INVITED DISCUSSION
Measurement of gluconeogenesis and mass isotopomer analysis based
on
[U-13C]glucose
Jerry
Radziuk1 and
W.-N. Paul
Lee2
1 The Ottawa Hospital and the
University of Ottawa, Ottawa, Canada K1Y 4E9; and
2 Department of Pediatrics,
Harbor-University of California Los Angeles Medical Center,
Torrance, California 90502
 |
ABSTRACT |
Two methods of measuring rates of
gluconeogenesis based on label redistribution after the introduction of
[U-13C]glucose into
the whole body are examined. These methods are compared with methods
previously derived for carbon-14 tracers. It is shown that the three
approaches (stoichiometric, dilution, and combinatorial) are
equivalent, provided the same set of assumptions are used. Barring a
factor of two [see Am. J. Physiol. 270 (Endocrinol. Metab. 33): E709-E717, 1996], the
differences (~10-15%) in the carbon-based dilutional and the
molecule-based estimates of the rate of gluconeogenesis from published
isotopomer data likely arise from small differences in the assumptions
that concern the relative rate of label loss from the different
isotopomers. The production of unlabeled substrate for glucose
synthesis (phosphoenolpyruvate) from
the different isotopomers of lactate is shown to be a potential source
of error in these methods. This error is estimated using models of the
interaction of the gluconeogenetic pathway and the tricarboxylic acid
(TCA) cycle and is shown to vary from negligible to 30% depending on
the relative flux of the two pathways through the oxaloacetate pool.
Because the estimates obtained by both methods considered are lower
than is physiologically expected, some of the assumptions made may not
hold. Future work will exploit the rich information content of
isotopomer data to yield improved estimates.
isotopomers; tracers; turnover; tricarboxylic acid cycle; mathematical models
 |
INTRODUCTION |
THE MEASUREMENT OF THE GLUCONEOGENETIC COMPONENT of
glucose production has been the goal of much developmental effort.
Briefly, gluconeogenesis is the conversion of nonglucose substrate to
glucose. A maximal rate of net gluconeogenesis can therefore be
estimated from the uptake of all possible substrates by the liver (let
us consider only this organ for the sake of simplicity) (1, 20, 28). An
alternative, direct measurement is the simultaneous determination of
glycogenolysis [by biopsy or NMR measurements (19, 25)] and
the rate of total glucose production, gluconeogenesis being the
difference. Clearly, these more direct methods cannot be frequently
implemented in humans because of the degree of invasiveness or expense
involved. Indirect measures of gluconeogenesis have therefore been
sought. These have almost always involved the use of tracers, or
isotopically labeled substrate and glucose. The basis of those
estimates is the dilution principle in the measurement of total hepatic
glucose production (HGP) and the transfer of label from substrate to
the product, glucose. The appearance of label in glucose, corrected for
the substrate specific activity or enrichment, yields an index of
gluconeogenic activity. For such an index to be an exact measure, the
substrate in question would have to be the only substrate or be in
complete equilibrium with all substrates so that its specific activity
or enrichment would be representative of that of all the substrates. In
addition, there should be no loss of label either by dilution or
exchange along the conversion pathway.
Clearly, these assumptions do not hold in general. Lactate, perhaps the
predominant substrate, is not in complete equilibrium even with alanine
(3), for example. Moreover, it was recognized (12) that carbons
involved in the gluconeogenic flux can exchange with those originating
in acetyl-CoA without any net synthesis from fatty acids. Early
estimates of the degree of incorporation of fatty acid carbon into
glucose (29) were initially applied as a correction for the loss of
labeled carbon in the exchange with tricarboxylic acid (TCA) cycle
carbon (6).
Such exchanges with labeled CO2
(22), acetate (2), and water (4, 13, 21), furthermore, have been used
as markers or probes of the gluconeogenetic process at various points
along its pathway. Again, assumptions must be made about the
completeness of the equilibration, i.e., the rate of the exchange
process relative to the flux to glucose and whether any spurious
labeling can take place, such as labeling with no net flux to glucose.
Methods in the context of incomplete equilibration have also been
developed (18). This very brief overview has been provided to emphasize the importance of the assumptions that underlie any of the methods proposed.
