## Abstract

Tayek and Katz proposed calculating gluconeogenesis’s contributions to glucose production and Cori cycling from mass isotopomer distributions in blood glucose and lactate during [U-^{13}C_{6}]glucose infusion [Tayek, J. A., and J. Katz. *Am. J. Physiol.* 272 (*Endocrinol. Metab.* 35): E476–E484, 1997]. However, isotopic exchange was not adequately differentiated from dilution, nor was condensation of labeled with unlabeled triose phosphates properly equated. We introduce and apply corrected equations to data from subjects fasted for 12 and 60 h. Impossibly low contributions of gluconeogenesis to glucose production at 60 h are obtained (23–41%). Distributions in overnight-fasted normal subjects calculate to only ∼18%. Cori cycling estimates are ∼10–15% after overnight fasting and 20% after 60 h of fasting. There are several possible reasons for the underestimates. The contribution of gluconeogenesis is underestimated because glucose production from glycerol and amino acids not metabolized via pyruvate is ascribed to glycogenolysis. Labeled oxaloacetate and α-ketoglutarate can exchange during equilibrium with circulating unlabeled aspartate, glutamate, and glutamine. Also, the assumption that isotopomer distributions in arterial lactate and hepatic pyruvate are the same may not be fulfilled.

- lactate
- alanine
- CO
_{2}fixation

tayek and katz (19) introduced a novel method for estimating the contribution of gluconeogenesis to glucose production from mass isotopomer distribution (MID) values in blood glucose and lactate during [U-^{13}C_{6}]glucose administration. However, calculations from observed distributions yielded overestimates (20). Two factors were calculated, one for dilution by unlabeled carbon of [^{13}C]lactate formed from the blood glucose and the other for dilution in the conversion of that lactate to glucose. The product of those factors times an estimated fraction of the blood glucose carbon recycled via lactate to glucose and times glucose production was equated to the rate of gluconeogenesis (19).

Most recently, the same authors presented a new procedure for calculation (20), giving lower estimates of gluconeogenesis. Rates are calculated from the product of glucose production, the factor for the dilution by unlabeled carbon of the labeled lactate formed from the blood glucose, and an estimate of the fraction of glucose molecules recycled, the latter estimate also considered the measure of Cori cycling. However, exchanges of ^{13}C with ^{12}C in the process of gluconeogenesis are not adequately differentiated from dilution of^{13}C by^{12}C from unlabeled gluconeogenic precursors. Also, the condensation of labeled with unlabeled triose phosphate is not properly equated.

We now present corrected equations for calculating the contributions of gluconeogenesis and Cori cycling from MID. Applying them, we have estimated the contribution of gluconeogenesis in humans after an overnight fast and after fasting for 60 h. If the approach is adequate, the contribution at 60 h should be nearly 100% (12, 18). After an overnight fast, it would be expected to be ∼40–50% (6, 11, 17). A critical assumption in the approach is that the MID in arterial blood lactate accurately measures that in pyruvate in liver and in kidney, to the extent kidney contributes to gluconeogenesis. To test that assumption, distributions in arterial blood, lactate, and alanine were compared with distributions in hepatic vein and renal vein lactate and alanine.

## METHODS

#### Subjects.

Seven healthy normal men, aged 26–31 yr with body mass indexes of 20.5–24.4 kg/m^{2}, were studied. The study was approved by the Human Investigation Committees at the Karolinska Hospital and University Hospitals of Cleveland. Informed consents were obtained.

#### Materials.

[U-^{13}C_{6}]glucose, 99% enriched, purchased from Isotec (Miamisburg, OH), was dissolved in isotonic saline and filtered through a sterile Millipore 0.22-μm porosity filter. The solution was shown to be sterile and pyrogen free by the Pharmacy Department of the Karolinska Hospital.

#### Procedure.

At 8 AM, three of the subjects, after 60 h of fasting, were given a priming dose and then an infusion for 5 h of the solution of [U-^{13}C_{6}]glucose, 9.8 ml/h, into an antecubital vein of one arm at a rate of ∼0.4 μmol of [U-^{13}C_{6}]glucose ⋅ kg body weight^{−1} ⋅ min^{−1}. The priming dose equaled the amount infused in 1 h. Also at 8 AM, a catheter was inserted into the brachial artery of the other arm. At 3 h into the infusion, catheters were inserted under fluoroscopic control into a hepatic vein and a renal vein via a femoral vein. The catheters were kept patent by periodic saline rinses.

