A mathematical model of compartmentalized neurotransmitter
metabolism in the human brain
Rolf
Gruetter1,
Elizabeth R.
Seaquist2, and
Kâmil
Ugurbil1,2,3
Departments of 1 Radiology, 2 Medicine, and
3 Biochemistry, Center for Magnetic Resonance Research and
General Clinical Research Center, University of Minnesota, Minneapolis,
Minnesota 55455
 |
ABSTRACT |
After administration of enriched
[1-13C]glucose, the rate of 13C label
incorporation into glutamate C4, C3, and C2, glutamine C4, C3, and C2,
and aspartate C2 and C3 was simultaneously measured in six normal
subjects by 13C NMR at 4 Tesla in 45-ml volumes
encompassing the visual cortex. The resulting eight time courses were
simultaneously fitted to a mathematical model. The rate of (neuronal)
tricarboxylic acid cycle flux (VPDH), 0.57 ± 0.06 µmol · g
1 · min
1,
was comparable to the exchange rate between (mitochondrial) 2-oxoglutarate and (cytosolic) glutamate (Vx,
0.57 ± 0.19 µmol · g
1 · min
1), which
may reflect to a large extent malate-aspartate shuttle activity. At
rest, oxidative glucose consumption [CMRGlc(ox)] was
0.41 ± 0.03 µmol · g
1 · min
1, and
(glial) pyruvate carboxylation (VPC) was
0.09 ± 0.02 µmol · g
1 · min
1. The
flux through glutamine synthetase (Vsyn) was
0.26 ± 0.06 µmol · g
1 · min
1. A
fraction of Vsyn was attributed to be from
(neuronal) glutamate, and the corresponding rate of apparent
glutamatergic neurotransmission (VNT) was
0.17 ± 0.05 µmol · g
1 · min
1. The
ratio [VNT/CMRGlc(ox)] was
0.41 ± 0.14 and thus clearly different from a 1:1 stoichiometry,
consistent with a significant fraction (~90%) of ATP generated in
astrocytes being oxidative. The study underlines the importance of
assumptions made in modeling 13C labeling data in brain.
nuclear magnetic resonance; glutamate; neurotransmission; in vivo
spectroscopy
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INTRODUCTION |
IN THE TRADITIONAL
CONTEXT of neuroscience, the brain's tasks are mainly
accomplished by the neurons, with the surrounding glial cells
performing simple, passive tasks of maintaining the milieu required for
optimal neurotransmission. However, the glial cells are more than just
passive components in neuronal function, in that they are intimately
involved in the process of neurotransmission through glial uptake of
glutamate (Glu) from the synaptic cleft (64, 77, 78). Glu
is the major excitatory neurotransmitter (62); it is
present in the mammalian brain in high concentrations and is
dynamically stored in presynaptic vesicles (73). Despite the high intracellular concentration of Glu, the extracellular concentration must be maintained very low (~0.004 mM) to avoid excitotoxicity. Presynaptic release of Glu into the synaptic cleft therefore requires efficient uptake mechanisms, which are achieved by
Glu transporters (2). Most of the metabolic evidence
suggests that uptake by glia is the most important process. Most of the Glu is in neurons (51), as is most of the glutaminase
activity (52), whereas astrocytes contain most of the
glutamine (Gln) (51), all of the glutamine synthetase
(42), and pyruvate carboxylase (63); they
predominantly take up and metabolize acetate (74). Early
studies showed that cerebral Glu metabolism is compartmentalized, involving two major metabolic pools of Glu (7, 16, 71). The large pool has been associated with the neuronal compartment and
the small pool with the glial compartment. Recent studies have again
supported the participation of glia in neurotransmission through rapid
clearance of Glu from the synaptic cleft into neighboring glia, on the
basis of conductance currents associated with Glu uptake
(6) and consequent metabolism. The uptake of Glu into the
astrocytes is associated with uptake of glucose into the glial compartment (39), thereby linking stimulated energy
metabolism between glial and neuronal cells during neurotransmission.
In summary, the glial-neuronal metabolic relationship mediated by
Glu-Gln interconversion appears to be essential for glutamatergic neurotransmission. This compartmentation of metabolic pathways into
both the glial and neuronal fractions extends to other systems as well
and may represent a fundamentally important biochemical process for
cerebral tissue. For instance, aspartate-like immunoreactivity was
recently found to colocalize with Glu in brain slices
(25), and aspartate aminotransferase stained the neuronal
compartment most intensely (75).
In recent years, 13C NMR spectroscopy of brain slices
(4), extracts (37, 64), and cell cultures
(9, 26, 46) has corroborated and extended the initial
findings of compartmentalized cerebral energy and Glu metabolism. Given
the specific compartmentation of critical enzymes for cerebral energy
metabolism, the use of 13C NMR spectroscopy offers an
unprecedented amount of highly specific information (17).
Such data are obtained from the amount of label incorporated into the
different positions of one or more molecules after administration of a
specifically labeled metabolic precursor, such as glucose, the major
source of energy in brain (3, 5, 57, 68). From the
specific labeling pattern, the relative and absolute fluxes through a
given pathway can be calculated. For example, the incorporation of
multiply labeled glucose into multiply labeled Glu at the C2 position
is indicative of pyruvate carboxylase flux at low enrichment
(37). The specific information gained by 13C
NMR spectroscopy can also be used to estimate rates of pyruvate recycling and of malic enzyme activity (17, 47). In
addition to the analysis of isotopomers (33, 40), which
has been in widespread use for analyzing 13C NMR spectra of
brain extracts (68), dynamic incorporation of label into a
given position can be observed. Metabolic rates can be quantitatively
extracted from the rate of label incorporation. These approaches
require by necessity that accurate temporal data be obtained in vivo,
but the derivation of metabolic rates depends more critically on the
specific model used to analyze the data and the assumptions made
(76). In brain, several models have been proposed, some of
which have been used to calculate metabolic rates (17, 23, 44,
67, 72). Given the compartmentation of cerebral enzymes,
such as glutamine synthetase, the landmark observation that Gln
labeling can be detected noninvasively in the brain (19, 21,
23) is thus of crucial importance to the study of metabolic
compartmentation, as pointed out in a recent review (3).