These assumptions are also involved in specific ways in the development
of the isotopomer-based methods discussed here. Isotopomers can be
defined as compounds that are chemically identical but that differ in
the degree of isotopic substitution. Isotopomers may be characterized
by their mass (M,
M+1,
M+2... or
M0,
M1, M2...) or by the
position at which different isotopes
(13C,
2H) are substituted (positional
isotopomers). The distribution of glucose mass isotopomers after the
introduction of
[U-13C]glucose in vivo
has been proposed as the basis of methods to estimate fractional
gluconeogenesis (or the rate of gluconeogenesis if the total rate of
glucose production is known) (8, 14, 16, 26, 27, 30). This is based on
the premise that this distribution, along with that of lactate,
contains the necessary information both on the dilution of substrate
molecules by unlabeled substrate and on the dilution of labeled carbons
by 12C. Depending on the approach
taken, this information is used to estimate these dilution factors (26)
or to obviate the necessity of this calculation (14).
 |
APPROACHES AND ASSUMPTIONS |
The two recently published methods under consideration here (14, 26)
are based on the same measurements and therefore depend on the same
assumptions. It is useful to list these assumptions explicitly:
1) The
13C distribution in lactate is
representative of that in intrahepatic pyruvate, which is the direct
substrate for the gluconeogenic process. This implies either that
lactate is the principal substrate, and therefore its labeling pattern
essentially determines that of the pyruvate, or that hepatic pyruvate
and circulating lactate are in rapid equilibrium so that their labeling patterns are identical.
2) Flux through pyruvate
dehydrogenase is negligible so that the TCA cycle dilution of labeled
carbons is exclusively with 12C
arising from acetyl-CoA.
3) Pyruvate kinase flux can also be neglected.
4) No other exchanges of
13C occur to a measurable degree.
The possible impact of 13C
incorporation from circulating
13CO2/H13CO
is, however, discussed in Ref. 14.
5) The tracer concentration is low
enough that the probability of combinations of two labeled molecules is
negligibly low.
The contributions of glycerol are neglected for the purposes of this
calculation. It is also implicitly assumed that all of the corrections
for background glucose (and derivative) enrichments and for tracer
contamination with nonuniformly labeled glucose molecules have been made.
When it is the carbon atoms that are labeled in the glucose molecule,
glycolysis and subsequent resynthesis of lactate or pyruvate to glucose
induce a redistribution or randomization of the labeled carbon
(14C or
13C). It is therefore
distinguishable from the original label. For [1-14C]glucose, for
example, the recycled 14C is found
in all the other positions, although primarily in positions 1, 2, 5, and 6. The amount of recycled label can thus be quantitated (24), and
its rate of appearance in the glucose molecule can be used as an index
of gluconeogenesis (23). Identical considerations hold for
[U-13C]glucose. The
recycled molecule will be labeled as
M1,
M2, and M3, a measure
that is somewhat more quantitative than the radioactive label because
with small amounts of tracer no
M6 glucose will be reformed. The rate of appearance of these isotopomers can then also
be used as an indicator of gluconeogenesis. It may be instructive to
first derive an estimate of the gluconeogenetic rate based on the
14C label.
Let us define the following quantities:
Ra |
Rate of appearance of glucose
|
 |
Rate of infusion of tracer
([1-14C]glucose)
|
R+a |
Rate of appearance of recycled
[14C]glucose
|
C |
Plasma concentration of glucose
|
C* |
Plasma concentration of
[1-14C]glucose
|
C+ |
Plasma concentration of recycled
[14C]glucose
|
a: |
Specific activity of infused label in plasma,
C*/C
|
F: |
Dilution of labeled gluconeogenic flux by exchange with unlabeled
carbon arising from the TCA cycle
|
It follows that
|
(1)
|
|
(2)
|
The reason that the rate of appearance of glucose corresponds to
Eq. 1 and that of recycled label to
Eq. 2 is that
/C*
defines a steady-state measure of the metabolic clearance of glucose
(MCR, ml/min or ml · kg
1 · min
1),
which then clearly applies to both glucose and labeled glucose. This
can be formalized as
The applicability of MCR to either glucose or tracer is inherent in the
linearity property of tracers. Any tag that is attached to glucose will
be cleared in the same way as glucose so long as the tag itself does
not affect the clearance mechanisms. Thus, barring isotope effects at
the level of enzymes,
[14C]- or
[13C]glucose will be
removed (proportionally) at the same rate as [12C]glucose, but
3-O-methylglucose might not. It does
not take any extrapolation to conclude that each molecule of glucose,
as well as each carbon within the glucose molecule, will be cleared at the same MCR.
[1-14C]glucose is a
good example of a tracer where the measurement of the label
concentration, C+ (dpm/ml), yields
what could either be considered a carbon or a molecular approach. In
the terminology of mass spectrometry, each labeled glucose molecule has
one carbon labeled originally at the first position, and therefore
corresponds to an M + 2 (because 14C has two additional mass
units). Clearly, with the very low enrichments in
14C, any metabolic process that
recycles the label back to glucose will also yield an
M + 2 molecule. If the label is lost
(e.g., in exchanges), only an M + 0 molecule will remain. Therefore, we have a situation in which only
M + 2 and
M + 0 molecules will exist. If one
considers carbons, C+/C = (1)M2, where
C+/C is the specific activity, and
M2 is the
enrichment in M + 2 or
14C-labeled molecules, and there
is only one 14C per molecule. If
one considers molecules, then C+/C = M2, which is
identical to the above.
