physiology forum:
commentary
Estimating gluconeogenesis with [U-13C]glucose:
molecular condensation requires a molecular approach
JOANNE K. KELLEHER
Department of Physiology, The George Washington University School of Medicine
and Health Sciences, Washington, District of Columbia 20037
glucose; molecular condensation; stable isotopes; gas chromatography-mass spectrometry
of the American Journal of Physiology: Endocrinology and Metabolism may be aware of a recent
series of papers proposing distinct equations for estimating gluconeogenesis in vivo after constant infusion of
[U-13C]glucose. The three key papers are by Tayek and
Katz (4, 5) and Landau et al. (3). The issues raised in
these studies are important, illustrating fundamental
principles for the development of tracer methods. The
papers cited have produced three different equations
for fractional gluconeogenesis (Table 1). These equations are based on identical assumptions, yet they are
algebraically different. This manuscript employs binomial probability to address this issue.
Deriving mathematical relationships that can be
solved for useful information is fundamental to the
study of metabolism. A derivation must be accurate; it
should always produce a mathematically correct anREADERS
swer under the stated assumptions. Once a derivation
has been presented, investigators may test it with
experimental data. Often, as the history of gluconeogenesis estimates attests, application of the equation resulting from the derivation will fail to produce results
consistent with experimental experience. This may
occur because the assumptions underlying the derivation do not apply. In this case, a new derivation should
be built on the previous one, differing only when the
new set of assumptions dictates that a different relationship is required. Estimating gluconeogenesis by use of
stable isotope tracers and mass or positional isotopomers is a relatively new field. The optimal method may
not yet be in hand. Thus it is essential that correct
forms of derivations are used in the earliest stages so
that future studies may build on this framework.
In these studies, gas chromatography-mass spectrometry (GC-MS) is used to quantify the relative amount of
each mass isotopomer of plasma glucose and lactate
molecules. The terminology used here is consistent
with the three published papers. The amount of each
isotopomer is expressed as fractional abundance, that
is, the amount of each isotopomer divided by the sum of
all isotopomers. From our perspective, fractional abundances are required, because they are equivalent to
probabilities. A different letter represents the isotopomers of each compound, and the subscript ‘‘i’’ indicates
mass: Mi for isotopomers of plasma lactate; Mi for
isotopomers of plasma glucose. We add ‘‘Pi’’ for the
isotopomers of phosphoenolpyruvate (PEP), ‘‘Gi for
gluconeogenic glucose, and ‘‘Qi’’ for lactate from glycolysis of plasma glucose. By this convention, m3 represents
the fractional amount of plasma 13C-13C-13C lactate.
Tayek and Katz also use the term ‘‘molar enrichment,’’
which they define as the weighted sum of the isotopomer fractions of a molecule ‘‘x’’ with n carbons as
n
molar enrichment ⫽
兺 i·x
i⫽1
i
(1)
Accordingly, the molar enrichment of lactate ⫽ m1 ⫹
2 ⫻ m2 ⫹ 3 ⫻ m3. The protocol used in the studies is
simple: a constant [U-13C]glucose infusion serves two
purposes; it allows calculating the rate of appearance of
plasma glucose (Ra ) as rate of infusion divided by M6. It
also provides a 13C precursor for gluconeogenesis, labeled plasma lactate, that is easily sampled.
0193-1849/99 $5.00 Copyright r 1999 the American Physiological Society
E395
Downloaded from http://ajpendo.physiology.org/ by 10.220.33.5 on June 17, 2017
Kelleher, Joanne K. Estimating gluconeogenesis with
[U-13C]glucose: molecular condensation requires a molecular
approach. Am. J. Physiol. 277 (Endocrinol. Metab. 40): E395–
E400, 1999.—Recently three equations for estimating gluconeogenesis in vivo have been proposed, two by J. A. Tayek and
J. Katz [Am. J. Physiol. 270 (Endocrinol. Metab. 33): E709–
E717, 1996, and Am. J. Physiol. 272 (Endocrinol. Metab. 35):
E476–E484, 1997] and one by B. R. Landau, J. Wahren, K.
