1 Department of Radiology, A kinetic model of the citric acid cycle for
calculating oxygen consumption from
13C nuclear magnetic resonance
(NMR) multiplet data has been developed. Measured oxygen consumption
(M
13C isotopomer analysis; citric acid cycle flux; heart metabolism; nuclear magnetic
resonance
FUNCTIONAL IMAGING STUDIES have stimulated interest in
measurement of tissue oxygen consumption, yet few methods exist that provide this measurement noninvasively. Nuclear magnetic resonance (NMR) spectroscopy in combination with
13C tracers could in principle
fulfill this need. A number of recent papers (22, 25, 27) have analyzed
the rates of appearance of 13C in
metabolites associated with the citric acid cycle, with models similar
to those developed for 14C
fractional enrichment measurements. In 1983, Chance et al. (1) were the
first to determine citric acid cycle flux from
13C NMR measurements of the change
in glutamate fractional enrichment with time. A number of studies with
similar approaches have followed, obtaining fractional enrichments from
1H-observed,
13C-edited spectra in rat (3, 20)
and human (19) brain and direct
13C-observed spectra in rat liver
(8), the canine heart in vivo (26), perfused rat heart (2, 28, 31, 32),
and perfused rabbit heart (11, 23, 33-35). Citric
acid cycle flux has also been estimated empirically with the difference
in time to one-half of enrichment of glutamate C-3 and C-4 (30, 31). In
most of these studies, however, a direct comparison between oxygen
consumption estimated by these methods and measured experimentally was
not made, and in several cases oxygen consumption was used as one of
the inputs to the model.
Information that can be derived from a
13C NMR spectrum is not limited to
13C fractional enrichments. We
have presented numerous 13C NMR
isotopomer methods, both isotopic steady-state and non-steady-state methods (15-17), for analysis of relative flux through the citric acid cycle. Chance et al. (1) in their early NMR study collected high-resolution spectra from heart extracts and designed a model that
would have allowed for the analysis of multiplets contained within the
spectra. However, they elected to use only
13C fractional enrichment data.
Although measurement of 13C
multiplets in vivo is certainly not routine and may require a
high-field magnet, it has been demonstrated that multiplets can be
observed in the human brain (4). Therefore, it was decided to develop a
model for calculating oxygen consumption directly from intact tissue
with 13C multiplet data and to
compare this with the more typical measurement of total resonance areas
(a reflection of 13C fractional
enrichment). Furthermore, because the glutamate C-4 resonance appears
in a relatively uncrowded region of the spectrum and the doublet
component of this resonance (referred to here as C4D34) is resolved in
spectra of human brain (4), our kinetic analysis was also applied to
the temporal evolution of the C4D34 doublet as the only NMR measurement.
A necessary component of the analysis of the time course of glutamate
enrichment is the rate of exchange between The purpose of this work was to develop a kinetic model capable of
analyzing 13C NMR multiplet data,
as well as fractional enrichment data, and to evaluate which data
variables provide the most reliable estimation of oxygen consumption.
Experiments were performed under both "ideal" conditions
(13C NMR of extracts) and those
more likely to be achieved in vivo (measurements from intact hearts
under conditions of low signal-to-noise). A statistical analysis was
performed to determine the benefits of including multiplet data, the
correlation between parameters, and the influence of uncertainty in
Vx on
VTCA and hence
oxygen consumption. It was found that the addition of
13C multiplet data significantly
improved the measurement of oxygen consumption. The same benefit was
found in the analysis of the C4D34 doublet as the only NMR measurement.
Because the glutamate C-4 resonance is reasonably well resolved from
other carbon resonances in in vivo spectra, temporal measurement of the
C4D34 doublet may offer certain advantages for in vivo studies. The
C4D34 doublet could be detected with single-frequency
13C excitation and narrow-band
1H decoupling, thereby making
spatial localization schemes simpler and potential concerns about
tissue heating less of an issue.
[2-13C]sodium acetate,
[3-13C]sodium
pyruvate, and
[1-13C]glucose (all
99%) were purchased from Cambridge Isotopes (Andover, MA). [3-13C]sodium
propionate (99%) was obtained from Isotec (Miamisburg, OH). Other
common materials were obtained from Sigma (St. Louis, MO). Perfusions
were conducted with Sprague-Dawley rats weighing 350-400 g and fed
ad libitum.
Heart perfusions. Rat hearts were
perfused by the Langendorff method with standard Krebs-Henseleit
bicarbonate buffer bubbled with 95%
O2-5%
CO2 at 37°C and a column
height of 100 cm. Hearts were placed inside the magnet, and the
temperature of perfusate surrounding the heart was monitored with a
fiber optic thermometry system (Luxtron, Santa Clara, CA). In addition
to water jacketing held at 37°C surrounding the perfusion rig, the
temperature was maintained with air flowing through the NMR probe at
35°C (Omega variable temperature accessory). The temperature,
recorded with the Luxtron probe, was 36.5-37.0°C during
acquisition of 13C NMR spectra
with broad-band proton decoupling. Heart rate was monitored with an
open-ended cannula in the left ventricle with a pressure transducer.
Coronary flow was measured with a stopwatch and measuring cylinder. The
oxygen tension of the perfusate and coronary effluent, the latter drawn
via a cannula placed in the pulmonary artery, was measured with a blood
gas analyzer (Instrumentation Laboratory, Lexington, MA). This was used
along with the coronary flow rate to calculate oxygen consumption.