The aim of this study was to fully incorporate the maximum information
achievable in in vivo localized 13C NMR spectra of human
brain using state-of-the-art sensitivity and methodology
(20) available at 4 Tesla. The resulting measurement of
label incorporation into eight distinct resonances in amino acids was
predicted to provide metabolic rates that are less dependent on each
other. Overall, on the basis of known cellular compartmentation of
metabolism and enzymes, we sought to determine whether sufficiently specific information could be obtained from the human brain to permit
assessment of cellular cerebral energy metabolism in vivo. This
information can then be used further to serve as a basis for unraveling
the relative contributions of both cell types to brain function in
health and disease.
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MATERIALS AND METHODS |
Subjects.
Six healthy human subjects were studied after giving informed consent
according to procedures approved by the Institutional Review Board:
Human Subjects Committee. On the morning of study, subjects reported to
the Center for Magnetic Resonance Research (University of Minnesota) in
the fasting state. In preparation for the clamp procedure, an
intravenous catheter was placed antegrade in each forearm and
retrograde in a lower leg/foot. Arms and legs were warmed by placing
preheated pads and water-soaked towels around the lower extremities.
Somatostatin was infused into one arm vein at a progressively
increasing rate up to 0.16 µg · kg
1 · min
1 to
suppress endogenous pancreatic insulin and glucagon secretion (61). Dextrose (50% wt/vol D-glucose) was
infused into the other arm vein at a variable rate adjusted to maintain
target glycemia at 15 mM plasma glucose concentration. The infusion
procedures have been described previously (23).
Alterations in the glucose infusion rate were made on the basis of
plasma glucose concentration measured on a nearby glucose analyzer
(Beckman, Fullerton, CA) in blood samples taken from the foot vein
every 3-5 min (60). Additional blood samples were
obtained every 20 min for the later determination of plasma insulin
concentration, and both before and after the study for assessment of
plasma ketone levels. When the subject was ready for spectroscopic
study, a bolus injection of 30 g of [1-13C]glucose
was given as 50% D-glucose in water, with a fractional enrichment of 99% over 1-2 min. As in our previous study
(23), the plasma glucose was then clamped at the peak
level of glycemia (~15 mM plasma glucose concentration) by the
infusion of 10 g [1-13C]glucose (prepared as 20%
D-glucose in water with a fractional enrichment of 70%) at
a variable rate determined by the plasma glucose concentrations. After
administration of [1-13C]glucose, additional plasma
samples were collected every 10 min to be used for the determination of
plasma glucose enrichment by use of gas chromatography-mass
spectrometry (GC-MS).
Chemical assays and GC-MS.
Insulin was measured in serum that had been frozen within 30 min of
acquisition with the double-antibody method of Morgan and Lazarow
(50). Plasma insulin was not detected in our study. Absence of serum ketones was verified in the clinical laboratory by a
qualitative test based on the nitroferrocyanide reaction.
Analyses of the 13C enrichment in serum glucose were
performed by the University of Minnesota General Clinical Research
Center GC/MS Core Laboratory by use of the following standard
procedures. After deproteinization, the supernatants were purified by
chromatography, as previously described (8). The fraction
containing glucose was converted to the pentatrimethylsilyl
O-methyloxime derivative by a modification of the procedure
of Laine and Sweeley (35). After the trimethylsilyl
derivative was produced, analysis by GC-MS was performed on a
Hewlett-Packard 5973 MSD system equipped with an HP6890 series gas
chromatograph in the selective ion-monitoring mode. Ions at 160 and 161 were analyzed to determine the enrichment of 13C in carbon
1 of glucose.
13C MR spectroscopy.
All studies used a 4-Tesla magnet with a 125-cm bore, equipped with a
standard clinical body gradient coil and amplifier (Siemens AS25,
Erlangen, Germany). The magnet and gradient system was interfaced with
a spectrometer console (Varian, Palo Alto, CA) by use of a
manufacturer-supplied interface board. Subjects were positioned supine
on the patient bed above the surface coil. After coil tuning, MR
imaging was performed to determine localization for spectroscopy according to anatomical landmarks. Subjects wore earplugs to minimize gradient noise and were placed into the coil holder with cushions to
minimize head movement. Shimming of the identified region of interest
was performed using FASTMAP (19), which resulted in water
linewidths of 7-9 Hz.
To efficiently separate the proton (169 MHz) and the 13C
frequency (42.5 MHz), we used a three-coil design in which the circular polarized 1H radio frequency (RF) field was generated by
two distinct 14-cm-diameter coils driven by a quadrature hybrid. The
13C coil was a single-loop 9-cm-diameter surface coil. This
three-coil design was recently described elsewhere (1).
Observation of the Federal Drug Administration guidelines for power
absorption was verified using methods and procedures presented in
detail elsewhere (1, 20, 23). RF power for excitation,
polarization transfer, and decoupling was carefully calibrated using a
small sphere containing 0.5 ml of 13C-labeled formic acid
placed at the 13C coil center, as described previously (for
example, see Ref. 20). These calibrations were used to
ensure proper power settings for decoupling as well as to minimize RF
power needed for the experiment.
Localization was performed on the longitudinal proton
z-magnetization, which was transferred to the
13C magnetization using a semi-adiabatic polarization
transfer method, PRoton Excited
Carbon-13 Image SElected in vivo
Localized spectroscopY, or PRECISELY
(20), as described recently (23). Editing
delays were set to correspond to a heteronuclear coupling constant of JCH = 137 Hz.
Spectra were analyzed after 3-Hz apodization, zero-filling, and
fast-Fourier transform by use of the fitting algorithm supplied by the
spectrometer software. To reduce variability, linewidths of
13C-13C doublets were set to the linewidth of
the corresponding center peak, and the fitted frequencies of the
13C-13C doublets were fixed to be symmetrical
to the main resonance, according to the homonuclear
13C-13C coupling constants. After correction
for field frequency drift, the frequencies and linewidths of the fitted
peaks were determined on the basis of fit to a spectrum representing
the average of
60 min of data accumulation. This procedure was
justified on the basis of the observation of <3-Hz changes in
1H spectra (corresponding to <0.75-Hz changes in
13C spectra) in studies performed over similar time periods
with the identical equipment. Convergence of the fit procedure was verified by inspecting the residuals of the fit point by point.
