(Received for publication, May 25, 1994; and in revised form, November 28, 1994)
From the
Absolute metabolic fluxes in isolated perfused hearts have been
determined by a nonlinear least squares analysis of glutamate labeling
kinetics from [1-C]glucose,
[4-
C]
-hydroxybutyrate, or
[2-
C]acetate using
C NMR
spectroscopy. With glucose as substrate, the malate-aspartate shuttle
flux was too slow to account for the reducing equivalents generated by
glycolysis and to predict the observed oxygen consumption rate. For
acetate and
-hydroxybutyrate, the malate-aspartate shuttle had to
be reversed for the network to agree with the observed oxygen
consumption and glutamate labeling. Thus, an additional redox shuttle
was required to reoxidize the NADH produced by cytoplasmic malate
dehydrogenase. Using this model there was good agreement between the
experimentally determined oxygen consumption and glutamate labeling and
the calculated values of these parameters from the model for all
substrates. The contribution of exogenous substrate to the overall
tricarboxylic acid (TCA) cycle flux, 89.6 ± 6.5% (mean ±
S.D.) as measured in the tissue extracts compared well with 91.4
± 4.2% calculated by the model. The ratio of TCA cycle flux to
oxygen consumption for acetate, was 2.2 ± 0.1, indicating that
NADH production is principally accounted for by TCA cycle flux. For
glucose or
-hydroxybutyrate, this ratio was 2.9 ± 0.2,
consistent with the existence of other NADH producing reactions (e.g. glycolysis,
-hydroxybutyrate oxidation).
C NMR spectroscopy has been used to study
intermediary metabolism in a wide range of biological systems including
isolated
cells(1, 2, 3, 4, 5, 6) ,
organs (both in vitro(7, 8, 9, 10, 11, 12) and in vivo(13, 14, 15, 16) ),
and most recently in humans(17, 18) . As
C-enriched substrates are metabolized, the
C
label is transferred to various metabolic intermediates. The specific
location of the label is dependent on the chemistry of the enzyme
reactions, and the rate of incorporation is determined by the flux
through particular metabolic pathways. If the concentration of the
intermediates is high enough (approximately 10
M), the time course of
C label
incorporation can be determined using
C NMR spectroscopy.
In many biological systems the intermediates in glycolysis and the TCA (
)cycle are below the limit of detection by NMR. However,
glutamate is present in sufficient concentration for detection by NMR
and is in exchange with the TCA cycle intermediate
-ketoglutarate,
via two transaminase reactions. There have been many studies that have
analyzed the steady state
C labeling of glutamate to
determine the relative contribution of various substrates to the
overall TCA cycle
flux(8, 11, 19, 20, 21) .
These approaches, however, are limited in that they do not provide
estimates of absolute metabolic fluxes, which can be obtained by
analysis of
C labeling kinetics(22) .
If
glutamate is in rapid exchange with the TCA cycle, measurement of the
time course of C label incorporation into glutamate by
C NMR spectroscopy may provide a means for noninvasively
determining the oxygen consumption of an organ in vivo.
However, such an analysis is critically dependent on knowing the
mechanism by which the glutamate pool is labeled, since only a small
fraction of the total glutamate pool is in exchange with
-ketoglutarate. Consequently, there has been much interest in
analyzing the kinetics of isotopic incorporation in order to estimate
TCA cycle fluxes in vivo. Such calculations of absolute fluxes
cannot be made from the measurement of steady state enrichment data and
external fluxes alone, due to the complexity of the reaction networks
involved.
In this study, we have built upon the earlier work by
Chance et al.(22) who reported that modeling of C NMR kinetic data from rat hearts perfused with
[2-
C]acetate and
[3-
C]pyruvate lead to accurate estimates of the
TCA cycle flux and the aspartate and alanine aminotransferase reaction
rates. We have developed a mathematical description encompassing both
glycolysis and the TCA cycle and analyzed the rate of labeling of
glutamate in the isolated perfused heart with three different labeled
substrates. Analysis of the kinetics of glutamate labeling in
combination with measured values for pool size, fractional enrichments,
and oxygen consumption have enabled us to show how small unlabeled
influxes affect the end point enrichments and increase the accuracy of
the calculated fluxes, yielding insight into the nature of the network
of significant reactions that occur in the intact heart.
