Content uploaded by David Andrew Fell
Author content
All content in this area was uploaded by David Andrew Fell
Content may be subject to copyright.
Available via license: CC BY 4.0
Content may be subject to copyright.
THE
JOURNAL
OF
BIOLOGICAL
CHEMISTRY
Vol.
269,
No.
41,
Issue
of October
14,
pp.
25502-25514, 1994
Printed
in
U.S.A.
Control
of Glucose
Utilization
in
Working
Perfused
Rat Heart*
(Received for publication, April 22, 1994, and in revised form, July 14, 1994)
Yoshishiro Kashiwaya, Kiyotaka SatoS, Naotaka Tsuchiya, Simon Thomas§, David
A.
Fells,
Richard
L.
Veechn, and Janet
V.
Passonneau
From the National Institute on Alcoholism and Alcohol Abuse, Rockville, Maryland
20895
and the §School of Biological
and Molecular Sciences, Oxford Brooks University, Headington, Oxford
OX3
OBP,
United Kingdom
Metabolic control analyses of glucose utilization were
performed for four groups of working rat hearts per-
fused with Krebs-Henseleit buffer containing 10
m~
glucose only, or with the addition of
4
mM
D-p-
hydroxybutyratell
m~
acetoacetate, 100
IIM
insulin (0.05
unitlml), or both. Net glycogen breakdown occurred in
the glucose group only and was converted to net glyco-
gen synthesis in the presence of all additions. The flux of
[2-3Hlglucose through P-glucoisomerase
(EC
5.3.1.9) was
reduced with ketones, elevated with insulin, and un-
changed with the combination. Net glycolytic
flux
was
reduced in the presence of ketones and the combination.
The
flux
control coefficients were determined for the
portion of the pathway involving glucose transport to
the branches of glycogen synthesis and glycolysis. Major
control was divided between the glucose transporter
and hexokinase
(EC
2.7.1.1)
in the glucose group. The
distribution of the control was slightly shifted to hexo-
kinase with ketones, and control at the glucose trans-
port step was abolished in the presence of insulin. Anal-
ysis of the pathway from 3-P-glycerate to pyruvate
determined that the major control was shared by eno-
lase
(EC
4.2.1.1)
and pyruvate kinase
(EC
2.7.1.40) in the
glucose group. Addition of ketones, insulin, or the com-
bination shifted the control to P-glycerate mutase
(EC
5.4.2.1) and pyruvate kinase.
These results illustrate that the control of the meta-
bolic
flux
in glucose metabolism of rat heart is not ex-
erted by a single enzyme but variably distributed among
enzymes depending upon substrate availability, hormo-
nal stimulation, or other changes of conditions.
With
the demonstration
that
the
concentration of intracellu-
lar
glucose was very low
in
skeletal muscle, it was
first
sug-
gested
that
insulin might act primarily by increasing glucose
transport into the cell
(1).
The evidence
that
administration of
insulin increased
the
galactose space in eviscerated dogs
(2)
confirmed
that
a
major action of insulin was to increase
intra-
cellular hexoses in insulin-sensitive tissues.
It
was subse-
quently shown
that
glucose transport was mediated
in
muscle
by
a
carrier-facilitated process (3).
In
retrograde perfusion of
isolated
rat
hearts, administration of insulin did not alter the
apparent
K,
of 3-0-methyl glucose transport
in
the forward
direction but
rather
increased its apparent
V,,,
from near
1
*
The costs of publication
of
this article were defrayed in part by the
“aduertzsement”
in accordance with
18
U.S.C. Section 1734 solely to
payment of page charges. This article must therefore be hereby marked
indicate this fact.
$
Present address: Dept. of Medicine, Kitasato University School
of
Medicine, Sagamihara, Kanagawa 210, Japan.
1
To whom correspondence should be addressed: National Institute on
Alcoholism and Alcohol Abuse, 12501 Washington Ave., Rockville, MD
20852. Tel.: 301-443-4620; Fax: 301-443-0930.
pmol/min/g to 12 pmol/min/g while
at
the same time decreasing
the
K,,,
in
the
reverse direction from
7
to
3
mM
(4).
The further
finding
that
hearts
perfused in the retrograde manner had
unmeasurable [GlcJl
at
concentrations of extracellular glucose
[Glc,] from
2
to 16 mM contributed to the belief
that
[Glc,] was
very low and that, therefore, glucose transport was rate-limit-
ing for reactions utilizing glucose
(5).
However, in the same
study
it
was also observed
that
[Glc,] was about
1.5
mM when
hearts were perfused in the working mode, provided
that
ex-
tracellular glucose was elevated
to
the mildly hyperglycemic
concentration of 16 mM and
that
the
atrial
pressure was main-
tained below
5
cm
H,O
to limit the work-related requirement
for substrate. Under very slight differences in experimental
conditions, therefore, limitations imposed on
a
particular
en-
zyme step were
altered
so
that
this step was no longer rate-
limiting.
It
is, therefore, to be expected
that
a
step
that
exerts
a
dominant effect upon flux under one set of conditions, such
as
insulin deprivation, may exert
a
quantitatively different effect
upon flux under different experimental conditions
(6,
7).
In
contrast to the view
that
glucose transport
is
the
“rate-
limiting” or “pacemaker” reaction of glucose utilization,
an
al-
ternative view
has
been expressed
that
many, if not all, of the
enzymes of glycolysis have activities similar to the
rate
of gly-
colysis itself and
that
one or another of these enzymes may
control flux under different conditions. Decreases of only 33%
in the activity of
an
enzyme, P-glucoisomerase, thought to op-
erate
in
vivo
very close to near-equilibrium, have been reported
(8)
to decrease significantly
the
ratio of [products] to [reactants]
(r)
measured
in
tissue
and
at
the same time to cause
a
propor-
tionate decrease
in
the
rate of complex carbohydrate synthesis.
One way to deal quantitatively
with
the distribution
of
the
control of the rate of
flux
through
a
metabolic pathway exerted
by individual enzymatic steps or groups of enzymatic steps
has
been formalized
in
the concept of control strength
(91,
which
The abbreviations used are: Glc,, intracellular glucose; Glc,, extra-
cellular glucose; Pyr, pyruvate;
HK,
hexokinase; UDPGPlase, UDP-Glc
pyrophosphorylase (EC 2.7.1.1); GlycS, glycogen synthase; Plase, phos-
phorylase; PGK, 3-P-glycerate kinase; PGlyM and PGM, P-glycerate
mutase; Eno, enolase; PK, pyruvate kinase; UDPG, UDP-Glc; Glc-6-P
and G6P, glucose 6-phosphate; Fru-6-P and F6P, fructose 6-phosphate;
Glc-1-P and GlP, glucose 1-phosphate; Fru-l,6-P2, fructose 1,6-bisphos-
phate; Fru-2,6-P,, fructose 2,6-bisphosphate; DHAF’, bishydroxyacetone
phosphate; GAP, glyceraldehyde-3-phosphate; 1,3-P2-glycerate and
1,3DPG,
1,3-bisphosphoglycerate;
2,3-P2-glycerate, 2,3-bisphosphoglyc-
erate; 3-P-glycerate, 3-phosphoglycerate; 2-P-glycerate and 2PG,
2-phosphoglycerate; P-enolpyruvate and PEP, phosphoenolpyruvate;
a-glycero-P, a-glycerophosphate; Glut4, glucose transporter 4; P-glu-
comutase and PGM, phosphoglucomutase; P-glucoisomerase and PGI,
phosphoglucoisomerase; P-fructokinase, phosphofructokinase; triose-P
isomerase, triose phosphate isomerase; MCA, metabolic control analy-
sis;
J,
metabolic
flux;
C,
flux
control coefficient;
E,
elasticity;
K‘,
equi-
librium constant;
r,
ratio of products to reactants in the tissue for a
given reaction.
H
denotes all ionic species of a compound; therefore, we
have used
[X...]
throughout.
25502
Ketone Bodies and Insulin Action on Glucose Utilization
25503
was subsequently termed
flux
control coefficient (10).
Flux
con-
trol coefficients
(C)
are defined
as
the fractional change in
flux
resulting from an infinitesimal fractional change in enzyme
activity. The
flux
control coefficient can be determined indi-
rectly by first calculating the elasticity
(E),
the fractional
change in the net rate of a reaction catalyzed by a particular
enzyme brought about by infinitesimal fractional change in the
concentration of its substrate
or
product (Equation
6).
The de-
gree of control exerted by each enzyme step can be determined
using bottom-up analysis
(9,
11).
In
a
steady state, net rate
(14
can be calculated from known kinetic and thermodynamic pa-
rameters using the Haldane equation (Equation 4) (12)
to
ob-
tain the elasticity (Equation
8).
The degree of control exerted by
groups of enzymes can also be determined using top-down anal-
ysis
(11,
13,
14).
In this paper, the method of analysis is closest
to
that of Groen
et
al.
(15). Flux
can be varied in different ways:
the activity of a particular enzyme may be decreased by inhib-
itor titration (16) or by the selection of mutants with lower
activity of a specific enzyme
(8);
enzyme activities may be in-
creased by addition of pure enzyme to
a
tissue homogenate
(17)
or by genetically engineered overexpression
(18).
Other meth-
ods to formalize analysis of
flux
control coefficients have also
been developed (19-25).