Blood was drawn from the artery at 3 h into the infusion and from 4 h to 5 h every 15 min for determination of MID in plasma glucose, lactate, and alanine. Blood was drawn from the hepatic and renal veins every 15 min from 4 h to 5 h for determination of MID in lactate and alanine. Concentrations of blood glucose and β-hydroxybutyrate were determined at 4 and 5 h. Breath was collected at 4 and 5 h for the determination of ^{13}C excess enrichment in breath CO_{2}. Breath was collected before the beginning of [U-^{13}C_{6}]glucose infusion to measure the natural^{13}C enrichment in breath CO_{2}.

The other four subjects were treated the same as the first three except that the 5 h of infusion of [U-^{13}C]glucose were begun after 12 rather than 60 h of fasting. Then blood was drawn for the determination of MID in arterial glucose and in arterial, hepatic vein, and renal vein lactate every 15 min from 16 h to 17 h into the fast. Breath was collected at 16 h and 17 h.

#### Analyses.

Blood glucose concentrations were determined using glucose oxidase (YSI, Yellow Springs, OH). β-Hydroxybutyrate concentrations were also determined enzymatically (22). Plasma for MID analyses, collected rapidly after blood drawing, was frozen immediately and shipped to Cleveland. MID values of glucose were determined from the aldonitrile pentaacetate derivative, as described by Tayek and Katz (19), and of lactate from the pentafluorobenzyl derivative as described by Hazey et al. (7). Measured isotopomer distributions were corrected for natural^{13}C enrichment at all masses (5). To measure ^{13}C enrichment of breath CO_{2}, the CO_{2} was collected in NaOH, and BaCl_{2} was added. The rinsed and dried precipitate of BaCO_{3} was introduced in a vial that was flushed with CO_{2}-free N_{2} before injection of H_{2}SO_{4}. The evolved CO_{2} was injected with a gas syringe into a gas chromatograph-mass spectrometer. Linear calibration curves of^{13}CO_{2}enrichments (0.1–1.5%) were obtained using NaH^{13}CO_{3}standards. Measured enrichments of expired CO_{2} ranged from 0.7 to 1.0%.

#### Calculations.

Rate of appearance of glucose (R_{a}glucose) in the circulation was calculated using the equation
Equation 1 where R is the rate of infusion of [U-^{13}C_{6}]glucose in μmol ⋅ min^{−1} ⋅ kg^{−1}, and *M*
_{6} is the percentage of glucose molecules having six^{13}C atoms.*M*
_{6} was 94% of the [U-^{13}C_{6}]glucose infused in the present study. Endogenous glucose production (GP) equals R_{a} glucose minus R. Because R is small relative to the R_{a} glucose, GP is a little less than R_{a}glucose.

D, the dilution by unlabeled lactate of labeled lactate undergoing Cori cycling, was calculated using the equation
Equation 2 where*M*
_{1},*M*
_{2},*M*
_{3}, and*M*
_{6} are, respectively, the percentages of blood glucose molecules with 1, 2, 3 and 6 ^{13}C atoms, i.e., isotopomers*M*1, *M*2, *M*3, and *M*6. Correspondingly,*m*
_{1},*m*
_{2}, and*m*
_{3} are the percentages for blood lactate of isotopomers *m*1,*m*2, and *m*3, respectively.

F, the fraction of glucose molecules in the blood that recycled, was calculated using the equation
Equation 3 The rate of gluconeogenesis (GNG) equals R_{a} glucose × D × F. The percent contribution of GNG (%GNG) to glucose production (GP) equals 100(GNG/GP). The amount of blood glucose undergoing Cori cycling equals (R_{a} glucose) × F and the percent 100F. *Equations 2
* and *
3
* are applicable only when the rate of glucose infused is small relative to GP. Thus, in the present study, [U-^{13}C_{6}]glucose was infused at only ∼4% of the rate of GP. That resulted in relatively low enrichments and with negligible formation of*M*4 and*M*5 as well as*M*6 isotopomers. Small quantities of [U-^{13}C_{6}]glucose must be infused to avoid altering metabolism, even if the cost of [U-^{13}C_{6}]glucose allowed giving quantities to achieve high enrichments (19).