A total of six
hearts were perfused under one of four substrate conditions: 1)
glucose, 5 mM plus insulin (0.05U/ml), n = 2;
2) -hydroxybutyrate, 11 mM plus glucose, 5 mM and insulin (0.05 unit/ml), n = 2; 3) acetate, 11
mM, n = 1 or 4) acetate, 11 mM plus
glucose, 5 mM, and insulin (0.05 unit/ml), n =
1. After approximately 30-min equilibration with unlabeled substrates
the perfusate was switched to that containing
C-labeled
substrates: 1) [1-
C]glucose, 5 mM; 2)
[4-
C]
-hydroxybutyrate, 11 mM plus
glucose, 5 mM; 3) [2-
C]acetate, 11
mM; or 4) [2-
C]acetate, 11 mM plus glucose, 5 mM. In all experiments the composition of
the perfusate before and after switching to labeled substrates was
identical except for the presence of the
C label. In each
group the
C-labeled substrates were 99% enriched. In the
groups with two substrates (i.e.
-hydroxybutyrate plus
glucose and acetate plus glucose) the glucose was unlabeled. The
C-labeled glucose and acetate were purchased from
Cambridge Isotope Laboratories (Woburn, MA), and the
[4-
C]
-hydroxybutyrate was purchased from
Isotech Inc. (Miamisburg, OH).
High
resolution C NMR spectra of heart extracts were collected
using a Bruker MSL-500 NMR spectrometer equipped with an 11.74T magnet
(89-mm diameter bore) and a commercial 10-mm probe. Extract spectra
were obtained under fully relaxed conditions (8-s total interpulse
delay, 12 µs (60°) pulse) with a 25 KHz sweep width, and stored
in 32K data blocks. Spectra were proton decoupled using composite pulse
decoupling during data acquisition only (to avoid nuclear Overhauser
enhancement).
High resolution spectra of extracts were analyzed using standard integration routines. Spectra were zero-filled to 64 or 128K and filtered with a 2-Hz line broadening prior to Fourier transformation.
Figure 1:
Reaction network used to analyze the
kinetics of glutamate labeling for one of the experiments with
[1-C]glucose as substrate and the calculated
steady state enzyme velocities (glucose Exp. 1 from Table 2). The
abbreviations of steady state fluxes and flux relationships are as
follows: Fg = total influx from glycolysis; Fpcp = pyruvate influx; Fms = malate-aspartate
shuttle flux; Fs = proteolysis influx; Fb = flux from endogenous substrates; MVO
= oxygen consumption; RFO
=
MVO
/TCA cycle flux; +2e/-2e =
two electron reduction/oxidation. The abbreviations of steady state
enzyme velocities are defined in Table 1. Reactions with double-headed arrows indicate that the reaction is near
equilibrium with a net flux in the direction of the double-headed
arrows. Note that an additional redox shuttle was required to
provide a hydrogen balance between the cytoplasm and the mitochondria;
see ``Results'' and ``Discussion'' for more
details.
Figure 2:
Reaction network used to analyze the
kinetics of glutamate labeling for one of the experiments with
[4-C]
-hydroxybutyrate and unlabeled glucose
as substrates and the calculated steady state enzyme velocities
(
-HB Exp. 1 from Table 2). Fat = total
-hydroxybutyrate influx; see legend to Fig. 1for other
definitions.
Figure 3:
Reaction network used to analyze the
kinetics of glutamate labeling with [2-C]acetate
only as substrate and the calculated steady state enzyme velocities
(see Table 2). Fat = total acetate influx; see
legend to Fig. 1for other
definitions.
The model requires that intermediate pool sizes be
defined in order for fluxes to be calculated. Although it was evident
that the glutamate pool size would effect the flux calculations, it was
not clear what effect differences in TCA cycle intermediate pool sizes
would have on these calculations. An extensive sensitivity analysis was
carried out to determine the effect of changes in these pools on the
calculated fluxes. We found that if the intermediate pool sizes were
small relative to glutamate, changes in pool size had no effect on the
calculated fluxes. Since these intermediates were below the limits of
detection in the C NMR spectra from both the intact heart
and the tissue extracts, it was felt appropriate to assume that they
were small relative to glutamate. Consequently the pool sizes for most
of the TCA cycle intermediates were taken from the earlier work of
Chance et al.(22) and converted to micromoles/g of
wet weight. For TCA cycle intermediates that were not measured in that
paper, such as succinate, fumarate, and oxaloacetate, an arbitrary
value of 0.1 µmol/g of wet weight was used.