Perfusions were begun with a 30-min period with unenriched substrates
to ensure metabolic steady state before switching to perfusate
containing enriched substrates at the same concentration. Two substrate
mixtures were studied, the first consisting of 5 mM glucose plus 5 mM
[2-13C]acetate. The
NMR data were collected from hearts perfused with this mixture by two
different methods. In the first case, the data were collected from
extracts, and after exposure to
13C-enriched substrates for 3, 5, 8, 12, 15, 30, 45, or 60 min, the hearts were freeze-clamped.
Perfusions were performed in triplicate at each time point. Oxygen
consumption was measured in the initial perfusion period and during
incubation with enriched substrates. In the second method, the NMR
spectra were collected from hearts perfused inside the magnet. Toward
the end of the 30-min perfusion period with unenriched substrates, a
10-min period was used to collect NMR spectra that were then discarded,
which allowed the temperature to stabilize during proton decoupling. An
initial (background) spectrum was then saved, and spectra were acquired continuously after being switched to perfusate containing enriched substrates. Perfusion was continued for 60 min, during which oxygen consumption measurements were made. Hearts were then freeze-clamped for
1H NMR and biochemical analysis. A
second mixture of substrates, 5 mM glucose plus 1 mM
[3-13C]pyruvate, was
also used. In this case, NMR data were collected from hearts perfused
in the magnet until isotopic steady state was reached. Hearts were then
removed from the magnet, freeze-clamped, extracted, and subjected to
high-resolution NMR to evaluate the estimate for the fractional amount
of [2-13C]acetyl-CoA
(Fc2) and the relative
anaplerotic flux (Y) with steady-state isotopomer methods.
Tissue measurements. Freeze-clamped
tissue was held at liquid nitrogen temperatures before treatment. The
tissue was pulverized in the presence of liquid nitrogen, and a small
portion of tissue was removed and weighed before and after drying in an
oven to determine the wet-to-dry ratio. The remainder of the tissue was extracted with perchloric acid (3.6%, 4 ml/g wet tissue wt),
centrifuged, neutralized with KOH, and centrifuged a second time. A
portion of the supernatant was used to perform enzymatic assays and ion chromatography measurements, while the remainder was freeze-dried and
dissolved in 0.5 ml of phosphate buffer (pH 7.7) containing 2H2O
for NMR spectroscopy.
Aspartate and glutamate were measured by spectrophotometric assay (12),
and NMR methods. A General Electric Omega
400-MHz spectrometer (Bruker Instruments, Billerica, MA) was used to
collect 13C spectra at 100.6 MHz
and 1H spectra at 400.1 MHz.
13C NMR spectra obtained from
extracts were collected in 32K data blocks with a sweep width of 20,000 Hz and WALTZ-16 broad-band proton decoupling in a 5-mm broad-band
probe. Pulses (45°) were applied every 3 s. These pulsing
conditions were optimal for achieving maximal signal-to-noise without
differential saturation of the protonated glutamate resonances. The
number of scans acquired varied from 4,000 (hearts freeze-clamped after
30 min) to 18,000 (hearts freeze-clamped at 3 min).
[3-13C]propionate (2 µmol) was added as an internal standard.
13C NMR spectra of intact hearts
were acquired in a 20-mm broad-band probe. Data were collected in 16K
data blocks with 45° pulses with a 3-s interpulse delay. Spectra
were collected in 5-min blocks (100 scans). Broad-band proton
decoupling was performed with WALTZ-16 with bilevel decoupling; 3 W
were applied during acquisition of the free induction decay (0.82 s)
and 0.3 W between pulses. An external standard consisting of a small
bulb with 80 µl dioxane was placed close to the aorta of the hearts.
1H NMR spectra of extracts were
obtained with 45° pulses with a 7.0-s interpulse delay and
presaturation of water; 256 transients were collected in 8K data blocks.
Free induction decays were analyzed by baseline correction (to remove
direct current voltage offsets), exponential multiplication, and
Fourier transformation. A line broadening of 0.5 Hz was used to analyze
the data collected from extracts. To measure the multiplet areas from
spectra collected from intact hearts, 4-Hz line broadening was used.
The total area of signals corresponding to the glutamate carbons
collected from intact hearts was measured after subtracting the initial
background spectrum from all subsequent spectra. These were then
analyzed after being processed with 35-Hz line broadening. To measure
directly the fractional enrichment in glutamate C-4, 1H NMR spectra were analyzed in
spectra processed with 0.5-Hz line broadening. The area of the
13C satellite signals was divided
by the total area of the H4 resonance (sum of the
12C and
13C components).
Peak areas were measured by line fitting to the Voigt line shape (18)
with custom-written software. The line widths of peaks arising from
individual carbons were set to a single (optimized) value. The areas of
the multiplets contributing to each resonance were expressed as a
fraction of total resonance area, as described elsewhere (6, 15, 16).