Quantification of integrated 13C signals was performed
relative to the signals of N-acetyl-aspartate (NAA) at 22.7 (C6) and 54.0 ppm (C2) set to correspond to 0.12 mM on the basis of our previous observation of a stable NAA C2 signal at 54.0 ppm
(23). Stability of the NAA signals was verified for 2 h after start of the [1-13C]glucose infusion for both the
C2 and C6 resonances (data not shown). This calculation assumes that
the 1H saturation factors are identical in vivo, which was
supported by inversion-recovery nulled spectroscopy at 4 Tesla
(49) and the relatively long repetition time of 3 s.
Signal differences due to differential T2 were neglected,
because the measured linewidths of 2-3 Hz implied that
T2 is longer than 100 ms, which is much longer than the
T2 evolution time of the sequence (9 ms).
Modeling of compartmentalized neurotransmitter metabolism in the
human brain.
The time courses were used as the experimental data to fit the model
recently proposed in Ref. 23, which is
redrawn in Fig. 1A. Because
the scheme does not explicitly describe the mechanisms by which label
is scrambled in the tricarboxylic acid (TCA) cycle, we have
added the scheme in Fig. 1B.

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Fig. 1.
A: proposed model of cerebral compartmentation
based on published enzymatic compartmentation in the brain.
Left: glial compartment; right: neuronal
compartment. This figure is adapted from one in Ref. 23,
with the following abbreviations for metabolic fluxes:
CMRGlc, glucose consumption; VPDH,
neuronal tricarboxylic acid (TCA) cycle; VPC,
rate of pyruvate carboxylase;
Vg+VPC, glial pyruvate
dehydrogenase + VPC;
Vx, exchange between cytosolic amino acids and
mitochondrial TCA cycle intermediates; Vsyn,
glutamine synthetase; VNT, apparent rate of
glutamate neurotransmission; Vefflux, loss of
glutamine (Gln) from the glial compartment;
Vout, VLout, label
dilution and exchange of lactate across the blood-brain barrier;
Vgase, glutaminase rate;
, rate of Gln
flux from the astrocyte to the glutamatergic neuron. Also,
Lac3/Pyr, C3 of lactate and pyruvate; OAA2,3,
C2 & C3 of oxaloacetate; OG2,3,4, C2, 3, & 4 of
2-oxoglutarate (OG). B: scheme illustrating label scrambling
from [1-13C]glucose due to activity of the TCA cycle.
Label transfer from OG C3 to OAA C2 at the succinate level is modeled
by the bidirectional arrow between OAA C3 and OG C3. Note also the
distribution of label including flux through pyruvate carboxylase and
pyruvate dehydrogenase and the relationship with cytosolic amino acids.
Vx denotes the exchange between mitochondrial
TCA cycle intermediates and cytosolic amino acids. In neurons,
VPC = 0, and in glia, Aspartate (Asp) was
assumed to be negligible. Boldface indicates NMR-measurable molecules
and respective positions.
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|
The scheme in Fig. 1B explicitly accounts for potential
finite exchange between the amino acids in the cytosol and the TCA cycle intermediates in the mitochondrion. The differential Eqs. 5-21 that follow are derived by the generalized procedure
described in Ref. 23. Label scrambling in the amino acids
due to TCA cycle activity was modeled according to the scheme in Fig.
1B, derived as a special case of the general model by Chance
et al. (10).
Briefly, label derived from the C1 or C6 of glucose arrives at the C3
of pyruvate/lactate, where depending on whether the label enters the
TCA cycle via pyruvate carboxylase (flux VPC) or
pyruvate dehydrogenase (VPDH) reaction, it
ultimately is detected in the C4 or C2 position of Glu. Label
scrambling due to TCA cycle activity results in the C2 and C3 of
2-oxoglutarate (OG) receiving label from the C4 of OG (Fig.
1B). In neurons, VPC was neglected, and in astrocytes, conservation of mass required that the flux through
glial pyruvate dehydrogenase be equal or larger than
VPC, which was modeled by setting the flux
through glial pyruvate dehydrogenase to VPC + Vg, with Vg
0 (Fig.
1A), where Vg accounts for the difference in flux between glial pyruvate dehydrogenase and pyruvate carboxylase.
Label accumulation into Gln proceeds almost exclusively in glia because
of the exclusive localization of glutamine synthetase (EC 6.3.1.2) in
astrocytes (Fig. 1A).
The effect of a sizable brain glucose concentration on the isotope
kinetics cannot be completely ignored (22, 43). Therefore, we calculated the enrichment of brain glucose from the measurements of
plasma glucose concentration and isotopic fraction by use of the
reversible Michaelis-Menten model of glucose transport, which has been
shown to provide a more consistent depiction of brain glucose
concentrations and transport (12, 24). The differential equation describing the change in total brain glucose
[Gbrain(t)] and in 13C-labeled
brain glucose [13Gbrain(t)] is
given by
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(1)
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(2)
|
where Kt is the Michaelis-Menten constant
of glucose transport, Tmax is the corresponding maximal
transport rate, and CMRGlc is glucose consumption. For a
more detailed description see Ref. 24. Brain glucose is
metabolized by glycolysis to pyruvate, which is assumed to be in rapid
exchange with lactate, given the high activity of cerebral
L-lactate dehydrogenase (EC 1.1.1.27). We assumed cerebral
lactate to have the same isotopic enrichment in both cell types because
of the small lactate concentration and large distribution volume
(55), in agreement with a high lactate transport
efficiency (47). Therefore, only one single cerebral rate
of glucose consumption was taken into account; this, however, does not
assume that all glycolysis occurs in glia.
The rate of label incorporation into cerebral lactate is thus a
function of changing fractional enrichment of brain glucose and the
metabolic rate CMRGlc and the dilution/efflux
Vout (29)
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(3)
|
This equation assumes that Vout models
the exchange of label with unlabeled plasma lactate, whose fractional
enrichment is given by FELac, which was assumed to be 0.011 in this study. CMRGlc was set to 0.45 µmol
g
1 min
1, and oxidative CMRGlc
[CMRGlc(ox)] was set to 0.97 CMRGlc. Equations 1-3 were solved using a
fourth-order Runge-Kutta algorithm based on the measured time course of
plasma glucose and its fractional enrichment, yielding the time course
of fractional enrichment for lactate C3,
Lac3(t)/Lac.