Correction of *M*
_{1}, to the extent of its formation via fixation by pyruvate of^{13}CO_{2}formed from the [U-^{13}C_{6}]glucose, can be made by infusing NaH^{13}CO_{3}or NaH^{14}CO_{3}under the same study conditions. Measurements are made of the enrichments or specific activities of blood glucose and breath CO_{2}, combined with measurement of the enrichment of breath CO_{2} from the [U-^{13}C_{6}]glucose. Thus
The only unknown is then the enrichment of^{13}CO_{2}from [U-^{13}C_{6}]glucose fixed in glucose.

Contributions of fixation can also be estimated from just the enrichment of breath^{13}CO_{2}labeled from [U-^{13}C_{6}]glucose. For example, assume that^{13}CO_{2}in breath from [U-^{13}C_{6}]glucose was 1% enriched in a 60-h-fasted subject in whom GNG is responsible for 100% of GP. Also, assume that this is the enrichment of the CO_{2} fixed by pyruvate in liver and that there is complete isotopic equilibration with fumarate of the oxaloacetate formed before its conversion to glucose. Then the carboxyls of the oxaloacetate and carbon 3 and carbon 4 of blood glucose would each have 0.5% enrichment, giving a ratio of the enrichment in glucose to that in breath of (2 × 0.5)/1 = 1.0. Therefore, if *M*
_{1}determined by MID was 2%, the corrected*M*
_{1} would be 1%.

We infused both NaH^{13}CO_{3}and NaH^{14}CO_{3}into normal subjects fasted 60 h (4, 9). The ratio of the enrichments and specific activities in blood glucose to breath CO_{2} was ≈0.65. The ratio being lower than 1.0 is due in large part to incomplete equilibration of the oxaloacetate and the contribution of glycerol to GP. Therefore, the correction to *M*
_{1}has been estimated in the present study by multiplying the enrichment in the breath CO_{2} by 0.65. To measure the contribution of^{13}CO_{2}fixation to *m*
_{1},^{13}CO_{2}or^{14}CO_{2}from carbon-labeled bicarbonate fixed in lactate would have had to be measured.

## RESULTS

Arterial glucose concentration of the first three subjects at 65 h into the fast was 3.5 mM in *subject 1*, 3.4 mM in *subject 2*, and 2.4 mM in*subject 3* and was about the same at 64 h into the fast. Concentrations of β-hydroxybutyrate were, respectively, 2.7, 3.8, and 2.9 mM at 65 h and slightly lower at 64 h into the fast. These concentrations are in accord with the subjects having fasted for 65 h.

The percentage of isotopomer*M*6 in the MID in glucose did not change between 64 h and 65 h (Table 1). There is a suggestion of a gradual increase in*M*
_{1},*M*
_{2}, and*M*
_{3} between 64 h and 65 h. This is particularly apparent for*M*
_{3}, being 9–15% more at 65 h than at 64 h. There is the suggestion during the hour of a small increase in distributions in lactate from*subjects 1* and*3*.*M*
_{6} was ∼4%, and *m*
_{3} was about one-half that percentage. Other isotopomers were present at 0.78% or less. *M*
_{2} was about the same as*M*
_{3}, and*m*
_{2} was about one-half of *M*
_{2}.*M*
_{1} was similar to*M*
_{2} and*M*
_{3}, and*m*
_{1} appeared to be somewhat more than*m*
_{2}.

The R_{a} of glucose from*Eq. 1
*, by reference to the data in Table 1, calculates to 9.1–10.4 μmol ⋅ min^{−1} ⋅ kg^{−1}(Table 2), with endogenous GP only 0.4 μmol less. Unlabeled lactate diluted lactate from blood glucose undergoing Cori cycling, D, ∼1.5-fold. About 20% of the R_{a} of glucose was cycled. The percentage of GP contributed by GNG ranged from 23.4 to 40.4%.

%Excess ^{13}C breath CO_{2} at 64 h and 65 h, multiplied by 0.65, is recorded in Table 3. Comparison is made with the*M*
_{1} measured in the glucose. As is evident, while quantitation is uncertain, most of*M*
_{1} arose by fixation of^{13}CO_{2}formed from the [U-^{13}C_{6}]glucose. In the calculations that follow and those in Table 2, no corrections have been made for the contributions of^{13}CO_{2}to *M*
_{1} and*m*
_{1}. If, for example, *M*
_{1} and*m*
_{1} were set to zero, Cori cycling estimates, F in Table 2, would reduce to 0.152, 0.125, and 0.134, and %GNG in Table 2 would reduce to 30.7, 20.4, and 30.0%.