One of the other uncertainties in the model was the distribution of metabolites between the mitochondrial and cytosolic compartments. To determine whether this distribution was important in calculating the fluxes the ratio of these compartments was varied between 5 and 40%. This covers the range of values for the fraction of the total cell volume occupied by the mitochondria in skeletal and cardiac muscle (28) . Analysis indicated that the relative sizes of these two compartments over this range did not have a significant effect on the calculated fluxes.
The reactions used in construction of the model along with the
number of differential equations necessary to describe each reaction
are listed in Table 1. The total number of differential equations
required to describe the network of reactions is 340. The reason for
this large number of equations is that one equation is used to describe
the reaction between two specific labeled intermediates. The number of
possible labeled species for any intermediate is 2, where n is the number of carbon atoms. For example, a total of 32
differential equations are required to describe the interconversion
between
-ketoglutarate and glutamate via one aminotransferase
reaction.
The C-labeled substrates enter the network as
influxes and are assumed to be the principle sources of energy and of
C label in the system. Due to the cleavage of the
[1-
C]glucose and
[4-
C]
-hydroxybutyrate molecules into 3- and
2-carbon fragments, respectively, the maximum possible fractional
enrichment at acetyl-CoA C-2 is 50% (in contrast to that of
[2-
C]acetate, which is 100%). In order to
account for our observation that end point enrichments of glutamate
were significantly less than the maximum possible enrichment,
additional unlabeled endogenous influxes had to be included in the
network. Isotopic dilution at glutamate C-4 originates from influxes
into the acetyl-CoA pool; this is a common end point of many different
pathways. Two principal pathways that could be responsible for isotopic
dilution of acetyl-CoA are glycolysis (Fgl) and
-oxidation of
endogenous fatty acids (Fb). Depending on the perfusion conditions, Fgl
could arise from unlabeled glucose or from glycogen breakdown; it is
not possible to distinguish between these pathways in our network.
Entry of unlabeled substrates into the TCA cycle other than via acetyl-CoA, such as metabolism of amino acids, was represented by a single unlabeled influx (Fs) at succinyl-CoA. It should be noted that since succinyl thiokinase is freely reversible, both succinate and succinyl-CoA were treated as a single pool in our model. Although Fs has been restricted to influx at succinyl-CoA, the network cannot discriminate between unlabeled substrate influx here or via other anaplerotic pathways; the net result is the same i.e. dilution of glutamate C-3 enrichment relative to C-4
In order to maintain constant pool size in the TCA cycle intermediates and to allow the possibility of achieving a steady state, a branch point in the network at the malate pool via malic enzyme had to be included. Malic enzyme has been shown to be active in rat heart mitochondria by a number of workers(29, 30, 31, 32) . In terms of the reaction network, the branching opens an alternative pathway from malate to citrate with different fates for the individual carbon atoms. It would be impossible to maintain constant pool sizes if the pathway from mitochondrial malate to mitochondrial pyruvate were omitted from the network.
Examination of the networks in Fig. 1Fig. 2Fig. 3indicates that the absence of
malic enzyme in combination with proteolysis would lead to the flux
into acetyl-CoA being less than cycle flux and the flux into
oxaloacetate being greater than TCA cycle flux. The result of this
would be a decrease in acetyl-CoA and malate pools and an increase in
oxaloacetate and citrate. A depletion of acetyl-CoA would ultimately
lead to a cessation of the TCA cycle due to the lack of entry of
2-carbon fragments and thus a decline in function and ultimately an
imbalance in the demand and supply of ATP. However, cardiac function
and high energy phosphates are stable in our experiments. It is
possible that the additional acetyl-CoA moieties could be supplied by
-oxidation; if this were the case then the fractional enrichment
of glutamate C-4 would be significantly less than we measured.