Insulin and work were known to increase glucose transport
into heart muscle (4,26). Glucose transport was later shown to
result from the translocation of Glut4 from the endoplasmic
reticulum to the plasma membrane (27-31). Because insulin
administration increases rapidly the number of Glut4 mol-
ecules located within the plasma membrane, glucose transport
into the interior of perfused working
rat
heart increases as
well. However, with the provision of
a
preferred fuel such
as
ketone bodies (32-34) for energy production, the transport of
glucose
to
supply the energy requirements for the heart should
decrease. We have used these two approaches: first, increasing
the activity of the glucose transporter by
a
saturating dose
of
insulin (100 nM); and second, reducing the need for glucose
transport by supplying 4 mM sodium o-P-hydroxybutyrate and
1
mM sodium acetoacetate
as
an alternative energy source.
Using these strategies, we have determined for the first time in
one set of data the concentrations of the intermediate metabo-
lites, the kinetic constants of the enzymes of glucose metabo-
lism, the values of equilibrium constants
(K')
for intracellular
conditions of pH and free
[Me],
and the
flux
of the pathway.
With this information we have examined the effects of different
physiological states
on
the control of
flux
exerted by the enzy-
matic steps of glycolysis and glycogen metabolism of perfused
working
rat
heart.
EXPERIMENTAL PROCEDURES
Preparation and Perfusion
of
Rat Hearts
450-500-g male Wistar
rats
(Charles River Laboratories, Wilming-
ton,
MA)
fed
ad
libitum
were given
50
mgkg of sodium pentobarbitalkg
of body weight intraperitoneally (Sigma). Hearts were removed and
perfused in
a
nonrecirculating hemoglobin-free system (35)
as
previ-
ously described (36). Briefly, following rapid excision, hearts were per-
fused in the retrograde manner
(a
modified Langendorfftechnique (37))
with modified Krebs-Henseleit buffer, pH 7.4, containing 1.2 mM Pi, free
[Mp] of
0.5
m,
free [Ca,']
of
1.07 mM, and 10 mM glucose for
-15
min.
During this period, the vena cavae and the pulmonary veins were li-
gated, and the pulmonary artery was catheterized to collect the effluent
of the coronary sinus and the right ventricular thebesian veins. Hearts
were then switched to the working mode (35) with
a
10 cm H,O preload
and
80
mm Hg
(108
cm H,O) afterload for
15
min for
a
period of
stabilization. During the succeeding 30 min, hearts were perfused with
one of four buffer solutions containing:
1)
10
mM glucose; 2) 10 mM
glucose plus
1
mM sodium acetoacetate and 4 mM sodium D-P-hydroxy-
butyrate (Sigma); 3) 10 mM glucose plus
0.05
unitfml (-100 nM) recom-
binant soluble human insulin (100 units
or
4 mg per ml) (Novo-Squibb,
Princeton, NJ),
a
dose
of
insulin found in skeletal muscle preparations
to
give maximal insulin response
in
vitro
(38);
or
4)
10
mM glucose plus
the combination of ketone bodies and insulin. During this period, a
number of parameters of cardiac function were measured
as
previously
described (36): aortic flow, coronary flow, left ventricular dPldt (Gould
G4615-71, Valley View, OH), systolic aortic pressure (Spectramed
P23X1, Oxnard CA), diastolic aortic pressure, mean aortic pressure,
and left ventricular systolic pressure (Millar SPR477, Houston
TX).
At
the end of the 30-min period, hearts were freeze-clamped to a thickness
of <2 mm, submerged under liquid nitrogen, and the atrium and any
adherent perfusate were removed with
a
dental drill. Extracts for me-
tabolite and ion analyses were made
as
previously described (36), except
that the extracts for Fru-2,6-P, analysis were prepared in
0.05
M
NaOH
(39) and those for glycogen were prepared by heating the tissue samples
in 0.5
M
NaOH
at
100
"C for
15
min to destroy the glucose and solubilize
the glycogen.
Enzyme Measurements
For most enzyme determinations, heart tissues were minced with
scissors; homogenized at low speed on
a
Potter-Elvehjem glass homog-
enizer in
10-20
volumes of a
1:l
H,O:glycerol mixture containing
10
mM
&HPO,:KH,PO,, pH 7.4, 20 mM imidazole, pH 7.4, 5 mM mercapto-
ethanol, 0.5 mM EDTA, and 0.02% bovine plasma albumin; and used
without centrifugation. Where two substrates were involved, the
K,
of
the
first
substrate was determined in the presence of saturating con-
centrations of the second substrate. To preserve the interconvertible
forms of glycogen synthase (EC 2.4.1.11) and phosphorylase (EC 2.4.1.1)
separate homogenates were prepared in 20 mM imidazole buffer, pH 7,
containing
0.5
mM dithiothreitol, 5 mM EDTA, and 20 mM
KF.
All of the
enzyme activities were determined at 37 "C using fluorometric proce-
dures measuring the oxidation
or
reduction of pyridine nucleotides (40).
The basic reagent was
10
mM &HPO,; KH,PO, buffer, pH 7.2, 20 mM
imidazole HCl, pH 7.2, 150 mM
KC],
and
5
mM MgCl,; substrates, aux-
iliary enzymes, and cofactors were added
as
necessary. The kinetics of
all of the enzymes of glycolysis were measured
as
well as the kinetics of
glycogen synthase, phosphorylase, P-glucomutase (EC 5.4.2.21, and glu-
cose-6-phosphatase (EC 3.1.3.9). The analyses were conducted at high
dilution by fluorometric procedures that minimize disturbing side re-
actions. Appropriate blanks were included to correct for nonspecific
reactions. When more than one form of an enzyme might be present, the
numbers represent an average value in the crude tissue; the homoge-
nates were not purified in any manner and thus should represent
as
closely
as
possible the activity of the tissue itself. In specific instances,
the reverse reactions were measured in order
to
do metabolic control
analysis (Tables V,
VI,
and
VII).
Certain equilibrium and kinetic con-
stants were obtained from the literature as noted in Tables
IV
and V (4,
41-57).
Analytical Measurements
Intra- and extracellular water spaces were measured with perfusate
containing
1
pCi/ml 3H,0 (DuPont NEN) and 0.05 pCi/ml [l4C1mannitol
(ICN Biochemicals, Costa Mesa, CA) for
5
min
as
previously described
(36). Unless otherwise stated, glycolytic intermediates were measured
using
a
ratio fluorometer (Optical Technology Devices, Inc., Elmsford,
NY)
by established methods (40). 2,3-P2-glycerate was measured by a
fluorometric adaptation
of
the method of Rose and Liebowitz (58).
Fru-2,6-P, was measured by
a
fluorometric adaptation of a published
enzymatic method (39). CAMP was measured by radioimmunoassay
(DuPont NEN). Values for metabolites, nucleotides, and cofactors are
given
as
micromoles per milliliter of intracellular water;
to
convert mi-
cromoles per gram wet weight, to micromoles per milliliter of intracel-
lular water the values were multiplied by 2.88
as
determined by space
measurements.
Metabolic
Flux
The rate of glucose utilization was determined with high pressure
liquid chromatography purified [2-3Hlglucose (DuPont NEN). Tritiated
glucose (0.75 mCi) was added to 200 ml of perfusate (375 pCi/mmol).
The coronary outflow was collected during a timed interval, usually 2
min. The phosphorylated intermediates and glucose were removed by
passing the sample over formate and borate Dowex
50
columns in
sequence (59). The tritiated water remaining was a measure
of
the flux
through P-glucoisomerase; no correction was made for incomplete equil-
ibration
at
this step (60). The removal of the labeled glucose and inter-
mediates was confirmed by evaporating a portion of the effluent from
the column; less than
0.1%
of the counts remained. The rates of glyco-
genolysis
or
glycogenesis were calculated from the Aglycogen as glu-
cosy1 units from the end
of
the initial perfusion of
15
rnin to the end of
the 30-min experimental treatment (Fig.
1).
25504
Ketone Bodies and Insulin Action on Glucose Utilization
Calculations
Statistical analyses
of
the significance of the difference between
means were calculated using a Mann-Whitney
U
test (Stat-View-4,
Abacus Concepts, Inc., Berkeley, CAI. Cytoplasmic [Pi] was determined
by 31P NMR; the cytoplasmic pH was taken from the shift of the intra-
cellular
Pi
from phosphocreatine,2 and the cytoplasmic free IMP] was
calculated using the measured
[Hcitratel/[Xisocitratel
ratio (61) (Table
11).
Cytoplasmic [ZATPl/[HADPl ratios were calculated as previously
described (36).
All
equilibrium constants were corrected, where appro-
priate, for the pH and free [Me] by methods previously described (62)
using the equilibrium constants that had been determined under con-
ditions approximating the intracellular environment. The values for
[GAP], [Fru-1,6-Pzl, and [1,3-Pz-glyceratel are calculated from the equi-
librium constant of triose-P isomerase (EC 5.3.1.1), aldolase (EC
4.1.2.13), and 3-P-glycerate kinase (EC 2.7.2.3) using the individual
values
of
measured metabolites. All other calculations were made cor-
recting for intra- and extracellular volumes (36). Changes in metabolite
levels are presented as proportionate change, which is equal to
n
x
(experimental value/control values)";
n
=
1
when the experimental
>
control, and
n
=
-1
when the experimental
<
control, thus assigning
equal value to increases and decreases (63). Cardiac hydraulic work was
calculated as follows,
cardiac hydraulic work(J/min/g wet weight)
=
cardiac output (mumin)
X
aortic pressure (mm Hg) 101,325 (Nm-2)
left ventricle weight (g wet weight)
X
760 (mm Hg)
where
1
atm
=
760 mm Hg
=
101,325 newtons/m2 (Nm-2).
Method
of
Calculation
of
Metabolic Control Parameters
A variable property of a system will respond to a variation of some
parameter; for example, metabolic
flux
will respond
to
changes in en-
zyme activity or metabolite concentration. A simple model is shown
below.
