sufficiently fast that the Gl --, G6 and G6 + Gl conversion rates reached steady state within each computational iteration (or “instant of time”) of the rest of the model. A modular representation of the phosphoglucomutase reaction was constructed according to the scheme shown in Fig. 9. At any instant Zx and Zy are predicted by the whole-system model with known initial concentrations of Cl and G6. It is possible to impose the known values of Zx, Zy, and GNEO to obtain the value of GA as follows

dW1 -

VlPH

pyrophosphorylase

III Enzyme

(18)

2.4 .I .I 1) [UD]VMlST KJST + [UD]

Using equation 23 and the fact that GA is the sum of Gl and G6, the ratio of G6 to G1 (K,,) is calculated as a function of GA and Zx. The steady-state values of Gl and G6 were thus predicted and reinserted in the whole-system model. After one successive iteration, new Zx and GA values were predicted, and the process was repeated. A steady state rather than equilibrium model was used. Although near-equilibrium conditions were usually predicted, the Gl/G6 ratio deviates from the equilibrium value when maximum glycogenolysis is induced. Glucose transport into hepatocyte. It is known that glucose diffuses freely in and out of the hepatocyte (10). The dynamics of this process have been modelled by Williams et al. (52), and based upon their results, we assumed a time constant for glucose diffusion of 0.67 min.

(19)

II Enzyme

Because detailed kinetic studies of liver glycogen phosphorylase (EC 2.4.1.1) have been presented by Maddaiah and Madsen (32), we chose to use their formulation to represent this enzyme system in the model. Thus, the rates of glycogen degradation and synthesis via this enzyme alone are given as follows: Degradation VM2PR V2PR = (2W K!K3 K3 + [GLY] [Pi] [Pi]

r I I I

GI 4

\ VIGM

V2GM at

1 I I

I I

G6

4;

4 . L -- -- -lI

I

GNEO

Synthesis VlPR

Kinetic

parameters

VMlPR

=& 1.0 + [GLY] were

supplied

Wb)

WG -- KS + [Gl] + [GLY] [Gl] by Maddaiah

and

Madsen.

The

FIG. 9. Model for phosphoglucomutase enzyme. Gl, G6 are glucose l-phosphate and glucose 6-phosphate. VlGM, V2GM are unidirectional velocities between moieties. GNEO, gluconeogenesis; GA = Gl + G6. Zx and Zy, net velocities into GA from surrounding metabolites.


1618

M.

Thus, the net rate follow ing reaction rate

of glucose

of movement

movement

into

= & .

(EPI

the cell is given

- [GUI)

by the

(24)

Cyclic adenylate system. A highly simplified version of the mechanism by which glucagon and insulin affect hepatic glucose production via the cyclic AMP-protein kinase system was included in the model (17). It was assumed that the CAMP level was determined by a balance between cyclic adenylate and phosphodiesterase activity. Most elements of the glycogen phosphorylase system (protein kinase, phosphorylase kinase, phosphorylase phosphatase) were not included in the model, and VM2PR was assumed to be directly proportional to the CAMP level. The cAMP/VM2PR relation was adjusted such that flux through phosphorylase was 0.06 mg/min g liver if CAMP = 7.0 x 10eg mol/g liver and flux = 0.25 mg/min l g liver (a maximum hepatic glucose production rate) if CAMP = 7.0 x lo-’ mol/g liver. Thus l

d[cAMP] p dt

= y - p [CAMP]

(25)

GLOSSARY Symbol

[ 3 GP GU G6 Gl UD GLP GLY iGAl pi UTP ppi

Explanation concentration of substance plasma glucose glucose in liver cell water glucose 6-phosphate in liver cell water glucose l-phosphate in liver cell water uridine diphosphate glucose in 1iver cell water glycogen in liver cell water kinetically effective glycogen in liver cell water

El1 + WI cytosol inorganic phosphate uridine triphosphate inorganic pyrophosphate

VM K, V 1 2 PH PP GK ST PR GM KI GNEO ZX

ZY

EL-REFAI

AND

R. N.

BERGMAN

maximum velocity of an enzymatic reaction Michaelis constant velocity of an enzymatic reaction denotes reaction in the direction of glycogen synthesis denotes reaction in the direction of glycogen breakdown glucose-6-phosphatase UDP-glucose pyrophosphorylase glucokinase glycogen synthase glycogen phosphorylase phosphoglucomutase inhibition factor rate of G6 production via gluconeogenesis net flux of mass into Gl compartment from the upper part of the pathway (Fig. 9) net flux of mass between G6 and GU compartments (Fig. 9)