Vout is assumed to be equivalent to label
dilution due to pentose phosphate shunt activity and label dilution at
the lactate level (32) and, in principle, also at the
acetyl-CoA level. Because the brain relies almost entirely on glucose
for energy metabolism, and because fatty acid uptake is small and
ketone bodies were not detected in our study, we assumed that dilution at the acetyl-CoA level in brain is negligible. Net loss of
lactate can be modeled by assuming VLout
Vout. In the resting brain, VLout ~ Vout, or
almost complete oxidative metabolism of glucose, defined as
2 CMRGlc = 2 CMRGlc(ox)
VLout + Vout.
In our scheme (Fig. 1A), total CMRGlc(ox)
(defined as the rate of glucose equivalents entering the TCA cycle) is
related to the fluxes in glial and neuronal TCA cycles by the
relationship
|
(4)
|
where Vg denotes the flux through glial
pyruvate dehydrogenase corresponding to complete oxidation of pyruvate,
i.e., Vg + VPC is the
total flux through glial pyruvate dehydrogenase (as outlined in the
scheme in Fig. 1A), VPDH is the
analogous flux in neurons, and VPC is the rate
of net oxaloacetate (OAA) and net citrate formation (anaplerosis). The
net carbon compound formed is in our steady-state model removed by net
consumption of OG and biosynthesis of Gln.
Throughout this section, the superscript 13 denotes the 13C
label, and the numeral subscripts indicate the position at which the
label is observed, e.g., 13Glu4 denotes the sum
of all isotopomers of Glu with 13C label at the C4
position. The derivation of these and the following differential
equations follows from tracer kinetics and is mathematically equivalent
to the procedure outlined previously (23) and used in many
earlier studies (10, 14, 40, 57).
Because the gluconeogenic capacity, as well as the capacity to generate
pyruvate or lactate from amino acids, is generally small in the
neuronal compartment (38), we assumed that the net flux of
Glu carbon skeletons into the neuronal TCA cycle was negligible
compared with VPDH.
The NMR signal represents total tissue Glu concentration, (and Gln,
conversely) of which the vesicular neurotransmitter pool is generally
viewed to constitute a small fraction. Neglecting the contribution of
extracellular Glu (0.004 µmol/g) to the NMR signal, the neuronal Glu
pool [Glu(n)] can be partitioned into a vesicular (small)
neurotransmitter signal GluNT plus a metabolic pool
Glumet. Based on studies showing 1) rapid
redistribution of label between vesicular and extravesicular Glu
(73), 2) that isolation of Glu-containing
vesicles requires rapid isolation procedures (58), and
3) that influx of Glu results in simultaneous efflux of Gln
from glial cells (34, 48), we assumed that the exchange
between Glumet and GluNT is rapid compared with
, the rate of
Gln flux from the astrocyte to the glutamatergic neuron. For
definitions of symbols, see also Fig. 1A. In this case, the
label incorporation into the observed Glu signal will reflect the label
incorporation into the neurotransmitter Glu pool, GluNT.
The lack of metabolic pathways branching off at the level of neuronal
Gln, or Gln(n), and the metabolic steady-state requirement
that no net concentration changes occur, e.g.,
dGln(n)/dt = 0, imply that the rate across the
glial-neuronal interface be
. Under these
assumptions, the rate of unidirectional Glu transport out of the neuron
is equal to
, and
the rate of OG and
labeling
can be written, accordingly, as
|
(5)
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|
(6)
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|
(7)
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(8)
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By equating the forward and backward exchange rates between Glu
and OG, we have assumed that net flux of neuronal Glu into the neuronal
TCA cycle is negligible compared with the unidirectional exchange rates
(Vx) that describe the exchange rate between
(mitochondrial) OG and (cytosolic) Glu (see also Fig. 1). Therefore,
Vx is a composite figure that describes the
combined effect of glutamate dehydrogenase, aspartate transaminase, and
transport across the mitochondrial membranes. Given the slow
incorporation of nitrogen into Glu compared with the glutamine amide
group (15), glutamate dehydrogenase flux must be small
compared with the flux through glutamine synthetase; it was, therefore,
neglected. This assumption is also consistent with studies showing a
reduced Glu concentration when aspartate transaminase was inhibited
(11). The differential equations for Glu3 are
equivalent to those for Glu4 and are simply derived by
replacing the subscript. Likewise, analog equations can be written for
Glu2 simply by replacing the subscript. Label incorporation into OAA, which is in exchange with Asp, is described by the following equations
|
(9)
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|
(10)
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|
(11)
|
|
(12)
|
The lack of metabolic pathways branching off at neuronal Gln was
based on observation of little or no Gln efflux into the medium of
cultured neurons, as shown in, for example, Ref. 38. The
rate of change in
is thus given by
|
(13)
|
and likewise for the other positions in Gln(n),
because the glutaminase reaction does not change the positional
13C labeling between Gln and Glu.
Glial metabolism: glutamine synthetase and pyruvate carboxylase.
In reference to the majority of evidence that links the Glu/Gln
interrelationship to excitatory neurotransmission (77), we
have denoted the rate from Gln(n) to Glu(n) and
from Glu(n) to Glu(g) as
, the apparent
rate of neurotransmission. In view of the low glutaminase (EC 3.5.1.2)
activity in glia (28), we assumed that the glutaminase
rate (Vgase) is negligible compared with
. Although we
assumed in this study that Vgase = 0 (as
indicated by the dashed arrow in Fig. 1A), the equations
below are written to allow for some Vgase.
The steady-state requirement
assumes that anaplerosis leads to glial loss of Gln. Loss of Gln
from the glial cell to the extracellular space is, in this case,
modeled by the term Vefflux = VPC. The rate of
labeling is thus given by
|
(14)
|
and equivalent equations can be written for the 2 and 3 positions of glial Gln simply by replacing the subscript 4 with 2 and
3, respectively
|
(15)
|
|
(16)
|
In addition to label derived from neuronal Glu(n),
label can be incorporated into glial glutamate [Glu(g)]
from the glial TCA cycle, the rate of which is given by
Vg (Fig. 1). Pyruvate carboxylase (PC, EC
6.4.1.1) transfers label from pyruvate C3 to OAA C3 in the glial
compartment. In this model, reverse flux from OAA to fumarate was
neglected, on the basis of previous reports suggesting a substantial
difference in labeling at the C1 and C4 position of OAA
(31), which is supported by differential labeling of Glu
C2 and C3 in astrocytes (41). Neglecting any backflux to
fumarate underestimates the pyruvate carboxylase flux when assessed
from the differential labeling of the C2 and C3 positions in Glu and
Gln. Given the small pool size of cerebral OAA and most TCA cycle
intermediates, label equilibration is assumed to be relatively fast
until it reaches OG. The small pool size of glial Glu(g)
relative to the high activity of the malate-aspartate shuttle is
assumed to result in rapid label equilibration of Glu(g)
relative to OAA(g).
is also labeled
from neuronal
as
well as from glial
on
subsequent turns of the TCA cycle.
