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Circulation. 2000;101:2090-2096

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(Circulation. 2000;101:2090.)
© 2000 American Heart Association, Inc.


Basic Science Reports

ATP Synthesis During Low-Flow Ischemia

Influence of Increased Glycolytic Substrate

Alison C. Cave, PhD; Joanne S. Ingwall, PhD; Jan Friedrich, MD, DPhil; Ronglih Liao, PhD; Kurt W. Saupe, PhD; Carl S. Apstein, MD; Franz R. Eberli, MD

From the Cardiac Muscle Research Laboratory, Whitaker Cardiovascular Institute, Boston University School of Medicine, and the NMR Laboratory for Physiological Chemistry, Cardiovascular Division, Department of Medicine, Brigham and Women’s Hospital (J.S.I., J.F.), Boston, Mass.

Correspondence to Carl S. Apstein, MD, 715 Albany St, Room X720, Boston, MA 02118. E-mail capstein{at}acs.bu.edu


*    Abstract
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*Abstract
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Background—Our goals were to (1) simulate the degree of low-flow ischemia and mixed anaerobic and aerobic metabolism of an acutely infarcting region; (2) define changes in anaerobic glycolysis, oxidative phosphorylation, and the creatine kinase (CK) reaction velocity; and (3) determine whether and how increased glycolytic substrate alters the energetic profile, function, and recovery of the ischemic myocardium in the isolated blood-perfused rat heart.

Methods and Results—Hearts had 60 minutes of low-flow ischemia (10% of baseline coronary flow) and 30 minutes of reperfusion with either control or high glucose and insulin (G+I) as substrate. In controls, during ischemia, rate-pressure product and oxygen consumption decreased by 84%. CK velocity decreased by 64%; ATP and phosphocreatine (PCr) concentrations decreased by 51% and 63%, respectively; inorganic phosphate (Pi) concentration increased by 300%; and free [ADP] did not increase. During ischemia, relative to controls, the G+I group had similar CK velocity, oxygen consumption, and tissue acidosis but increased glycolysis, higher [ATP] and [PCr], and lower [Pi] and therefore had a greater free energy yield from ATP hydrolysis. Ischemic systolic and diastolic function and postischemic recovery were better.

Conclusions—During low-flow ischemia simulating an acute myocardial infarction region, oxidative phosphorylation accounted for 90% of ATP synthesis. The CK velocity fell by 66%, and CK did not completely use available PCr to slow ATP depletion. G+I, by increasing glycolysis, slowed ATP depletion, maintained lower [Pi], and maintained a higher free energy from ATP hydrolysis. This improved energetic profile resulted in better systolic and diastolic function during ischemia and reperfusion. These results support the clinical use of G+I in acute MI.


Key Words: creatine kinase • glucose • insulin • ischemia • metabolism


*    Introduction
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up arrowAbstract
*Introduction
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down arrowResults
down arrowDiscussion
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During normoxia, ATP delivery to the myofilaments and membrane ion pumps is ensured by ATP synthesis from glycolysis and oxidative phosphorylation. The creatine kinase (CK) reaction contributes to the ability of cardiac muscle to increase and sustain high levels of work, as shown during the ATP supply-demand mismatch of hypoxia1 and high cardiac work loads2 when phosphoryl transfer from phosphocreatine (PCr) to ADP slows the rate of ATP depletion. Moreover, maintaining high ATP and low ADP and inorganic phosphate (Pi) levels maximizes the free energy available from ATP hydrolysis.

The relative contributions of oxidative versus glycolytic ATP synthesis rates to total ATP synthesis; the time course and extent of changes in [ATP], [ADP], [Pi], pH, and the free energy of ATP hydrolysis; and concomitant systolic and diastolic dysfunction that occurs during the low-flow ischemia of an acute myocardial infarction (MI) region are not known. Previous work in animals has suggested that oxidative metabolism remains the major ATP source in the ischemic region immediately after coronary ligation.3 Despite its importance in supporting cardiac function under stress, changes in CK reaction velocity are also undefined during low-flow ischemia. Thus, our first goal was to define the alterations that occur in anaerobic glycolysis, oxidative phosphorylation, and CK velocity simultaneously with changes in systolic and diastolic function in isolated blood-perfused rat hearts during a degree of low-flow ischemia that exists in the acute MI region in humans.4

During low-flow ischemia, the activity of aerobic and anaerobic pathways are determined in part by the amount of residual coronary flow and available carbon substrates. Increasing glycolytic substrate with high glucose and insulin (G+I) has been reported to be beneficial in low-flow ischemia and patients with acute MI,5 6 7 8 9 but the bioenergetic consequences of G+I in this setting are unknown. G+I increases glycolysis,5 but it may also affect oxidative phosphorylation and CK velocity by increasing pyruvate delivery to the Krebs cycle, by worsening tissue acidosis, and by changing ADP and/or Pi concentrations. Therefore, our second goal was to define the effects of increased glycolytic substrate on each of these possibilities.