For example, the glutamate C-4 resonance always consisted of a singlet
(C4S) and a doublet (C4D34) in the experiments reported here, with
C4D34 representing the area of the doublet expressed as a fraction of
the total C-4 resonance area (i.e., C4S + C4D34 = 1). Because only one
of these fractional measurements is independent, the C4D34 was chosen
for analysis. The peaks corresponding to the C2D12 multiplet were small
in hearts perfused with enriched acetate and not very well resolved
from lines corresponding to the C2D23 multiplet. Therefore, only the values for the quartet (Q) and singlet from the C-2 spectrum (C2Q and
C2S, respectively) were included in the data for kinetic analysis. Similarly, the C-3 resonance consists of an overlapping singlet (typically small) and triplet plus a well-resolved doublet. Rather than
introducing error by attempting to separate the C3S and C3T areas, the
C-3D multiplet was included as the only independent measurement from
this resonance.
Model. A schematic of the model used
for the kinetic analysis of the citric acid cycle is shown (Fig.
1). This model is similar to the original
used by Chance et al. (1) except that the exchange reaction between
alanine and pyruvate was not included, the pathways of anaplerosis were
added, and the four-carbon intermediates of the cycle are represented
by malate only. The exchange between alanine and pyruvate was not
included because pyruvate is not a citric acid cycle intermediate, so
the size of the alanine pool has little effect on the kinetic analysis
(this was evidenced in the kinetic analysis presented by Chance et al.
where pyruvate-alanine exchange flux was reported to be small). All
possible pathways of anaplerosis were represented by a single flux, of
rate
Y · VTCA
and the disposal reactions by a single flux with the same rate. The
number of intermediates used to represent the citric acid cycle was
limited to four because 13C
enrichment was measured in molecules external to the cycle only. Without direct measurement of the labeling of the citric acid cycle
intermediates, the reactions with which they are involved can be
grouped into single steps. Citrate was therefore used to represent the
six-carbon intermediates, and malate was used to represent the
four-carbon intermediates. Oxaloacetate must not be included with the
other four-carbon metabolites because, as a result of exchange with
aspartate, the curves generated by the model would not adequately
describe the experimental data (results not shown). Hence, the minimum
number of citric acid cycle intermediates that must be represented
under the conditions to which this model was applied is four. To model
the exchange of mitochondrial intermediates with (mainly cytoplasmic)
amino acids, the same principle applies: there is no information
available with respect to the labeling of intermediates in the two
cellular compartments, and hence the exchange process can be treated as
a single step
(Vx) even
though it involves both a transaminase and a transport process.
ABSTRACT
TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
REFERENCES
O2) was
compared with M
O2 predicted by the model with 13C NMR data
obtained from rat hearts perfused with glucose and either
[2-13C]acetate or
[3-13C]pyruvate. The
accuracy of M
O2 measured
from three subsets of NMR data was compared: glutamate C-4 and C-3
resonance areas; the doublet C4D34 (expressed as a fraction of C-4
area); and C-4 and C-3 areas plus several multiplets of C-2, C-3, and
C-4. M
O2 determined by
set 2 (C4D34 only) gave the same degree of accuracy as
set 3 (complete data); both were superior to
set 1 (C-4 and C-3 areas). Analysis of the latter suffers from the
correlation between citric acid cycle flux and exchange between
-ketoglutarate and glutamate, resulting in greater error in
estimating M
O2. Analysis of
C4D34 is less influenced by correlation between parameters, and this
single measurement provides the best opportunity for a noninvasive
measurement of oxygen consumption.
INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
REFERENCES
-ketoglutarate and
glutamate (Vx)
(33). However, estimates of this parameter have varied considerably,
ranging from 0.2 (2) to 4 (1) times the citric acid cycle flux
(VTCA) in the
perfused rat heart. The effect of uncertainty in the exchange rate on
citric acid cycle flux estimates must be evaluated because these two
parameters are correlated (33), and it has been recognized that the
exchange parameter is responsible for much of the uncertainty in
estimating citric acid cycle flux (8).
MATERIALS AND METHODS
TOP
ABSTRACT
INTRODUCTION
MATERIALS AND METHODS
RESULTS
DISCUSSION
REFERENCES
-ketoglutarate was measured by fluorimetric assay (13). Citrate,
fumarate, isocitrate, succinate, and malate content was determined with
a DX500 Chromatography System (Dionex, Sunnyvale, CA). An IonPac(R)
AS11 analytical column was used
with an anion self-regenerating suppressor and CD20 conductivity
detector. Intermediates were eluted with a gradient of NaOH (0.5 mM,
increased linearly to 5 mM over 7 min). Concentration measurements were made after the calibration curves with standards were prepared. The
malate and succinate peaks coeluted at the same time, and hence their
combined tissue contents were obtained. Chromatography peak areas were
measured with the PeakNet software supplied with the instrument.
View larger version (18K):
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Fig. 1.
Model of citric acid cycle. Parameters to be estimated from model
include: Fc2, fraction of
acetyl-CoA from (in this study)
[2-13C]acetate or
[3-13C]pyruvate;
Pyr3, fraction of anaplerotic
substrate, from, for example,
[3-13C]pyruvate in the
glucose + [3-13C]pyruvate group;
VTCA, citric acid
cycle flux; Vx,
exchange flux; and Y, influx of
anaplerotic substrate relative to
VTCA. Rate of
disposal pathways is equal to anaplerotic flux.