Ekberg, S. F. Previs, D. Yang, and H. Brunengraber [Am. J.
Physiol. 274 (Endocrinol. Metab. 37): E954–E961, 1998].
Both groups estimate gluconeogenesis from cycling of
[U-13C]glucose to lactate and back to glucose, detected by
mass spectrometry. Landau’s approach is based on analysis of
labeled molecules, whereas Tayek and Katz’s is based on
labeling of carbon atoms by use of the concept of ‘‘molar
enrichment,’’ which weights each mass isotopomer by the
number of labeled carbons. We derived an equation very
similar to Landau’s using binomial probability. Our analysis
demonstrates that the molecular-based approach is correct.
Additionally, equations appropriate for 14C studies are not
appropriate for 13C studies, because the method used to detect
14C, decay of atoms, differs from 13C mass isotopomers
detected as labeled molecules. We conclude that the molar
enrichment carbon-based approach is not useful in the derivation of equations for the polymerization of molecules detected
by mass spectrometry of molecules, and we confirm the
findings of Landau et al.
E396
COMMENTARY
Table 1. Comparison of equations for fractional gluconeogenesis
Fractional Gluconeogenesis ⫽
Source (Ref No.)
Fig. 1
3 · (M1 ⫹ M2 ⫹ M3 )
Tayek and Katz (4)
m1 ⫹ 2 · m2 ⫹ 3 · m3
1.01
(M1 ⫹ M2 ⫹ M3 ) · (M1 ⫹ 2 · M2 ⫹ 3 · M3 ⫹ 6 · M6 )
Tayek and Katz (5)
(M1 ⫹ M2 ⫹ M3 ⫹ M6 ) · 2 · (m1⫹ 2 · m2 ⫹ 3 · m3 )
Landau et al. (3)
2 · (m1 ⫹ m2 ⫹ m3 )
0.69
M1 ⫹ M2 ⫹ M3
0.45
M1 ⫹ M2 ⫹ M3
Eq. 11 binomial
2 · m0 · (m1 ⫹ m2 ⫹ m3 )
0.50
Fractional gluconeogenesis by application of equations to example in Fig. 1.
Fig. 1. Gluconeogenesis from [U-13C]glucose infusion
(rrrrrr) and cycling at steady state. Glucose enters
the plasma compartment from three sources: [U-13C]glucose infusion, glycogenolysis, and gluconeogenesis. Fractional abundances of each isotopomer are indicated to
right of symbol. Isotopomers of lactate derived from
plasma glucose (compartment Qi ) are as predicted from
plasma glucose. Mi, isotopomers of plasma glucose. Pi,
isotopomers of phosphoenolpyruvate (PEP). As lactate
travels back to glucose, the tricarboxylic acid (TCA)
cycle reduces the number of labeled carbons per molecule but retains the number of labeled molecules.
Gluconeogenic glucose (Gi ) isotopomers are formed, as
indicated in text, by use of binomial probability. For
example, (G1 ⫹ G2 ⫹ G3 ) ⫽ 2 ⫻ P0 ⫻ (P1 ⫹ P2 ⫹ P3 ).
Other refers to formation of glucose from 2 labeled PEP
precursors (see Eq. 10). When values here are used,
fractional gluconeogenesis ⫽ 15/30 ⫽ 0.5.
ing the Ra (M6 ) and part (M1 ⫹ M2 ⫹ M3 ) for gluconeogenesis. The model allows several sites for dilution or exchange of isotope. Unlabeled carbon enters
plasma glucose via glycogenolysis and unlabeled lactate from muscle mixes in the plasma with lactate
derived from glucose. The tricarboxylic acid (TCA) cycle
exchanges labeled carbon atoms for unlabeled ones.
Both groups use the same assumptions, which we
summarize.