To achieve these goals, 31P NMR spectroscopy and magnetization transfer (MT) measurements were performed in isolated blood-perfused hearts subjected to a clinically relevant degree of low-flow ischemia (10% of baseline coronary flow) and provided with either normal levels of insulin and the major physiological substrates (glucose, free fatty acid, and lactate) (the control group) or to the control levels of free fatty acid and lactate but with increased levels of glucose and insulin (the G+I group).


*    Methods
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*Methods
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Heart Preparation
Isovolumic LV and coronary perfusion pressures were recorded5 10 in RBC-perfused rat hearts (balloon in LV) isolated from fasted male Wistar rats (300 to 350 g). For experiments using NMR spectroscopy, the heart was placed in a 20-mm glass NMR tube in an NMR spectrometer and perfused with phosphate-free Krebs-Henseleit buffer containing bovine RBCs at a hematocrit of 40% as described.10 Animal care was in accord with the protocol of the Boston University School of Medicine and Harvard Medical School Institutional Animal Care and Use Committees.

Experimental Protocols
After 60 minutes of baseline normoxic perfusion at a constant coronary flow rate (coronary perfusion pressure 80 mm Hg), hearts underwent 60 minutes of low-flow ischemia (constant coronary flow at 10% of baseline), were reperfused for 30 minutes at the baseline coronary flow rate, and then were freeze-clamped. In control hearts (n=12), the initial concentrations of 5.5 mmol/L glucose and 15 µU/mL insulin were maintained throughout the protocol. In the G+I group (n=12), from 5 minutes before the onset of low-flow ischemia until the end of reperfusion, high glucose and insulin were infused into the aortic cannula; final concentrations were 19.5 mmol/L glucose and 250 µU/mL insulin. Half of the experiments (n=6 per group) were performed without NMR spectroscopy to permit the collection of venous effluent for measurement of MO2 and lactate.

31P NMR Measurements
Standard 1-pulse 31P NMR spectra (Figure 1Down) obtained at 161.94 MHz as previously described11 were acquired over 2 minutes by signal-averaging 52 scans of 60° (27 µs) read pulses separated by an interscan delay of 2.3 seconds immediately before and after each MT experiment and each change in coronary flow. Four MT experiments (Figure 2Down) were carried out: 1 before ischemia, 1 after 10 minutes and again after 38 minutes of ischemia (early and late ischemia, respectively), and 1 after 10 minutes of reperfusion.



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Figure 1. Representative 31P NMR spectra obtained from erythrocyte-perfused control and high-G+I rat hearts during preischemia, early (10 to 30 minutes) and late (35 to 55 minutes) low-flow ischemia, and late reperfusion. Major resonances are monophosphate ester (MPE) (also contains any residual 2,3-DPG); Pi; PCr; {gamma}-, {alpha}-, and ß-phosphates of ATP; and NAD. Integrated peak intensities are proportional to metabolite contents. During ischemia, as pH decreases, chemical shift of Pi peak moves (dashed lines) closer to PCr peak.



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Figure 2. Representative stacked plot of 31P NMR spectra obtained during preischemic perfusion from same erythrocyte-perfused control rat heart as shown in Figure 1Up. Major resonance is as assigned in Figure 1Up. This plot illustrates MT method used to measure kfor for CK reaction in the direction of ATP synthesis. Saturation pulse was applied at resonance frequency for [{gamma}-P]ATP. Saturation duration is shown on right of each spectrum. Spectrum with no [{gamma}-P]ATP saturation is shown as first and last spectra. Spectra were obtained by signal averaging 40 scans of high-power broadband 90° (41 µs) read pulses following low-power narrow-band saturation pulse, interleaved in groups of 8 and separated by a constant delay of 7 seconds, including saturation pulse time (total time, 22 minutes).