Kss

DWWI

CAMP Y P

cyclic 3’,5’-adenosine parameter proportional parameter proportional

monophosphate to adenylate cyclase to phosphodiesterase

activity activity

The authors thank Ms. Suzonne Z. Oliver for her aid in producing this manuscript. Thanks to Dr J. Radziuk for helpful suggestions and to Dr. Jacob Blum of Duke University, and to Dr. Joseph Larner of the University of Virginia for making comments on the manuscript. This work was supported by National Institutes of Health Grant AM-17236-02. M. El-Refai was a Predoctoral Trainee of the National Institutes of Health (Grant GM-01724). Present address of M. El-Refai is: Dept. of Physiology, Vanderbilt University, Nashville, Tenn. Send reprint requests to: R. N. Bergman, Dept. of Biomedical Engineering, University of Southern California, Olin Hall 500, Los Angeles, Calif. 90007. Received

for publication

3 December

1975.

REFERENCES 1. AHLBORG, G., P. FELIG, L. HAGENFELDT, R. HENDLER, AND J. WAHREN. Substrate turnover during prolonged exercise in man. Splanchnic and leg metabolism of glucose, free fatty acids, and amino acids. J. CZin. Inoest. 53: 1080-1090, 1974. 2. ALBRECHT, G. J., S. T. BASS, L. L. SEIFERT, AND R. G. HANSEN. Crystalization and properties of uridine diphosphate glucose pyrophosphorylase from liver. J. BioZ. Chem. 241: 2968-2975, 1966. 3. ARION, W. J., AND R. C. NORDLIE. Liver microsomal glucose-6phosphatase, inorganic pyrophosphatase and pyrophosphateglucose-phosphotransferase. J. BioZ. Chem. 239: 2752-2757,1964. 4. BERGMAN, R. N., AND R. J. BUCOLO. Interaction of insulin and glucose in the control of hepatic glucose balance. Am. J. Physiol. 227: 1314-1322, 1974. 5. BISHOP, J. S., R. Steele, N. ALTSZULER, A. DUNN, C. BJERKNES, AND R. C. DE BODO. Effects of insulin on liver glycogen synthesis and breakdown in the dog. Am. J. Physiol. 208: 307-316, 1965. 6. BISHOP, J. S., AND J. LARNER. Rapid activation-inactivation of liver uridine diphosphate glucose-glycogen transferase and phosphorylase by insulin and glucagon in vivo. J. BioZ. Chem. 242: 1354-1356, 1967. 7. BODANSKY, 0. Kinetics of phosphoglucomutase action. J. BioZ. Chem. 236: 328-332, 196.1. 8. BUCOLO, R. J., R. N. BERGMAN, D. J. MARSH, AND F. E. YATES. Dynamics of glucose autoregulation in the isolated, blood-perfused canine liver. Am. J. Physiol. 227: 209-217, 1974. 9. BUSCHIAZZO, H., J. H. EXTON, AND C. R. PARK. Effect of glucose on glycogen synthetase, phosphorylase and glycogen deposition in perfused rat liver. Proc N&Z. Acad. S&US 65: 383-387, 1970. 10. CAHILL, G. F., JR., J. ASHMORE, A. S. EARLE, AND S. ZOTTU. Glucose penetration into liver. Am. J. Physiol. 192: 491-496, 1958. 11. CLELAND, W. W. The kinetics of enzyme-catalyzed reactions with

12.

13.

14.

15.

16.

17.

18.

19.

20. 21.

two or more substrates or products. Biochim. Biophys. Acta 67: 104-137, 1963. DE WULF, H., AND H. G. HERS. The stimulation of glycogen synthesis and of glycogen synthetase in the liver by the administration of glucose. European J. Biochem. 2: 50-56, 1967. DE WULF, H., W. STALMANS, AND H. G. HERS. The influence of inorganic phosphate, adenosine triphosphate, and glucose-6phosphate on the activity of liver glycogen synthetase. European J. Biochem. 6: 545-551, 1968. DE WULF, H., AND H. G. HERS. The interconversion of liver glycogen synthetase a and b in vitro. European J. Biochem. 6: 552-557, 1968. DE WULF, H. The control of glycogen synthesis in the liver. Verhandel. Koninkl. VZaam. Acad. Geneeskunde Belg. 33: 76101, 1971. EXTON, J. H., S. B. LEWIS, R. J. Ho, G. A. ROBISON, AND C. R. PARK. The role of cyclic AMP in the interaction of glucagon and insulin in the control of liver metabolism. Ann. NY Acad Sci. 185: 85-100, 1971. . EXTON, J. H., S. B. LEWIS, R. J. Ho, AND C. R. PARK. The role of cyclic AMP in the controrof hepatic glucose production by glucagon and insulin. Advan. Cyclic NucZeotide Res. 1: 91-101,1972. FELIG, P., AND J. WAHREN. Influence of endogenous insulin secretion on splanchnic glucose and amino acid metabolism in man. J. Clin. Invest. 50: 1702-1711, 1971. GLINSMANN, W. H., E. P. HERN, AND A. LYNCH. Intrinsic regulation of glucose output by rat liver. Am. J. Physiol. 216: 698-703, 1969. GOLD, A. H. The effect of diabetes and insulin on liver glycogen synthetase activation. J. BioZ. Chem. 245: 903-905, 1970. HELDT, H. W. Phosphataltige Metabolite in Anionenaustaushchromatogrammen sfiureloslicher Extrakte ans Rattenleber im Nano-Bereich. Biochem. 2. 337: 397-413, 1963.