CM2 can therefore
be substituted for C+ in the
equations given above. For 14C,
M2 is extremely
low, not easily detectable by use of mass spectrometry, but
C+ or
CM2 can be
measured using liquid scintillation counting.
To convert R+a into a rate of
gluconeogenesis, the immediate precursor of the glucose molecule needs
to be considered. If, as assumed here, lactate is well equilibrated with hepatic pyruvate, it is the nearest measured representative of
such a precursor, and dilution of label at this level (e.g., peripheral
glycogenolysis) can be taken into account. Each labeled molecule
incorporated into glucose (recycled molecule) is now representative of
a certain number of unlabeled pyruvate (lactate) molecules. By the same
token, each labeled carbon is representative of a certain number of
unlabeled carbons. Therefore, under steady-state conditions, dividing
the rate of incorporation of labeled carbons into glucose
(Ra) by this ratio of labeled to
unlabeled molecules (or carbons) would yield the mass rate of
appearance of new glucose. The (net) stoichiometry of lactate and
lactate tracer conversion to glucose is as follows
If this reaction is considered from the point of view of the simplest
chemical kinetics, then the equilibrium constant,
K, for the reaction is defined by
|
(i)
|
Now consider a perturbation of the system in which a (very) small
amount of tracer lactate is added. This will have the effect of
producing a small amount of additional glucose, which will also be
labeled. By the definition of a tracer, it is distinguishable from the
perspective of measurement but indistinguishable in terms of its
physical, chemical, or metabolic behavior. Equation
i can therefore be rewritten for the new concentrations
of glucose and lactate in the system as
|
(ii)
|
Because the volume of distribution of the glucose and tracer is the
same, we can also write
and
It follows then, from the chemical and physical equivalence of
metabolite and tracer, that Eq. ii can
be rewritten as
|
(iii)
|
where
[glucose*] and [lactate*] are the
concentrations of label. Expanding, subtracting Eq.
i and dropping the term in
[lactate*]2, because
it is small, will yield the following
|
(iv)
|
Dividing Eq. iv by
Eq. i then gives
This implies that a = 2al (where
al is the measured molar specific
activity of lactate), if no dilution takes place. This is equivalent to
the probabilistic expression of this issue: because we have a mixture
of m0 and
m2, we must consider the number of possible ways in which these two molecules can
combine. The probability of each combination can be determined from the
binomial expansion (5, 11)
where
Because
m0 is essentially
1, M2 is simply
equal to 2m2.
Thus, because two molecules of lactate condense to form one molecule of
glucose, but only one lactate label has a detectable probability of
entering the glucose molecule, we finally have
|
(3)
|
where
Ra(gng) is the rate of
gluconeogenesis. Again, the factor two is included in the denominator
because the combination of two lactate molecules leads to one glucose
molecule, and therefore the molar specific activity of glucose (with
respect to 14C) will be double
that of lactate.
Finally, to account for TCA cycle dilution, an appropriate correction
factor, F, should be used (6, 7, 10, 17). Often this is extrapolated
from another experiment. The final formula is therefore
|
(4)
|
An analysis very similar to this one was used to estimate glycogen
synthesis by the gluconeogenic pathway in humans (23).
 |
[U-13C]GLUCOSE:
TRACKING CARBONS |
The development proposed by Tayek and Katz (26) also stems from a
previous analysis to assess this "indirect" pathway of glycogen
synthesis (9). In these studies (9, 26),
M6 glucose was
infused. Converting the molar infusion rate to labeled carbons, we have
|
(1`)
|
where
R is the rate of infusion of
[U-13C]glucose in
millimoles per minute, and
M6 is the
measured enrichment of plasma glucose in this isotopomer.
Equation 1' is thus (for small
enrichments) exactly equivalent to Eq. 1, with 6 × M6 equivalent to
a. It should be noted that because the infusions of tracer are not
massless, the calculated Ra should
be corrected for this rate of infusion
The next step involves estimating the fraction of newly produced
glucose that is recycled. This can be viewed from the perspective of
either molecules or carbons. Since, because of its extremely low
specific activity, the recycled
14C-labeled glucose considered in
the last section is labeled at one
14C atom per molecule,
considerations of numbers of atoms and molecules are essentially the
same. Equation 3 can therefore be
rewritten as
|
(5)
|
where
and
Cl are the labeled and unlabeled
lactate concentrations, and al =
/Cl.
The second factor in Eq. 5,
(C+/C)/[(C+ + C*)/C] or
C+/(C+ + C*) represents the fraction of
[14C]glucose label
that is recycled, and
[(C+ + C*)/C]/(2
/Cl)
is the dilution of labeled glucose carbon by unlabeled lactate. Hence
the fraction in Eq. 5,
C+/(C+ + C*), applies to both cases.
With the use of
[U-13C]glucose, the
issue is less transparent. Tayek and Katz in their first paper (26)
chose the alternative of considering the problem entirely in terms of
carbon fluxes and treating it analogously to that based on a
[14C]glucose tracer.