Metabolite Contents and Conversion to Concentrations
Integrated signal intensities in 31P NMR spectra corresponding to the ATP, phosphocreatine (PCr), and Pi contents of the heart were measured by NMR1 curve-fitting routine (New Methods Research Inc). Signal intensities of the [ß-P]ATP resonance peaks during baseline perfusion were indistinguishable for the glucose and insulin and the control groups and were assigned a concentration value of 10.8 mmol/L, independently determined by high-pressure liquid chromatography,12 to convert content to concentration. Other metabolite concentrations were determined from the ratio of their signal intensities (corrected for differential relaxation) relative to that of [ß-P]ATP during the stabilization period multiplied by 10.8 mmol/L. Intracellular pH was determined by comparing the chemical shift difference between the Pi and PCr resonances with values obtained from a external standard curve.

[ADP] was calculated by 2 methods. The first makes the assumption that the CK reaction was at or near equilibrium throughout the protocol: Keq=[ATP][free creatine]/[ADP][PCr][H+], where Keq was set to 1.66x109 per mole at pH 713 for baseline and reperfusion periods, and 1.47x109 per mole at pH 6.2 for ischemia.14 The second method assumes that the CK reaction is at equilibrium only during the baseline period. The pseudo–first-order rate constant of the CK reaction, kfor, measured by MT is the product of the second-order rate constant, k', and free [ADP]. We calculated the second-order rate constant at baseline (by dividing kfor by [ADP]) and assumed it remained constant. [ADP] for ischemia and reperfusion was estimated by dividing kfor (measured by MT) by k', referred to as [ADP]'. This second method of [ADP]' calculation recognizes that k' may vary during the experimental protocol. Total tissue creatine measured in a subset of hearts15 was not different between groups and was unaffected by ischemia and reperfusion (22 to 23 mmol/L).

The free-energy release from ATP hydrolysis was calculated from the equation {Delta}G~P={Delta}G°+RT ln[ATP]/[ADP][Pi], where {Delta}G° (30.5 kJ/mol) is the value of ATP hydrolysis under standard conditions of molarity, temperature, pH, and [Mg2+], R is the gas constant (8.314 J · mol-1 · K-1), and T is temperature in kelvin. Input values for ATP and Pi were obtained from 31P NMR measurements, [ADP], and [ADP]' were calculated as described above, and the 2 [ADP] values were used to calculate {Delta}G and {Delta}G', respectively. Free energies are presented as absolute values.

Lactate concentration was measured in coronary arterial and venous sample supernatants after digestion with perchloric acid. Lactate production rates (µmol · g dry wt-1 · min-1) were calculated from the coronary flow rate and heart weight. Total lactate production was determined from the area under the curve of lactate production rate versus time during ischemia and the first 90 seconds of reperfusion. Tissue lactate and glycogen were measured in the hearts frozen at the end of reperfusion.5 MO2 was calculated from the arteriovenous O2 content differences derived from O2 saturation curves for the Krebs-RBC perfusate over the experimental range of pH and PO2. Lactate production and MO2 are reported as (mmol/L)/s by using measured wet/dry heart weight ratios and a value of 0.5 mL intracellular water per gram wet weight.16 Dry/wet weight is constant during low-flow ischemia and decreases by only 6% after reperfusion.5

CK Reaction Velocity
The CK reaction is

The MT measurements of the forward CK reaction (PCr->[{gamma}-P]ATP) were analyzed according to the 2-site chemical exchange model yielding the pseudo–first-order rate constant, kfor.11 Multiplying kfor by [PCr] yields the measured reaction velocity, Vfor=kfor[PCr]. CK velocity can also be calculated from the rate equation15 : Vcalc=Vmax[ADP][PCr]/(1+D)KaKib. Measured input values are 55 (mmol/L)/s for Vmax (total CK activity under saturating conditions at 37°C), the cytosolic concentrations of PCr and ADP for each heart and kinetic constants from Reference 1717 .