J
-
Substrate
[Xo]
s
Product
[X,]
"r
ur
(Eq.
1)
El
where
i
is number of the step,
1-n
(in this model,
i
=
1);
[XI
is concen-
tration of the metabolite
([X,]
=
[Xc-LJ,
concentration of the substrate,
[SI; [X,]
=
[XJ,
concentration of the product, [PI);
ur
is rate
of
conversion
of substrate to product;
u,
is rate of conversion
of
product to substrate;
u
is net rate of an individual enzyme step;
J
is
flux
through the pathway
of the system (in this one-step model
J
=
u
=
uf
-
ur);
and
E,
is enzyme
catalyzing step
i
denoted by the subscript.
1.
Michaelis-Menten Initial Rate Equation with One Substrate or
One Product
(64)
where
Km,s
is Michaelis constant
(K,)
of
[SI,
forward direction; is
Michaelis constant
(K,)
of [PI, reverse direction; V,, is maximum
velocity of an enzyme step in the forward direction; and Vmaa is maxi-
mum velocity of an enzyme step in the reverse direction.
2.
Law
of
Microscopic Reuersibility, Haldane Relationship, and
Steady-state Rate Equation with One Substrate and One Product,
Assuming Michaelis-Menten Kinetics
(12)
At equilibrium,
where
K'
is the equilibrium ratio of [PI to [SI determined
in vitro
under
specified conditions.
3.
Flux
Control Coeficient
The
flux
control coefficient
(C)
is the fractional change in the
flux
of
the system
(SJIJ)
that results from an infinitesimal fractional change in
K.
Clarke and C. Keon, unpublished observations.
the rate of enzyme catalytic activity
(Se/e)
in step
i.
(Eq.
5)
C
can be calculated in two ways.
In
the direct method,
flux
is meas-
ured and the enzyme concentration is titrated by the addition of enzyme
or inhibitors and does not require the calculation
of
elasticities
(17,
65-67). In the indirect method, elasticities of the steps must first be
determined (see step 4 below), and
C
can be calculated from these data
(9, 15, 19, 20).
4.
Elasticity
The elasticity
(E)
of an enzyme is the fractional change in the net rate
for
an individual reaction
(Su,/ui),
caused by an infinitesimal fractional
change of metabolite concentration
(S[Xl/[XI)
in step
i.
In this model,
X,-,
is the substrate and
X,
is the product of
Ei
(for review see Ref. 23).
(Eq.
6)
4a.
Calculation of
E
from Change in Flux
This equation can be regarded as the finite approximation
to
the elas-
ticity definition. To calculate
E
by this method one needs measurements
of net rate (Table
I)
and substrate concentrations (Table
11).
The above
relationship (Equation
7)
allows estimation of the block elasticity if the
following conditions are met:
1)
the
flux
(J)
through a block
of
the
reaction is equal to the net rate
(u)
of the step,
2)
the
flux
is dependent
on the concentration
of
only one metabolite outside of the block, and 3)
the
flux
is changed by a perturbation in some other part of the metabolic
pathway that causes a change in
[SI.
4b.
Calculation of
E
from Kinetic Data-If
a steady state prevails and
if the tissue reactions follow Michaelis-Menten kinetics, the net rate of
the steady-state equation (Equation
4)
can be substituted into Equation
6.
The derivative of Equation 6 yields Equation
8.
To
calculate
E
from
the kinetic parameters of the enzymes one needs the following:
(a)
the
K,,,
and
V,,
of forward and backward direction of each enzyme involved
and the
K,
and
K,
of
other substances that alter the kinetic parameters
(Table
V);
(b)
the concentration of the substrates
([SI)
and products ([PI)
of
each reaction (Table
11)
and the ratio of the products
to
reactants in
the tissue
(r)
(Table
IV);
(c)
the equilibrium constant
(K')
of the reaction
under appropriate conditions of temperature, ionic strength, pH, and
free [Me] under which the reactions are occurring (Table
IV);
and
(cl)
the architecture of the pathway, that is whether it is linear or branched,
and the ratio of
fluxes
at the branch points (Table
I
and Equation
11).
(Eq.
8)
€EL
-
___
-
-
r/K',,
[PYKm,P(Ez
I
-
r/K',,
Vr8,
-
-
r/K'E,
+
[sYKm,S(E,]
+
[PYKm,P(E,j
-
'IK',;
VmuR,E;
u~/u,
=
r/K
The expressions
u,JV,,,
and
ur/VmarR
represent the fractional satu-
ration of the enzyme with
[SI
and [PI, respectively
(to
the extent that
Km,s
and
Km,p
approximate true dissociation constants).
5.
Summation Theorem
all of the
n
enzymes in a metabolic sequence is
1.
The sum of all
flux
control coefficients of any chosen linear
flux
(J)
for
t=1
where
n
is the number of steps in the sequence chosen.
6.
Connectivity Theorem
The
flux
control
coefficients
are related to the elasticities
of
all en-
Ketone Bodies and Insulin Action on Glucose Utilization 25505
zymes that respond to the concentration
of
a
single metabolite
[XI.
7.
Branch Point Theorem
At a branch point under steady-state conditions, the sum of the flux
control coefficients of enzymes
in
the branches
is
equal to the ratio
of
flux through the branches.
Glycogen synthase
(x4.~)Glycogen
(E5.a)
/
(X4
a)
UDPG
,
/Phosphorylase
Ry)
(J4.y)
(X3,)GlP
J
PGM
VPGM
(E3.a)
T
(J3.a)
v
Flux
in
glucose
group
SCHEME
1
In Scheme
1,
branch point
at
Glc-6-P, the equation would be
C.
c:,/c&3
=
U3.,/%.pr
1.3
for
the glucose group specifically,
(C&
+
Ci,,)/G,p
=
U3.a/u3.p, (Eq.
11)
and for the other groups,
where
a,
p,
and
y
are branched steps in step
i.
8.
Matrix Method
of
Control Analysis
(11,
681
E.C
=
M,
C
=
E".M
(Eq. 12)
where
E
is the elasticity matrix;
C
is the flux control coefficient matrix;
and
M
is
the matrix
that
defines the relationships between the elements
of E and the flux control coefficients in
C.
Application
of
Metabolic Control Analysis
We performed "bottom-up"
(11,
23) and "top-down"(11, 13,141 analy-
ses. Bottom-up analysis considers individual enzyme steps with regard
to their elasticities. In contrast, top-down analysis considers groups of
enzymes, using group elasticities. In
our
applications, the differences
between top-down and bottom-up analyses are:
1)
top-down analysis
applies
to
the whole
of
glucose metabolism,
i.e.
the effects
of
reactions
beyond the block analyzed are included; 2) because different block elas-
ticities were derived by taking different pairs of the experimental sets,
there
is
a
single result from the top-down method, which is an approx-
imate average over the states considered, Fuller explanations
as
models
are given below.
1.
Model
of
Bottom-up Analysis
E
was determined for the individual enzyme steps
of
the branched
pathway from glucose transport to glycogen metabolism and P-gluco-
isomerase step (Scheme
1)
and also for the steps of the terminal linear
pathway
of
glycolysis from 3-P-glycerate kinase to pyruvate kinase
(Scheme 2) using the data from Tables
11-V.
For each pathway ana-
lyzed,
xCJ
=
1.
1A.
Glucose Dansport
to
the Branches
of
Glycogen Metabolism and
P-glucoisomerase
Step-Scheme
1
is a model of glycogen metabolism
and illustrates both glycogenolysis and glycogen synthesis. The activity
of Glc-6-P dehydrogenase (EC 1.1.1.49) in the heart was 102-103 lower
than that of P-glucomutase and P-glucoisomerase (Table
V),
and the
oxidative portion of the hexose monophosphate pathway was, therefore,
ignored. In the presence of glucose alone, there was net phosphorolysis
of
glycogen (shown as
dashed arrow)
and the net rate of the P-glu-
comutase reaction was in the direction
of
Glc-6-P formation;
J3,,,
=
J4,,,
J4.a
=
0.
The value
of
glycogen synthase was not considered, In the
presence of ketones and/or insulin, there was net glycogen synthesis,
and the net rate
of
the P-glucomutase reaction was in the direction
of
Glc-1-P formation (shown
as
a
solid arrow
j;
J3,=
-
J4.0, J4
-
0.
In these
cases, phosphorolysis was not considered, Elasticities were calculated
using kinetic data (Equation
8).
25506
Ketone Bodies and Insulin Action on Glucose Utilization
-
c;,,t*
GK
times higher than the
K,,,
of
hexohnase for glucose,
so
the use of glucose
CiG,
CJ,DPGPl,,,
-
CJGlYCS
1
algebra.
In
the glucose and ketones groups,
r
for the glucose transport
step was far from equilibrium; intracellular glucose was low but several
';GM
=
by hexokinase would be favored. The elasticity calculation does include
a
contribution for
the
reversibility in the term involving the disequilib-
rium ratio, but the smaller contribution from the fractional saturation
of the carrier
(u,/V,,&
approaches
0
in the glucose and glucose plus
(Eq. 17) ketones groups where [Glc,]
>>
[Glc,] and has been taken to be
1
in the
presence
of
insulin where [Glc,]
-
[Glc,]. The reaction of UDP-Glc py-
rophosphorylase was assumed to be in
a
state of near-equilibrium, and
the elasticities were assigned
as
described above. The reaction
of
gly-
glycogen synthase was assigned the calculated
uf
from the Michaelis-
Menten equation (Equation 4) and substituted in Equation 6, and the
11
1
1
0
cogen synthase was taken to be irreversible (Table
IV).