Thus the fraction of labeled carbon that is recycled and that would
correspond to
C+/(C+ + C*) or
(C+/C)/[(C+ + C*)/C] is
|
(6)
|
Whether this fraction is representative of the fraction of recycled
glucose carbon can be questioned. In this context it should be noted
that when
[1-14C]glucose is the
starting label, it is clear (because of the very low final specific
activity) that as 14C is
distributed among the different positions of the glucose molecule,
there will not be more than one
14C per molecule. Each measured
14C will therefore represent both
a single labeled carbon and a single labeled molecule. When
[U-13C]glucose is the
starting label, all of the carbons of one molecule are substituted with
13C. Whether the fractions of
Eq. 3 and Eq. 6 will lead to the same estimates may therefore be open
to discussion.
[14C]glucose can be
considered as six positional isotopomers of the M2 mass
isotopomer. For
[13C]glucose, we could
consider M1,
M2, and
M3 to be in some
sense equivalent, so that it may not be relevant whether the
13C is on the same molecule or on
different molecules. Certainly without carbon dilution by label
exchange in oxaloacetate (OAA), these labels would recycle onto
themselves in a similar manner as the
14C label. Only with the
M6 isotopomer may
other considerations hold. Clearly each
M6-labeled
glucose (with no TCA cycle exchange) will yield two
M3 glucose
molecules. The number (or mass) of recycled carbons, however, remains
the same.
When the strategy of dealing with
13C in the same way as with
14C is used, the rate of
appearance of labeled glucose carbons can then be calculated
analogously to Eq. 2
|
(2`)
|
Note that to illustrate the analogy with
[14C]glucose, we
consider C (M6 × 6) and
C ·
31 iMi which correspond to the mass of labeled glucose carbons divided by
volume of plasma.
The remaining problem is twofold: accounting for the dilution of
pyruvate carbon by unlabeled substrate (e.g., amino acids or lactate
from muscle glycogen) and for the loss of labeled carbon in label
exchange with the TCA cycle.
Approaching the first problem analogously with
[14C]glucose, the
equation equivalent to Eq. 3 is
|
(3`)
|
where
mi is the molar
enrichment of lactate mass isotopomers for
i = 1 to 3. The factor 2 is included
in the denominator for the same reasons as before. Again,
Eq. 3' can be expressed as
|
(5`)
|
The
second factor in the equation represents the fraction of recycled
labeled carbon, and the third, the dilution of the labeled carbon in
the lactate (or, by assumption, liver pyruvate) pool. This demonstrates
the equivalence of the development here, for both the
14C- and
13C-labeled glucose, with that of
Ref. 26, where fractional gluconeogenesis was estimated from a product
of labeled carbon dilution factors.
Finally, there is the issue of loss of labeled carbon atoms by exchange
with unlabeled TCA cycle carbon. Tayek and Katz (26) used a simple
method based on the enrichments of the different mass isotopomers,
information which is not available with radioactive labels. Because
there would be no loss of label without this exchange, all recycled
glucose would be
M3, and the
fraction of labeled carbons would be
3
31 Mi. The
appearance of M1
and M2
isotopomers quantifies the loss of 13C in the OAA pool. The dilution
factor is therefore
simply
and
the final equation for the rate of gluconeogenesis
|
(6`)
|
or
|
(4`)
|
which
(except for a factor of 2) corresponds to the final equation proposed
in Ref. 26.
One major assumption in the exchange dilution factor, and therefore in
Eq. 4', is that there is no loss
of labeled glucose molecules, i.e., that
where,
however, M'0 refers
only to the unlabeled molecules arising from the previously labeled
molecules. To the extent that
M '0 is
generated, an error in the dilution factor will occur; this will be
approximated by the ratio of the two terms in the above equation.
Second, the dilution correction is essentially applied to all of the
terms in the second factor of Eq. 6'. As discussed in Ref. 26, it only applies exactly to the
M+3 situation, because it accounts
(with the exception of the production of
M0) for the loss of 13C in the TCA cycle.
Clearly this loss of labeled carbons is not proportional for those
molecules starting as
M2 or
M1. The
correction should be smaller, and the overall correction made will
overestimate the rate of gluconeogenesis. As pointed out in Ref. 26,
the proportion of
M2 and
M1 is small
relative to
M3+2M6,
so the error will not be large.
 |
[U-13C]GLUCOSE: THE MOLECULAR
APPROACH |
An alternative approach to estimating the rate of gluconeogenesis
[Ra(gng)] using
[U-13C]glucose and
mass isotopomer analysis was provided by Landau et al. (14). The same
equation (Eq. 1') clearly
holds for total glucose production. The development of the remaining
equations remains completely analogous to that for
[14C]glucose. When
14C is used as the label, each
molecule is either labeled or unlabeled. In an exactly similar fashion,
when 13C is used as the label,
each molecule is also considered to be labeled
(M1,
M2, or
M3) or
unlabeled. The appearance of labeled (and recycled) glucose molecules
is therefore simply
|
(2'')
|
As before, because the immediate substrate is hepatic pyruvate
(represented by circulating lactate), the appearance of labeled molecules can be converted to the rate of gluconeogenesis by the enrichment of lactate in labeled molecules. This corresponds to
31 mi since
different isotopomers are not distinguished. Therefore,
Eq. 3 becomes
|
(3'')
|
with
the factor of 2 again present, because two molecules of lactate yield
one of glucose, so that twice the fraction of glucose molecules will be
labeled relative to lactate molecules.