Downloaded from http://ajpendo.physiology.org/ by 10.220.33.5 on June 17, 2017
An overview of the flow of tracer glucose in this
protocol is described in Fig. 1. To make the diagram
easy to follow, higher values for [U-13C]glucose infusion
and for all labeled isotopomers are shown than were
used in the studies discussed here. Because the actual
enrichment of plasma lactate is not high in vivo,
generation of glucose from two labeled lactate is ignored in Fig. 1. Under these conditions, part of the
isotopomer profile of glucose can be used for determin-
E397
COMMENTARY
equations to represent the fraction of glucose carbon or
molecules that recycles. These cycling equations are
then used to derive fractional gluconeogenesis. To bring
a fresh view to this discussion, we develop a derivation
without involving cycling. Instead of working with the
cycling of glucose, we simply take the fractional abundances of lactate as known. The resulting derivation
illustrates principles for developing equations for the
rate of production of molecules formed by condensation
of two or more identical precursors. The derivation will
be built as a two-step modeling process.
FIRST MODEL: 2 LACTATE = GLUCOSE
We begin with the simpler model. Assume that
lactate travels directly to glucose, bypassing oxaloacetate and the TCA cycle. TCA cycle has no effect on
isotopomer labeling. Ignore the fact that the tracer
enters as [U-13C]glucose infusion, and consider the
synthesis to begin with a population of isotopomers of
lactate that are all either m0 or m3. Note that m0 and m3
represent fractional enrichment values, so that m0 ⫹
m3 ⫽ 1. Thus m0 and m3 equal the probability that a
randomly selected molecule from the gluconeogenic
lactate pool is labeled, ⫽ m3, or unlabeled, ⫽ m0. In this
simple model, gluconeogenesis is the polymerization of
two lactate molecules. The probability distribution for
the various possible labeled forms of glucose is derived
from binomial probability by expanding the polynomial
representing this dimer
1 ⫽ (m0 ⫹ m3)2 ⫽ m02 ⫹ 2 · m0 · m3 ⫹ m32
(2)
Accordingly, the probability of each isotopomer of gluconeogenic glucose (Gi ) is
G0 ⫽ m02
(3)
G3 ⫽ 2 · m0 · m3
(4)
G6 ⫽ m32
(5)
These simple expressions provide the key to understanding the relationship between precursor and product
molecules.
No comparable equation exists for carbon atoms.
Equation 4 is most important, because G3 is produced
solely by gluconeogenesis. The isotopomers of newly
synthesized glucose enter plasma glucose by mixing
with glucose derived from glycogenolysis and tracer
infusion. When plasma glucose is considered, glycogenolysis will contribute to M0 and tracer [U-13C]glucose
infusion will contribute to M6, leaving M3 as the glucose
isotopomer supplied only by gluconeogenesis. The fractional contribution of gluconeogenesis to the plasma
glucose is
fractional gluconeogenesis ⫽ M3 /G3 ⫽ M3 /(2·m0 ·m3)
(6)
This equation simply states that M3 glucose will be
directly proportional to the fraction of glucose derived
from the condensation of an m0 and m3 lactate. An
Downloaded from http://ajpendo.physiology.org/ by 10.220.33.5 on June 17, 2017
1) The amount of [U-13C]glucose infused is small relative to other fluxes, so that correction of Ra for tracer
infusion may be ignored.
2) The fractional abundance of labeled lactate is low,
and the probability of glucose formed from two labeled
lactate moieties is negligible.
3) Data are corrected appropriately for natural abundances of heavy isotopes, and all isotopomer data are
expressed as fractional enrichments.
4) Labeled carbon enters the TCA cycle only via pyruvate through pyruvate carboxylation. If 13C enters the
TCA cycle via 13C acetyl-CoA or 13CO2 fixation, gluconeogenesis will be overestimated. An exception occurs if
the data are corrected for 13CO2 fixation, as in Landau
et al. (3).
5) Gluconeogenesis from glycerol is negligible.
6) Isotopic enrichment of intrahepatic pyruvate is equal
to that of plasma lactate.
7) Except for pyruvate carboxylation, unlabeled carbon
enters the TCA cycle only at acetyl-CoA. Thus exchange
with TCA cycle intermediates, via amino acid transamination, for example, is negligible. (The impact of assumptions 4, 5, 6, and 7 is discussed below).
8) The exchange of labeled molecules with the TCA
cycle yields PEP molecules with fewer labeled carbons
but does not yield significant unlabeled molecules.