MID values in arterial blood lactate (from Table 1) and arterial alanine and in hepatic and renal vein blood lactate and alanine are recorded in Table 4. Means ± SE are for the five determinations made of each subject from 64 h to 65 h. Distributions in lactate were remarkably similar in arterial, hepatic vein, and renal vein bloods. That was also so for alanine, although*M*
_{3} in hepatic vein blood was in all three subjects ∼10% less than in arterial blood. *M*
_{3} in alanine was one-half to two-thirds that in lactate.

In Table 5, means ± SE are recorded for the five determinations of MID in glucose and lactate from blood collected at 16–17 h from the four subjects fasted for 12 h and then infused with [U-^{13}]glucose while the fast continued. The values every 15 min are not shown, but*M*
_{3} increased by 12 ± 4% and*m*
_{3} increased by 16 ± 6% between 16 h and 17 h. Also not shown are the enrichments in breath CO_{2} and*M*
_{1} at 16 h and 17 h. Multiplying the enrichments in breath CO_{2} by 0.65 and assuming a contribution of GNG to GP of ∼50% (11), again, most of the*M*
_{1} appears to have arisen by^{13}CO_{2}fixation. The fraction of glucose molecules in the blood that recycled (*Eq. 3
*) was 15.1 ± 1.7%. Enrichments in lactate from arterial, hepatic vein, and renal vein blood were similar (Table 6).

## DISCUSSION

Percent GNG, as proposed for calculation most recently by Tayek and Katz (20), derives from two equations, *Eqs.4
* and *
5
*
Equation 4
Equation 5Note that, in *Eq. 4
*, the percentages of mass isotopomers are weighted for the number of their^{13}C atoms. The product of those equations times 100 is then equated to %glycogenolysis, and*Eq. 5
* times 100 is equated to percent Cori cycling (20). Introducing the distributions of isotopomers in Table 1 into *Eqs. 4
* and *
5
* yields percent contributions of GNG of 68.8, 43.0, and 62.0%, respectively, rather than 40.4, 23.4, and 34.9% (Table 2). In addition, Cori cycling would range from 28 to 36% rather than from 16 to 22% (Table 2).

Before examination of the reasons why *Eqs.4
* and *
5
* give higher estimates than *Eqs. 2
* and *
3
*, the difference between isotopic exchange and dilution requires further emphasis (10). Assume that two molecules of lactate, each with three atoms of^{13}C, are converted to glucose. Assume that in the conversion each undergoes exchange of^{13}C for^{12}C in the tricarboxylic acid (TCA) cycle, so that each triose phosphate converted to glucose has only one ^{13}C atom. One molecule of glucose was formed with one-third of its atoms being^{13}C. The same amount of glucose would have been formed if there had been no exchange. Assume instead that the two molecules of [^{13}C]lactate are diluted by four unlabeled lactate molecules, and then the six lactates are converted to glucose without exchange. Of the 18 carbons of glucose formed, one-third will again have^{13}C, but the net synthesis will be three molecules of glucose. Thus dilution, not exchange, results in a net increase in GNG.

Because *Eq. 4
* includes isotopomer percentages weighted for ^{13}C atoms, “dilution” includes both exchange and dilution.*Equation 2
* removes the contribution of exchange by treating each labeled triose unit in lactate and glucose, no matter how many of its carbons are labeled with^{13}C, as having all three carbons labeled. In the calculation of GNG originally proposed by Tayek and Katz (19), the other dilution factor, now *Eq. 6* in Ref. 20, was for dilution of pyruvate in the TCA cycle in its conversion to glucose and was set equal to 3 (*M*
_{1} +*M*
_{2} +*M*
_{3})/(*M*
_{1}+ *M*
_{2} +*M*
_{3}). Because that factor is only more than 1.0 to the extent of exchange (20), its use (19) contributed to the overestimations of GNG.

In *Eqs. 2
* and *
3
*, the factor 0.5 is required because one-half of the triose units forming the glucose molecules of masses*M*1,*M*2, and*M*3 are unlabeled and are not derived from [U-^{13}C_{6}]glucose. The equations must represent the dilution and fraction only of the [U-^{13}C_{6}]glucose cycled if the [U-^{13}C_{6}]glucose is to be used to trace the fate of unlabeled glucose endogenously produced.

