Control of Glucose Utilization in Working Perfused Rat Heart*

Metabolic control analyses of glucose utilization were performed for four groups of working rat hearts perfused 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 glycogen 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 hexokinase with ketones, and control at the glucose trans- port step was abolished in the presence of insulin. Analysis of the pathway from 3-P-glycerate to pyruvate determined that the major control was shared by enolase (EC 4.2.1.1) and pyruvate kinase (EC 2.7.1.40) in the glucose group.

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-limiting 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 extracellular glucose was elevated to the mildly hyperglycemic concentration of 16 mM and that the atrial pressure was maintained 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 enzyme step were altered so that this step was no longer ratelimiting. 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 "ratelimiting" or "pacemaker" reaction of glucose utilization, an alternative view has been expressed that many, if not all, of the enzymes of glycolysis have activities similar to the rate of glycolysis 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 operate 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 proportionate 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 was subsequently termed flux control coefficient (10). Flux control 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 indirectly 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 degree 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 parameters using the Haldane equation (Equation 4) (12) t o obtain the elasticity (Equation 8). The degree of control exerted by groups of enzymes can also be determined using top-down analysis (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 inhibitor titration (16) or by the selection of mutants with lower activity of a specific enzyme (8); enzyme activities may be increased by addition of pure enzyme to a tissue homogenate (17) or by genetically engineered overexpression (18). Other methods to formalize analysis of flux control coefficients have also been developed (19)(20)(21)(22)(23)(24)(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)(28)(29)(30)(31). Because insulin administration increases rapidly the number of Glut4 molecules 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)(33)(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 metabolites, the kinetic constants of the enzymes of glucose metabolism, the values of equilibrium constants ( K ' ) for intracellular conditions of pH and free [ M e ] , 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 enzymatic 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, Wilmington, M A ) 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 previously described (36). Briefly, following rapid excision, hearts were perfused in the retrograde manner (a modified Langendorfftechnique (37) 1) 10 mM glucose; 2) 10 mM glucose plus 1 mM sodium acetoacetate and 4 mM sodium D-P-hydroxybutyrate (Sigma); 3) 10 mM glucose plus 0.05 unitfml (-100 nM) recombinant 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 metabolite 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 homogenizer 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 mercaptoethanol, 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 concentrations 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 a t 37 "C using fluorometric procedures 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, auxiliary 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 glucose-6-phosphatase (EC 3.1.3.9). The analyses were conducted at high dilution by fluorometric procedures that minimize disturbing side reactions. 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 homogenates 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 constants 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, N Y ) 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 micromoles per gram wet weight, to micromoles per milliliter of intracellular 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 equilibration at this step (60). The removal of the labeled glucose and intermediates was confirmed by evaporating a portion of the effluent from the column; less than 0.1% of the counts remained. The rates of glycogenolysis 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).

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 intracellular Pi from phosphocreatine,2 and the cytoplasmic free I M P ] 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 appropriate, for the pH and free [ M e ] by methods previously described (62) using the equilibrium constants that had been determined under conditions approximating the intracellular environment. The values for [GAP], [Fru-1,6-Pzl, and [1,3-Pz-glyceratel are calculated from the equilibrium 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 correcting 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 enzyme activity or metabolite concentration. A simple model is shown below. ; 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 = ufur); and E, is enzyme catalyzing step i denoted by the subscript.

Michaelis-Menten Initial Rate Equation with One Substrate or One Product (64)
where Km,s is Michaelis constant (K,) of [SI, forward direction; is maximum velocity of an enzyme step in the forward direction; and Vmaa is maximum velocity of an enzyme step in the reverse direction. (12) At equilibrium, where K' is the equilibrium ratio of [PI to [SI determined in vitro under specified conditions.

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 measured and the enzyme concentration is titrated by the addition of enzyme or inhibitors and does not require the calculation of elasticities (17,(65)(66)(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).

Elasticity
The elasticity ( E ) of an enzyme is the fractional change in the net rate (Eq. 6)

4a. Calculation of E from Change in Flux
This equation can be regarded as the finite approximation to the elasticity definition. To calculate E by this method one needs measurements of net rate ( Table I ) (Table 11) and the ratio of the products to reactants in the tissue (r) ( Table IV) (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) VmuR,E; u~/u, = r/K The expressions u,JV,,, and ur/VmarR represent the fractional saturation of the enzyme with [SI and [PI, respectively (to the extent that Km,s and Km,p approximate true dissociation constants).

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 where n is the number of steps in the sequence chosen.

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 [ X I .

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. 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 analyses. 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 elasticities were derived by taking different pairs of the experimental sets, there is a single result from the top-down method, which is an approximate average over the states considered, Fuller explanations as models are given below.