The rate of lactate labeling is calculated as described in Eq. 3 and set to that of pyruvate, which is the label precursor for
acetyl-CoA; thus
|
(17)
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(18)
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(19)
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(20)
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(21)
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Numerical procedures.
The cerebral Glu(g) + Glu(n) pool size
labeled by [13C]glucose was estimated at 5.7 µmol/g, in
agreement with previous studies (53, 54, 56), from the
amount of 13C-labeled Glu signal divided by the fractional
enrichment determined from the 13C-13C
isotopomers as described previously (21, 37, 40).
Likewise, the cerebral aspartate pool was estimated at 1.5 µmol/g,
and this neurotransmitter was assumed to be mainly in the neuronal compartment.
The set of differential equations (see Eqs. 5-21) was
solved, and
13[Glu(n)+Glu(g)]2,3,4
and
13[Gln(n)+Gln(g)]2,3,4
were simultaneously fitted using commercially available software (SAAM
II, The SAAM Institute, Seattle, WA) to the separately measured time
courses of Glu C4 and Gln C4 as well as the C2 and C3 positions. In
addition, we included the combined signal of Asp C2 and C3 in the
modeling, Asp23, because the smaller pool size of Asp makes
the labeling curve less dependent on the exchange Vx compared with the rate of OAA labeling.
All metabolite pools [except for cerebral glucose
(Glcbrain)] were assumed to be constant during the
duration of the [13C]glucose infusions: 14% of the total
glutamate pool was assumed to be in the glial compartment; see Ref.
17 and references therein. Consistent with most evidence
(51), we assumed that the neuronal Gln,
Gln(n), was small (e.g., 0.2 µmol/g), and we verified
that this assumption did not influence substantially the labeling time
course of Gln. The glutamine pool, Gln(n) + Gln(g), turned over by [13C]glucose
metabolism, was estimated at 1.7 µmol/g with the same methods as for
Glu. We assumed cerebral OG and OAA pools to be very small,
i.e., OG(n) = OG(g) = OAA(n) = OAA(g) = 0.1 µmol/g. The
cerebral lactate pool was set to a fixed value of 1.0 µmol/g. The
pool sizes of other glycolytic and TCA cycle intermediates were also
assumed to be small and without effect on isotope kinetics; they were
validated to be without effect on the conclusions of this paper up to a
total mass of several micromoles per gram. On the basis of our
inability to detect signals from TCA cycle intermediates, even when
summing spectra over extended measurement periods from all measured
subjects, we assumed the pool sizes to be below 0.05 µmol/g, which we
verified to have a negligible impact on the calculated fluxes (not shown).
The following rates were varied to achieve the best fit to the data:
VPDH, Vx,
Vout, VNT,
Vg, VPC. All fluxes were
constrained to be positive in the fitting process. To take into account
that the malate-aspartate shuttle is the major mechanism by which the brain maintains the cytosolic redox state under normoxic conditions, we
constrained the exchange rate Vx to be equal or
greater than the pyruvate dehydrogenase flux,
VPDH.
 |
RESULTS |
The improved sensitivity achieved at 4 Tesla was used to reduce
the volume of interest being investigated and to achieve localization to a metabolically more homogenous area in the human brain. Figure 2 illustrates the excellent sensitivity
achieved with our approach. The spectrum was acquired 1 h after
the start of [1-13C]glucose infusion and represents data
collection corresponding to 45 min from a volume of 45 ml. In addition
to the three dominant resonances from Glu, resolved peaks were detected
from the corresponding three positions in Gln, and resonances from NAA
and GABA were routinely observed. Furthermore, the resolution and
sensitivity afforded the simultaneous detection of the homonuclear
isotopomers in all three Glu resonances, C2, C3, and C4.

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Fig. 2.
13C NMR detection of
label incorporation into cytosolic amino acids in a 45-ml volume in the
human occipital lobe at 4 Tesla. This is a representative spectrum
obtained from a 3 × 3 × 5-cm3 volume in the
human visual cortex in 45 min. Resonance assignments are as follows:
Glu C2 at 55.6 ppm, Gln C2 at 55.0 ppm, N-acetyl-aspartate
(NAA) C2 at 54.0 ppm, Asp C2 at 53.7 ppm, NAA C3 at 40.5 ppm, GABA C4
at 40.45 ppm, Asp C3 at 37.6 ppm, GABA C2 at 35.3 ppm, Glu C4 at 34.2 ppm, Gln C4 at 31.7 ppm, Glu C3 at 28.0 ppm, and Gln C3 at 27.7 ppm. In
addition to these resonances, those ascribed to the homonuclear
13C-13C coupling were readily detected at
positions of all Glu resonances (brackets). The spectrum was processed
with a mild Lorentz-to-Gauss apodization (3 Hz) and is shown without
baseline correction.
|
|
The spectral data shown in Fig. 2 exemplifies the spectral resolution
and suppression of extraneous lipid signal achieved in our study. The
resonance intensity for Glu C2, C3, C4 and Gln C2, C3, C4, as well as
Asp C2 and C3, was determined with a temporal resolution of 15 min,
resulting in eight simultaneously recorded time courses of label
incorporation into cytosolic amino acids. To improve sensitivity, the
labeling curves for aspartate C2 and C3 were averaged and accordingly
fitted. Intersubject reproducibility of 13C label
incorporation was evaluated from the standard deviation, which was on
average 0.1 µmol/g.