The assumptions of the model include
1) metabolic steady state;
2) rate of labeling of intermediates
feeding into acetyl-CoA and involved in anaplerotic pathways is fast
with respect to citric acid cycle turnover;
3) all reactions can be treated as
irreversible without influencing the rate of labeling of glutamate,
except of course for exchange between oxaloacetate, -ketoglutarate, aspartate, and glutamate; 4) no
incorporation of
13CO2;
and 5) rapid equilibration of
enrichment between the inner carbons and between the outer carbons of
the symmetrical four-carbon intermediates.
The parameters that can be estimated from the model are listed in the caption to Fig. 1. In principle, the model can be extended to analyze the other labeling patterns in acetyl-CoA ([1-13C]acetyl-CoA, corresponding to Fc1, and [1,2-13C]acetyl-CoA, corresponding to Fc3). Furthermore, a mixture of substrates generating the different acetyl-CoA isotopomers could be analyzed simultaneously. However, to apply this method in vivo, conditions that provide the simplest spectra for analysis will be the most successful. Therefore, only one labeled substrate was used for each experiment in this study (either [2-13C]acetate or [3-13C]pyruvate). These substrates generate [2-13C]acetyl-CoA only, which, as noted above, results in a glutamate C-4 spectrum that consists of a singlet and double only.
To illustrate the system of equations needed for a solution to this
model, the following indicate the change in the unlabeled isotopomers with time
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The model consists of a system of 88 equations (16 for each of citrate,
-ketoglutarate, glutamate, and aspartate; 12 for both malate and
oxaloacetate). The model was implemented as a Fortran program, with the
routine LSODE (5) for the solution of stiff ordinary differential
equations. This provided the fraction of each
13C isotopomer at each time point,
from which total resonance area and fractional multiplet values were
calculated as previously described (6). These calculated values were
then optimized to the experimental measurements to obtain the model
flux parameters with nonlinear least squares methods (21). The model
was implemented as a FORTRAN
program,1 written to be flexible
in handling data sets consisting of different measurements (total
resonance areas, fractional contribution of an individual multiplet to
any glutamate resonance, or both) yet also to provide Monte Carlo
simulations for assessing parameter errors.
Data used with model. The tissue
contents of intermediates included in the model were measured except
acetyl-CoA, for which the value of 0.2 µmol/g dry wt was used (25),
and oxaloacetate, calculated from ([aspartate]
[-ketoglutarate])/(6.6 [glutamate]) (1).
Both estimates are small relative to the total pool size and,
consequently, have little influence on flux calculations. These tissue
metabolite contents were used as fixed values in the model in all analyses.
The time-dependent 13C NMR measurements input to the model were separated into three different data sets. Data set 1 consisted of the total glutamate C-4 and C-3 (or C-2) resonance areas. The C-2 was used in spectra from hearts perfused with glucose plus pyruvate (the signal from [3-13C]pyruvate present in the perfusate overlapped somewhat with glutamate C-3, see Fig. 4A), whereas the C-3 resonance was used for hearts perfused with glucose plus acetate. Values for Fc2 and Y were used as fixed values. These were obtained with multiplet values measured from the last spectrum in the time course, applying a steady-state isotopomer analysis previously reported (6, 15, 16). The values for VTCA and Vx were estimated from the model. Data set 2 consisted of C4D34 as the sole NMR data. As with data set 1, values for Fc2 and Y were used as fixed inputs and VTCA and Vx were estimated from the model. Data set 3 included the sum of data sets 1 and 2 plus time-dependent estimates of C2Q, C2S, and C3D. Because more data were available in this set, Fc2 and Y were fit in the kinetic model along with VTCA and Vx.
Finally, the actual fractional enrichment in glutamate C-4 measured with 1H NMR of extracts from hearts at steady state was input as a fixed value in the model. As explained in RESULTS, the C-4 fractional enrichment measured by 1H NMR can differ from the value for Fc2, indicating that the entire glutamate pool was not involved with the citric acid cycle. This would affect the absolute flux value calculated by the model. Therefore, the measured glutamate content was adjusted by the ratio of Fc2 over the absolute fractional enrichment before calculation of the change in glutamate isotopomers with time.
Because not all of the glutamate pool is involved with the citric acid cycle, this would also introduce error if fractional enrichments were measured with an external 13C standard. Therefore, the C-4 and C-3 (or C-2) total resonance areas were not converted to actual 13C fractional enrichments before input of the data into the kinetic model. Instead, these experimentally determined resonance areas were converted to fractional enrichment before each iteration of the fitting process, with the values for Fc2 and Y (provided as input, as in the case of analysis of data sets 1 and 2, or estimated by the model). {The fractional enrichment of glutamate C-4 is equal to [2-13C]acetyl-CoA at steady state, whereas the enrichment of C-2 and C-3 is equal to Fc2/(2Y + 1); Ref. 16}.
An additional benefit of the above process was avoidance of additional experimental error introduced by the extra step of measuring the area of an external standard. This step requires correction for differences in nuclear Overhauser effects and relaxation between glutamate and the standard. Even after avoiding such steps, the standard deviation of the fit contributed by the C-4 and C-3 (or C-2) resonance areas tended to be higher (6-7%) than that of the multiplet data (1-4%). This indicates that fractional multiplet areas (given adequate resolution for area measurements) are less subject to the uncertainties associated with 13C fractional enrichment measurements.