Furthermore, if there was an accumulation of citrate this would be
evident in the NMR spectra as a resonance at approximately 45 ppm,
which was not observed. It therefore seems justified to include the
malic enzyme in the network.
All the reactions in the network are considered to be irreversible with the exception of the transaminases and fumarase. The reverse flux of the cytosolic transaminase was varied as an unknown parameter. The best agreement between the experimental and calculated results was obtained when the reverse reaction was slow compared with the forward reaction, indicating that the cytosolic transaminase is out of equilibrium. High forward and backward rates for fumarase relative to the TCA cycle were required to maintain a positive velocity and to achieve and maintain the fumarate and malate pool sizes at their equilibrium values.
Although there is evidence of pyruvate
carboxylase activity in the
heart(19, 33, 34, 35) , this pathway
has not been included in the network. Flux through this enzyme is
usually activated in response to an increase in TCA cycle intermediate
pool sizes as occurs following potassium arrest or alterations in
available substrates(34, 35, 36) . In our
experiments metabolite pool sizes are constant; thus, it is unlikely
that there is significant flux through pyruvate carboxylase.
Furthermore, even if there was a small flux through pyruvate
carboxylase, in the experiments with unlabeled glucose plus C-labeled acetate or
-hydroxybutyrate, this flux
would be accounted for by Fs, as the net result would be a dilution of
glutamate C-2 and C-3 enrichment. Although metabolism of
[1-
C]glucose via pyruvate carboxylase would
initially lead to an inequality in the enrichments of glutamate C-2 and
C-3, the high forward and backward rates of fumarase will result in
complete randomization in the labeling of glutamate C-2 and C-3.
Therefore, a small contribution from pyruvate carboxylase to the
overall TCA cycle flux cannot be ruled out. However, even if there is a
small flux through pyruvate carboxylase, this would not affect the
calculated MVO
, the exchange of reducing equivalents
between the mitochondria and the cytosol or the labeling of the
glutamate pool via the malate-aspartate shuttle.
A typical series of C NMR spectra recorded from
a heart perfused with [4-
C]
-hydroxybutyrate
is shown in Fig. 4. The label first appeared in the C-4 position
of glutamate and subsequently in the C-2 and C-3 positions; no other
resonances were observed. With [1-
C]glucose as
substrate the only differences were the additional incorporation of the
C label into lactate, alanine, and glycogen. The time
course of labeling of glutamate C-4 and C-3 when perfused with
[1-
C]glucose,
[4-
C]-
-hydroxybutyrate plus unlabeled
glucose, or [2-
C]acetate as substrates is shown
in Fig. 5. Since the enrichment time curves for glutamate C-2
and C-3 were indistinguishable, only the C-3 data were used in the
model. The optimized fit of the mathematical model to the experimental
data is plotted along with the experimentally determined values.
Figure 4:
Series of C NMR spectra from
isolated perfused rat heart with
[4-
C]
-hydroxybutyrate as substrate for 50
min. The spectra have been expanded to show the glutamate region
only.
Figure 5:
Time
course of labeling of glutamate C-4 and C-3 with
[1-C]glucose as substrate from the same
experiment as the data in Fig. 1(a); with
[4-
C]
-hydroxybutyrate plus unlabeled
glucose as substrate (data from Fig. 2) (b); and with
[2-
C]acetate as substrate (data from Fig. 3) (c). The data points are the experimentally
determined values and the lines have been calculated by the reaction
network.
The unknown fluxes and rates of oxygen uptake (which to some extent depend on these fluxes) calculated by nonlinear least squares analysis for all six experiments are given in Table 2. The topology of fluxes, which includes those fluxes that depend on the net influxes, is presented schematically in Fig. 1Fig. 2Fig. 3for each perfusion condition.
Although proteolysis was not well determined by the network, in five of the six experiments the flux was significantly greater than zero (Table 2). That is, although the confidence limits may be relatively large, omission of Fs from the network resulted in a poorer fit between the calculated glutamate labeling kinetics and the experimental data. The calculated rate of proteolysis was between 0.02-0.12 µmol/min/g of wet weight, which is in good agreement with other studies of proteolysis in the isolated perfused rat heart(38, 39, 40) , which report rates of 0.01-0.05 µmol/min/g of wet weight. In one experiment the influx from proteolysis was not significantly different from zero. In other words, it was not possible to determine differences in end point enrichments between glutamate C-4 and C-3.