One major goal of this study was to assess the rate of label exchange
between the cytosolic amino acids and their mitochondrial TCA cycle
counterparts. This exchange is mediated by the malate-aspartate shuttle
(Fig. 3A), which provides a
mechanism by which Asp and Glu can be labeled from the TCA
cycle through transport of Asp and Glu by the Asp/Glu antiporter
(11, 36). On the basis of this mechanism, we analyzed the
exchange between Asp and OAA as well as between Glu and OG with a
single reaction rate, Vx. The use of the label
incorporation into the amino acids ideally assumes that the rate of
label incorporation into the cytosolic amino acids is a good
approximation of label incorporation into the metabolic counterpart,
e.g., OG in the mitochondrion. However, as stated previously, this
assumption generally is true only when the exchange between OG and Glu
is fast compared with the TCA cycle flux (45). In
addition, as shown in Fig. 3B, the accuracy by which the
amino acid represents the label incorporation into the TCA cycle
intermediate also depends on the relative pool sizes. For example, Asp,
whose concentration is at least three times less than that of Glu, much
more closely represents the fractional enrichment of OAA (dotted curves
in Fig. 3B) at an otherwise equal relative rate
Vx/VPDH, whereas Glu
labeling is a much poorer indicator of the corresponding OG labeling
(solid curves in Fig. 3B). The effect of assuming widely
varying Vx had a quantitatively negligible impact on calculating the TCA cycle flux from the measurement of Asp
C2+C3 (Asp23) alone (second column in Table
1). On the other hand, the measurement
from Glu C4 (Glu4) alone illustrates a more profound effect
of the assumed value of Vx on the derived TCA
cycle flux, as shown in the third column of Table 1.

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Fig. 3.
A: fluxes participating in the
malate-aspartate shuttle (adapted from Stryer). The overall flux
between mitochondrial OG/OAA and cytosolic Asp/Glu is modeled by
Vx. B: to illustrate that the pool
size does affect the fidelity by which the corresponding amino acid
reflects the rate of labeling of its corresponding TCA cycle
intermediate, the label in Asp relative to OAA (dotted curves) was
compared with the label in Glu C4 relative to OG C4 (solid curves) for
Vx = 5.7 and 0.55 µmol · g 1 · min 1,
assuming VPDH = 0.7 µmol · g 1 · min 1.
Concentrations of the participating amino acids were assumed in this
simulation to be 5.7 µmol/g for Glu and 1.5 µmol/g for Asp.
|
|
The model proposed in Ref. 23 and shown in the scheme in
Fig. 1A was fitted to the curves showing label incorporation
into Glu C4, C3, and C2 as well as Gln C2, C3, and C4 and Asp C2 and C3
(Fig. 4). The fits resulted in a
covariance matrix whose normalized off-diagonal elements were in
magnitude <0.6 for all but one element. The resulting fitted fluxes
are shown in Table 2, along with the
normalized covariance matrix in Table 3.
Because glucose is the dominant fuel for generation of energy in brain,
the fitting was constrained, in that Vx was not
allowed below the minimum required flux by the malate-aspartate
shuttle, which was assumed to be VPDH, where the
fitting process converged.

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Fig. 4.
Observed rates of label incorporation into the main amino
acids Glu, Gln, and Asp. Lines represent the best fit of model shown
schematically in Fig. 1A.
|
|
Provided that flux through glutamine synthetase is exclusively due to
the flux from neuronal Glu(n), Gln should be equally
labeled relative to Glu at each carbon atom. Table
4 shows the relative amount of
13C NMR signal at the C2, C3, and C4 positions determined
60-120 min after the start of the glucose infusion, which was
found to be measurably higher at the C2 compared with the C3 and C4
positions (P < 0.01). In addition to the different
isotopomer populations in Gln relative to Glu, fitting to the label
incorporation curves also indicated a substantial contribution of
pyruvate carboxylase to the total flux through glutamine synthetase.
 |
DISCUSSION |
In the present study we have for the first time comprehensively
measured and analyzed multiple curves of label incorporation into
resonances from three different amino acids in the human brain. The
inclusion of the amino acid Asp with a much lower concentration than
Glu helped to reduce the mathematical covariance between fitted fluxes
compared with that present in previous studies (45, 76),
as judged from Table 3 and Fig. 3B. Even higher sensitivity can be obtained, for example by higher static field strength (such as 7 Tesla) and by increasing the fractional enrichment of the amino acids
through the use of multiply labeled glucose, e.g., [1,6-13C2]glucose. It should then be possible
to achieve much more robust measures of TCA cycle flux than through the
measurement from Glu alone, as suggested by the comparisons presented
in Fig. 3B and Table 1. Nevertheless, some of the advances
presented in this study were achieved on the basis of the improved
sensitivity afforded by the use of a human 4-Tesla system. The
sensitivity shown in Fig. 2 obtained from a 45-ml volume in 45 min is
comparable to that of a 144-ml volume at 2.1 Tesla in 60 min
(65). This illustrates the substantial gain in sensitivity
(approximately threefold) achieved at 4 Tesla compared with 2.1 Tesla.
The reduced volume size measured in this study currently is the
smallest reported for this type of experiment. Thus partial volume
effects were smaller because of a higher contribution of gray matter to
the overall signal. In addition to the size, the location of the voxel assured that signals were acquired predominantly from gray matter, consistent with the very high cerebral blood flow and the high metabolic glucose consumption rate measured by fluorodeoxyglucose and
[11C]glucose positron emission tomography (PET) in this
region (70). Furthermore, 1H MRS
(59) consistently showed a choline-to-creatine ratio
associated with a predominantly gray matter composition of the human
occipital lobe (unpublished data), according to Hetherington et al.
(27). We therefore assumed that interindividual
differences in tissue composition were minimized for the volumes used
in the present study.
Our study indicates a rate of neuronal TCA cycle flux
(VPDH, Fig. 1A) of 0.57 µmol · g
1 · min
1 (Table
2). The small but measurable glial pyruvate dehydrogenase flux,
VPC + Vg, is consistent
with active glial metabolism of acetate (74).
Incorporating the small glial TCA cycle flux rate of 0.06 µmol · g
1 · min
1 and the
rate of pyruvate carboxylase, VPC, of 0.09 µmol · g
1 · min
1, an
oxidative glucose consumption rate [CMRGlc(ox)] of
0.41 ± 0.03 µmol · g
1 · min
1 was
derived, which is in excellent agreement with PET measurements of total
CMRGlc in resting gray matter (70) and the
nearly complete oxidation of cerebral glucose under resting conditions.