Error and parameter sensitivity analysis. Parameter errors are reported as confidence levels (analysis of extract data) or actual range (analysis of intact heart data), both being more accurate descriptions of the uncertainty in the estimates than standard deviations (7). The 13C NMR data from heart extracts were combined for analysis, giving one time course with replicates at each time point, from which one set of parameter values was estimated. The error in these parameters was obtained with Monte Carlo simulation, a robust technique for error estimation that is subject to fewer assumptions than other methods (24, 29). The simulation was used to determine the 5 and 95% confidence levels. The 13C NMR data obtained from intact hearts provided the complete time course for each heart. Rather than combine measurements from all hearts, the data from each heart were analyzed to obtain parameter estimates. The error in the parameters was then reported with the actual range of values obtained from hearts in each experimental group. (Confidence levels could not be determined because of the small sample size).
A parameter sensitivity analysis was also performed with Monte Carlo simulation. Synthetic 13C measurements were generated and subdivided into the three data sets (described in Data used with model) and analyzed with the model. This was used to test the effect of available data on parameter estimates. Different values for Vx were also used in generating the synthetic data to examine the consequences of uncertainty in determination of this parameter. (Further details are given in RESULTS section.) The results of these simulations were used to determine the confidence levels and correlation between model parameters.
Calculation of oxygen consumption from model parameter
estimates. This was performed with
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Statistical analysis. Data are reported as means ± SD or, in the case of parameter estimates, means (5-95% confidence levels in the case of extract data, actual range in the analysis of data from intact hearts). Absolute flux rates are reported as micromoles per minute per gram of dry weight of tissue. Tissue contents are reported as micromoles per minute per gram of dry weight. Statistical analysis was conducted with paired two-tailed t-tests.
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RESULTS |
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Size of intermediate pools involved with the citric
acid cycle. The tissue content values of the more
readily measured intermediates are shown in Table 1. The
total amount of the citric acid cycle intermediates was only 5-7%
of all measurements (citric acid cycle intermediates + amino acids)
combined. Hence, the content of the amino acids must be the more
accurately determined, as errors in measuring the amounts of citric
acid cycle intermediates have little effect on flux
estimates.
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The extent to which the intermediates are involved in the citric acid cycle also affects the calculation of citric acid cycle activity. It has been reported that a fraction of glutamate remains unlabeled in rabbit (9, 10) and rat hearts (28). The actual fractional enrichment in glutamate C-4 (measured by 1H NMR spectroscopy) was compared with that calculated from acetyl-CoA enrichment (estimated by 13C isotopomer analysis) with extracts of hearts freeze-clamped at the final point in the time series. With the use of paired t-tests, a significant difference (P = 0.0010) was found in hearts perfused with 1 mM [3-13C]pyruvate and 5 mM glucose (0.70 ± 0.01 and 0.84 ± 0.02, n = 6, 1H NMR and 13C NMR, respectively). Hence, the value obtained for the extractable amount of glutamate in this group (Table 1) was adjusted by the ratio 0.70 to 0.84 for use in the kinetic analysis. In hearts perfused with 5 mM [2-13C]acetate plus 5 mM glucose, the difference was not significant: 0.92 ± 0.05 and 0.95 ± 0.02, n = 8. Similar measurements were not possible for the other intermediates, but because their tissue contents were much lower than glutamate and assuming the required correction factor (~10% for glutamate) is the same for all intermediates, this will have little effect on the measurement of citric acid cycle flux.
Kinetic analysis of data. Spectra from
the first 30 min of exposure to glucose plus
[2-13C]acetate are
shown in Figs.
2A (data
collected from extracts) and
3A
(data collected from intact hearts). Figure
2B shows the multiplet measurements
made from the extract data, along with the curves generated after
fitting the data to the kinetic model. All of the data shown were used
in the analysis; the values measured in triplicate at each time point
were included as individual values. Figure
3B shows the same measurements
obtained from intact hearts. The signal-to-noise of the spectra in this
case was lower, as can be expected, so the scatter in the measurements
is higher and measurements at the earlier time points were not always
possible. The curves in this figure show the result of fitting the
combined data. However, this is for demonstration purposes only; the
data from individual hearts were analyzed separately to allow
statistical evaluation of the parameter estimates. Figure
4A shows hearts perfused with glucose plus
[3-13C]pyruvate.
Hearts perfused with these substrates had less glutamate (Table 1) and
a lower enrichment in acetyl-CoA. As a result, the signal-to-noise in
spectra collected from hearts in this group was worse, and the scatter
in the NMR measurements was greater (compare Fig.
4B with Figs.
2B and
3B).
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Table 2 lists the means and ranges of
VTCA and
Vx estimated by
analysis of the three different NMR data sets. Not shown in this table
are the estimates for Fc2 and
Y. The analysis of data set 3 from each experimental group gave values for
Fc2 of 0.96 (0.94-0.97), 0.94 (0.88-0.96), and 0.84 (0.81-0.87) and values for
Y of 0.04 (0.03-0.05), 0.03 (0.02-0.05), and 0.05 (0.00-0.10) for hearts perfused with
glucose plus acetate (extracts and intact hearts) and glucose plus
pyruvate, respectively. No evidence was found for the entry of labeled
pyruvate as anaplerotic substrate (Pyr3 = 0.0). Because
Fc2 and
Y were not as well determined in the
analysis of data sets
1 and
2, these parameters were estimated from spectra of tissue extracts at steady state and were used as fixed
values during the fitting. The values of
Fc2 and
Y obtained from extract spectra were
identical to those listed above as determined by the fitting of data
set
3.