Note that, again, Eq. 3
can be
written (14) as
|
(5'')
|
where
the second factor is the recycled fraction of glucose molecules, and
the third factor is the dilution of labeled lactate molecules arising
from glucose by unlabeled lactate.
M6 is multiplied by 2 because each molecule of glucose labeled in all 6 carbons yields 2 molecules of labeled lactate and, therefore, 2 molecules of recycled glucose.
The innovative feature of Eq. 3
is that, so long as one assumes (as before)
that there is no loss of labeled molecules (i.e., no complete loss of
carbon from any labeled molecule) in the TCA cycle, then the number of
labeled (in any way) molecules remains the same between the
lactate/pyruvate pool and the
phosphoenolpyruvate (PEP) pool, and
hence the recycled glucose. No additional correction for loss of
labeled molecules, therefore, needs to be made.
Based on the consideration of the existence of only two types of
molecules, labeled (in any way) and unlabeled, an alternative approach
based on the probabilities of different molecular combinations can be
used to calculate the isotopomer distribution in glucose synthesized
from the set of labeled lactate molecules
(m0,m1,m2,m3). The probabilities can be obtained from the expansion of
The
newly synthesized glucose will have the following distribution
with
the remainder of the terms neglected, because the probability of the
combination of two labeled molecules is very low. When this model is
used, the fractional gluconeogenesis is expressed as
Because
m0 in studies
such as these is ~95-97%, the fractional rate of
gluconeogenesis will be corrected slightly, by ~3%.
Finally, as before,
M0 isotopomers
will be formed in the process of recycling, and exactly the same
correction as before will hold
|
(7)
|
where
M'0 again refers
only to unlabeled molecules that were previously labeled. A relatively
subtle correction needs to be considered when a factor such as the
above is applied. The lactate labeled as
m3,
m2, and
m1 will not
become M0(PEP) at
the same rate. Therefore, a labeled lactate that starts as m3 will have a
much smaller chance of losing all its label than, for example,
m1, on a single
pass through the TCA cycle or even the OAA pool. Stated differently, in
the presence of any equilibration with the TCA cycle,
Eq. 3
used with pure
m1 lactate tracer
and pure m3
lactate tracer will yield very different answers. A single correction
factor is thus unlikely to apply to all three terms in the numerator of
Eq. 3
. A factor such as
Eq. 7 needs to be generated for each
set of
(m3,m2,m1)
and will not simply be dependent on properties of the enzymes in the
TCA cycle. Thus the nonequivalence of the three isotopomers (the factor
will be larger for
m1 and m2 than for
m3) will yield
an underestimation of the gluconeogenic rate if a correction factor
dependent only on the TCA cycle and derived on the basis of the
conversion of m3
to M0(PEP) is
used. This relative underestimation will again be small, because the m3 value is
higher than
m1+m2.
The two formulas attributed to Tayek and Katz (26) (without including
the factor of 2, Eq. 5') and
Landau et al. (Ref. 14, Eq. 3
) are similar. Both formulas will be
exact (given the assumptions) and therefore identical, if
there is no 13C exchange and if
only m3 is
present. This is illustrated by the calculated fractional
gluconeogenetic rate of 56.3% using both formulas, in Fig. 1 of Ref.
14. On the other hand, Table 1 shows a comparison of the estimates of fractional gluconeogenesis made
from data in Refs. 14 and 26. It can be seen that the estimates using
both formulas are similar, although those arising from
Eq. 4' are consistently somewhat
higher, by ~15-20%. Because of the nonequivalence of the three
isotopomers of lactate, the (corrected) formula of Tayek and Katz (26)
should slightly overestimate, and that of Landau et al. (14) slightly
underestimate the rate of gluconeogenesis, relative to the theoretical
case in which we have only
m3. These
approximations may very well account for a significant part of the
difference observed.
One could attempt to remove the influence of
m2 and
m1 in the
calculations by considering only
(M3+2M6)
m3
M3, and
then applying a TCA cycle correction based on label dilution. This would, however, neglect the contributions from
m1 and
m2 to
M1 and
M2, and perhaps
further illustrates the complexity of the problem.