In principle, the metabolic relationship between Glu and Gln implies
that the relative distribution of label in the different positions of
Gln must be the same as that of Glu, with the assumption that the large
(neuronal) pool is the dominant source of label for the (glial) pool of
Gln. Any differential extent of labeling in brain Gln therefore implies
that other, glial, reactions, such as pyruvate carboxylase, must
contribute significantly to the flux through glutamine synthetase. In
this investigation, we extended our previous work to measure pyruvate
carboxylase activity in the human brain by use of a single,
isotopically enriched substrate that can be obtained at comparatively
low cost, namely D-[1-13C]glucose. Our
measurement is in excellent agreement with previous studies using
D-[U-13C6]glucose
(37) and our previous report from larger volumes in the
human brain (23). The 95% confidence interval for the rate of pyruvate carboxylation in this and our previous study (23) overlaps well with the upper limit of a more recent
study, which assessed the rate of anaplerosis from the Glu C4 and Gln C4 resonances only (65). However, when label incorporation
is measured into only one or two positions, the complexity of cerebral energy metabolism is likely to result in ambiguous numerical solutions because four different fluxes were simultaneously fitted. Consequently, the previous assertion of a very small activity of pyruvate carboxylase must be considered with caution.
It should be stressed in this context that our modeling does not assume
that the rate of pyruvate carboxylation must result in a net loss of
Gln into the bloodstream. Because Gln is the single most concentrated
amino acid in the cerebrospinal fluid, it can be metabolized by many
other reactions and compartments. Regardless of the specific
quantitative value of pyruvate carboxylation, the consistent
observation that isotopomers of Glu and Gln are not identical suggests
that the Glu/Gln interconversion is not the sole source of flux through
glutamine synthetase, in that pyruvate carboxylation can contribute
substantially to the labeling pattern in glial Gln. In fact, our study
suggests that the flux from (neuronal) Glu to (glial) Gln is only on
the order of 41 ± 14% of the oxidative glucose consumption,
which is much lower than the 1:1 stoichiometric relationship that has
been claimed on the basis of analysis of C4 time courses only in whole
rat head studies (67). It should also be emphasized that
pyruvate carboxylation that leads to net formation of Glu, and
eventually Gln, is energetically favorable, because each Gln molecule
synthesized from glucose via pyruvate carboxylase (one-half of the
glucose is used in the form of pyruvate for formation of OAA; the other one-half is used for the formation of acetyl-CoA needed for the net
formation of citrate required to generate the extra OG required for the
net synthesis of Gln) generates a total of 4 NADH molecules (two are
produced by glycolysis, one by pyruvate dehydrogenase, and one by
isocitrate dehydrogenase, and two ATP are formed by glycolysis and two
are used by PC and glutamine synthetase), resulting in a net formation
of ~10 ATP molecules (assuming a P/O ratio of 2.5), thereby removing
two
, which is an energetically highly favorable reaction compared with the purely anaerobic combustion of glucose. Including the glial TCA cycle flux of
Vg = 0.06 µmol · g
1 · min
1 (Table
2), we calculate an oxidative ATP production of
Vg × 32 + VPC × 10, which represents 87 ± 5%
of the glial ATP generation, because the term CMRGlc × 2 is added when we assume that all of the glycolysis is confined to
the glial compartment. This calculation results in 3 µmol · g
1 · min
1 of ATP
produced in the glial compartment, a rate that can easily sustain the
energy requirements for maintaining glutamatergic neurotransmission by
removal of extracellular Glu via energy-dependent Glu transporters
(39), because the VNT of 0.17 µmol · g
1 · min
1 (Table 2)
requires ~0.35
µmol · g
1 · min
1 of ATP
for glutamine synthetase and the Na-K pump. An important consequence of
the measured energetics is that it underlines the importance of coupled
glial energy metabolism to that in neurons, as previously pointed out
by Magistretti et al. (39). However, it also stresses the
importance of oxidative metabolism, in that even minor fluxes in
oxidative glucose combustion can easily produce more ATP than the much
larger flux through glycolysis, even in glia (18).
In neurons, if glial lactate is assumed to be the major energy source,
the rate of neuronal ATP generation (i.e., 30 × VPDH) is 17 µmol · g
1 · min
1,
suggesting that, although glial oxygen consumption is significant, it
is a minor component of total brain oxygen consumption, contributing one-fifth to one-seventh of the oxygen consumption measured by 13C MRS.
Ideally, it is desirable to have a sufficiently large metabolic pool
directly associated with the metabolic reactions, as is the case, e.g.,
for lactate in tumors (69). In the case of the TCA cycle,
however, it appears that mitochondrial TCA cycle intermediates are
below detectability in vivo. This requires the detection of isotope
kinetics via the amino acids, which are in exchange with the TCA cycle
intermediates. Of critical importance in this regard is the delay by
which the isotope labeling kinetics of the (cytosolic) amino acid lag
behind those of the associated (mitochondrial) TCA intermediate.
Consider, for instance, the two pairs OAA/Asp and OG/Glu: it is clear
that the rate of exchange Vx relative to the
pool size dictates to what extent the isotope kinetics in the amino
acid reflect those of the associated intermediate. Hence, for a given
Vx, Asp kinetics approximate those of OAA
approximately four times faster than the kinetics of Glu mimic those of
OG (Fig. 3B) because of the approximately fourfold lower Asp
pool size.
Previous studies have focused on the question of whether the rate of
label exchange between cytosolic Glu and mitochondrial OG is fast
compared with the TCA cycle rate, VPDH
(44, 45, 66, 76). In the heart, this ratio was shown to
vary and to be closer to 1 (66, 76). This appears also to
be the case in skeletal muscle (30). In contrast, a report
in brain estimated Vx at 57 µmol · g
1 · min
1
(44, 45). Such a high rate of exchange of negatively
charged OG or Glu represents a rather high rate of exchange of ions
that must occur in the presence of the electrochemical gradient.
Our exchange rates are clearly lower than those reported in Refs.