This could be due to greater noise in the data in this experiment,
or it could be because there was no proteolysis in this experiment. The
results from the model were also consistent with the contribution of
anaplerosis to the overall TCA cycle determined from the ratio of
glutamate C-3/C-4 intensities in the tissue extracts(20) . The
calculated values for proteolysis ranged from 0 to 5.4% of the total
TCA cycle flux compared with 1.9-8.3% calculated from the high
resolution C NMR spectra for all six experiments. The mean
of experimentally measured values of proteolysis for the glucose (2.9%)
and acetate (2.4%) experiments compared well with those calculated by
the model (2.7 and 2.1%, respectively), despite the fact that these
values were not statistically well determined. In the ketone body
experiments the model underestimated proteolysis at a mean of 2.3%
compared with 7.7% calculated from the high resolution
C
NMR spectra of the extracts.
Previous C NMR experiments
with the rat heart showed that alanine is labeled only on pyruvate or
glucose perfusion and not on acetate perfusion(22) . This was
confirmed in the current study, as we did not observe any alanine or
lactate labeling with mitochondrial substrates. This observation
suggests that the only extramitochondrial pathway is the labeling of
cytoplasmic glutamate by the malate-aspartate shuttle. This agrees with
the previous results from
C-tracer experiments (41, 42) and suggests that in these experiments the
pathway from propionyl-CoA to pyruvate via malic enzyme is located
entirely in the mitochondria. Although extramitochondrial activity has
been observed in rat heart(30) , the observations mentioned
above suggest that extramitochondrial malic enzyme is not active in
these perfusions and therefore was not included in the analysis. In
contrast to the earlier study (22) where the pathway of
glutamate labeling in the cytosol was by direct exchange, we have
included metabolite transport across the mitochondrial membrane by the
malate-aspartate shuttle.
The magnitude of the specific fluxes in Table 2is dependent on the work carried out by the heart for each
experiment. For the six experiments in this study, the work load,
defined as the rate pressure product (i.e. heart rate
developed pressure) ranged from 18,800 to 39,200 mmHg/min. In order for
the network to adequately describe the experimental results, both the
calculated kinetics of glutamate labeling and the calculated oxygen
consumption had to agree with the experimentally measured values. Good
agreement between the calculated and experimental MVO
required inclusion of a redox shuttle in addition to the
malate-aspartate shuttle to export reducing equivalents from the
cytosol to the mitochondria (Fig. 6). In the absence of any
evidence to the contrary, we have assumed that this additional redox
shuttle is the glycerol phosphate shuttle; however, the precise nature
of the shuttle is unimportant as long as the net effect is to transfer
reducing equivalents from the cytosol to the mitochondria.
Figure 6:
Comparison between the experimentally
measured and the calculated oxygen consumption (MVO) with
and without the glycerol phosphate shuttle. Error bars represent 5 and
95% confidence limits of calculated values.
In the
case of the glucose experiment, the rate of the malate-aspartate
shuttle as determined by the kinetics of glutamate labeling was too
slow to account for the total reducing equivalents generated by the
rate of glycolysis and too slow to produce the observed value of
MVO. For the acetate-perfused and the
-hydroxybutyrate
plus glucose-perfused hearts, the malate-aspartate shuttle had to be
reversed in order to produce a network which would: 1) maintain a
constant metabolite pool size, 2) account for the observed labeling
kinetics of glutamate, and 3) predict the observed MVO
. As
a consequence, an additional hydrogen shuttle was required to reoxidize
the NADH produced by cytoplasmic malate dehydrogenase. A comparison
between the measured and calculated MVO
in the presence and
absence of the additional redox shuttle is shown in Fig. 6. It
is clear from these data that inclusion of the glycerol phosphate
shuttle significantly improves the agreement between the calculated and
measured MVO
for all the experiments.