The net rate of
'UDPGlc
'UDPGlc
0
'hGM
-"%GI '/%DPGPlase
l/uGlycS
UDPGPlase GlyeS
derivative was taken.
J
glycogen synthesis
1,3DPG- 3PG
2PG
TF$'pKi
glucose transport
('O)
PGK
('I)
PGlyM
En0
(El)
(Si)
(E3)
(FA)
phosphorylation
SCHEME
2
glycolysis
IB.
Terminal Linear Pathway in Glycolysis (Scheme
2)
SCHEME
3
[~PGI
[~PGI glucose metabolism
as
a
single system (Schemes
3
and
4).
-m&K
-
m+
2. Model
of
Top-down
Analysis
'PGK
-
3ffi
-
-
Two
forms of top-down analysis were performed considering all of
2A.
Glc-6-P as Intermediate Metabolite (Scheme
3)
[3PGYKm,3PG~t'GKl
-
Ah
J/Aln[GGP],
+
[1,3DPGyKm,,,3,PG(PCK)
+
[3pGyKm,3PCWK,
-Aln Jm/Aln[G6P],
1
'Eno
-
[2PGyKm.ZPG(Enol
2PG
-
+
[2PGyKm,ZFG(Eno)
+
[pEpyKm,PEP(En~)
glucose transport glycogen synthesis
and glycolysis
Whenever
T/K
was
21
we assumed an equilibrium state, and where cp
and
cs
approached negative and positive infinity, respectively, the num-
bers -100
or
100
were assigned to solve the equations using matrix
SCHEME
4
In
the
first
case, centering
on
Glc-6-P, glucose transport and phos-
phorylation was taken
as
block 1, glycogen synthesis
as
block 2, and
glycolysis as block
3.
Because insulin markedly increases the
V,,,
of the
glucose transporter and thus cLp (Equation 21), it is inappropriate to
calculate a
flux
control
coefficient
for block
1
from
a
comparison of
changes of
flux
induced by addition of insulin to glucose-perfused
hearts. We may, however, compare changes of
flux
induced by addition
of ketones to glucose-perfused hearts (Equation 22, column
1)
and by
the addition of insulin to hearts perfused with glucose plus ketones in
blocks 2 and
3
(Equation 22, columns 2 and 3).
In
this
case, insulin was
regarded
as
perturbing block
1,
allowing calculation of the elasticity of
blocks
2
and
3;
and ketones were regarded
as
perturbing block
3,
al-
lowing calculation of blocks
l
and 2. Where an elasticity could be cal-
culated in more than one way, an error analysis was performed to
identify the more reliable value.
RESULTS
Cardiac hydraulic work was significantly elevated from
0.30
to
0.37
and
0.34
J/min/g wet weight, in the presence
of
ketones
Ketone Bodies and Insulin Action on Glucose Utilization
25507
or insulin, respectively, but was not altered in the presence of
both effectors (Table I). The increase in cardiac hydraulic work
was primarily the result of an increase in systolic aortic pres-
sure from 90.5
to
96.0 mm Hg.
In
the
presence of glucose alone,
glycogen decreased
at
a
rate of 0.46 pmol of glucosyl units/
midml of intracellular water. After the addition of ketones, in-
sulin, or the combination, glycogen was synthesized at the rates
of 0.67, 2.6, and 2.5 pmol of glucosyl units/min/ml of intracel-
lular water, respectively (Table I). In the presence of insulin, the
production of
3H,0
from [2-3Hlglucose increased from 4.58
to
6.36 pmoVmidm1 of intracellular water but decreased to 2.36 in
the presence of ketones. When glycogen synthesis
or
breakdown
was combined with the measurement of 3H,0 release at the P-
glucoisomerase step, net glycolytic flux in hearts perfused with
glucose alone was 5.04 pmoVmidm1 of intracellular water in
glucose-perfused hearts (Table I).
As
expected, net glycolytic flux
decreased 3.0-fold on provision of the alternative substrate
of
ketone bodies and 2.3-fold on addition of insulin plus ketones;
the addition of insulin alone caused no statistically significant
change. The production of L-lactate
at
10 cm H,O right atrial
pressure accounted for only 0.3% of the glucose use in the glu-
cose group and increased to
1,
7, and 0.7% in the ketones, in-
sulin, and ketones plus insulin groups, respectively.
[Glc,] was 1.91 pmoVml of intracellular water (Table
11)
in
these working hearts, far above the
K,,,
of 0.072 mM for the
hexokinase reaction (Table
V).
Decreasing the requirement for
glucose by substituting ketone bodies for pyruvate
as
the major
provider of
NADH
for electron transport increased [Glc,]
to
3.4
pmoVml of intracellular water, whereas the addition of 100 nM
insulin equilibrated [Glc,]
with
[Glc,]. [Glc-6-P] was 0.17 and
[Fru-6-P] was 0.04 pmoVml of intracellular water in hearts
perfused with glucose alone. The increase in [Glc-6-P] was 3.5-
fold with ketones, 7.5-fold with insulin, and 10-fold with the
combination (Table 11, Fig. 1). However, equilibrium was main-
tained in the P-glucoisomerase reaction;
T/K'
was near
1
under
all conditions studied (Table
IV).
[Glc-1-PI was 0.02 pmoVml of
intracellular water and increased slightly in the presence of
ketones
or
insulin, but it increased 10-fold in the ketones plus
insulin group, near-equilibrium for the P-glucomutase reaction
(Table
IV).
[Glycogen] was
35.3
pmol of glucosyl unitdm1 of intracellular
water (Table 11, Fig.
1)
at the end of the 15-min stabilization
period. After 30 min of perfusion in the experimental period,
[glycogen] decreased to 21.4 pmol of glucosyl unitdm1 of intra-
cellular water in the glucose group and increased
to
55.5
in the
presence of ketones, 112 in the presence of insulin, and 109 in
TABLE
I
Physiological and metabolic parameters in perfused working rat hearts
Except for cardiac hydraulic work, the data are given
as
pmol/min/ml of intracellular water
f
S.E. with the number of observations given in
parentheses. Significant differences from glucose alone for lines
1
and 2 are indicated. Calculations in lines 3 and 4 are average values; standard
error is based on the combination of
error
formula for the sum
or
difference of two figures,
ie.
for
z
=
x
-
y:
S,
=
d\/CSJz
+
(SJZ
where
S,
is the
standard error in
z,
etc. Hydraulic work and 3H,0 production from [2-3Hlglucose were determined as described under "Experimental Procedures."
Glucose Glucose
+
ketones Glucose
+
insulin
Hydraulic work (J/min/g 0.30
f
0.01
(8)
0.37
f
0.01"
(8)
0.34
t
0.01" (4) 0.32
f
0.01
(4)
3Hz0
production from 4.58
-c
0.75 (3) 2.37
f
0.69"
(3)
6.36
*
0.32" (3) 4.66
f
0.5
(3)
Glycogen synthesis -0.463 0.12 2.56
2
0.43 2.46
c
0.15
Net glycolytic flux through 0.673
f
0.14 2.20
t
0.52
L-Lactate exiting heart 0.030 (2)
0.050
(2)
0.400 (2) 0.066 (2)
Glucose
+
ketones
+
insulin
wet weight)
[2-3Hlglucose
5.04
t
0.76 1.70
f
0.70 3.80 0.53
P-glucoisomerase
p <
0.05,
Mann-Whitney
U
test
TABLE
I1
Metabolite concentrations in perfused working rat hearts
Metabolites in extracts from freeze-clamped hearts were measured
as
described under "Experimental Procedures" and given
as
means
S.E.
in
pmoliml of intracellular water. The numbers of observations in each group
are
as
follows: glucose
=
8, ketones
=
3,
insulin
=
3,
and ketones and
insulin
=
4,
except for the following: pyruvate
=
4,
5,
7, and 7; 2-P-glycerate and P-enolpyruvate
=
5,
3,3, and 3; and glycogen and Fru-2,6-P2
=
3,
2, 2, and 3, respectively. Significant differences from glucose-perfused hearts are indicated. When there were only two samples, S.E.
=
rang&.
Metabolite Glucose Glucose
+
ketones Glucose
+
insulin
Glucose
+
ketones
+
insulin
Glycogen" 21.4
t
1.62
55.5
f
2.95*
Glc-1-P 112
f
12.4' 109
f
3.31'
0.035
f
0.020 0.057
f
0.012 0.198
f
0.077'
0.013
f
0.003'
Glc-6-P 0.169
f
0.010 0.612
f
0.082' 0.009
f
0.001
1.268 0.020'
Glc, 1.626
c
0.508'
FN-6-P 1.91 0.503 3.40 1.12 11.5
2
1.09'
0.041
t
0.005
0.155
t
0.026b 9.94
f
0.712'
Fru-1,6-P2 (total) 0.035
t
0.003 0.342
t
0.003' 0.321
t
0.053'
0.016
t
O.OOOb
0.678
t
0.149 0.040
f
0.002 0.033
f
0.005
DHAP
0.036
t
0.005
0.155
t
0.062 1.40
f
0.047' 0.593
f
0.158
GAP (x103) (calculated) 0.017
t
0.004
1.62
c
0.241
0.055
f
0.001
0.035
f
0.005
1,3-Pz-glycerate
(x103)
0.869
2
0.081
0.791
f
0.179 2.50 0.042'
3.32
f
0.076'
3.57
f
1.10'
1.58
2
0.221
2.57
c
0.440'
2,3-P2-glycerate 0.010 0.004
3-P-glycerate 0.071
t
0.004
0.008
f
0.001
0.007
2
0.002
0.010
f
0.004
0.063
t
0.003
2-P-glycerate 0.064
t
0.018
0.009
f
0.002 0.042
t
0.006h
0.003
f.
