## Abstract

We have derived equations, by employing [U-^{13}C]glucose and mass isotopomer analysis, to determine the pathways of glycogen synthesis (J. Katz, W. P. Lee, P. A. Wals, and E. A. Bergner.*J. Biol. Chem.* 264: 12994–13004, 1989). More recently, by use of these methods we have derived equations to determine the rate of glucose recycling and of gluconeogenesis [Tayek and Katz. *Am. J. Physiol.*270 (*Endocrinol. Metab.* 33): E709–E717, 1996 and 272 (*Endocrinol. Metab.* 35): E476–E484, 1997, and Katz and Tayek.*Am. J. Physiol.* 275 (*Endocrinol. Metab.* 38): E537–E542, 1988]. The former equations have been criticized and challenged by C. Des Rosiers, B. R. Landau, and H. Brunengraber [*Am. J. Physiol.* 259 (*Endocrinol. Metab.* 22): E757–E762, 1990], and the latter recently by B. R. Landau, J. Wahren, S. F. Previs, G. K. Ekberg, D. Yang, and H. Brunengraber [*Am. J. Physiol.* 274 (*Endocrinol. Metab.* 37): E954–E961, 1998]. Landau et al. claimed that our equations were in error and “corrected” them. Their analysis, and their values for recycling and gluconeogenesis (GNG) differ markedly from ours. We show here our equations and estimates of recycling and GNG to be correct. We present here a theoretical analysis of recycling and discuss the determination of the Cori Cycle and GNG. We illustrate by numerical examples the difference in parameters of glucose metabolism calculated by the methods of Katz and Landau. J. Radziuk and W. N. P. Lee [*Am. J. Physiol.* 277 (*Endocrinol Metab.* 40): E199–E207, 1999] and J. K. Kelleher [*Am. J. Physiol.* 277 (*Endocrinol. Metab.* 40): E395–E400, 1999] present a mathematical analysis that, although differing in some respects from Landau’s, supports his equation for GNG. We show in theappendix that their derivation of the equation for GNG is incorrect.

- glucose
- mass isotopomer analysis

## THE SYSTEM

We assume a steady state and, as in fasting, no formation of liver glycogen from glucose. In mass isotopomer analysis with [U-^{13}C]glucose, the fractions (%) of labeled glucoses and lactate in blood are designated, respectively, as “*M*” and “*m*” values, with a subscript, the index, indicating the number of^{13}C carbons per molecule. Thus*M*
_{0},*M*
_{1},*M*
_{2}...*M*
_{6}is glucose containing no, or 1, 2, 3...6^{13}C carbons per labeled molecule, and *m*
_{0},*m*
_{1},*m*
_{2},*m*
_{3} are lactate molecules and contain no, or up to 3^{13}C carbons. We designate the sum of labeled molecules as Σ*M* or Σ*m*. Thus
We also designate the product of the *M* or*m* values with the index as Σ*M _{n}
* or Σ

*m*. Thus These expressions show the number of

_{n}^{13}C carbons per 100 molecules of glucose or lactate.

In the numerical examples we assume net glucose production (replacement of label by nonlabeled carbon) to be 2 mg ⋅ min^{−1} ⋅ kg^{−1}. There is a continuous infusion of 0.1 mg ⋅ min^{−1} ⋅ kg^{−1}of [U-^{13}13C]glucose. For simplicity, we neglect the mass of infused [U-^{13}C]glucose. We also assume in some examples the direct conversion of pyruvate to phospho*enol*pyruvate (PEP), without loss of ^{13}C by exchange in the operation of the tricarboxylic acid (TCA) cycle. As we show later, this assumption does not affect the recycling of molecules.

## RECYCLING OF GLUCOSE MOLECULES AND OF GLUCOSE CARBON

Lactate-pyruvate is the product of glycolysis and is also the major precursor for gluconeogenesis (GNG). Thus there is always recycling of glucose. This does not affect the net production of glucose but increases the synthesis of glucose by liver in kidney, as will be discussed in a later section.

As long as infusion of U-^{13}C and net glucose production are constant, the concentration of [U-^{13}C]glucose,*M*
_{6} containing six^{13}C carbons per molecule, will be constant. In our example, glucose rate of appearance (R_{a}) is also constant.
The general expression is
An identical value, 2 mg ⋅ min^{−1} ⋅ kg^{−1}, would be obtained with a nonrecycling tracer, such as [3-^{3}H]glucose.