44 and 45, which were based on early studies
performed in the late 1980s and early 1990s. For example, the
measurements were performed in large volumes encompassing a significant
fraction of the brain. Because of the complexity of the modeling and
scarcity of experimental detail in these early studies and differences in modeling, it is difficult to pinpoint exactly the reason why our
results are much lower. The early modeling studies in brain apparently
did not involve simultaneous fitting of all measured time courses, as
judged from the absence of a covariance matrix or discussion thereof,
and from the absence of a described total cost function. Furthermore,
the sensitivity of the TCA cycle flux on the precise value of
Vx has not been reported in brain. As pointed
out by others (76), the assessment of
Vx from Glu results in a large covariance
between VPDH and Vx, and
this covariance may have contributed to some numerical inaccuracy. In
contrast, our simulations shown in Table 1 suggest that the measurement of Asp-labeling kinetics alone can greatly reduce the influence of
Vx on the measured TCA cycle rate. Therefore,
the measurement of Asp kinetics allows in the fitting process a rather
robust measurement of the TCA cycle rate, which (once known) allows a more precise measurement of Vx. A similar
approach has been applied in the heart, where oxygen consumption
measurements were combined with Glu turnover to achieve excellent
quantification of Vx by elimination of the large
numerical covariance (76), whereas in Refs.
44 and 45, the reported errors in
Vx are high.
The exchange between OG and Glu on one hand and between Asp and OAA on
the other hand is also an integral component of the malate-aspartate
shuttle, which transports the two NADH produced by oxidative glycolysis
into the mitochondrion to maintain the cytosolic redox potential (Fig.
3B). Therefore Vx cannot be smaller than VPDH, inasmuch as the glycerol phosphate
shuttle plays a quantitatively minor role in maintaining the cytosolic
redox potential in brain. Therefore, the TCA cycle rate was assumed to
provide a lower limit for the exchange rate Vx
(Fig. 1B). We also used the fact that isotope
kinetics in a detected amino acid mimic the isotope kinetics in the
corresponding TCA cycle intermediate much better if the pool size is
reduced, as illustrated in Fig. 3A. Therefore, we also
incorporated Asp labeling in our analysis, in addition to Glu and Gln.
The resulting exchange rate had a skewed error distribution to higher
values but was statistically not different from the theoretical minimum
afforded by VPDH. A low rate of exchange between
OG and Glu on the order of the flux through pyruvate dehydrogenase
implies that the malate-aspartate shuttle is a substantial mechanism by
which label is exchanged between the cytosolic amino acids Glu and Asp
and their metabolic partners in the TCA cycle. This points to the
potential that the rate of exchange between Glu and OG can change under
widely varying metabolic conditions and thus cannot a priori be assumed
to be at a constant high level.
Recently, it has been postulated that the rate of glutamatergic action,
assumed to correspond to the rate of neuronal Glu uptake into glia and
interconversion to Gln (also termed the glutamate-glutamine "cycle") is stoichiometrically related to the oxidative glucose consumption, CMRGlc(ox). In our study, this ratio was found
to be substantially lower than the 1:1 ratio reported in rat brain (57, 67). The differences can potentially be ascribed to
two assumptions in that study, namely that turnover of Glu C4 was assumed to represent total CMRGlc(ox) and turnover of Gln
C4 was assumed to represent exclusively the glutamate-glutamine
"cycle." Indeed, in our study we find that when the flux through
glutamine synthetase, Vsyn, was correlated with
the oxidative glucose consumption, CMRGlc(ox), a
ratio of 0.8 ± 0.2 was calculated that is much closer to the
reported relative rates. However, the contribution of pyruvate carboxylase needs to be subtracted from the flux through glutamine synthetase, resulting in a substantial reduction of this ratio. In this
calculation, it should be noted that nonoxidative contributions to the
overall flux through hexokinase, glycogen metabolism (13), as well as metabolism of GABAergic neurons, have not been taken into
account, which would lead to an even larger discrepancy between the ATP
produced by the glial compartment and the ATP required for the Glu-Gln
cycle. Furthermore, it has been shown that astrocytes can increase
their oxygen consumption after glutamate uptake (18). Nevertheless, it is quite possible that some form of monotonic relationship exists between energy metabolism and glutamatergic action,
yet the precise relationship still remains to be fully characterized.
The presented results can depend on the assumed distribution of
glutamate between the glial and neuronal compartments. For example, the
assumed intercellular distribution of glutamate has a strong effect on
the calculated rates (Table 5). The
parameter that was systematically varied was
, which was defined
through the following relationships: Glu(g) =
Glutot, Glu(n) = (1
Glutot), where Glutot = Glu(g) + Glu(n). Likewise, the effect of
changing the cellular distribution of glutamine was shown by varying
the parameter
, defined by the relationships
Gln(n) =
Glntot,
Gln(g) = (1
Glntot), where
Glntot = Gln(g) + Gln(n),
which was without effect on the modeling (Table
6). However, even the assumption
that all but 3.3% of the metabolic glutamate pool is in neurons does
not affect our suggestion that the relationship between glutamatergic
action and glucose consumption is not stoichiometric, because this
relationship increased only to ~0.6, oxidative generation of ATP in
astrocytes decreased to ~82%, and glial relative to neuronal ATP
generation was reduced to ~10%. Interestingly, in all simulations,
the total oxidative glucose consumption remains a very stable
measurement. The proposed modeling is subject to further refinement,
but we think we have attempted the most complete modeling with the
least number of assumptions to date. Our study, therefore, underlines
the importance of making such assumptions in modeling complex
biological data, and the recognition that previous models based on
simpler data need to be considered with appropriate caution.
We conclude that pyruvate carboxylation may be a significant
contributor to the flux though glutamine synthetase in the human brain
in vivo. Glutamatergic action contributes to the flux through glutamine
synthetase, but we conclude that, at rest, oxidative glucose
consumption is not necessarily 1:1 stoichiometrically correlated with
glutamatergic action. Finally, we conclude that the exchange of label
between 2-oxoglutarate and glutamate may be affected by the cellular
energy status.
 |
ACKNOWLEDGEMENTS |
This study was supported by National Institutes of Health Grants
RR-08079 (K. Ugurbil) from the Biotechnology Resource Program and
RR-00400 from the Clinical Research Center program of the National
Center for Regional Resources, R01-NS-35192 (E. R. Seaquist), R01-NS-38672 (R. Gruetter), and a grant from the Whitaker Foundation (R. Gruetter).
 |
FOOTNOTES |
Address for reprint requests and other correspondence: R. Gruetter, Center for MR Research and General Clinical Research
Center, 2021 6th St. SE, Minneapolis, MN 55455 (E-mail:
gruetter{at}cmrr.umn.edu).
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. Section 1734 solely to indicate this fact.
Received 7 June 2000; accepted in final form 22 February 2001.
 |
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