Neither group offers an equation to correct for the
formation of unlabeled PEP molecules from labeled
lactate molecules. Landau et al. (3) state this assumption explicitly. Tayek and Katz state that the correction
factor used for dilution of carbon in the TCA cycle does
not correct for the formation of unlabeled PEP (5). Both
groups justify this assumption because the tracer entering the TCA cycle is predominately m3, and the rate of
pyruvate carboxylation relative to the TCA cycle is
substantial, resulting in significant M3 and M2 glucose.
The major differences in the approach of the two
groups are that Tayek and Katz use carbon-based
calculations, estimating ‘‘recycling of glucose carbon’’
and ‘‘dilution by unlabeled carbon.’’ In contrast, Landau
uses a molecular approach, calculating ‘‘fraction of
glucose molecules recycled.’’ These differences are most
apparent when the interaction with the TCA cycle is
considered. The TCA cycle effectively reduces the number of labeled carbon atoms but produces no change in
the number of labeled molecules (assumption 8). The
derivations presented by Tayek and Katz employ factors to correct for the loss of labeled carbon in the TCA
cycle (4) or recycling of carbon atoms (5). To quantify
this loss of carbon, they use the concept of molar
enrichment defined above. In contrast, Landau et al.,
using a molecule-based approach, state that no correction is required for loss of labeled carbon in the TCA
cycle so long as labeled molecules are conserved. Thus
the central issue defining the differences between the
two groups is the use of carbon-based calculations that
involve corrections for lost carbon vs. molecule-based
calculations that do not use this correction. Molar
enrichment is used for carbon-based calculations.
A common feature of the presentations of both groups
is the use of glucose cycling. Both groups produce
E398
COMMENTARY
alternative statement of this relationship based on
probability is
G1 ⫹ G2 ⫹ G3 will appear in glucose only as a result of
gluconeogenesis, so that
probability of M3
fractional gluconeogenesis
⫽ fractional gluconeogenesis (2 · m0 · m3)
(6a)
Equation 6a emphasizes the fact that expressing the
amounts of isotopomers as fractional abundances is
equivalent to probabilities. For this reason, fractional
abundances are required for this type of analysis.
Terminology based on mole or atom percent excess
cannot be used. Before moving on, we emphasize that
the binomial probability equation allowing this simple
derivation for fractional gluconeogenesis is a property
of molecules and not carbon atoms.
We now consider the interaction of the labeled lactate
with the TCA cycle and introduce hepatic PEP as the
immediate gluconeogenic precursor (Fig. 1). The net
effect of the TCA cycle is that some labeled atoms are
lost in the TCA cycle carbon exchange. Lactate, largely
m3, enters the TCA cycle as oxaloacetate via intrahepatic pyruvate, and P3, P2, P1, or even P0 PEP emerges.
However, P0 PEP produced by this process is negligible
(assumption 8). Tayek and Katz clearly and correctly
state that their equation for TCA cycle carbon dilution
does not correct for P0 (see p. E481 of Ref. 5). They also
indicate that much of the carbon loss observed is due to
conversion of m3 lactate to M2 glucose, a process that
does not produce loss of labeled molecules (see p. E714
of Ref. 4). The example shown in Fig. 1 tests the effects
of loss of labeled carbon but conservation of the fraction
of labeled molecules between lactate and glucose. Thus
the fraction of labeled lactate molecules equals that of
PEP, (m1 ⫹ m2 ⫹ m3 ) or (9/90) ⫽ (P1 ⫹ P2 ⫹ P3 ) or (3/30).
To test the carbon vs. molecular approach, this example
includes loss of labeled carbon via the TCA cycle. The
molar enrichment of PEP (6/30) is less than that of
plasma lactate (24/90 ⫽ 8/30).