In the resynthesis of glucose from dilute solutions of labeled lactate (<5%), the statistical chance of recombining two labeled trioses is very small and is neglected. The resynthesized glucose will contain^{13}C either in carbons 1, 2, 3 or 4, 5, 6 of glucose. If there were no recycling, the isotopomer spectrum would be 5*M*
_{6} + 95*M*
_{0}. In the limit, at 100% recycling, the isotopomer spectrum will be 5*M*
_{6} + 10*M*
_{3} + 85*M*
_{0}. Thus, in the limit, the concentration of labeled glucose will be one-third*M*
_{6} and two-thirds*M*
_{3}, and the concentration of labeled molecules will be trebled. The recycled fraction will be
With 50% recycling the fraction of recycled molecules will be
and for 10% recycling
Recycling will also increase the content of^{13}C carbons in glucose. Because*M*
_{3} contains three^{13}C carbons, and with the assumption of direct conversion of pyruvate to PEP without loss of^{13}C, the fraction of recycled carbon in the above example will be
at 100% recycling, and
at 10% recycling. However, although the exchange of^{13}C with^{12}C carbon does not affect the recycling of molecules, as discussed below, it causes loss of^{13}C from recycled molecules.

In the conversion of pyruvate to PEP there occurs a loss of labeled carbons by exchange with ^{12}C. When the flux of oxaloacetate (OAA) to citrate predominates, labeled pyruvate containing three ^{13}C carbons will be converted to a mixture of*m*
_{3},*m*
_{2},*m*
_{1}, and*m*
_{0}. However, in the fasted state the flux of OAA to PEP is much larger than the flux to citrate (7). We show elsewhere (Katz and Tayek, unpublished) that, in fasted humans, the predominant change is the conversion of*m*
_{3} to*m*
_{2}, with little loss of *m*
_{2} and negligible loss of*m*
_{1}. Thus the sum of *m*
_{1} +*m*
_{2} +*m*
_{3} or*M*
_{1} +*M*
_{2} +*M*
_{3} changes little. This has also been accepted by Landau et al. (10) and the other reviewers. Thus we have used*M*
_{3} in the above example rather than the sum of recycled M values.

The general expression for the fraction of recycled molecules is
However, in the conversion of pyruvate to PEP there is a loss of^{13}C carbons. The actual^{13}C content per molecule is shown by the index, which indicates the number of^{13}C carbons for each*M* and*m* of glucose or lactate. Thus the fraction of recycled carbon is
The numerator represents the number of carbons in 100 molecules of recycled glucose, and the denominator is the number in total glucose. We illustrate in Table 1 our calculations for a 40-h-fasted man (6). The table also shows the average number of^{13}C carbons per molecule of PEP. This is 2.07 ^{13}C carbons per molecule. Thus, neglecting the recycling of lactate, ∼29% of labeled carbons of pyruvate were lost in its conversion of PEP.

We stress, in contradiction to Landau and co-workers (9, 10) and Kelleher (8), the fact that the isotopomer spectrum provides for a complete description, not only of the pattern of labeled molecules but also of the labeled carbon. There is also equivalence in “enrichment,” the ^{13}C content of glucose, and relative specific activity obtained with [U-^{14}C]glucose. This has been confirmed by experiment, by comparing the metabolism of [U-^{13}C]- and [U-^{14}C]glucose (7). We have previously derived (13) and show in Table2 the apparent R_{a} if [U-^{14}C]glucose were infused. Because of recycling, the specific activity of [U-^{14}C]glucose in blood is increased, and apparent R_{a} is decreased.

The recycling of carbon and the recycling of molecules are two independent parameters of physiological interest, and we routinely report both in our studies. On the other hand, according to Landau et al. (10), they are the same. We quote, “The fraction of glucose carbon recycled must be the same as the fraction of recycled molecules, contrary to Tayek and Katz.”