The fractional
enrichment at glutamate C-4 that results from the metabolism of labeled
substrates can be determined from the high resolution C
NMR spectra of tissue extracts(20) . For glucose and
-hydroxybutyrate, the maximal fractional enrichment is 50% and for
acetate it is 100%; enrichment less than these maximal values indicates
entry of unlabeled substrate at acetyl-CoA. We compared the calculated
fractional enrichment at
-ketoglutarate C-4 with the measured
enrichment at glutamate C-4; at steady state these should be equal. The
mean of the experimentally measured values of glutamate enrichment for
the glucose (41%), ketone body (47.2%), and acetate (92.4%) experiments
compared well with those calculated by the model (46.1, 47.2, and 86.7%
respectively). The contribution of exogenous substrate to the overall
TCA cycle flux for all six experiments was 89.6 ± 6.5% (mean
± S.D.) as measured in the tissue extracts which was in good
agreement with the value 91.4 ± 4.2% calculated by the model.
It is apparent from these data that there was significant dilution
at glutamate C-4. Isotopic dilution at glutamate C-4 is a result of an
influx of endogenous substrates into the acetyl-CoA pool. Two principal
pathways that could be responsible for isotopic dilution of acetyl-CoA
are glycolysis (Fgl) and -oxidation of endogenous fatty acids
(Fb). The best fit with the experimental data was obtained with the
majority of this unlabeled influx entering via glycolysis rather than
-oxidation (i.e. Fgl > Fb).
Inspection of the
observed mathematical form of label incorporation into glutamate C-3
shows a hyperbolic form for the glucose experiments and a marked delay
in -hydroxybutyrate and acetate experiments. As a result, a
sigmoidal curve for the labeling kinetics of glutamate C-3 provides a
more accurate representation for hearts perfused with
-hydroxybutyrate plus glucose or acetate as sole substrate(s). In
all cases labeling of glutamate C-4 showed a direct, hyperbolic
response. On closer examination of the results, this was also observed
in the earlier work by Chance et al.(22) . The
sigmoidal response in the calculated curves was obtained when the
cytoplasmic transaminase reaction was out of equilibrium. This was
achieved by allowing the reverse flux to vary as an unknown parameter.
Although the experimental data indicate that a similar situation may exist in the glucose perfused hearts, this observation is critically dependent on the early time points, which are poorly defined in this experiment. Thus, it is not possible to distinguish mathematically between a rectangular hyperbole or a sigmoid curve for the glutamate C-3 enrichment kinetics in the glucose experiments. In the studies using extracts(22) , earlier time points are better defined and clearly demonstrate the sigmoidal nature of the glutamate C-2 labeling with acetate. Fitting these data with the new model using both a fast reverse reaction and a slow reverse reaction is shown in Fig. 7. It is clear from these data that the fast reverse reaction overestimates all the observed values for glutamate C-3 (Fig. 7a). In contrast, with a slow back reaction, statistical analysis indicates that there is a random distribution of residuals and a lower sum of squares of residuals (Fig. 7b).
Figure 7:
Time course of labeling of glutamate C-4
and C-3 with [2-C]acetate as substrate from the
original work by Chance et al.(22) comparing the
effect of rapid (a) and slow (b) exchange of the
cytosolic transaminase reactions.
The network described here results in excellent agreement between the measured and calculated metabolic parameters over a range of work loads and under different substrate conditions. The principal assumptions that we have made are: 1) that the reactions described by the network are consistent with the known biochemistry of the system and 2) that the glutamate pool is evenly distributed between the mitochondrial and cytosolic compartments. The relative size of these compartments had no impact on the calculated fluxes; varying the mitochondrial compartment between 5 and 40% of the total cell volume did not significantly affect the results. A sensitivity analysis on the effects of changes in intermediate pool sizes indicated that the only pool sizes that significantly affected the calculations were those large enough to be determined by NMR spectroscopy. Therefore the only metabolite pool size that was of significance in our experiments was the glutamate pool, which was determined by enzymatic analysis for each experiment.