Following the binomial expansion approach, we derive a second relationship for fractional gluconeogenesis. Because intrahepatic PEP cannot be sampled in
humans, (m1 ⫹ m2 ⫹ m3 ) is used in place of the
equivalent (P1 ⫹ P2 ⫹ P3 ). We lump together all labeled
molecules such that the synthesis of a dimer, glucose, is
described by the combination of labeled and unlabeled
lactate molecules
1 ⫽ [m0 ⫹ (m1 ⫹ m2 ⫹ m3)]2
fractional gluconeogenesis
⫽ (M1 ⫹ M2 ⫹ M3)/[2 · m0 · (m1 ⫹ m2 ⫹ m3)]
(11)
The substitution of lactate for the true gluconeogenic
precursor, PEP, in Eq. 11 is valid provided (m1 ⫹ m2 ⫹
m3 ) equals (P1 ⫹ P2 ⫹ P3 ). This requirement is related
to assumptions 4–7 above. If 13C enters the TCA cycle
via 13C acetyl-CoA or 13CO2 fixation (assumption 4),
gluconeogenesis will be overestimated. Overestimation
results because (m1⫹ m2 ⫹ m3 ) m0 will be less than
(P1⫹ P2 ⫹ P3 ) P0, and the smaller lactate terms in the
denominator of Eq. 11 lead to erroneously high fractional gluconeogenesis values. In contrast, if unlabeled
carbon enters the gluconeogenic pathway beyond
plasma lactate (assumptions 5–7), gluconeogenesis will
be underestimated because (m1⫹ m2 ⫹ m3 ) m0 will be
greater than (P1⫹ P2 ⫹ P3 ) P0.
COMPARING PUBLISHED MODELS
The binomial expansion equation (Eq. 11) is compared with the published equations (Table 1). Equation
11 very nearly equals Landau’s equation, differing only
in the presence of the term m0, representing the
fractional contribution of unlabeled lactate. This term
is part of the binomial expansion. However, for these in
vivo experiments where the [U-13C]glucose infusion is a
small fraction of Ra, m0 approaches 1. We include the m0
term to be mathematically correct and to remind
investigators that it might be significantly less than 1
in some situations. The effect of omitting m0 from the
equation is independent of the value for fractional
gluconeogenesis and varies linearly with m0 (Fig. 2). In
Landau’s experiments m0 was approximately equal to
0.97, signifying that Landau’s estimates of gluconeogenesis should be increased by the factor 1.03. In Table 1,
the larger numerical difference between Eq. 11 (bino-
(7)
Again, newly synthesized glucose will have the following distribution
G0 ⫽ m02
(8)
G1 ⫹ G2 ⫹ G3 ⫽ 2 · m0 · (m1 ⫹ m2 ⫹ m3)
(9)
Other Gi ⫽ (m1 ⫹ m2 ⫹ m3) = 0
(10)
2
Fig. 2. Effect of omitting m0 from equation for fractional gluconeogenesis is an underestimate. The fraction of the correct value resulting
from ignoring m0 term in denominator is plotted.
Downloaded from http://ajpendo.physiology.org/ by 10.220.33.5 on June 17, 2017
SECOND MODEL: 2 LACTATE = TCA CYCLE = PEP =
GLUCOSE
⫽ (M1 ⫹ M2 ⫹ M3)/(G1 ⫹ G2 ⫹ G3)
or
COMMENTARY
THE CARBON VS. MOLECULAR APPROACH FOR
CONDENSATION POLYMERIZATION EQUATIONS
Other than the factor of 2 discussed above, the
remaining difference between Tayek and Katz (1996)
and Landau et al. (1998) is the fact that Tayek and Katz
employ a correction for the loss of some labeled carbon
from labeled molecules, analogous to 14C studies. The
difficulty with analyzing 13C studies as analogous to 14C
studies stems directly from the carbon, rather than
molecular approach and the use of molar enrichment to
compensate for loss of carbon. In the 1996 paper, Tayek
and Katz utilize molar enrichment to correct for TCA
cycle dilution (4). In their 1997 paper, they state that
the estimate of gluconeogenesis is not dependent on
TCA cycle dilution (5). However, they continue to use
molar enrichment to calculate ‘‘dilution by unlabeled
carbon,’’ which again introduces a consideration of
carbon rather than molecules.