## THE CORI CYCLE

Cori pointed out the physiological role of recycling in maintaining blood glucose well before the advent of isotopic tracers. Early attempts to measure this recycling, named the Cori Cycle, were by randomization of [1-^{14}C]- and [6-^{14}C]glucose. These measure only the cycling of specifically labeled carbons. It is apparent that *Eq. 2*, the recycling of glucose molecules, equals the Cori Cycle. An essentially identical expression was used previously by Kalderon et al. (4) to measure the Cori Cycle in children. Thus the Cori Cycle equals *Eq. 2*
This equation was challenged by Landau et al. (10). Following a previous approach to recycling by Des Rosiers et al. (2), Landau introduced a factor of 0.5; thus, according to these authors, the expression for recycling is
They designated this expression as the Cori Cycle. The reason, to quote Landau, is “... the factor of 0.5 is required because only one-half of triose units of mass*M*
_{1},*M*
_{2},*M*
_{3} are not labeled and are not derived from [U-^{13}C]glucose. The equations must represent the dilution only of the [U-^{13}C]glucose cycled...” We do not understand their rationale and completely disagree. All the glucose molecules in blood, labeled and unlabeled, are cycled to the same extent, and isotopic tracers represent the fate of total glucose in blood. The reason that only one-half of*M*
_{1},*M*
_{2}, and*M*
_{3} contain^{13}C is because of the use of dilute solutions. If a 50% rather than a 5% solution of glucose were used, one-half of the recycled molecules would contain^{13}C in both halves of the glucose. Recycling would be the same as with the 5% dilution. Landau’s equation does not account for one-half of the recycled molecules and one-half of the recycled carbon, and it vitiates the conservation of mass. We believe Landau’s “corrected” equation does not represent any physiological parameter, and its designation as Cori Cycle is unfortunate.

## GLUCONEOGENESIS

In our previous studies (6, 13, 14), we derived an equation for GNG as the product of the Cori Cycle and the dilution of glycolytic by endogenous lactate. Landau et al. (10) accepted our approach, but their estimates of both the Cori Cycle and dilution differ markedly from ours. We present here an alternate direct approach and equation to measure GNG. In a later section we discuss dilution and compare the new expression and the calculated values of GNG with those derived by the two methods. We show that the two methods are algebraically identical.

Glucose is formed by a condensation of two trioses. For [^{14}C]glucose the two triose precursors are labeled, and the specific activity of [^{14}C]glucose is twice that of the triose. The stoichiometry of glucose formation from a diluted solution of [U-^{13}C]triose is different. It is a condensation of one labeled and one unlabeled triose. If the labeled triose is*m*
_{3}, the stoichiometry is
Thus the ^{13}C content of*m*
_{3} and*M*
_{3} is equal, with three ^{13}C carbons per molecule, and the ratio*M*
_{3}/*m*
_{3}is 1 when GNG is 100%.

Consider the direct interconversion of [U-^{13}C]glucose and lactate. Assume 100 micromoles (18 mg) of glucose containing 5% [U-^{13}C]glucose, or 30 microatoms of ^{13}C converted to 200 micromoles of lactate, or to 10*m*
_{3} + 190*m*
_{0} molecules. As required from the conservation of mass, the lactate will contain 30 microatoms of ^{13}C. On further interconversions, the steps are
Thus*m*
_{3} and*M*
_{3} will always contain 30 microatoms of ^{13}C. Mass spectroscopy measures the fractions of mass of glucose or lactate containing ^{13}C carbons. It does not count molecules. The fraction of mass containing 1, 2, or 3^{13}C carbons from either lactate or glucose remains the same. Both*M*
_{3} and*m*
_{3} contain three^{13}C, and their fraction of mass in the example of ^{13}C is 30^{13}C carbons. This is not affected by the conventional, arbitrary representation of*M* and*m* values as fractions (%) per 100.

In a dilute solution of glucose, the mixture of*M* values results from a combination of the corresponding *m* and*m*
_{0}, with the^{13}C content of the*m* and*M* being equal. If 100% of glucose production is by GNG
This is supported by experiment (6). In 40-h-fasted human subjects, when glycogen stores are depleted, the sum of*M*
_{1} +*M*
_{2} +*M*
_{3} is nearly the same as the sum of*m*
_{1} +*m*
_{2} +*m*
_{3}, the ratio is close to 1, and GNG accounts for 80–100% of glucose production.

The corresponding equation for GNG derived by Landau et al. (10), Kelleher (8), and Radziuk and Lee (11) is
differing from our equation by a factor of 2. It implies the synthesis of*M* values from two labeled precursors, with a doubling of ^{13}C content. The calculation for GNG by this equation yields values that are too low and physiologically untenable, that are in contradiction to experimental finding, and that are exactly one-half of the correct values obtained by us.