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-glucoisomerase 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 analyzed, x C J = 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-glucomutase 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). Insulin Action on Glucose Utilization c;,,t* G K 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 disequilibrium ratio, but the smaller contribution from the fractional saturation of the carrier ( glucose transport glycogen synthesis and glycolysis Whenever T / K was 2 1 we assumed an equilibrium state, and where cp and cs approached negative and positive infinity, respectively, the numbers -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 phosphorylation 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, allowing calculation of blocks l and 2. Where an elasticity could be calculated 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 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 pressure 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, insulin, or the combination, glycogen was synthesized at the rates of 0.67, 2.6, and 2.5 pmol of glucosyl units/min/ml of intracellular 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 Pglucoisomerase 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 glucose group and increased to 1, 7, and 0.7% in the ketones, insulin, and ketones plus insulin groups, respectively.
[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).

Metabolite Glucose
Glucose + ketones Glucose + insulin Glucose + ketones + 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  I and 111).
[ D m ] was 0.036 pmoVml of intracellular water in glucoseperfused hearts and increased 2.7-fold on addition of insulin, but it was unchanged on addition of ketones and the combination. [1,3-P2-glycerate], calculated from the K' of the 3-P-glycerate kinase reaction and the measured levels of [3-P-glyceratel and cytoplasmic [ZATPl/[XADPj, was 0.87 pmoVml of intracellular water in glucose-perfused hearts, increased %fold on addition 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 a t near-equilibrium in vivo (751, the latter reaction was chosen for the calculation of [1,3-P2-glyceratej because the V, , , , forward of 3-P-glycerate kinase is 15,000 ymoVmidm1 of intracellular 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 V,, and K,,,, denote the velocity and K,,,  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 unchanged 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. 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 calculated 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 metabolite were not measured but were calculated from the components of the 3-P-glycerate kinase reaction. The values of T/K' for the GAP dehydrogenase and the 3-P-glycerate kinase reactions 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 ketones and to >1 on perfusion with insulin. The apparent changes in the flux control coefficient at the enolase and P-glycerate mutase 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 hexokinase 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-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. Using bottom-up analysis of the upper portion of glucose metabolism (Scheme 11, from extracellular glucose to Fru-6-P and glycogen (Table VI,  In the terminal glycolytic portion of bottom-up analysis (Scheme 21, from 1,3-Pz-glycerate to pyruvate (Table VI, (Table   VII, part 2). Although these top-down results are approximate, they offer corroboration (via an independent method of analyzing 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. , metabolic control analysis attempts t o 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 metabolic 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, 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 explanation 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 T I K of an enzyme-catalyzed reaction is >0.5 (close to equilibrium), the elasticity depends primarily on the value of T I K , and as T I K increases, the value of E increases in a manner resembling a n exponential curve. In perfused hearts, this situation pertains to the P-glucoisomerase and P-glucomutase reactions (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 concentrations lend a degree of uncertainty to the measurement of these metabolites, which in some conditions were below the range of accurate detection.
When T I K 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 insulinsensitive glucose transporter, Glut4 (7). During perfusion with glucose alone, T I K was 0.19, and thus Glut4 would be sensitive not only t o 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 resulted in an increase in [Glc,] from 1.9 to 3.5 pmol/ml of intracellular water (Table 11). The elevation in [product] increased T I K from 0.19 t o 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 T I K near 1; and thus was increased to negative infinity (-100 was arbitrarily assigned) with a consequent 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 control of glucose utilization. In the case of the hexokinase reaction, 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-fmctokinase, and (in most cases) glycogen synthase and phosphorylase, the elasticity is totally insensitive to changes in T I K 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 pyrophosphorylase 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 proportion 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 alternative substrate for oxidative phosphorylation, permitting the accumulation of glucose and Glc-6-P. Second, in the presence of 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  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 results using metabolic control analysis. However, the use of the equations developed does provide a rigor that can help in avoiding 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 transporter would appear to share with hexokinase the major control of glucose utilization. There remain, however, unexplained observations 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 presence of insulin and unchanged in the presence of ketones plus insulin, when [Glc-6-P] was elevated 8-and 10-fold, respectively (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 phosphorylation, 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 glycolysis 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 Pfmctokinase is not the pacemaker, since only 0.26 of the control of glucose utilization is found in all of the steps below P-glucoisomerase. 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 nonoxidative portion of the hexose monophosphate pathway (80) and purine synthesis and salvage (81) and the flux through the branch of DHAP to a-glycero-P and the a-glycero-P shuttle (82) (Fig. 1) were not measured. The absence of precise flux measurements through P-fmctokinase and the multiple branch points above and below the P-fi-uctokinase reaction precludes the possibility of performing bottom-up analysis at the P-fmctokinase step in this study.
In addition to preventing misstatement, the application of this formal approach to an entire pathway provides new insights that may further our understanding of control. An example is the finding that T I K values for phosphorylase, pyruvate kinase, and P-glycerate mutase range from 0.01 to 0.5 and thus have characteristics more in common with the glucose transporter than with enzymes of the type such as hexokinase, P-fructokinase, and glycogen synthase on the one hand (where T I K is <0.01) or with P-glucoisomerase on the other (where T I K is >0.5). Enzymes that have intermediate values of T I K might be expected to change the degree to which they may affect flux through the lower portion of glycolysis in response to changes in substrate and product concentrations and to changes in their fundamental kinetic parameters.