The key to understanding the molecular approach is
that no correction is required for the loss of some 13C
atoms within a molecule if the number of 13C-labeled
molecules is conserved. The fractional abundances for
molecules with 1–3 13C atoms are combined in the
equations (see Eqs. 7–11). Thus it is of no consequence
whether a labeled molecule has one, two, or three
labeled carbons. Applying this concept to gluconeogenesis represents an important contribution of Landau
and co-workers. Mass spectrometry of molecules detects each mass isotopomer with identical efficiency. It
counts each molecule detected once regardless of the
number of labeled carbon atoms. Put another way, the
probability of detecting a 13C-labeled molecule by mass
spectrometry is not decreased by a decrease in the
number of labeled atoms/molecule. (We are not concerned here with signal-to-noise issues, which may
decrease the precision of detecting specific mass isotopomers). Thus 13C detected by mass spectrometry is
different from 14C detected by liquid scintillation counting. Starting with [U-14C]lactate, the probability of
detecting a labeled glucose molecule is directly proportional to the number of labeled atoms that survive to
reach the product. A correction factor analogous to that
used by Tayek and Katz for dilution of labeled carbon is
appropriate for 14C detected by liquid scintillation
counting but not for 13C detected by mass spectrometry
of molecules.
The concept of gluconeogenesis as the condensation
of two precursor molecules is fundamental for understanding how gluconeogenesis is estimated from tracers, both 14C and 13C. The binomial probability equation
(Eq. 11) underlies 14C calculations as well. Working
with 14C is disadvantageous because it deals with
atoms; liquid scintillation counting measures atoms by
emitted radiation, yielding disintegrations per minute
(dpm). The dpm detected may be used to convert atoms
to molecules by use of the specific activity of the traced
compound, dpm/(mole of the compound). However, in
doing this, one must carefully account for each atom of
14C lost in the path from precursor to glucose and
multiply by a dilution factor that effectively increases
the observed dpm to account for the missing 14C. This is
the basis of the elaborate 14C equations developed by
Katz (1) and Kelleher (2) in the 1980s to calculate
dilution factors. The calculations for 13C mass isotopomers are less complicated than for 14C dpm data, because
the labeling information is readily obtained in the form
in which it is used in the equations, as the fraction of
labeled molecules.
The differences in the 14C and 13C calculations described above are not differences inherent in the type of
tracer. Rather, they are consequences of the detection
method used. To illustrate this point, compare two
variations of the protocol described in Fig. 1. First,
Downloaded from http://ajpendo.physiology.org/ by 10.220.33.5 on June 17, 2017
mial probability) and Landau’s result is due to the
relatively low value of mo (0.9) in the example (Fig. 1).
Both equations of Tayek and Katz differ from the
derivation by binomial expansion and fail to produce
the correct answer for the test case shown in Fig. 1. The
mo term is also missing from the denominator of both of
their equations.
Binomial expansion (Eqs. 6 and 11) clearly includes a
factor of 2 in the denominator. This factor was omitted
by Tayek and Katz in 1996 (4). Landau was keenly
aware of the need for the factor of 2 in the denominator
of his equation. He explained the requirement for the
factor of 2 ‘‘because one-half the triose units forming
glucose molecules of masses M1, M2, and M3 are unlabeled and are not derived from [U-13C]glucose.’’ In view
of our reliance on binomial probability, we would rather
assert that the factor of 2 is required because it is the
coefficient in the binomial expansion. As such, it represents the two chances for making glucose one-half m0
and one-half m3, m0 ⫺ m3 and m3 ⫺ m0. It should be
noted that, in 1997, Tayek and Katz added a factor of 2
in the denominator (5). However, their 1997 equation
was still not equivalent to that derived by binomial
probability. We conclude that the equations of Tayek
and Katz for estimating gluconeogenesis are not appropriate, because they fail to produce a result consistent
with the binomial expansion.