The main limitation of these results is the quality of
the C kinetic data from the intact heart. The agreement
between the experimental and the calculated labeling kinetics is not as
good in the hearts perfused with labeled glucose as for those hearts
perfused with either labeled acetate or
-hydroxybutyrate. This
probably results from a 50% dilution of labeled acetyl-CoA units
originating from the [1-
C]glucose combined with
a relatively small glutamate pool. In the
[4-
C]
-hydroxybutyrate experiments there is
a similar dilution at acetyl-CoA (50%), but the glutamate concentration
is increased 2-fold compared with hearts perfused with glucose as the
sole substrate; thus, there is better agreement between the calculated
and experimental data. The best agreement between the calculated and
experimental data is observed with [2-
C]acetate
as substrate, since 100% of the acetyl-CoA units originating from
[2-
C]acetate are labeled.
One of major
differences between the three substrate conditions was the ratio of TCA
cycle flux to MVO (i.e. RFO
). In
acetate-perfused hearts RFO
was approximately 2, which
agrees well with earlier studies(23) , indicating that the NADH
produced is entirely accounted for by TCA cycle flux. However, in both
glucose and
-hydroxybutyrate perfused hearts the RFO
is significantly greater than that seen with acetate (Table 2), which is consistent with the existence of other NADH
producing reactions such as glycolysis and oxidation of
-hydroxybutyrate.
Based on current knowledge the only mechanism
for labeling the cytoplasmic glutamate pool from a very small
mitochondrial -ketoglutarate pool is via the malate-aspartate
shuttle. In all cases the calculated flux of this shuttle, determined
by the kinetics of glutamate labeling, is too slow to account for the
measured values of MVO
. With glucose as substrate the
expected pathway from cytoplasmic NADH to mitochondrial NADH would be
the malate-aspartate shuttle; however, the rate of the malate-aspartate
shuttle is of the order of only 20% of the total flux of reducing power
generated by glycolysis. In other words, the rate of cytoplasmic
glutamate labeling was too slow to account for the rate of NADH
production in the cytoplasm (i.e. Fgl > Fms). For the
mitochondrial substrates, the rate of endogenous glycolysis, calculated
from the dilution of label at glutamate C-4, was too small to account
for the rate of glutamate labeling (i.e. Fgl < Fms).
Consequently, as the labeling of cytoplasmic glutamate requires
oxidation/reduction reactions, it was necessary to add an additional
redox shuttle and to reverse the malate shuttle (compared with the
direction when glucose was sole substrate).
The precise nature of
this additional redox shuttle is unimportant as long as the net effect
is to transfer reducing equivalents from the cytosol to the
mitochondria; however, a promising candidate for this reaction is the
glycerol phosphate shuttle. Isaac et al.(43) provided evidence that the glycerol phosphate shuttle
was operational in cardiac tissue; however, Safer et al.(44) suggested that hydrogen flux through the shuttle was
limited under normal conditions by low concentrations of glycerol
3-phosphate. It is well known, however, that low concentrations of
metabolites can be assayed by cycling reactions, and thus low
concentrations of glycerol 3-phosphate need not preclude shuttle
activity. Furthermore, it should be noted that the incorporation of C label from [1-
C]glucose into
glycerol 3-phosphate has been observed under similar
conditions(45) , indicating that at least the cytoplasmic
portion of this shuttle is operative.
From our analysis we have
shown that relatively subtle changes in the network can have a
significant impact on the agreement between the experimental and
calculated results. From the experimental data for acetate and
-hydroxybutyrate, the labeling kinetics of glutamate C-3 shows a
lag compared with the labeling in the C-4 position. With the cytosolic
transaminase at near equilibrium (like fumarase) the mathematical form
of the curve does not adequately describe the experimental data; it
systematically overestimates the experimental findings (Fig. 7a). Some lag is the result of the necessity of
more than one complete turn of the TCA cycle in order for label to be
incorporated into glutamate C-3. This is insufficient, however, to
account for the experimental results. When the reverse flux of
transaminase was varied as an unknown parameter, the best fit to the
experimental data was obtained when this flux was exceedingly small (Fig. 7b). Although there also appears to be a lag time
in the C-3 labeling kinetics in the glucose experiments, there are
insufficient early time points to determine effectively the
mathematical form of the glutamate C-3 curve.