When there is production of glucose from hepatic glycogen, the value of is diluted, the ratio is <1, and

## DILUTION

Labeled lactate-pyruvate in blood formed by glycolysis is diluted by largely unlabeled lactate from amino acids and muscle glycogen. Landau et al. (10) agree with Katz that GNG is the product of recycling and dilution, but their values for recycling (the Cori Cycle) and dilution differ greatly. Endogenous lactate formation will dilute the concentration of labeled molecules and their^{13}C carbon content to exactly the same extent. Thus both parameters can be used to calculate dilution, and the results should be exactly the same. We estimated dilution by comparing the content of ^{13}C carbon in glucose to that of lactate in blood. The dilution is
The numerator is the^{13}C content of glucose, and the denominator is the ^{13}C content of blood lactate. The factor of 2 arises because the molecular weight of^{13}C glucose is twice that of lactate. This expression is exactly equivalent to the ratios of specific activities of [^{14}C]glucose and [^{14}C]lactate derived from glucose. Gluconeogenesis is the product of recycling, the Cori Cycle, and dilution, using dilution in terms of carbon, and we obtain gluconeogenesis as *Eq. 6.* We compare in Table 2 the values of GNG calculated by the equation
with the equation of GNG as the product of the Cori Cycle, and dilution
using the dilution obtained from ^{13}C carbon. The values for GNG are very similar, although the experimental data used in the calculation are different. This supports our assumptions, the validity of our analysis, and the expressions for the Cori Cycle and dilution. The dilution in fasted humans ranged in the great majority of subjects from 2- to 2.5-fold in the overnight fast, and from 2.5- to 3-fold in prolonged fasting. Thus GNG ranged from 2 to 3 times the rate of the Cori Cycle.

Landau et al. (10) estimated dilution from a comparison of the concentration of labeled molecules in glucose and lactate. Their results differ from those obtained with^{13}C carbon. Their expression for dilution is
The rationale for the factor of 0.5 appears to be the same as in their expression for the Cori Cycle. This expression neglects the fact that 200 molecules of lactate are formed from 100 molecules of glucose. The error is apparent by considering the dilution of glycolytic lactate derived from glucose by 100 moles of unlabeled lactate. According to this equation, the dilution will be 50% rather than the correct 33.3%. The correct expression for dilution in terms of molecules is
Substituting this expression for dilution, in the equation for GNG, as the product of Cori Cycle and dilution, we obtained the expression for GNG
Equation EEq._4We thus show that the apparently differing expressions for GNG are algebraically identical. We stress that the expression for GNG,
was derived solely from consideration of stoichiometry. It is independent of calculations of the Cori Cycle, of recycling or dilution, or of any assumptions on the pathways of gluconeogenesis. The algebraic identity of the equations employing stoichiometry, the Cori Cycle, and the different modes of dilutions establishes firmly the validity of our assumptions and analysis.

## CO_{2} FIXATION

The fixation of labeled CO_{2} in the operation of the TCA cycle leads to the incorporation of label in the carboxyl carbon of PEP. Because most of the pyruvate is unlabeled, there will be a formation of*M*
_{1} and*m*
_{1}, with^{13}C in the carboxyl carbon. The extent of the fixation will depend on the labeling of the body bicarbonate pool and the length of infusion, and in practice it will not approach steady state. It will have a negligible effect on the total ^{13}C content of glucose but may lead to a significant increase in fraction of recycled molecules. We find in overnight-fasted humans that the fraction of*M*
_{1} is very low (6) and the effect of CO_{2} fixation negligible. However, in extensive recycling or prolonged infusion, the*M*
_{1} fraction may equal and exceed*M*
_{3} (see Table 1).

In ionization in mass spectroscopy of lactate, the labile carboxyl is partially split off, and spectra of intact lactate and its 2,3 carbon moiety are obtained. This permits an estimate of*M*
_{1} containing^{13}C in the carboxyl carbon and a correction for^{13}CO_{2}fixation. At GNG values close to 100%, the overestimate in fasted humans is of the order of 5–10%. In extensive cycling, as in fasted young pigs (15), GNG is reduced by correcting for^{13}C fixation from an average of 104% to ∼90%.

## ASSUMPTIONS

In our studies with humans (6, 13, 14), the only assumption was that lactate-pyruvate in blood is equilibrated with that in liver. Of course, the concentration and specific activity or enrichment of pyruvate in the liver cell will depend on numerous inflows and outflows, labeled and unlabeled, into and from the TCA cycle (acetyl-CoA, amino acids), and on the reactions of pyruvate kinase, dehydrogenase, or carboxylase. We have shown perfect equilibration in rats (7). Rats were infused with [U-^{14}C]- and [U-^{13}C]lactate and alanine and lactate isolated from blood and liver tissue. The specific activity, the enrichment of ^{13}C, and the isotopic pattern of lactate and alanine were virtually the same and nearly identical in blood and liver. Such studies are impossible in humans. Landau et al. (10) infused U-^{13}C in fasted humans and found near equilibration of lactate and alanine in arterial but not in venous blood. Alanine is formed from protein breakdown, and it is likely that in a 5-h period steady state was not attained. The assumption of complete equilibration of pyruvate in blood and liver is widely held in the literature and appears to be shared by Kelleher (8) and Radziuk and Lee (11).