It is interesting that the binomial expansion derivation is not step by step identical to Landau’s and yet
produces an almost identical equation. This demonstrates that the glucose cycling properties of the model
are not essential to the measurement of gluconeogenesis. Finding a different derivation, yielding essentially
the same relationship, serves as a verification that the
molecular approach of Landau is correct. For those who
prefer examples to derivations, the values in Fig. 1
could be altered to test the validity of the molecular
approach. Glycogenolysis, tracer infusion, unlabeled
lactate flux, and TCA cycle activity could each be
changed. As long as the system is in steady state, and
the assumptions are not violated, Eq. 11 will yield the
correct result for gluconeogenesis. Alternatively, changing the values of the molar enrichment of lactate and
PEP, retaining the number of labeled molecules, will
have no effect on gluconeogenesis and will not affect the
estimates when Eq. 11 or Landau’s equation is used,
but it will change the values calculated with the
equations of Tayek and Katz.
E399
E400
COMMENTARY
with 14C as tracer or as a combustion IRMS study.
Other uses for molar enrichment should be carefully
justified.
Finally, our analysis agrees with that of Landau et al.
(3), supporting their conclusion that gluconeogenesis is
underestimated by the [U-13C]glucose technique. Investigations using the carbon-based molar enrichment
approach failed to detect this underestimation. As
Landau and co-workers pointed out, correct equations
can yield physiologically implausible answers (3). The
reason must be that some of the assumptions are not
valid or that we have overlooked some issue entirely. It
is now the task of interested researchers to build on
derivations consistent with binomial probability to
learn why the application of correct equations and
seemingly reasonable assumptions do not yield expected values.
This article was solicited by the Journal to resolve the differences
in the formulas developed in Refs. 3, 4, and 5. It was supported by
National Institute of Diabetes and Digestive and Kidney Diseases
Grant DK-45160.
Address for correspondence and reprint requests: J. K. Kelleher,
Dept. of Physiology, George Washington Univ. Medical Center, 2300
Eye St. NW, Washington, DC 20037 (E-mail: [email protected]).
REFERENCES
1. Katz, J. Determination of gluconeogenesis in vivo with 14Clabeled substrates. Am. J. Physiol. 248 (Regulatory Integrative
Comp. Physiol. 17): R391–R399, 1985.
2. Kelleher, J. K. Gluconeogenesis from labeled carbon: estimating
isotope dilution. Am. J. Physiol. 250 (Endocrinol. Metab. 13):
E296–E305, 1986.
3. 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.
4. 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.
5. 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.
Downloaded from http://ajpendo.physiology.org/ by 10.220.33.5 on June 17, 2017
consider a hypothetical experiment replacing the
[U-13C]glucose with [U-14C]glucose in the example
shown as Fig. 1. GC-MS could be used to detect
14C-labeled glucose and lactate molecules, just as with
the 13C experiments. The isotopomer would occur as M6
and M12, but the data could be analyzed as shown here
with binomial probability. Because GC-MS detects labeling of molecules, no correction would be required for
loss of 14C-labeled carbon atoms within labeled molecules. Alternatively, consider a 13C study isolating
glucose and lactate and combusting the molecules to
CO2. Isotope ratio MS (IRMS) of CO2 could measure the
labeling of carbon atoms. This method, like radioactivity, measures carbon atoms and requires a correction to
relate the number of labeled carbons to the number of
labeled molecules of glucose or lactate. These examples
illustrate the importance of using corrections appropriately to reflect both the type of data collected and the
mathematics of the underlying derivation. Biosynthesis of polymers by condensation of precursors is a
molecular process. To estimate its rate, equations must
deal with the labeling of molecules. Mass spectrometry
of molecules presents us with the data in the correct
form. The carbon-based molar enrichment approach
converts molecular isotopomer data to carbon data,
leading to errors. For this reason, the equations of
Tayek and Katz are not useful building blocks for the
future of this field.
One may ask whether molar enrichment may be used
to correct for the loss of labeled molecules in the TCA
cycle. Neither group directly accounts for this possibility. It is possible to derive equations to correct for loss of
labeled PEP molecules. These equations are functions
of the rate of pyruvate carboxylation relative to TCA
cycle flux (‘‘y’’) and of the fumarase equilibrium. The
resulting equations can be expressed in terms of m1, m2
and m3. However, these equations do not contain terms
that multiply the amount of each mass isotopomer by
the number of labeled carbons, as dictated by molar
enrichment. Molar enrichment is a concept that has
only one obvious use in our experience. It may be used
to predict the dpm to be found if a 13C study is repeated