0.003'
P-enolpyruvate 0.013
t
0.003 <0.002
0.008
t
0.008 0.002
f
0.001'
Pyruvate
0.011
t
0.006
0.055
t
0.004
0.002
t
0.002'
L-Lactate 0.036
0.003'
0.085
f
0.004' 0.060
f
0.009
0.683
t
0.053 0.288
t
0.064e 0.737
f
0.079
Citrate 0.778
f
0.247
Isocitrate 0.018
t
0.002
0.432
f
0.042 1.15
f
0.076* 0.883
t
0.031'
0.065
f
0.004b 1.56
t
0.210'
Fru-2,6-P2 (x103)
0.051
f
0.002' 0.092
f
0.009'
6.45
f
1.72 8.39
t
2.90 7.80 0.51'
0.020
t
0.004
Glc-1,6-P2 0.007
f
0.000
0.008
f
0.002
(calculated, x103)
(calculated)
11.3
f
1.54
a
[Glycogen] was 35.3
f
3.17 pmol of glucosyl units/ml of intracellular water
at
the end of the 15-min stabilization period,
'
p
<
0.05,
Mann-Whitney
U
test.
25508
Ketone Bodies and Insulin Action on Glucose Utilization
the ketones plus insulin group. The activities of the enzymes of
glycogen metabolism were analyzed
as
well
as
[CAMP], which
can affect these enzymes through
a
cascade
of
protein kinases
(69, 70).
No
significant change was found in [CAMP] (Table
111)
or in the percentage of phosphorylase
a,
the phosphorylated
form. Total phosphorylase activity
is
given in Table
V.
The
percentages in the
a
form were 5.6, 4.4, 5.4, and
5.0
in the
glucose, ketones, insulin, and ketones plus insulin groups, re-
spectively, suggesting that cytoplasmic free [Ca"] was not al-
tered by the treatments given. Total glycogen synthase was
measured (Table
V)
and did not vary among the experimental
groups. Despite the increases in phosphorylated hexoses, the
immediate precursor of glycogen, [UDP-Glc], remained invari-
ant; however, [UTP] decreased with addition of ketones plus
insulin, and [UDP] decreased 1.5-fold with all conditions even
though glycogen synthesis was increased (Tables
I
and
111).
In contrast to the up to 10-fold increases in metabolites pre-
ceding the P-fructokinase (EC 2.7.1.11) step, the concentrations
of total Fru-1,6-P2 were decreased 4-fold by provision of the
alternative substrate; ketone bodies increased 2-fold on addi-
tion of insulin, but remained unchanged by the combination
(Table
11,
Fig.
1).
Because of the large amount of Fru-l,6-P2
binding to aldolase (EC 4.1.2.13) (49), free [Fru-1,6-P21 was
calculated from the measured [DHAP] and the
K'
of the aldol-
ase and triose-P isomerase reactions (Table
IV).
The free [Fru-
1,6-P2] was calculated
to
be 0.68 nmol/ml
of
intracellular water
in hearts perfused with glucose alone and was altered by ad-
ditions to the perfusate to the same degree
as
total [Fru-1,6-P21
(Table
11,
Fig.
1).
The [Fru-2,6-P2], a positive effector of
P-
fructokinase (71,72), was
11.3
nmoVml of intracellular water in
the glucose-perfused hearts and was 6.5 on addition of ketones,
thus paralleling the changes in [Fru-l,6-P2]. In agreement with
previous reports, insulin did not increase [Fru-2,6-P2] in the
perfused hearts (73, 74).
[Dm] was 0.036 pmoVml of intracellular water in glucose-
perfused hearts and increased 2.7-fold on addition of insulin,
but it was unchanged on addition of ketones and the combina-
tion. [1,3-P2-glycerate], calculated from the
K'
of the 3-P-glyc-
erate kinase reaction and the measured levels of [3-P-glyceratel
and cytoplasmic [ZATPl/[XADPj, was 0.87 pmoVml of intracel-
lular water in glucose-perfused hearts, increased %fold on ad-
dition of ketones
or
insulin, and increased 2-fold on addition of
the combination, reflecting the increase in the [ZATPY[ZADPl.
Whereas both the GAP dehydrogenase (EC 1.2.1.12) and the
3-P-glycerate kinase reactions have long been considered to be
at near-equilibrium
in
vivo
(751, the latter reaction was chosen
for the calculation of [1,3-P2-glyceratej because the
V,,,,
for-
ward of 3-P-glycerate kinase is 15,000 ymoVmidm1 of intracel-
lular water, compared with 300 for that of the GAP dehydro-
genase reaction and is
1
or
2 orders of magnitude greater than
the
other enzymes of glycolysis (Table
V).
[3-P-glycerate] was 0.071 pmoVml of intracellular water in
hearts perfused with glucose alone and was unchanged on the
addition of either ketones
or
insulin but decreased 1.7-fold on
addition of ketones plus insulin. [2-P-glyceratel was decreased
>%fold in
all
groups
as
compared with glucose (Table
11,
Fig.
11,
Glq-
+
Glc,
v'
ATP
ADP
aglycero-P
ADP
iLNAD+
I.;'"
-?I
II
L-Lactate
FIG.
1.
Metabolite concentrations
(pmol/ml
of
intracellular wa-
ter) in working perfused rat heart following the addition
of
4
ll~~
sodium D-P-hydroxybutyrate and
1
IUM
sodium
acetoacetate
and/or insulin
(100
m).
The differences from hearts perfused with
glucose alone are shown as proportionate changes as described under
"Experimental Procedures," with the concentrations in hearts perfused
with glucose alone following the metabolite title; only glycogen is shown
as the actual concentration.
ICW,
intracellular water;
G,
glucose alone
in the perfusate;
GK,
glucose plus ketone bodies;
GI,
glucose plus insu-
lin;
GKI,
glucose plus ketones and insulin;
TCA
cycle, tricarboxylic acid
cycle.
TABLE
I11
Nucleotides, calculated
pH,
and free [Mg2+1 in perfused working rat hearts
[zATPV[XADPI are described under "Experimental Procedures." Cytoplasmic pH and [Pi] were from 31P
NMR.
Significant differences
from
Values are pmovml ofintracellular water
-c
S.E. for the number of observations given in Table 11. The calculations of free
[MFI
and cytoplasmic
glucose-perfused hearts are indicated.
Glucose Glucose
+
ketones Glucose
+
insulin Glucose
+
ketones
+
insulin
PH
7.06
-c
0.01
7.05
2
0.01 7.04
-c
0.02 7.02
f
0.00"
Free [Mg2+l
1.23
f
0.03 0.744
f
0.011" 0.730
f
0.029" 0.666
f
0.082"
UTP
0.194
-c
0.010
0.161
-c
0.021 0.179
f
0.006
0.159
f
0.005"
UDP
0.034
f
0.002 0.021
f
0.002" 0.025
-c
0.001"
0.022
f
0.001"
UDP-Glc
0.099
5
0.006 0.109 0.015 0.096
f
0.003 0.094
f
0.001
Phosphocreatine
6.84
f
0.376 14.7
-c
1.30" 17.1
f
0.530" 16.4
f
0.567"
Creatine
23.9
-c
1.51 12.1
f
1.49" 13.7 1.14" 12.5
f
0.488"
Cytoplasmic free [P,]
6.94
f
1.37 7.81
f
1.00 4.88
f
0.66 6.42
f
2.22
Cytoplasmic [IATPl/
45.4
f
2.55 168
-c
8.93" 166
f
9.50" 179 8.93"
(x103) 0.864
f
0.031 0.740
*
0.044 0.629
f
0.104 0.856
f
0.200
['ADPI
''p
<
0.05,
Mann-Whitney
U
test.
Ketone Bodies and Insulin Action on Glucose Utilization
25509
TABLE
IV
Equilibrium constants of the reactions ofglucose and glycogen metabolism compared with the ratio of[productsl to [reactants] in perfused
working rat hearts
The equilibrium constants
(K)
have been corrected (62) where necessary for differences in tissue pH and free [Me] (Table
11).
The values
of
Iproductsl/lreactantsl
(r)
are taken from Tables
I1
and
111.
The reactions
of
UDP-Glc pyrophosphorylase, aldolase, triose-P isomerase, GAP
dehydrogenase, 3-P-glycerate kinase, and pyruvate kinase are assumed to be at near-equilibrium, and
rlK
is given
as
1.
The values for
K
given
at various pH and free [Me] are those for the
sum
of
the species present. The reactions written are those of the most ionized species.
Reaction Glucose Glucose
+
ketones Glucose
+
insulin Glucose
+
ketones
+
insulin
Glycogen synthase (EC 2.4.1.11)
UDP-Glc'-
+
Glc,
+
UDP3-
+
GIC,,~
+
H'
Phosphorylase (EC 2.4.1.1)
Glc,
+
P,2-
-
Glc,_,
+
Glc-1-P2-
UDP-Glc pyrophosphorylase (EC 2.7.7.9)
Glc-1-P2-
+
UTP4-
+
H'
"-*
UDP-Glc'-
t
HPP?-
Glucose transporter
Glc,
-
Glc,
Hexokinase (EC 2.7.1.1)
Glc
+
ATP"
+
Glc-6-P2-
+
ADP3-
+
H
P-glucomutase (EC 5.4.2.2)
Glc-1-P2-
-
Glc-6-P2- (glucose group)
Glc-6-P2-
-
Glc-1-P2- (other groups)"
P-glucoisomerase (EC 5.3.1.9)
Glc-6-P2-
+
Fru-6-P2-
P-fructokinase (EC 2.7.1.11)
Fru-6-P2-
+
ATP4-
+
Fru-1,6-%-+ ADP3-
+
H'
Aldolase (EC 4.1.2.13)
Fru-1,6-e".