In order to account
for the observed isotopic dilution at the glutamate C-4, influxes from
unlabeled substrates via glycolysis (Fgl) or -oxidation (Fb) were
included in the network. In all the experiments where there was
significant dilution of glutamate C-4, Fgl was significantly greater
than Fb. For the mitochondrial substrates this flux from glycolysis
could be attributed to the metabolism of exogenous unlabeled glucose or
with acetate as the sole substrate resulting from glycogenolysis. In
the glucose experiments glycogen synthesis was clearly evident (data
not shown); thus, it is unlikely that the glutamate C-4 dilution is a
result of glycogen breakdown. An alternative explanation is that the
isotopic dilution is a result of metabolism via the pentose phosphate
pathway. When 6-phosphogluconate is metabolized to 5-ribulose
phosphate, the C-1 carbon of glucose is lost as CO
; thus,
if the C-1 position is labeled, there will be a loss of label which
will appear as an influx of unlabeled glucose into acetyl-CoA. The
dilution observed in these glucose experiments (i.e. 6-7%) is in agreement with a recent study by Chatham et
al.(46) which indicated a 5-6% dilution at alanine
and acetyl-CoA in hearts perfused with
[1-
C]glucose. Therefore it is possible that in
the glucose experiments Fgl is a measure of pentose phosphate activity.
The approach presented here is only one of many possible computational methods for modeling cardiac metabolism. For example, Cohen and Bergman (47, 48) recently presented a syntactical approach which avoided the use of differential equations. The problems inherent in the solution of large networks of differential equations as described by Cohen and Bergman(47, 48) , were minimized in our study by using FACSIMILE, a program designed specifically for the solution of complex reaction networks(36) . This enabled us to construct a network with few assumptions that included both cytosolic and mitochondrial compartments as well as the malate-aspartate shuttle. Therefore, we have been able to construct a more complete mathematical description of cardiac metabolism than previously published. Furthermore, although the syntactical approach (47, 48) may be computationally simpler, they required 1.5-14.5 h to execute a single simulation on a SPARCstation IPX. In contrast, using our more complete model a single simulation is obtained in a few seconds on a 486-DX2, 50 MHz laptop. In order to optimize the fit to the experimental data approximately 100 simulations are required and thus a complete solution was obtained within only a few minutes.
In order to completely
describe all the reactions included in the network a total of 340
differential equations are required. The complete set of differential
equations enables the position of every carbon atom in the network to
be accounted for at any one time. Clearly for any specific C-labeled substrate only a subset of equations will be
relevant since not all carbon atoms in all the intermediates will
become enriched. Thus, it would be possible to simplify the network for
a specific set of conditions; however, extensive coding changes would
be required. Consequently the time needed to simplify the network would
be excessive, given that the full network can used to fit the
experimental data in a matter of a few minutes on a personal computer.
Furthermore, if such simplification was made, a new model would have to
be constructed for each set of experimental of conditions. In contrast
using the full network it is straight forward to use different
substrates or combinations of labeled substrates.
Using the
mathematical system described above, we have obtained excellent
agreement between the calculated and experimentally determined oxygen
consumption rates for hearts perfused with glucose, with glucose plus
-hydroxybutyrate, and with acetate. The calculated time courses of
enrichment of glutamate C-4 and C-3 also agree well with the
experimental data. It should be emphasized that the network of labeling
equations used to calculated these fluxes is highly constrained. The
measured oxygen consumption rates, the kinetics of labeling of the
different glutamate isotopomers as well as their different steady state
enrichments all need to be satisfied by the model. Furthermore, the
network must be consistent with the known biochemistry of the system
and must maintain a steady state reflected by constant metabolite pool
sizes. As a result of the steady state constraint, the internal fluxes (i.e. enzyme activities) depend on the external influxes, and
the only unknowns are the exogenous and endogenous influxes and the
reverse flux of the transaminases. Thus, despite the complexity of the
network, the number of unknown parameters (i.e. total
substrate influx; rate of proteolysis (Fs); magnitude of the flux of
the malate-aspartate shuttle and reverse flux for the cytoplasmic
transaminase) is relatively small. The elucidation of the mechanism of
glutamate labeling offers the prospect of a noninvasive method for
determining the rate of oxygen uptake in tissue, in general, and
cardiac muscle in particular. This work provides a framework with which
to examine the complex relationship between oxygen consumption, work,
and substrate utilization.