The results (Table 1) calculated
on the basis of both formulas are also lower than physiologically
expected. Certainly after a 60-h fast it is anticipated that almost the
entire glucose output would be gluconeogenetic. A fraction of ~40%
is therefore low. Some possible reasons for this have been previously
discussed (14, 26). These include the dilution of hepatocyte pyruvate by a substrate that does not equilibrate well with lactate (e.g., glutamine, aspartate), as well as the formation of unlabeled PEP (M'0 above) from
labeled pyruvate. This would lead to a correction factor such as
Eq. 7. That this correction could be
significant can be surmised from previous estimates of ~1.4 (9) in
the context of gluconeogenic glycogen synthesis and from simulations to
be detailed below.
 |
INTERACTION WITH THE TCA CYCLE: PRODUCTION OF
M0 |
To appreciate the possible extent of the dilution of labeled glucose
molecules or carbons by exchange with unlabeled molecules or carbons in
the TCA cycle, simulations can be performed to predict the label
distribution in PEP relative to lactate (which is measured). This
prediction should be based on both the flux in the gluconeogenic pathway, relative to the TCA cycle, and the degree of equilibration of
OAA with fumarate (Fig. 1).

View larger version (11K):
[in this window]
[in a new window]
|
Fig. 1.
Interactions between the gluconeogenetic pathway and the tricarboxylic
acid (TCA) cycle: equilibration of oxaloacetate (OAA) with fumarate and
exchange with carbons arising from acetyl-CoA. The flux to citrate has
a nominal rate, 1, and the gluconeogenic flux, a relative rate,
y.
|
|
This can be done by considering the positional isotopomers of OAA that
compose the three mass isotopomers and that arise from the equivalent
isotopomers of lactate. We define these isotopomeric states in Fig.
2. The transition matrix, T, an extension of that defined in Ref. 15, and the isotopomer vector
are
|
(8)
|
where
C0 is the
M0 isotopomer of
OAA. The initial distribution,
Cij0, can be
defined, for example, by starting with m3 lactate, so
that
with
the remaining Cij = 0. Each
multiplication by T describes a turn of the TCA cycle. The final
distribution of the Cij can
then be defined either by
|
(9)
|
where
I is the identity matrix, or by solving the steady-state equation (15)
for
|
(10)
|
By use of approaches based on Eq. 10,
corrections ranging from 0.24% for y = 10 to 4.5% for y = 2 and 28% for
y = 0.5 were obtained.
Equation 9 was also used to estimate
m0(PEP) for
individual experiments, with account taken of the existence of
m1 and
m2. Iterating and
regrouping the Cij in terms of
the isotopomers of PEP, values were obtained for the
m0(PEP). The
correction factors obtained in this way were near 33% for
y = 0.5, or only somewhat higher than
the previous estimate, but they illustrate the fact that a significant
correction may arise under physiological circumstances. It may also be
interesting to note that pyruvate kinase (PK) flux (which is assumed to
be zero in the above developments) would contribute to a recycling of
PEP back through OAA, thus adding to the production of
m0(PEP). In some
investigations in which y was higher,
PK flux was also very significant (17). As already discussed, any major
remaining corrections are likely to arise from dilution of hepatocyte
pyruvate by nonlactate substrates.
In summary, the methods discussed (14, 26) appear to give very
consistent answers when applied to a specific situation: no TCA
interactions and only
m3 lactate as
substrate. All methods are based on assumptions that lead to certain
approximations. The stoichiometric, dilution, or combinatorial
approaches to determining fractional gluconeogenesis (or equivalently,
its rate) should all yield the same formulas when applied under exactly
the same set of assumptions. We have tried to illustrate that some of
the assumptions implicit in various derivations are not identical, leading to variances in the proposed formulas. A summary of the formulas based on the different approaches is presented in Table 2. It is left to the investigator to assess their
precise experimental situation and what approach might be most suitable
to build on. It should be restated that the principal difference
between the formula proposed by Ref. 26 and that shown above is a
factor of 2, which is not present in the presentation above. The
development made by Landau and colleagues (14) is conceptually and
mathematically simpler but does contain assumptions that increase its
theoretical accuracy only as
m3 becomes much
greater than
m1+m2,
or the TCA cycle interaction becomes negligible.
Gluconeogenesis is a complex metabolic process that is likely not
amenable to exact measurement. Advances in methodology have continuously yielded improvements in the approximations which must
perforce be made. The richness of information present in the mass
spectrometric determinations of mass isotopomers of precursors and
products has provided a major step forward in allowing consideration of
precursor-to-glucose flux and TCA cycle label exchange in the same
experiment. In addition to the potential in providing better estimates
of gluconeogenesis, much information can simultaneously be obtained
about interacting metabolic processes, such as the TCA cycle. Counting
labeled molecules is a major advantage in simplifying approaches. The
underestimation of gluconeogenesis that results in its use is an
indication that some of the assumptions do not hold. As illustrated
above in estimating the label distribution in PEP, one returns at that
point to the consideration of positional isotopomers and, therefore, by
definition, carbons. Clearly, given the present state of the
approximations, further work is needed to exploit the wealth of
information present in the isotopomer data.
 |
ACKNOWLEDGEMENTS |
The summary presented here was solicited by the Journal to resolve
and understand the differences in formulas developed in Refs. 14 and
26. The help of Dr. Joanne Kelleher (Dept. of Physiology, George
Washington University School of Medicine) in the combinatorial
approaches to determining product isotopomer enrichments is gratefully acknowledged.
 |
FOOTNOTES |
This work was supported by Medical Research Council (Canada) Grant 7334 and National Institutes of Health grants to the General Clinical
Research Center (M01-RR-00425) and to the Clinical Nutrition Research
Unit (PO1-CA-42710).