Statistical Analysis
Data acquired sequentially in individual hearts were tested by a 2-way ANOVA for repeated measures. When 2-way ANOVA gave a significant (P<0.05) difference either among the sequential measures or between the 2 groups, the data were further analyzed: (1) 1-factor ANOVA and 2-tailed paired Student’s t tests were used to test for statistical significance among the sequential experimental periods (stabilization, early ischemia, late ischemia, and reperfusion). (2) Either a 2-tailed unpaired Student’s t test or a Mann-Whitney rank sum test comparing control and G+I–treated hearts was used to test for statistical significance between the 2 groups. All calculations were aided by Statview 512+ (Brain Power Inc). All data are presented as mean±SEM.


*    Results
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*Results
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Hemodynamics
During ischemia, systolic function (and also developed pressure and rate-pressure product) decreased to {approx}20% of baseline (Table 1Down and Figure 3Down). G+I slightly increased systolic function during late ischemia and substantially increased it during early reperfusion (Figure 3Down). G+I exerted a highly protective effect on diastolic function, markedly blunting the increase in diastolic pressure during both ischemia and reperfusion. G+I also decreased coronary resistance (coronary perfusion pressure at constant coronary flow) during ischemia and reperfusion.


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Table 1. Cardiac Performance



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Figure 3. Hemodynamic measurements in control ({circ}) and G+I hearts (•). Data are shown during preischemic perfusion (0 to 60 minutes), low-flow ischemia (60 to 120 minutes), and reperfusion (120 to 150 minutes). n=12 per group. *P<0.05 vs equivalent control values.

Metabolite Concentrations
Control [ATP] and [PCr] decreased early and progressively during ischemia and did not recover during reperfusion (Figures 1Up and 4Down and Table 2DownDown). In contrast, for the G+I group, [ATP] did not decrease during early ischemia, [ATP] and [PCr] were higher than in controls at late ischemia, and neither increased during reperfusion. [ADP] calculated by 2 methods (see Methods) did not increase in either group during ischemia but tended to be lower in the G+I group. Pi increased 3-fold by end ischemia in controls but did not change with G+I. There were no differences in resonance areas for monophosphate esters between the 2 groups during ischemia or reperfusion. Intracellular pH decreased to {approx}6.2 in both groups during ischemia.



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Figure 4. ATP, PCr, and Pi concentrations and intracellular pH for control ({circ}; n=6) and G+I (•; n=6) hearts determined from 1-pulse 31P NMR spectra taken during protocol as in Figure 3Up. High G+I slows decrease in high-energy phosphate concentrations and protects against a rise in Pi during low-flow ischemia. Intracellular pH falls similarly for both groups. *P<0.05 vs preischemia; +P<0.05 vs control.


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Table 2. Substrate Concentration and Flux Through the Forward CK Reaction


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Table 2A. Continued

{Delta}G~P was similar and high in the control and G+I groups for preischemia and early ischemia. During late ischemia, {Delta}G~P (calculated with either set of [ADP] values) decreased by {approx}2 to 4 kJ/mol for the control group but stayed high in the G+I group.

Oxidative Phosphorylation
O2 consumption (MO2), used as the index of oxidative phosphorylation, was comparable in the 2 groups, declining to {approx}18% of baseline during ischemia and recovering to 72% to 95%. Thus, increasing the supply of glucose did not increase MO2.

Glycolysis
Glycolysis, assessed from ischemic lactate production (µmol · g dry wt-1 · min-1), was increased in the G+I hearts. In controls, lactate production peaked at 20 minutes (1.66±0.62) and thereafter gradually declined to 1.02±0.38 at end ischemia. In contrast, in G+I hearts, lactate production progressively increased to 40 minutes (2.93±0.38) and remained high (2.44±0.3) (P<0.01 versus controls at end ischemia). Total ischemic lactate production was 166±32 µmol/g dry wt for controls and 273±22 µmol/g dry wt for G+I hearts (P<0.05).

At end reperfusion, tissue lactate (10.6±1.2 versus 11.6±1.9 µmol/g dry wt, P=NS) and tissue glycogen (39.9±10.6 versus 23.9±7.3 µmol glucose equivalent/g dry wt, P=NS) were similar for the control and G+I groups.