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The range in VTCA indicates that there were only minor differences between the results of fitting data sets 2 and 3, whereas the range was greater for the fit of data set 1. This reflects correlation of VTCA and Vx, which is apparently magnified in the fitting of glutamate C-4 and C-3 (or C-2) resonance areas (see Numerical evaluation of model).
Oxygen consumption measurement. Table
2 shows experimental MO2 and
values estimated by the kinetic model. In no case was the calculated
M
O2 statistically different
from the experimental measurement. There was a ~30% difference in
experimental M
O2 between
hearts perfused with acetate and glucose vs. glucose plus pyruvate.
Note that the ranges for these two groups do not overlap. However, the
kinetic model did not predict differences in
M
O2 for these two substrate
groups when data sets
1 and
3 were analyzed. An analysis of data
set 2 did, however, successfully predict differences in
M
O2 for these two substrate groups.
Numerical evaluation of model. Monte
Carlo simulation was used to determine the extent of correlation
between parameters, measuring this for the three different subsets of
the data. Because the uncertainty in
Vx increases as
the size of this flux increases, four series of simulated data sets
were generated in which
Vx was varied
from 3 to 60 µmol · min1 · g
dry wt
1. The values of
other parameters were the same for each simulation (VTCA = 10 µmol · min
1 · g
dry wt
1,
Fc2 = 0.95, and
Y = 0.05). From each of these, a
further 300 data sets were constructed by adding random noise to give
standard deviations of 3% for multiplet data and 6% for C-4 and C-3
resonance areas (to compare with the experimental finding). Finally,
each data set was analyzed with the kinetic model in three ways,
selecting resonance areas only (corresponding to experimental data
set
1), the C4D34 multiplet only
(corresponding to experimental data
set 2), or resonance areas plus
multiplet data combined (corresponding to experimental data
set
3). The model parameter estimates
generated by this procedure were then used for correlation and
regression analysis. These parameter estimates were also used to
calculate oxygen consumption and hence the influence of
Vx on the error in this measurement.
Table 3 compares the degree of correlation between
parameters VTCA
and Vx, both as a
function of different subsets of the data and as the value of
Vx used in the
simulations increased. In the analysis of data
set
1, the correlation was negative,
declining ~20% as
Vx increased. The
absolute value of the correlation coefficient determined from data
set 2 was initially one-half of that obtained with data
set
1, fell to 35% of its absolute value
at Vx = 10, and
then gradually increased as
Vx increased.
These correlations, initially positive, were negative for values in
Vx of 10 µmol · min1 · g
dry wt
1 and greater. The
correlation coefficients obtained by analysis of data
set 3 were positive and smaller than in the analysis of the other two data
sets when Vx was
3 µmol · min
1 · g
dry wt
1, showed a small
increase at Vx = 10, and then decreased with increasing
Vx.
|
Although the correlation coefficient indicates the fraction of the error in a parameter estimate that can be explained by another, it does not indicate the magnitude of the influence. This was determined by examining the regression of one parameter on another (Table 3). For each data subset, the influence of Vx on the estimate of VTCA decreased dramatically as the value of Vx used in the simulations was increased. This reflects the fact that changes in the exchange rate when Vx is less than VTCA have more of an influence on the rate of glutamate labeling. The effect of Vx on VTCA estimates was some 3-10 times greater for data set 1 than for the other two sets of data. This indicates that the error in VTCA will be higher when estimated from temporal C-4 and C-3 resonance areas alone.
The overall influence of these two effects can be seen in two ways.
Histograms (not shown) of the parameter estimates frequently revealed
distributions that were not statistically normal, underlining the
importance of reporting confidence levels and not standard deviations
or errors (7). Second, Fig. 5 shows the 5 and 95% confidence levels for the calculated
MO2 as a function of the value of Vx used
in the simulations and the data subset fitted. The difference between
confidence levels increased as
Vx decreased, and
those obtained from fitting C-4 and C-3 resonance areas were two and
one-half to three times greater than those found with the other two
data groups. Furthermore, the confidence level determined by analysis
of data set
2 (the C4D34 multiplet alone) tended
to be smaller than in the analysis of the combined data when
Vx
20. This is
consistent with the finding that the measured influence of
Vx on
VTCA (the
regression coefficients in Table 3) was the smallest for this range of
Vx.
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DISCUSSION |
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The kinetic model introduced in this paper has been evaluated as a possible method for determining oxygen consumption in intact tissue. It has been examined with the substrate mixtures chosen in the pioneering work of Chance et al. (1) and by collecting the data in the same method as used in that paper and also from hearts perfused inside the magnet. With a view to the type of NMR data that may be obtained in vivo, different subsets of the data have been tested to determine the suitability of estimating oxygen consumption with a limited amount of data. In addition, the effect of correlation between model parameters was assessed, because this influences the accuracy of the calculated oxygen consumption.