Address for correspondence and reprint requests: J. Radziuk, Ottawa
Hospital (Civic Site), 1053 Carling Ave, Ottawa, Ontario, Canada K1Y
4E9 (E-mail: jradziuk{at}ottawahospital.on.ca).
 |
REFERENCES |
1.
Björkman, O.,
L. S. Eriksson,
B. Nyberg,
and
J. Wahren.
Gut exchange of glucose and lactate in basal state and after oral glucose ingestion in postoperative patients.
Diabetes
39:
747-751,
1990[Abstract].
2.
Consoli, A.,
F. Kennedy,
J. Miles,
and
J. Gerich.
Determination of Krebs cycle metabolic carbon exchange in vivo and its use to estimate the individual contributions of gluconeogenesis and glycogenolysis to overall glucose output in man.
J. Clin. Invest.
80:
1303-1310,
1987[Medline].
3.
Foster, D. M.,
G. Hetenyi, Jr.,
and
M. Berman.
A model for carbon kinetics among plasma alanine, lactate, and glucose.
Am. J. Physiol.
239 (Endocrinol. Metab. 2):
E30-E38,
1980[Abstract/Free Full Text].
4.
Guo, Z. K.,
W. N. Lee,
J. Katz,
and
A. E. Bergner.
Quantitation of positional isomers of deuterium-labeled glucose by gas chromatography/mass spectrometry.
Anal. Biochem.
204:
273-282,
1992[Medline].
5.
Hellerstein, M. K.,
and
R. A. Neese.
Mass isotopomer distribution analysis: a technique for measuring biosynthesis and turnover of polymers.
Am. J. Physiol.
263 (Endocrinol. Metab. 26):
E988-E1001,
1992.
6.
Hetenyi, G., Jr.
Correction for the metabolic exchange of 14C for 12C atoms in the pathway of gluconeogenesis in vivo.
Federation Proc.
41:
104-109,
1982[Medline].
7.
Katz, J.,
and
N. Grunnet.
Estimation of metabolic pathways in steady state in vitro. Rates of tricarboxylic acid and pentose cycles.
In: Techniques in Metabolic Research, edited by H. L. Kornberg. Amsterdam: Elsevier/North-Holland, 1979, pt. 1, B208, p. 1-18.
8.
Katz, J.,
W.-N. Paul Lee,
P. A. Wals,
and
E. A. Bergner.
Studies of glycogen synthesis and the Krebs cycle by mass isotopomer analysis with [U-13C]glucose in rats.
J. Biol. Chem.
264:
12994-13001,
1989[Abstract/Free Full Text].
9.
Katz, J.,
P. A. Wals,
and
W. N. P. Lee.
Determination of pathways of glycogen synthesis and the dilution of the three carbon pool with [U-13C]glucose.
Proc. Natl. Acad. Sci. USA
88:
2103-2107,
1991[Abstract].
10.
Kelleher, J. K.
Gluconeogenesis from labeled carbon: estimating isotope dilution.
Am. J. Physiol.
250 (Endocrinol. Metab. 13):
E296-E305,
1986[Abstract/Free Full Text].
11.
Kelleher, J. K.,
and
T. M. Masterson.
Model equations for condensation biosynthesis using stable isotopes and radioisotopes.
Am. J. Physiol.
262 (Endocrinol. Metab. 25):
E118-E125,
1992[Abstract/Free Full Text].
12.
Krebs, H. A.,
R. Hems,
J. Wiedermann,
and
R. N. Speake.
The fate of isotopic carbon in the kidney cortex synthesizing glucose from lactate.
Biochem J.
101:
242-272,
1966[Medline].
13.
Landau, B. R.,
J. Wahren,
V. Chandramouli,
W. C. Schumann,
K. Ekberg,
and
S. C. Kalhan.
Use of 2H2O for estimating rates of gluconeogenesis. Application to the fasted state.
J. Clin. Invest.
95:
172-178,
1995[Medline].
14.
Landau, B. R.,
J. Wahren,
K. Ekberg,
S. F. Previs,
D. Yang,
and
H. Brunengraber.
Limitations in estimating gluconeogenesis and Cori cycling from mass isotopomer distributions using [U-13C6]glucose.
Am. J. Physiol.