MODEL

OF

GLYCOGEN

SYNTHESIS

22. HETENYI, G., JR., AND K. ISHIWATA. Effect of n-ribose on the turnover of glucose in dogs. Am. J. Physiol. 214: 1333-1339,196s. 23. HORNBROOK, K. R., H. B. BURCH, AND 0. H. LOWRY. The effect of adrenalectomy and hydrocortisone on rat liver metabolites and glycogen synthase activity. Mol. PharmacoZ. 2: 106-108, 1966. 24. JAKOB, A., AND S. DIEM. Activation of glycogenolysis in perfused rat liver by glucagon and metabolic inhibitors. Biochim. Biophys. Acta 362: 469- 479, 1974. 25 JEFFERSON, L. S., J. H. EXTON, R. W. BUTCHER, E. W. SUTHERLAND, AND C. R. PARK. Role of cyclic 3’5’AMP in the effects of insulin and anti-insulin serum on liver metabolism. J. BioZ. Chem. 243: 1031-1038, 1968. 26 KNOP, J. K., AND R. G. HANSEN. Uridine diphosphate glucose pyrophosphorylase. J. BioZ. Chem. 245: 2499-2504, 1970. 27. KNOX, W. E. Appendix II. In: Enzyme Pattern in Fetal, Adult, and NeopZastic Tissues. Basel: Karger, 1972. 28. KREUTNER, W., AND N. D. GOLDBERG. Dependence on insulin of the apparent hydrocortisone activation of hepatic glycogen synthetase. Proc. NatZ. Acad. Sci. US 58: 1515-1519, 1967. 29. LELOIR, L. F., J. M. OLAVARRIA, S. H. GOLDENBERG, AND H. CARMINATTI. Biosynthesis of glycogen from uridine diphosphate glucose. Arch. Biochem. Biophys. 81: 508-520, 1959. * 30. LEVINE, R. A. Effect of glycogenolytic agents on phosphorylase activity of perfused rat liver. Am. J. Physiol. 208: 317-323, 1965. 31. LONDON, W. P. A theoretical study of hepatic glycogen metabolism. J. BioZ. Chem. 241: 3008-3022, 1966. 32. MADDAIAH, V. T., AND N. B. MADSEN. Kinetics of purified liver phosphorylase. J. BioZ. Chem. 241: 3873-3881, 1966. 33. MATSUURA, N., J. S. CHENG, AND N. KALANT. Insulin control of hepatic glucose production. Can. J. Biochem. 53: 28-36, 1975. 34. MICHAELIS, L., AND M. L. MENTEN. Die Kinetik der Invertinwirkung. Biochem. 2. 49: 333-369, 1913. 35. MILLER, T. B., JR., AND J. LARNER. Mechanism of control of hepatic glycogenesis by insulin. J. BioZ. Chem. 248: 3483-3488, 1973. 36. MILLER, T. B., JR., R. HAZEN, AND J. LARNER. An absolute requirement for insulin in the control of hepatic glycogenesis by glucose. Biochem. Biophys. Res. Commun. 53: 466-474, 1973. 37. MONDON, C. E., AND S. D. BURTON. Factors modifying carbohydrate metabolism and effect of insulin in perfused rat liver. Am. J. Physiol. 220: 724-734, 1971. 38. NORDLIE, R. C., AND W. J. ARION. ,Evidence for the common identity of glucose-6-phosphatase, inorganic pyrophosphatase, and pyrophosphate-glucose phosphotransferase. J. BioZ. Chem. 239: 1680-1685. 1965.