DHAP2-
+
GAP2-
Triose-P isomerase
(EC
5.3.1.1)
Dm2-
+
GAP-
GAP dehydrogenase (EC 1.2.1.12)
GAP2-
+
P,"-
+
NAD+
+
1,3-P2-glycerate4-
+
NADH
+
H'
3-P-glycerate kinase (EC 2.7.2.3)
1,3-P2-glycerate4-
+
ADP3-
-
3-P-glycerate3-
+
ATP4
3-P-glycerate mutase (EC 5.4.2.1)
3-P-glycerate3-
+
2-P-glycerate3-
Enolase (EC 4.2.1.11)
2-P-glycerate3-
+
P-enolpyruvate3-
Pvruvate kinase (EC 2.7.1.40)
"~-eno~pyruvate;-
+
ADP~'
+
H+
+
Pyruvate-
+
ATP-4
Lactate dehydrogenase (EC 1.1.1.28)
Pyruvate-
+
NADH
+
H'
+
L-Lactate-
+
NAD'
37.7
0.343
9.08
X
10-3
2.90
X
10-3
4.03
X
10-3
0.719
4.36
4.36
1
1
0.191
0.191
2.09
X
103
1.94
X
10-3
9.29
X
10-7
16.2
8.40
0.518
0.30
0.240
0.800
1.32
X
103
3.69
X
10-4
2.80
X
10-7
9.87
X
10-5
9.87
X
10-5
1
0.046
0.046
1
6.04
x
10"
6.04
x
10-1
1
3767
3767
1
0.11
0.125
>1
4.0
1.47
0.368
1.20
X
104
1.91
x
102
1.58
x
lo-'
7.85
x
10'
1
7.85
X
104
29.8
0.193
6.47
X
10-3
4.47
x
10-3
6.19
x
10-3
0.723
3.47
3.47
1
1
0.340
0.340
2.42
X
103
1.08
X
10-3
4.45
X
10-7
0.0617"
0.057
0.924
0.30
0.253
0.842
1.53
x
103
3.92
x
10-9
9.82
X
10-5
9.82
X
10-5
6.00
x
1
0.046
0.046
1
5.82
x
lo-'
5.82
x
10"
1
3094
3094
1
0.11
0.071
0.648
4.0
2.30
0.574
1.10
X
104
5.82
x
10'
5.32
x
lo-'
8.22
x
104
8.22
X
104
1
29.5
0.261
8.85
x
10-3
0.727
1.16
x
lo-'
1.60
x
lo-'
3.34
3.34
1
1
>1
>1
2.49
x
103
6.64
X
10-4
2.67
x
10-7
0.0617
0.045
0.725
0.30
0.270
0.898
1.58
x
2.47
x
11
1'
1.56
x
03
0-5
9.80
X
10-5
9.80
x
1
0.046
0.046
1
6.00
x
10-1
6.00
x
10"
1
3075
3075
1
0.11
0.047
0.424
4.0
>4.0
>1
1.07
X
104
1.18
X
103
8.03
x
104
8.03
X
104
1.11
x
10-1
1
28.6
29.14
8.23
x
10-3
0.716
3.08
x
lo-'
4.30
x
lo-'
3.46
3.46
1
1
0.994
0.994
2.43
x
103
9.14
x
10-4
3.76
x
10"
0.0617"
0.122
>1
0.30
0.198
0.659
1.54
X
103
1.03
x
10-5
6.70
x
10-9
9.83
x
10-5
9.83
x
10-5
1
0.046
0.046
1
5.50
x
10-1
5.50
x
10"
1
2942
2942
1
0.11
0.076
0.689
4.0
0.348
1.39
1.09
x
104
2.44
x
103
8.60
x
104
8.60
x
104
2.23
x
10-1
1
"p
c
0.05,
Mann-Whitney
U
test.
and after perfusion with insulin it was not detectable by our from lack of the cofactor for 3-P-glycerate mutase. [P-enolpyru-
methods. There was, however, no change in [2,3-P2-glycerate1, vatel
was
significantly decreased in the presence of ketones
indicating that the decrease in [2-P-glycerate] did not result with insulin but was unchanged
in
the other experimental
25510
Ketone Bodies and Insulin Action on Glucose Utilization
TABLE
V
Kinetic parameters
of
the enzymes
of
glucose
and
glycogen metabolism
The kinetics of the glycolytic enzymes were measured in 10 mM Pi, 20 mM imidazole buffer, pH 7.2, 150 mM KCI, and 5 mM total magnesium at
38
"C.
Activity is expressed as pmol/min/ml of intracellular water
t
S.E.,
and
K,,,,
values are expressed as mM. The number of observations is 3.
V,,
and
K,,,,
denote the velocity and
K,,,
in the direction of L-lactate formation (forward);
V,,
and
Kmp
denote the same parameters in the opposite
direction (reverse).
Enzyme
vu,,,
4s
Vd
KmP
K,
nucleotide or
P,
~~
Glycogen synthase
I
form 8.81
f
1.65
D
form
0.08"
8.81
f
1.65 1.42"
Phosphorylaseb 46.9
f
2.56
0.1'
3350 5'
P-glucomutase
116
f
16.6 0.045 67.2
f
3.15
0.67
Glc-1-P
-+
Glc-6-P
Glucose transportd
Glucose 4 2
3-U-Methylglucose
Without insulin
0.14-1
7-10
1-0.01 7
With insulin 13.2
6
6.6
3
Hexokinase 33
f
1.35 0.072 0.00637' 0.042' 0.236 (ATP)
Glucose-6-phosphatase NDf
Glc-6-P dehydrogenase 5.70
P-glucoisomerase 604
f
47.8 0.425 576
2
12.5 0.175
P-fructokinase
Aldolase
Triose-P isomerase 356
&
32.5 1.53
GAP dehydrogenase 321
f
28.7 0.042 0.058 (NAD+)B
1.42 (Pi)
3-P-glycerate kinase 15,060
f
175 0.021 959
&
169 0.51 0.008 (ADP)
0.565 (ATP)
3-P-glycerate mutase 674
f
77.8 0.145 2880
*
101 0.139
Enolase
111
&
6.22 0.045 120
-c
7.40 0.089
Pyruvate kinase 566
2
18.6 0.11 0.63h 10h 0.268 (ADP)
Lactate dehydrogenase 1436
&
36.6 0.125
0.001
(NADH)'
79.7
-c
8.26 0.224 0.127
59.5
2
2.50 0.038
a
K,,
for the
I
and D
forms
in the presence
of
Glc-6-P (55).
e
Ref. 56.
e
Calculated from Ref. 57.
V,,
was calculated by Haldane's relationship.
Ref. 4, pmoVg wet weight.
Not detected.
K,
for NAD+ was increased by increasing [Pi], and
K,
for
Pi was increased by increasing [GAP]. The value for NAD+ reported here is in the
Ref. 53.
presence of 5 mM Pi, and that for Pi is in the presence of 0.036 mM GAP.
'
K,
for NADH was increased in the presence of increased [pyruvate]. The value reported here was determined in the presence of 0.022 mM
pyruvate.
groups despite the decrease in the precursor, [2-P-glycerate].
[Pyruvate] was 0.055 pmol/ml of intracellular water in hearts
perfused with glucose alone, decreased 1.5-fold on addition of
ketones, increased 1.5-fold on addition
of
insulin, and was un-
changed on addition of ketones plus insulin.
la lac tat el
was
0.68 pmol/ml of intracellular water in hearts perfused with
glucose alone and decreased 2.3-fold on the addition
of
ketones
but was unchanged on the addition
of
insulin
or
insulin plus
ketones. The L-lactate efflux increased 1.7-, 13.3-, and 2.2-
fold in the presence
of
ketones, insulin,
or
the combination,
respectively.
The values of the equilibrium constants
(K)
of the reactions
catalyzed by the enzymes of glucose metabolism, corrected for
changes in pH and free
[M?]
when appropriate, were com-
pared with the values of the [productsY[reactantsl
of
the meas-
ured concentrations in heart tissue
(r)
(Table
IV).
The
r/K'
for
the glucose transport reaction was 0.19 during perfusion with
glucose alone, 0.34 after addition of ketones, and about
1
on
addition of insulin and the combination, showing that insulin
equilibrated [Glc,] and CGlc,]. The reactions catalyzed by
hexokinase and P-fructokinase had
T/K
ranging from
to
confirming previous reports in other tissues that these
steps were far from equilibrium
(45,
76).
For
the reactions of
glycogen synthase and phosphorylase, the
r/K'
ranged between
and lo". The
TIK'
of
the reaction catalyzed by P-glucoi-
somerase ranged from 0.90
to
0.66 despite the 10-fold increase
in [Glc-6-P], showing that this step is at near-equilibrium
under all conditions tested here.
Because the binding of
GAP
to
aldolase distorts the tissue
ratios, the
T1K'
values for the reactions catalyzed by aldolase
and triose-P isomerase were assumed
to
be at near-equilibrium
(49) and, therefore, were assigned a value of
1.
[GAP] was cal-
culated from the measured value of
[DHAP]
and the
K'
of
the
triose-P isomerase reaction.