Creatine Kinase
During preischemia, the measured pseudo–first-order rate constant of the CK reaction (kfor) and CK velocity (Vfor) were similar for the 2 groups (Figure 2Up and Table 2Up). During ischemia, measured CK velocity decreased similarly in both groups, to 36% to 49% of baseline, and remained depressed (41% to 42%) during reperfusion. Predicted CK velocity (Vcalc) was calculated by use of input values for both [ADP] and [ADP]'. The rate equation predicted that during preischemia, Vcalc would be equal for the control and G+I groups, and during ischemia, Vcalc would decrease similarly in both groups; both were observed. V'calc values were also depressed during ischemia but somewhat less than Vcalc. Thus, both measured and calculated estimates of CK velocity during ischemia showed a moderate inhibition and no influence of the G+I substrate. During reperfusion, the rate equation predicted higher velocities than those measured by MT for both groups.

Washout of CK Activity
Coronary venous effluent was collected and assayed for CK activity, and the cumulative CK leakage was calculated. G+I did not affect CK leakage during ischemia ({approx}2.6 IU/g wet wt) or reperfusion (32 IU/g wet wt). Thus, leakage was only {approx}0.2% of total tissue CK (1100 IU/g) during ischemia and only 3% during reperfusion.


*    Discussion
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*Discussion
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Model of Ischemia
In this study, red blood cell (RBC)–perfused hearts with a normal hematocrit were hypoperfused at a coronary flow rate that approximated myocardial perfusion levels that have been measured in acute MI in patients. Under these conditions, the coronary flow level and normal hemoglobin content provided enough oxygen delivery that oxidative phosphorylation was still the major source of ATP production and accounted for {approx}90% of ATP synthesis despite the ischemic state.

To simulate acute MI perfusion conditions, we imposed an ischemic coronary flow rate of 10% of normal. This value is representative of perfusion levels immediately after a coronary occlusion in humans4 and dogs.3 However, an acute MI region undoubtedly contains a gradation of perfusion levels. In regions of relatively more severe ischemia, both glycolysis and oxidative phosphorylation would be relatively more inhibited; with less severe ischemia, oxidative phosphorylation would probably contribute a relatively greater fraction of ATP synthesis.

Many characteristics of this model differ from either total (zero-flow) ischemia or high-flow hypoxia.12 With normal substrate availability, and like both total ischemia and hypoxia, ATP and PCr levels decreased while Pi accumulated. This was the case despite decreases of left ventricular (LV) developed pressure and rate-pressure product of {approx}85% from baseline, which would be expected to proportionally decrease ATP utilization. Unlike total ischemia, in which, to slow the rate of ATP depletion, PCr falls within minutes to undetectable levels, [PCr] was still nearly 40% of preischemic values at 30 minutes of low-flow ischemia, a time at which ATP had decreased by {approx}25%. Importantly, PCr levels decreased only slightly between 30 and 60 minutes of low-flow ischemia, even though ATP levels continued to fall. This pattern is like high-flow hypoxia. But unlike high-flow hypoxia, in which intracellular pH fell by only {approx}0.1 pH unit, intracellular pH decreased during low-flow ischemia by nearly 1 pH unit (from 7.1 to 6.2). Thus, the low-flow ischemia used in the present study is like high-flow hypoxia with regard to the fall in [ATP] and [PCr] but like total ischemia with regard to accumulation of protons.

Inhibition of CK
Our results for both measured and calculated CK velocity show that CK reaction velocity is lower during low-flow ischemia. This is also demonstrated by the failure of CK to use more of the available PCr to slow the rate of ATP depletion. This result was unexpected and suggests that, in contrast to minimal perturbation of CK velocity observed under conditions of mild underperfusion,18 CK is substantially inhibited in the metabolic milieu of an acute infarct region. Recently, Ponticos and colleagues19 presented evidence that CK can be inhibited by as much as 60% by phosphorylation by AMP kinase under conditions in which PCr/creatine and ATP/ADP levels fall. We suggest that inhibition of CK by this mechanism is likely to occur under the conditions of our study.

ATP Synthesis With Normal Substrates
At baseline, ATP synthesis rate from oxidative phosphorylation (estimated from MO2) and from glycolysis20 were {approx}1.0 and {approx}0.01 mmol/L of cell water/s, respectively. During low-flow ischemia, these rates were {approx}0.2 and {approx}0.02 (mmol/L)/s, respectively (assuming 1 net mole of glycolytic ATP produced per mole of lactate produced). Comparing low-flow ischemia to baseline, the ATP synthesis rate from oxidative phosphorylation decreased to 20%, while glycolytic ATP production doubled. The ratio of glycolytic/oxidative ATP synthesis increased 10-fold, from 0.01/1.0 (1%) at baseline to 0.02/0.2 (10%). Nonetheless, 90% of ATP synthesis in this simulated acute MI milieu was via oxidative phosphorylation.