Multiplying *Eq. 2
* by*Eq. 3
*, i.e., D × F, yields the contribution of GNG to the R_{a}glucose
Equation 6
*Equation 6
* provides evidence for the correctness of *Eqs. 2
* and *
3
*, because their product, if correct, must in theory yield *Eq. 6
*. That is because the estimation of the contribution of GNG by MID is analogous to measuring the ratio of the specific activity or enrichment in arterial blood glucose to that in arterial blood lactate on giving labeled lactate. At steady state, with the assumption that blood lactate specific activity or enrichment is that of intrahepatic pyruvate, if the ratio is 1.0, all blood glucose is formed by GNG. To the extent the ratio is less, the contribution of GNG is less. The need to use isotopomer analysis for quantitation rather than specific activities or enrichments is that the contributions of dilution can be separated from those of exchange in determinating the ratio.

For further understanding, these considerations are best illustrated by a numerical example. In Fig. 1, in the fasted state, 100 molecules/unit time of 100% enriched [U-^{13}C_{6}]glucose,*M*6, are infused into the blood, 500 molecules of glucose are released into the blood by GNG, and 1,000 molecules of unlabeled lactate enter the blood and are converted to glucose, i.e., via GNG. Twenty percent of glucose entering the blood is converted to lactate that is recycled to glucose, i.e., Cori cycling. There is assumed to be no exchange, so the movement of ^{13}C is in units of three and six ^{13}C atoms.

At steady state, 1,375 molecules of glucose/unit time enter the blood, 1,225 with no label, *M*0, 50 labeled *M*1 and 100 labeled*M*6. Twenty percent are recycled, i.e., 245, 10, and 20, respectively. The remaining 1,100 molecules are metabolized to CO_{2}and all else by brain and other tissues. The 275 glucose molecules cycled form 500 lactate molecules with no label,*m*0, and 50 with*m*3. Then the 1,550 molecules of lactate entering the blood by GNG are converted to 725*M*0 and 50*M*3. The percentage of the isotopomers of glucose and lactate in blood are recorded beside the numbers of molecules. If we apply *Eqs.1-3
*, R_{a}glucose = 100(100/7.27) = 1,375 molecules/unit time, D = (1.82 + 7.27)/3.23 = 2.82, and F = 1.82/(1.82 + 7.27) = 0.2. Then GNG = 1,375 × 2.82 × 0.2 = 775 molecules/unit time, GP equals 1,375 − 100 = 1,275 molecules/unit time, and the contribution of GNG = 100(775/1,275)= 60.8%. Thus, when the procedure for calculation proposed here is applied to MID in glucose and lactate that must exist under the set conditions, correct results are obtained.

Applying *Eq. 4
* gives the same dilution factor, 2.82, as *Eq. 2
*, because in the example there is no exchange of^{13}C with^{12}C. However, using*Eq. 5
*, the fraction recycled is 3.64/(3.64+7.27) = 0.33. Hence, the contributions of GNG are overestimated at 100(2.82)(0.33) = 92.7%, rather than 60.8%. Furthermore, Cori cycling is overestimated at 33%, rather than 20%. As is apparent from Fig. 1, *Eq. 5
*calculates the fraction of labeled glucose molecules in blood glucose no longer *M*6, i.e., 50/(50+100) = 0.33. However, the fraction of labeled molecules in the blood glucose that cycled is (10 + 20)/150 = 0.2. Because the fate of^{13}C is the same as that of^{12}C, if a true tracer-tracee relationship is to exist, 0.2 of the unlabeled carbon in blood glucose is cycled. The fraction of glucose carbon recycled must be the same as the fraction of molecules recycled, contrary to the conclusion in Ref.20, although of course six times as many carbon atoms as molecules of glucose are recycled.

Figure 2 depicts a prolonged fasting state when all glucose production is by GNG. Cori cycling is 10%, and 2,000 molecules of unlabeled lactate are converted to glucose. One-half the sum, 21.05, of the *m*3 molecules cycled, i.e., 1.05*m*3 molecules plus 20*m*3 molecules formed from the 10 *M*6 molecules, undergoes exchange to form 11.70 *m*1. If we apply the procedure for calculation proposed here, the results are correct, i.e., GP equals 1,122 molecules/unit time, Cori cycling is 10%, and the contribution of GNG to GP is 100%.