274 (Endocrinol. Metab. 37):
E954-E961,
1998[Abstract/Free Full Text].
15.
Lee, W.-N. P.
Analysis of mass isotopomer data.
J. Biol. Chem.
264:
13002-13004,
1989.
16.
Lee, W. N. P.,
S. Sorou,
and
E. A. Bergner.
Glucose isotope, carbon recycling and gluconeogenesis using [U-13C]glucose and mass isotopomer analysis.
Biochem. Med. Metab. Biol.
45:
298-309,
1991[Medline].
17.
Magnusson, I.,
W. C. Schumann,
G. E. Bartsh,
V. Chandramouli,
K. Kumaran,
J. Wahren,
and
B. R. Landau.
Non-invasive tracing of Krebs cycle metabolism in liver.
J. Biol. Chem.
266:
6975-6984,
1991[Abstract/Free Full Text].
18.
Neese, R. A.,
D. Faix,
J. M. Schwarz,
S. M. Turner,
C. Vu,
and
M. K. Hellerstein.
Measurement of gluconeogenesis and rate of appearance of intrahepatic triose-phosphate and its regulation by substrates by mass isotopomer distribution analysis (MIDA). Testing of assumptions and potential problems.
J. Biol. Chem.
270:
14452-14463,
1995[Abstract/Free Full Text].
19.
Nilsson, L. H.,
and
E. Hultman.
Liver glycogen in man
the effect of total starvation or a carbohydrate-poor diet followed by carbohydrate refeeding.
Scand. J. Clin. Lab. Invest.
32:
325-330,
1973[Medline].
20.
Owen, O. E.,
F. A. Reichle,
M. A. Mozzoli,
T. Kreulen,
M. S. Patel,
I. B. Elfenbein,
M. Golsorkhi,
K. H. Y. Chang,
N. S. Rao,
H. S. Sue,
and
G. Boden.
Hepatic, gut, and renal substrate flux rates in patients with hepatic cirrhosis.
J. Clin. Invest.
68:
240-252,
1981[Medline].
21.
Postle, A. D.,
and
D. P. Bloxham.
The use of tritiated water to measure absolute rates of glycogen synthesis.
Biochem. J.
192:
65-73,
1980[Medline].
22.
Radziuk, J.
Sources of carbon in hepatic glycogen synthesis during absorption of an oral glucose load in humans.
Federation Proc.
41:
110-116,
1982[Medline].
23.
Radziuk, J.
Hepatic glycogen in humans. II. Gluconeogenetic formation after oral and intravenous glucose.
Am. J. Physiol.
257 (Endocrinol. Metab. 20):
E158-E169,
1989[Abstract/Free Full Text].
24.
Reichard, G. A., Jr.,
N. F. Moury, Jr.,
N. J. Hochella,
A. L. Patterson,
and
S. Weinhouse.
Quantitative estimation of the Cori cycle in the human.
J. Biol. Chem.
238:
495-501,
1963[Free Full Text].
25.
Rothman, D. L.,
I. Magnusson,
L. D. Katz,
R. G. Shulman,
and
G. I. Shulman.
Quantitation of hepatic glycogenolysis and gluconeogenesis in fasting humans with 13C NMR.
Science
254:
573-576,
1991[Medline].
26.
Tayek, J. A.,
and
J. Katz.
Glucose production, recycling, and gluconeogenesis in normals and diabetics: a mass isotopomer [U-13C]glucose study.
Am. J. Physiol.
270 (Endocrinol. Metab. 33):
E709-E717,
1996[Abstract/Free Full Text].
27.
Tayek, J. A.,
and
J. Katz.
Glucose production, recycling, Cori cycle, and gluconeogenesis in humans: relationship to serum cortisol.
Am. J. Physiol.
272 (Endocrinol. Metab. 35):
E476-E484,
1997[Abstract/Free Full Text].
28.
Wahren, J.,
S. Efendi
,
R. Luft,
L. Hagenfeldt,
O. Björkman,
and
P. Felig.
Influence of somatostatin on splanchnic glucose metabolism in postabsorptive and 60-hour fasted humans.
J. Clin. Invest.
59:
299-307,
1977[Medline].
29.
Weinman, E. O.,
E. H. Strisower,
and
I. L. Chaikoff.
Conversion of fatty acids to carbohydrate: application of isotopes for this problem and role of Kreb's cycle as a synthetic pathway.
Physiol. Rev.
37:
252-272,
1957[Free Full Text].
30.
Wykes, L. J.,
F. Jahoor,
and
P. J. Reeds.
Gluconeogenesis measured with [U-13C]glucose and mass isotopomer analysis of apoB-100 amino acids in pigs.
Am. J. Physiol.
274 (Endocrinol. Metab. 37):
E365-E376,
1998[Abstract/Free Full Text].
Am J Physiol Endocrinol Metab 277(2):E199-E207
0002-9513/99 $5.00
Copyright © 1999 the American Physiological Society