ATP Synthesis With Increased G+I
A major result of the present study is that G+I increased [ATP] during low-flow ischemia primarily by increased glycolysis and not by increasing oxidative phosphorylation assessed by O2 utilization. G+I did not stimulate oxidative phosphorylation by increasing [ADP] or [Pi], because neither was increased by G+I. The increased [ATP] in the G+I group may be partly due to a slight increase in the P:O ratio due to a shift in substrate oxidation from free fatty acid to pyruvate. Finally, our results show that the increase in [ATP] in the G+I group was not the result of increased PCr utilization or of any mechanisms secondary to increased acidosis.

What was the fate of the ATP that resulted from G+I–mediated increase of glycolytic synthesis during ischemia? The amount of glycolytic ATP synthesis during the entire 60-minute ischemic period (estimated from lactate production) was 61 and 104 mmol glycolytic ATP/L cell water in the control and G+I groups, respectively (or {approx}30 and 52 µmol per heart, respectively). Therefore, the differential rate of ischemic glycolytic ATP synthesis attributable to the G+I was 0.37 µmol · heart-1 · min-1, or {approx}0.7 mmol/L cell water/min. This would have increased [ATP] markedly above the controls, by {approx}42 mmol/L, at end ischemia if no increase in ATP utilization had occurred in the G+I group. The observation that there was only a 6.8 mmol/L differential in high-energy phosphate concentration between groups at end ischemia suggests that the major portion of the "extra" glycolytic ATP resulting from the G+I substrate was used to support the better systolic and diastolic function of the G+I group. Only a small fraction was used to preserve a higher level of high-energy phosphates during ischemia.

Despite the increase in glycolytic flux, the G+I substrate did not cause more severe tissue acidosis during low-flow ischemia. There are at least 2 explanations for this. First, the presence of even a very low flow provides substantial washout of lactate and protons; tissue lactate does not accumulate significantly unless perfusion is <5% of control.21 Second, intracellular pH also depends on ATP hydrolysis (a proton-generating reaction),22 which was less with G+I.

Higher {Delta}G~p With G+I
Another major finding is that G+I markedly increased the free energy release from ATP hydrolysis, {Delta}G~p . Free energy release from ATP hydrolysis is not constant but rather depends on the concentrations of ATP, ADP, and Pi. With G+I, [ATP] was higher, [ADP] was relatively unchanged, and [Pi] was lower than for controls. We calculated {Delta}G~p . and {Delta}G'~p . using values of [ADP] and [ADP]'. Regardless of which estimate of [ADP] was used, at late ischemia, greater free energy (4.0 to 4.4 kJ/mol) was available for all cellular ATPase reactions for the G+I group.

Study Limitations
Our protocol was designed to simulate, as closely as possible, the myocardial metabolic milieu present in an acutely infarcting region in humans. However, because the G+I was started 5 minutes before the onset of ischemia, our protocol does not mimic the timing of drug administration of an acute MI. Because global ischemia was imposed, the entire LV of the isolated heart served as a model of the acute MI region. Despite the imposition of global coronary flow reduction, heterogeneous ischemia most likely exists in this model, as it does in acute clinical MI.4 Our NMR spectra report average tissue values for the entire heart and do not report any intracellular or regional variations and/or gradients; such average values may belie the extent of metabolite and free energy changes in different regions. Because it is impossible to measure free [ADP] directly, we calculated its value by 2 independent methods. Although there were some differences in estimates for [ADP] according to the method of calculation, both methods resulted in the same overall conclusions regarding the bioenergetic benefits of the G+I substrate.


*    Acknowledgments
 
This work was supported by grants from the NHLBI (HL-48715 to Dr Apstein, HL-52350 to Dr Ingwall, and K08-HL-03574 to Dr Eberli), and from the American Heart Association, National and Massachusetts Affiliate to Drs Eberli, Cave, and Friedrich. We acknowledge the assistance of Jonathan Rose, Soeun Ngoy, and Adam Silverman.

Received June 24, 1999; revision received November 2, 1999; accepted November 29, 1999.


*    References
up arrowTop
up arrowAbstract
up arrowIntroduction
up arrowMethods
up arrowResults
up arrowDiscussion
*References
 
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