Glycerol serves as an important substrate for glucose formation. Glycerol entering gluconeogenesis at the triose-P stage will be recycled just as glucose is. Indeed, Landau et al. (9) have shown that glycerol carbons are randomized just as those of glucose. Thus the formation of glucose from glycerol is included in our equations. This is supported by the experiments of Sunehag et al. (12) with premature babies, where glycerol was a major source of glucose.

In our analysis we have not considered the operation of cycling between glucose and glycogen. As discussed by us previously (6), the operation of such a cycle in the fasted state is controversial. Further studies are required to resolve the issue and the question whether the operation of such a cycle will affect our equations and our estimates of Cori Cycle and GNG.

Our equations employ ratios such as
It appears likely that a nonsteady state, incomplete equilibration, or recycling with glycogen would affect in a similar manner the*M* and*m* values. The ratios and our equations would hold under such conditions. Further studies are needed to test our equations under diverse conditions.

Landau et al. (10) faulted our analysis and calculations because, and we quote, “...isotopic exchange was not adequately differentiated from dilution, nor was condensation of labeled with unlabeled triose-P properly equated.” The claim is baseless. Indeed, it would be difficult to maintain that any errors affecting metabolic pathways would lead to equations differing exactly by the factor of two, yielding one-half of our correct estimates. They claimed to support their analysis and calculation by graphic models of glucose metabolism. In their model they divided the glucose pool arbitrarily into two subpools: a large one, as much as 80% “in brain, etc.” that is oxidized to CO_{2} and not recycled, and a small one, where recycling occurs. However, recycling affects the whole body glucose pool. Isotopomer patterns taken from systemic blood will be the same from whichever site the blood is sampled. It can be readily shown that correct numerical calculations differ widely from those shown by Landau et al. (10) for his models. The models are untenable and provide no support for their equations.

## THE PHYSIOLOGICAL ROLE OF RECYCLING

The net production of glucose, the replacement of glucose carbon by unlabeled precursors, is not affected by recycling. In steady state, the net production R_{a} can be determined using nonrecycling tracers, such as [3-^{3}H]glucose from the ratio of the rate of infusion and specific activity of glucose, or with [U-^{13}C]glucose, from the ratio of the rate of infusion and*M*
_{6}. If there were no recycling, the concentration of [U-^{13}C]glucose would equal *M*
_{6}. However, as shown here, recycling increases the concentration of labeled glucose molecules and the content of labeled carbon,^{13}C or^{14}C in blood glucose. In the limit, at 100% recycling, the ^{13}C content of glucose or the specific activity of [^{14}C]glucose will be doubled. Thus recycling increases the actual rate of glucose synthesis, the output of glucose by liver and or kidney, or of GNG.

We have found in overnight-fasted humans the recycling of glucose, the Cori Cycle, to be ∼20 and 40% of glucose production contributed by GNG and 60% by glycogenolysis. After a 40-h fast, R_{a} declined from ∼2.2 mg ⋅ min^{−1} ⋅ kg^{−1}overnight to ∼1.8 mg ⋅ min^{−1} ⋅ kg^{−1}. Recycling increased to 35–40%, and GNG contributed 85–100% of glucose production. Thus the synthesis of glucose in the overnight-fasted humans was increased by some 20%. In the 40-h fast, the role of hepatic glycogen was negligible, and GNG, the production of glucose, was increased by 30–35%. Thus recycling serves to maintain the concentration of blood glucose and the size of the body glucose pool, when net synthesis of glucose decreases. It is likely that, without recycling, the 40-h-fasted subjects would be dangerously hypoglycemic.