Estimating citric acid cycle flux. The
first part of this discussion will be limited to the results from the
analysis of data set
3 in Table 2. In hearts perfused with
glucose plus
[2-13C]acetate and
extracted for analysis, acetate provided ~95% of the acetyl-CoA
pool, and the citric acid cycle flux rate was estimated to be 11.3 µmol/g dry weight. The latter value agrees well with the literature:
in hearts perfused with acetate and glucose, Randle et al. (25)
reported a value of 14, whereas studies with acetate only as the
substrate have found ~11
µmol · min1 · g
dry wt
1 (31, 33, 35). These
values are somewhat higher than those estimated by Chance et al. (1;
8.3 µmol · min
1 · g
dry wt
1); this cannot be
explained by a lower workload in the hearts used in the Chance et al.
study, because the oxygen consumption was higher (30.2 in the Chance et
al. study vs. 24.7 µmol · min
1 · g
dry wt
1 here; Table 2). The
difference in
VTCA estimates is
not due to differences in modeling results: when the kinetic model of this study was used to analyze the time course of fractional
enrichments in Fig. 4 of Chance et al., the citric acid cycle flux
estimated (8.2 µmol · min
1 · g
dry wt
1, 5-95%
confidence levels: 7.5-8.9) agreed very well with that obtained by
Chance et al. (8.3 µmol · min
1 · g
dry wt
1, 5-95%
confidence levels: 7.9-8.7).
When the same analysis was performed with data collected from intact
hearts, the estimated citric acid cycle flux agreed very well between
the two sets of experiments (Table 2). The difference in the confidence
levels obtained from the analysis of extract data (0.6 µmol · min1 · g
dry wt
1) is smaller than
the range of values obtained from intact heart data (5.2 µmol · min
1 · g
dry wt
1). This is largely
a result of differences in data treatment. Measurements collected from
extracts were, by necessity, analyzed as one data set, and the
confidence levels calculated represent the uncertainty in parameter
estimates resulting from the fit. The data from intact hearts, on the
other hand, provided the complete time course for each heart and were
analyzed separately. The data range obtained by this method represents
both the variation between samples and the uncertainty in estimating
parameters from the data. The variation between samples is the larger
source of error for
VTCA but not
necessarily Vx.
When all of the data from intact hearts were combined into a single
data set and fit, the confidence levels were very similar to those
found in the analysis of extract data.
In hearts perfused inside the magnet with glucose plus
[3-13C]pyruvate,
pyruvate provided the majority (84%) of the substrate for oxidation
and VTCA was
estimated at 6.07 µmol · min1 · g
dry wt
1. This is lower than
that found in hearts perfused with acetate plus glucose, which can be
explained by the additional NADH produced by oxidation of pyruvate and
the lower oxygen consumption measured in this group (Table 2). When
these two factors are taken into account,
VTCA estimated
from hearts perfused with these two substrate mixtures agreed well with
each other. However,
VTCA determined in this substrate group was less than one-half of that estimated by the
Chance et al. study. As noted above, this discrepancy is not due to
modeling differences: when the glutamate measurements taken from Fig.
11 of Chance et al. were analyzed with the present model,
VTCA was
estimated at 10.6 (9.86-11.6)
µmol · min
1 · g
dry wt
1, in good agreement
with that estimated by Chance and et al., 11.9 µmol · min
1 · g
dry wt
1 (11.3-12.6).
The higher flux in this case may be partly explained by a higher oxygen
consumption (34.9 µmol · min
1 · g
dry wt
1) reported by
Chance et al. for this same substrate mixture.
Exchange between -amino- and
-keto
acids. It is apparent from Table 2 that the
Vx is not well
determined. This has already been noted by Chance et al. (1) in their
1983 report, where they described a "rather poorly determined value
for isotope exchange between
-ketoglutarate and glutamate." This
results simply from the nature of exchange reactions, where the system
is more sensitive to changes at relatively low flux rates. With the use
of this model, it was found that the exchange parameter is poorly
determined when rates are equal to or greater than the citric acid
cycle flux. A review of the literature indicates that values of
Vx determined by
fitting glutamate C-4 and C-3 enrichment curves (equivalent to our data
set
1) to kinetic models of varying
complexity have been quite variable. Chance and et al. reported
Vx-to-VTCA
ratios (Vx/VTCA)
of 2.8 (acetate + glucose) and 4.4 (pyruvate + glucose) (1), whereas
Weiss et al. (31, 32), with acetate only, reported values for
Vx/VTCA
ranging 0.85-2.5, and we reported a ratio of 1.0 (28). In a later
report (2), the original model of Chance et al. (1) was modified to
generate a more complex model that calculated
Vx based on
oxygen consumption, which was used as an input to the model. That
treatment gave much lower values for
Vx/VTCA
(~0.2). Work with 14C in the rat
heart has also yielded
Vx/VTCA
values of 1.0 (22) and 13 (25). In the rabbit heart, Lewandowski and
co-workers (11, 23, 33-35) have reported values for the
Vx/VTCA
that are generally around 1.0. The variability in
Vx was also found
to be large, i.e., 10.18 ± 6.57 µmol · min
1 · g
dry wt
1 (means ± SD),
from the analysis of data from individual hearts (33). This variation
is not significantly different from the range obtained here in intact
hearts with data set
1 (Table 2). Taken together, we
conclude that Vx
is not well determined in the heart with either
14C fractional enrichments or
13C measurements (enrichments
alone or combined with multiplet data).