For
similar reasons and because
of
the instability
of
1,3-P2-glycerate, the tissue levels of this me-
tabolite were not measured but were calculated from the com-
ponents of the 3-P-glycerate kinase reaction. The values of
T/K'
for the GAP dehydrogenase and the 3-P-glycerate kinase reac-
tions were assigned a value of 1(51,75).
T1K'
for the components
of
the 3-P-glycerate mutase reaction was
>1
during perfusion
with glucose alone and decreased
to
0.65 on addition of ketones
or
0.69 with ketones plus insulin, but it decreased
to
0.42 on
perfusion with insulin alone.
T/K'
for the enolase reaction was
0.37 on perfusion with glucose alone and 0.35 in the presence of
ketones plus insulin, but it increased
to
0.58
on addition of ke-
tones and
to
>1
on perfusion with insulin. The apparent changes
in the
flux
control coefficient at the enolase and P-glycerate mu-
tase steps were an unexpected outcome of this type of analysis.
The changes did not correlate with changes in the measured
amounts of the cofactor of the mutase, 2,3-P2-glycerate (Table
11).
In contrast
to
the findings with the substrates of the hex-
okinase and P-fructokinase reactions where
T/K'
was
or
the 3-P-glycerate kinase reaction where
TtK
was
1,
the
T/K'
values for the substrates of the pyruvate kinase reaction were
a factor of e100 from equilibrium.
TIK'
for the pyruvate kinase
reaction was 0.016 during perfusion with glucose alone and in-
Ketone Bodies and Insulin Action on Glucose Utilization
25511
TMLE
VI
Flux
control coefficients determined by bottom-up analysis
Standard errors and coefficients
of
variation were calculated using MetaCom (68).
Errors
of
10%
were arbitrarily assigned to the elasticities and
fluxes used in the calculation
of
flux control coefficients in order
to
calculate the sensitivity and error analysis. Values are given
*
S.E.;
the
coefficient
of
variation
(S.D.
mean
x
100) in percent is given in parentheses.
Glucose Glucose
+
ketones Glucose
+
insulin Glucose
+
ketones
+
insulin
1.
Branched pathway
from
glucose transport
to
glycogen metabolism and P-glucoisomerase"
-0.237 -0.516 0.159
-0.128
-1.22
1.81
4.75
NAb
NAb
NA
-0.011
0.396 0.34 (9.2)
0.590
f
0.033 (5.6)
<0.001
0.016
f
0.002 (13)
NA
NA
-0,001
?
0.0001
(10)
0.248
-0.232
12.9
-12.5
5.91
100
-100
0.929
NA
0.314
f
0.030 (9.6)
0.653
-t
0.029 (4.4)
0.001
2
0.0002 (20)
0.024
f
0.003 (13)
<0.001
0.009
2
0.002 (22)
NA
2.
Linear pathway from 3-P-glycerate kinase to pyruvate kinase'
EPGK
3PG
-100
-100
GAYM
100
2.50
E;%
1.43 2.27
EW
0.859 0.929
CJSK
CJSlyM
Gno
GK
&ffil~M
2PG
-100 -1.82
&Eno
PEP
-0.687 -1.45
0.008
2
0.002 (25) 0.008
f
0.001 (13)
0.008
t
0.001 (13) 0.326
f
0.036
(11)
0.547
2
0.034 (6.2) 0.260
f
0.019 (7.3)
0.438
2
0.035 (8.0) 0.406
f
0.039 (9.6)
-100
0.164
-0.159
3.18
-2.94
9.39
100
-100
0.455
NA
0.002
f
0.0002 (10)
0.972
f
0.003 (0.31)
0.001
f
0.0002 (20)
0.016
f
0.003 (19)
<0.001
0.009
f
0.002 (22)
NA
-100
1.39
-0.702
100
-100
0.981
0.008
f
0.001
(13)
0.575 0.048 (8.3)
0.004
f
0.0004
(10)
0.412
f
0.048 (12)
-100
0.224
-0.218
100
-100
2.36
100
-100
0.461
NA
0.002
f
0.0003 (15)
0.862
f
0.017 (1.9)
<0.001
0.066
f
0.008 (12)
<0.001
0.069
f
0.011 (16)
NA
-100
3.00
-2.24
1.47
-0.577
1.23
0.009
f
0.002 (22)
0.306
f
0.31
(11)
0.466
f
0.025 (5.4)
0.219
f
0.029
(11)
Scheme
1.
Scheme
2.
'
NA,
not applicable.
creased to 0.053 on addition of ketones, 0.11 on addition
of
in-
sulin, and
0.22
on addition of the combination. There was no
correlation between the shifts for the pyruvate kinase reaction
and the [Fru-1,6-Pzl
or
[Fru-2,6-P2].
Using bottom-up analysis of the upper portion
of
glucose
metabolism (Scheme
11,
from extracellular glucose to Fru-6-P
and glycogen (Table
VI,
part
11,
the
flux
control coefficient of
glucose transporter
(C&,,)
was
0.40,
of hexokinase
(CJ,,)
was
0.59,
of P-glucoisomerase
(CJ,,)
was 0.02, and
of
phosphorylase
(C&J
was -0.001 during perfusion with glucose alone. The
activity of glucose-6-phosphatase was not considered since we
were unable to detect
it
in
vitro,
although
this
activity has been
inferred from
NMR
data.3 The addition of ketones slightly in-
creased control
at
the hexokinase and P-glucoisomerase steps;
some control appeared at the glycogen synthase step
(C&ycs).
Insulin essentially abolished control
at
the glucose transporter;
CJGlutl
=
0.002,
CJ,,
=
0.97,
C$,
=
0.02,
and
C&y,s
=
0.01. In the
presence of insulin and ketones, control was shared by hexoki-
nase, P-glucoisomerase, and glycogen synthase;
CJ,
=
0.86,
Ck,
=
0.07,
and
C&,,
=
0.07.
In the terminal glycolytic portion of bottom-up analysis
(Scheme
21,
from 1,3-Pz-glycerate to pyruvate (Table
VI,
part
2)
in the presence of glucose only, the
flwr
control coefficient of
K.
Clarke, personal communication.
enolase
(C&J
was
0.55
and of pyruvate kinase
(C$,)
was
0.44,
whereas the
flux
coefficients of 3-P-glycerate kinase
(CJ,,)
and
3-P-glycerate mutase
(CgGIYM)
were ~0.01. After addition of ke-
tones, insulin,
or
both,
CkIyM
was 0.33,
0.58,
and 0.31, respec-
tively.
Cgn0
was decreased to
0.26
aRer addition of ketones and
to
0.47
in the presence of ketones plus insulin, but
it
was
reduced to nearly
0
in the presence of insulin and absence of
ketones.
C<,
was not changed in the presence of ketones or
insulin, but it was decreased
to
0.22
in the presence of the
combination.
Using top-down analysis with Glc-6-P as the intermediate
between blocks (Scheme
31,
Cf
comprising the block of glucose
transport and phosphorylation step was
0.58,
C;
of the block
comprising glycogen synthesis was
0.17,
and
Ci
of
the block
comprising glycolysis was 0.26. This type of analysis confirmed
that
glucose entry and phosphorylation dominated the control
of glucose metabolism, with glycolysis exerting about
a
quarter
and glycogen synthesis
17%
of the control of
the
total rate
(Table VII, part
1).
Top-down analysis was performed with
[Glc,]
as
the intermediate between blocks composed of (Scheme
4)
C:,
the glucose transporter, and
C;,
all of the other reactions
of glucose utilization. In the presence of ketones, the control
distribution was similarly shared between the two blocks;
Cf
=
0.55
and
C;
=
0.45
(no significant difference). This contrasts
with
the
states
involving addition of insulin where
C<
de-
25512
Ketone Bodies and Insulin Action on Glucose Utilization
creased to nearly zero, while the control exerted by the com-
bined pathways of glucose utilization increased
to
0.99 (Table
VII,
part 2). Although these top-down results are approximate,
they offer corroboration (via an independent method of analyz-
ing the results) of the conclusion from the bottom-up analysis
that in the absence of insulin the transporter shares some of
the control but that in the presence of insulin the control shifts
to
glucose utilization.
DISCUSSION
In
a
metabolic pathway in the steady state,
J
PGM,, GIP
Glut4
HK
Gk0-
Glc,”---+
G6P
u1
VZ
T1
u3P
F6P
the flux
(J)
through the pathway is equal
to
the net rate
(u)
for
any single enzyme step,
all
of which are equal. Since
u1
=
u2
=
us,
+
uSp
=
J,
it
is
true, but misleading, to say that the flux
through the pathway is equal
to
the “slowest”
or
“pacemaker”
enzyme since the flux through all of the steps is equal in the
steady state. By assigning flux control coefficients to each step
or
to
blocks of steps and by setting
x
CJ=l (the summation
theorem, Equation 91, metabolic control analysis attempts
to
define formally the proportion of
a
change in the flux that
is
caused by changes either in the reactants or in the kinetic
properties of each particular step in an arbitrarily defined
pathway. This analysis shows that control of metabolic flux can
be distributed between several enzymatic steps and that the
site and degree
of
control may vary. Thus control of the flux of
glucose utilization vanes with the nutrient presented or the
receptor stimulated. This has implications for both genetic and
pharmacological therapy in that alteration in the degree of flux
control
at
one step will result in the development of flux control
at other steps. It
is
therefore necessary to understand the met-
abolic system as
a
whole and not simply focus narrowly on one
or another enzyme step within the pathway.
Flux control coefficients may be derived from the elasticity of
each enzyme step using the connectivity theorem (Equation 10,
x
CgZ
E:
=
0).