## EXPERIMENTAL ASPECTS

The criterion for the truth of a theory is agreement with experimental data. We have in a recent publication (6) compared our estimates of GNG in humans with values reported by other investigators, and the agreement is close. Of special significance is the comparison with data obtained by Landau and co-workers (1, 9) with glucose deuterated in*positions 2 *and *5*. This method is based on minimal assumptions and is well validated. Both Landau and we find that %GNG is ∼40% after an overnight fast and 80–100% in prolonged fasting. On the other hand, Landau’s “corrected” equations show 20 and 40% for these conditions. Landau and co-workers acknowledge that our values are much the same as those determined by his method, but he persists in claiming that his equations are “theoretically correct.” They failed to realize that their “corrected” value is one-half of the true value as calculated by us. They dismiss our values as being accidental, a fluke.

The use of [U-^{13}C]glucose is preferable to radioactive tracers for human studies. Calculations by mass isotopomer analysis are simple. They provide much more information about carbohydrate metabolism than can be attained by a combination of several glucoses labeled with ^{14}C or ^{3}H. The infused amount of U-^{13}C is small, approaching tracer levels, and does not affect endogenous metabolism. The required blood sample is small, as available in studies of neonatal babies. The equipment is much cheaper than NMR and widely available. Kalderon et al. (4) were the first to use mass isotopomer analysis in their studies of children. We have used this approach for studies with fasted humans (6), cancer patients (14), and diabetics (13), and Sunehag et al. (12) employed it with premature babies kept on parenteral nutrition. Resolution of current disputes should lead to a wider application of our analysis and equations.

## Acknowledgments

This study was supported by a National Institute of Diabetes and Digestive and Kidney Diseases Clinical Investigator Award, K08-DK-02083 (to J. A. Tayek) and a Harbor-UCLA General Research Center Grant, M01-RR-00425.

## Appendix

### Recycling in Glycogen Synthesis and GNG

The analysis of recycling in the present paper is an extension of that used by Katz et al. (5) in the study of the indirect path of glycogen synthesis. This was challenged by Des Rosiers, Landau, and Brunengraber (2). With a dilute solution of [U-^{13}C]glucose, one-half of the glycogen molecule formed in the indirect path is unlabeled, just as in GNG. This led Des Rosiers et al. to introduce the factor of 0.5 in their equation, just as in their equation for the Cori Cycle. Accordingly, they calculated the contribution of the indirect path to be ∼35% rather than 50% according to Katz. They did not distinguish the recycling of molecules from the recycling of carbon. The error of Des Rosiers et al. was not realized at the time by Katz and was not commented upon. A critique of Des Rosiers’s rationale and calculations would parallel closely the present critique of Landau et al. and is not presented here.

## Appendix

### Response to Kelleher, Radziuk, Lee, and Landau

Kelleher misunderstood our equations and misquotes them (see Table 1 of Ref. 8). A statement in her abstract, “Landau’s approach is based on analyses of labeled molecules, while Tayek and Katz’s is based on labeling of carbon atoms...” is not correct, and this should be apparent to readers of our review.

Kelleher does not consider recycling nor the equations of Landau et al. She claims to derive the expression for GNG from binomial probability. The binomial theorem serves to predict the frequency of the products as a function of the concentration of precursors. It also serves, as used by Hellerstein and Neese (3), to obtain the concentration of the precursor from that of the products. The frequency depends solely on the fractional concentration of the precursor. For example, with a 20% solution of [U-^{13}C]lactate, the direct conversion to glucose would yield
This tells us nothing about recycling or GNG, which may range from 0 to 100%. To equate the equation for GNG with the term “2 ab” in the expression (a + b)^{2} with GNG, and use it to prove Landau’s equation, is simplistic and incorrect.

Radziuk and Lee (11) offer, by employing an awkward, formal notation, a review of tracer theory with ^{14}C. Most of it is well established and noncontroversial. They fail to realize the distinction between^{14}C and [U-^{13}C]glucose. They do not realize that*m*
_{3} and*M*
_{3} both contain three ^{13}C carbons. We quote, “... a factor of 2 is 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.” True, but only for ^{14}C. We have dealt with the fallacy of this statement, the cardinal error of Landau, in our review.

Our fundamental difference with the array of investigators disputing our analysis is on the role of theory and experiment in research. They admit that the equations of Landau and his supporters yield physiologically untenable values. They fail to account for the discrepancy. In accord with Landau, Kelleher quotes, “[a] correct equation can yield incorrect answers.” In our judgment, incorrect answers, discrepancy between experiment and theory, discredit the theory. We provide practical equations that provide solutions for physiological parameters and that are admittedly valid. We believe that the submission of theories in conflict with experiment is irresponsible, and their publication unfortunate.

- Copyright © 1999 the American Physiological Society