Parameters estimated from different data subsets. The mean value for VTCA determined by kinetic analysis of 13C NMR data did not vary greatly among the three data subsets (Table 2). However, although the range of values was similar when derived from data sets 2 and 3, the range was consistently higher when analyzed with data set 1. As a result, a statistically significant difference in VTCA was found between hearts perfused with the two substrate mixtures when analyzed with data sets 2 and 3, but not when data set 1 was analyzed.
The poorer determination of VTCA when analyzed with data set 1 is likely due to correlation between VTCA and Vx. The mean and range of Vx values were higher when estimated with data set 2. However, because the degree of correlation and the influence of Vx on VTCA are the smallest with this data set (Table 3), the uncertainty in VTCA was similar to that found by analysis of data set 3. In contrast, the correlation between parameters and their influence on each other is stronger when data set 1 is analyzed.
The nature of the correlation between VTCA and Vx in the analysis of fractional enrichment data has previously been discussed by Yu et al. (33). We believe the correlation exists and is negative simply because both parameters tend to alter the rate of 13C appearance in glutamate C-4 and C-3 in a similar manner; thus an increase in one or another of these parameters will increase the rate at which enrichment levels reach steady state. In contrast, VTCA and Vx have different influences on the evolution of 13C multiplets. Increasing the citric acid cycle flux rate increases the rate at which 13C enters all intermediate pools. This, in turn, affects the rate at which multiply enriched molecules appear while causing a correspondingly more rapid decline in sparsely labeled glutamate. Hence, in the 13C spectrum C2Q, C3T, and C4D34 multiplets increase, whereas the singlets decline to their steady-state values more rapidly at higher VTCA. An increase in Vx, however, promotes the interchange of newly labeled intermediates with unlabeled pools early in the perfusion period, thus temporarily prolonging the existence of singly labeled molecules at the expense of multiply enriched products: the reverse of increasing the citric acid cycle flux rate. The net outcome of these two opposing effects is a reduction in the degree of correlation and a tendency toward positive correlation.
Calculating oxygen consumption from kinetic
parameters. In hearts perfused with glucose and
acetate, MO2
determined by analysis of data sets
2 and
3 gave very similar results (Table 2).
Although the mean M
O2
obtained from analysis of data set
1 was not very different, the range of
M
O2 values was significantly
greater than the other two data sets. The span was approximately five times larger (7.2 µmol · min
1 · g
dry wt
1) and
approximately two times larger (26.5) in the analysis of extracts and
intact hearts, respectively. Thus, even under ideal conditions (data
collected from extracts with high signal-to-noise), the addition of
multiplet data improved the precision of the
M
O2 estimate.
In hearts perfused with glucose plus pyruvate, the signal-to-noise was
poor and perhaps represents more closely what may be obtained in vivo.
This did not affect the analysis of data
sets 2 or
3 because the parameter ranges
actually were smaller in this substrate group. However, the range of
MO2 values (26.6 µmol · min
1 · g
dry wt
1) estimated by
analysis of data set
1 was four times that of the other two
data sets.
To conclude, the addition of 13C
multiplets to kinetic analysis of time-dependent data significantly
improves estimates of MO2 in
intact tissues. The principal reason for this benefit is the reduced
correlation between model parameters involved in calculation of
M
O2 in the heart.
Under conditions of reasonable signal-to-noise (data collected from
intact hearts perfused with acetate + glucose), the use of multiplet
data would allow one to detect a 60% increase or decrease in oxygen
consumption. Conversely, a twofold increase in
M
O2 would not be reliably
detected using the appearance of 13C in glutamate C-4 and C-3
alone. Hence, the use of multiplets will make it easier to distinguish
between different physiological and pathological states that influence
oxygen utilization. Not only is the addition of multiplet data
beneficial, we have demonstrated that analysis of temporal changes in
C4D34 alone can reliably predict
M
O2 in the heart. For
technical reasons, this may be a significant advantage for measuring
M
O2 in vivo. Because C4D34 is
obtained from a single glutamate resonance, narrow-band frequency excitation may be used and broad-band
1H decoupling is unnecessary. It
has already been shown that this multiplet is resolved in spectra of
human brain at 2.1 tesla (4). Thus, use of the C4D34 multiplet to
estimate M
O2 in vivo could extend recent studies that employed appearance of
13C in glutamate C-4 and C-3 (3,
19, 20, 26) while minimizing the error in
VTCA estimates
introduced by the uncertainty in
Vx (8).
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ACKNOWLEDGEMENTS |
---|
This work was supported by National Institutes of Health Grant HL-34557 and P41-RR-02584. R. A. Carvalho acknowledges a Ph.D. grant from Junta Nacional de Investigação Cientifica e Tecnológica Portugal (BD-3604-94).
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FOOTNOTES |
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The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact.
1 The program tcaFLUX is available to others as a service to the scientific community. Please contact the authors for further information.
Address for reprint requests and other correspondence: F. M. H. Jeffrey, The Mary Nell and Ralph B. Rogers Magnetic Resonance Center, Dept. of Radiology, Univ. of Texas Southwestern Medical Center, 5801 Forest Park Road, Dallas, TX 75235-9085 (E-mail: Mark.Jeffrey{at}emailswmed.edu).
Received 1 March 1999; accepted in final form 12 July 1999.
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