Elasticities of small magnitude are critical; large
elasticities have relatively little influence on the flux control
coefficient. If two adjacent enzymes have
a
large and small
elasticity, respectively, for
a
common intermediate, the enzyme
with the small elasticity
will
have the larger flux control coef-
ficient.
A
negative value for elasticity means an inhibitory ef-
fect (elasticities embody the kinetic effects). For example, with
[Glc,]
as
the common intermediate, the glucose transporter and
hexokinase are adjacent enzymes. Equation 10 can be de-
scribed
as
C&,t4~~1~Lt4
+
CGKe;ki
=
0.
The value of
E:::‘
was
-0.24, and was 0.16 in the glucose group;
C&ut4
was 0.40,
and
CGK
was 0.59.
As
long as the flux control coefficient can be obtained from
the elasticities, the change in flux
is
a
result of changes in
either the inherent kinetic properties
of
the enzyme or in the
ratio of [products] to [reactants] for that enzyme, The explana-
tion for this relationship may be seen from the derivation of
elasticities (Equation
8),
which are a function of
K’
for the
reaction, the
ratio
of [products] to [reactants] actually achieved
under the condition studied (here called
TI,
and
K,,,
and
V,,
in
the forward and backward direction for each enzyme. In the
case of the enzymes of glucose utilization in the perfused heart,
the elasticities for each step fall into three classes depending
upon how close they come to catalyzing equilibrium between
their products and reactants under the conditions studied.
When
TIK
of an enzyme-catalyzed reaction
is
>0.5 (close to
equilibrium), the elasticity depends primarily on the value of
TIK,
and as
TIK
increases, the value of
E
increases in
a
manner
resembling an exponential curve. In perfused hearts, this situ-
ation pertains to the P-glucoisomerase and P-glucomutase re-
actions (Table IV). Analytically,
it
is
difficult to distinguish
between 0.5 and
1
of
TIK’;
however, in this range the elasticity
will change by orders of magnitude and will, in turn, affect the
calculation of the flux control coefficients. In some instances,
this relationship assigns flux control coefficients that appear to
vary disproportionately with the observed changes in [SI.
For
example, in the cases of enolase and P-glycerate mutase, small
changes in [2-P-glyceratel and [P-enolpyruvate] resulted in the
shift of control from one enzyme
to
the other. The low concen-
trations lend a degree of uncertainty to the measurement of
these metabolites, which in some conditions were below the
range of accurate detection.
When
TIK
is
>0.01
but <0.5, elasticity is
a
function both of
the ratio of [products] to [reactants] and of the kinetic constants
for the enzyme.
An
example of such
a
reaction is the insulin-
sensitive glucose transporter, Glut4
(7).
During perfusion with
glucose alone,
TIK
was 0.19, and thus Glut4 would be sensitive
not only
to
changes in the ratio of [products] to [reactants] but
also to changes in the kinetic constants of the enzyme. Both
mechanisms were demonstrated here. By the first mechanism,
addition of ketones decreased the demand for glucose and re-
sulted in an increase in [Glc,] from 1.9 to 3.5 pmol/ml of intra-
cellular water (Table
11).
The elevation in [product] increased
TIK
from 0.19
to
0.34, altering
E:;;‘
from -0.24 to -0.52 (Table
VI). Second, addition of insulin changed the kinetic constants of
the glucose transporter by increasing
V,,
10-fold (Table V),
which increased [GlcJ to near 10 pmoyml of intracellular water
(Table
111,
making
TIK
near 1; and thus was increased
to
negative infinity (-100 was arbitrarily assigned) with
a
conse-
quent decrease in
CJGlUt4
to nearly zero. The very low flux control
coefficient
of
the glucose transporter in the presence of insulin
means that under conditions of saturating doses of insulin,
glucose transport no longer plays
a
significant role in the con-
trol of glucose utilization. In the case of the hexokinase reac-
tion, product inhibition by Glc-6-P significantly decreases the
flux control coefficient of this step below what
it
might be were
such inhibition not present. The significance of this effect has
been pointed out by other workers
(77).
In those enzymes that catalyze reactions that are far from
equilibrium
so
that
r/K
is
<0.01, such
as
hexokinase, P-fmc-
tokinase, and (in most cases) glycogen synthase and phospho-
rylase, the elasticity
is
totally insensitive to changes in
TIK
and responds only to changes in kinetic constants.
The flux control coefficient
is
also affected by the ratio of the
fluxes in the branches, which
is
equivalent to the ratio of the
flux control coefficients (the branch point theorem, Equation
11).
Despite the small elasticities of glycogen synthase and
phosphorylase,
CJ,,,,,
in the presence of ketones, insulin, and
ketones plus insulin and
CJ,,,,
in the presence of glucose were
small; this is in part
a
consequence of the flux ratios.
C&ycs
and
CJ,,,,
were also affected by the neighboring UDP-Glc pyrophos-
phorylase and P-glucomutase reactions with large elasticities.
Finally, the flux control coefficients were obtained by using
matrix algebra (Equations 12,
15,
17, 20, 22, and 24); the pro-
portion of control will be affected by each elasticity, the ratio of
the fluxes, and the other flux control coefficients in the system.
The conversion from glycogen phosphorolysis
to
glycogen
synthesis was achieved in two ways. First, the requirement for
glucose was decreased by providing ketone bodies as an alter-
native substrate for oxidative phosphorylation, permitting the
accumulation of glucose and Glc-6-P. Second, in the presence of
Ketone Bodies and Insulin Action on Glucose Utilization
25513
TABLE VI1
Flux
control
coefficients
determined
by
top-down
analysis
Standard errors
and
coefficients
of
variation
were
obtained and
are
presented
as
described
in
Table VI.
1.
Glc-6-P
as
intermediate"
Block Control Addition
E
C
1.
Glucose
transport
and
Glucose
Ketones
&P
-0.51
f
0.26
c:
0.58
?
0.17 (29)
2.
Glycogen synthesis Ketones Insulin
EbP
1.34
f
0.47
C:
0.17
-c
0.07
(42)
3.
Glycolysis
Ketones
Insulin
46P
0.264
*
0.48
c;
0.26
f
0.11 (42)
phosphorylation
2.
Glc,
as
intermediateb
Block
2
Control Change Value
EL,
Glycogen
synthesis
E;,.,
Ketones Insulin
Glucose
Insulin
0.18
-c
0.10
0.63 0.35
and
glycolysis
Glucose Glucose
+
ketones Glucose
+
insulin
-0.237 -0.516
-100
-100
Glucose
+
ketones
+
insulin
Ehk,
&,
0.18
0.63
0.18
0.63
c:
0.43
f
0.14 (33)
0.55
f
0.14
(25)
0.002
-c
0.001
(50)
c;
0.57
*
0.14 (25) 0.45
*
0.14 (31) 0.998
-c
0.001 (0.10) 0.994
-c
0.004 (0.40)
0.006
f
0.004 (67)
Scheme
3.
*
Scheme
4.
~gi;~~
of
the glucose transporter
as
given
in
Table VI
was
used
for calculation.
insulin, [Glc,] was equal to [Glc,]
as
a
result of the mobilization
of Glut4, and [Glc-6-P] was elevated up to 10-fold. In both
instances, the elevated [Glc-6-P] can increase the affinity of
glycogen synthase for UDP-Glc as much
as
6-fold, regardless of
the phosphorylation state of the synthase
(55).
From the point of view of the kinetics of the enzymes of
a
pathway and the thermodynamics of the reactions catalyzed,
there
is
nothing fundamentally new in the presentation of re-
sults using metabolic control analysis. However, the use of the
equations developed does provide a rigor that can help in avoid-
ing imprecise conclusions. The idea that glucose transport
is
rate-limiting for the reactions of glucose utilization (4,
5,
18)
would not appear to be true in working perfused rat heart even
in the absence of insulin (Table
VI).
Rather, the glucose trans-
porter would appear to share with hexokinase the major control
of glucose utilization. There remain, however, unexplained ob-
servations about hexokinase. The accumulation of Glc-6-P
would lead us to predict that hexokinase would be strongly
inhibited (781, but the glucose flux was unrelated to [Glc-6-P];
3H,0
released was reduced in the presence of ketones when
[Glc-6-P] was increased 3.6 times but was elevated in the pres-
ence of insulin and unchanged in the presence of ketones plus
insulin, when [Glc-6-P] was elevated 8- and 10-fold, respec-
tively (Table I).
In bottom-up analysis, the flux control coefficients indicate
the distribution within that selected pathway only; they would
all be scaled down if the whole of glucose metabolism was
considered. Viewed from the perspective of the processes of
glucose utilization, and using top-down analysis, the proportion
of control of the block
of
glucose transporter and phosphoryla-
tion, glycogen metabolism, and glycolysis was determined with
rGlc-6-PI assigned as the intermediate metabolite. The flux
control coefficient of glucose transport and phosphorylation
was 0.58, that of glycogen synthesis was 0.17, and all of glycoly-
sis was 0.26, which
is
an approximate average over the states
considered (Table VII, part
1).
It
is
clear from this study that,
considering glucose metabolism
as
a
whole, the activity of P-
fmctokinase is not the pacemaker, since only 0.26 of the control
of glucose utilization is found in all of the steps below P-glu-
coisomerase. That is not to say that P-fmctokinase does not
have an elegant system of controls
that
involve an increasing
number of previously unknown effectors formed by enzymes
undergoing covalent modification (71, 72, 79). However, the
flux through the branches of Fru-6-P and GAP into the nonoxi-
dative portion of the hexose monophosphate pathway (80) and
purine synthesis and salvage
(81)
and the flux through the