1619 39. NORDLIE, R. C., AND W. J. ARION. Liver microsomal glucose-6phosphatase, inorganic pyrophosphatase, and pyrophosphateglucose phosphotransferase. J. BioZ. Chem. 240: 2155-2164, 1965. 40. RUDERMAN, N. B., AND M. G. HERRERA. Glucose regulation of hepatic gluconeogenesis. Am. J. Physiol. 214: 1346-1351,196s. 41. SALAS, M., E. VIXWELA, AND A. SOLS. Insulin-dependent synthesis of liver glucokinase in the rat. J. BioZ. Chem. 238: 3535-3538, 1963. 42. SEGAL, H. L. Some consequences of the “non-competitive” inhibition by glucose of rat liver glucose-6-phosphatase. Am. Chem.. Soc.J. 81: 4047-4050, 1959. 43. SMITH, E. E. Control of glycogen structure. Control of Glycogen MetaboZism, edited by E. J. Whelan. Oslo: Universitetsforlaget, 1968, vol. 5, p. 205-213. 44. STADTMAN, E. R. Allosteric regulation of enzyme activity. Aduan. Enzymol. 28: 41-154, 1966. 45. STALMANS, W., H. DE WULF, L. HUE, AND H. G. HERS. The sequential inactivation of glycogen phosphorylase and activation of glycogen synthetase in liver after the administration of glucose to mice and rats. European J. Biochem. 41: 127-134, 1974. 46. STEELE, R., J. S. BISHOP, A. DUNN, N. ALTSZULER, I. RATHGEB, AND R. C. DE BODO. Inhibition by insulin of hepatic glucose production in the normal dog. Am. J. PhysioZ. 208: 301-306,1965. 47. STEINER, D. F., V. RAUDA, AND R. H. WILLIAMS. Effects of insulin, glucagon and glucocorticoids upon hepatic glycogen synthesis from uridine diphosphate glucose. J. BioZ. Chem. 236: 299304, 1961. 48. STEINER, D. F., AND J. KING. Induced synthesis of hepatic uridine diphosphate glucose-glycogen glucosyl-transferase after administration of insulin to alloxan-diabetic rats. J. BioZ. Chem. 239: 1292-1298, 1964. TSENG, J. K., AND E. GURPIDE. Uptake and metabolism of exogenous uridine by superfused rat liver slices. Biochem. Biophys. Acta 353: 399-406, 1974. 50. TURNQUIST, R. L., T. A. CRILLETT, AND R. G. HANSEN. Uridine diphosphate glucose pyrophosphorylase. J. BioZ. Chem. 249: 7695-7700, 1974. 51. VINUELA, E., M. SALAS, AND A. SOLS. Glucokinase and hexokinase in liver in relation to glycogen synthesis. J. BioZ. Chem. 238: 1175, 1963. 52. WILLIAMS, T. F., J. H. EXTON, C. R. PARK, AND D. M. KEGEN. Stereospecific transport of glucose in the perfused rat liver. Am. J. PhvsioZ. 215: 1200-1209. 1968.


Effect of insulin and glucose on the glucose consumption and glycogen synthesis by the rat diaphragm.

Insulin control of hepatic glucose production.

Deficiency of a glycogen synthase-associated protein, Epm2aip1, causes decreased glycogen synthesis and hepatic insulin resistance.

Regulation of glycogen synthesis in rat-hepatocyte cultures by glucose, insulin and glucocorticoids.

Dynamic control of hepatic glucose metabolism: Studies by experiment and computer simulation.

4-Hydroxyisoleucine improves hepatic insulin resistance by restoring glycogen synthesis in vitro.

Stimulation of hepatic glycogen synthesis by amino acids.

Control of insulin gene expression by glucose.

Evidence for the indirect utilization of glucose for the synthesis of hepatic glycogen in man.

Effect of starvation on hepatic glycogen metabolism and glucose homeostasis.

Hepatic metabolism of glucose and glycogen in fed rats.

Regulation of glycogen synthesis from glucose and gluconeogenic precursors by insulin in periportal and perivenous rat hepatocytes.

Control of hepatic glucose metabolism by islet and brain.

Regulation of fetal lung phosphatidyl choline synthesis by cortisol: role of glycogen and glucose.

Hepatic miR-378 targets p110α and controls glucose and lipid homeostasis by modulating hepatic insulin signalling.

Glycogen synthase in the rat tapeworm, Hymenolepis diminuta--II. Control of enzyme activity by glucose and glycogen.

Actions of insulin-potentiating peptides on glycogen synthesis.

Hepatic insulin signalling is dispensable for suppression of glucose output by insulin in vivo.

A mathematical model and computer simulation study of insulin sensitive glucose transporter regulation.

The role of cell swelling in the stimulation of glycogen synthesis by insulin.

Insulin and the stimulation of glycogen synthesis. The road from glycogen structure to glycogen synthase to cyclic AMP-dependent protein kinase to insulin mediators.

Hepatic glucose-6-phosphate cycling has no bearing on recently used isotopic procedures to investigate the pathways of glycogen synthesis.

Glycogen synthesis by rat hepatocytes.

Insulin alters the sensitivity of glycogen synthesis to inhibition by okadaic acid, a protein phosphatase inhibitor.