If conditions are altered, so that the exchange occurred in the conversion of lactate to glucose, i.e., in the TCA cycle rather than in the conversion of glucose to lactate, the percentage of mass isotopomers *m*
_{1}and *m*
_{3} would be different, i.e.,*m*
_{1} = 1.17/2,244 = 0.052% and *m*
_{3} = 21.05/2,244 = 0.938%. But because*M*
_{1} and*M*
_{3}, as well as*m*1, and*m*3, are treated the same in the equations, correct results are still obtained, i.e.,*M*
_{1} +*M*
_{3} = 1.82% and*m*
_{1} +*m*
_{3} = 0.99% in either case. When *Eqs. 4
* and *
5
* are applied to the conditions of Fig. 2, GNG is overestimated at 161% and Cori cycling at 18.2%.^{1}

Figure 3 also depicts a prolonged fast when all GP is by GNG, and Cori cycling is 10%. As in Fig. 1, movement is only in three and six ^{13}C units. However, per unit of time, of the 133.34 molecules of lactate from blood glucose mixing with 2,000 molecules of unlabeled lactate, 1,000, rather than being converted to glucose, return to the tissues, producing unlabeled lactate. This is also an exchange (10) that must be considered, because the equilibration between blood lactate and tissue pyruvate is extensive. The result in the example is the net production of 566.67 molecules of glucose from 1,334.34 molecules of lactate per unit time.

From *Eqs. 2
* and *
3
*, D = 15.84/0.99 = 16.0, and F = 0.84/15.8 4 = 0.053. The rate of GNG is then 666.67 × 16 × 0.53 = 566.67, and therefore the %contribution of GNG to GP still calculates to 100%. However, the introduction of the pyruvate ↔ lactate exchange results in an underestimation of Cori cycling, 5.3% rather than 10%. Therefore, the Cori cycling estimates in Table 2should be considered underestimates, to the extent labeled lactate formed in the cycling exchanges with unlabeled lactate before conversion to glucose.

Exchanges in the conversion of glucose to lactate and lactate to glucose, resulting in the formation of*m*0 from*m*3, are assumed negligible. This is justified because*M*
_{3} ≈*M*
_{2} >>*M*
_{1}, with correction for the contribution of^{13}CO_{2}fixation (Table 3), and*m*
_{3} >>*m*
_{1}. The formation of *m*0 from*m*3 should be less than the formation of *m*1 from*m*3. That*M*
_{1} is much less than *M*
_{2} and*M*
_{3} is to be expected, because other than by^{13}CO_{2}fixation, *M*1 can only be formed via the pentose cycle and by label from [U-^{13}C_{3}]lactate after experiencing a turn of the TCA cycle.*M*2 and*M*3 can be formed via lactate conversion to oxaloacetate, equilibration between fumarate and oxaloacetate, and then conversion of oxaloacetate to glucose. If the formation of *m*0 occurred by exchange during the conversion of labeled glucose to lactate, the estimated contribution of GNG would be unaffected, but Cori cycling would be underestimated.

In normal subjects fasted overnight and infused with [U-^{13}C]glucose for 3 h (19) and 4 h (20), from the reported data applying *Eq.6
*, percent contribution of GNG to GP is 18.5 ± 1.3% (*n* = 14). From the data in Table5, applying *Eq. 4
*, the percent contribution calculates to 17.3 ± 2.5% (*n* = 4). That is one-half or less than in other quantitations (6, 11, 17, 21). After 60 h of fasting, GNG calculates to a contribution of 41% or less (Table 2). At 60 h, ∼85% would have been expected, allowing for a 10% contribution by glycerol (11, 12) and a 5% contribution by glycogenolysis (20).

There are several reasons why the correct equations give underestimates. Glycerol’s conversion to glucose is included in glycogenolysis rather than GNG. The conversion of amino acids to glucose without pyruvate as an intermediate also results in an underestimation of GNG and an equivalent overestimation of glycogenolysis. Thus the conversion to glucose of aspartate [via oxaloacetate → phospho*enol*pyruvate (PEP)] and of glutamine and glutamate (via α-ketoglutarate → oxaloacetate → PEP) would calculate as glycogenolysis, except to the extent of PEP cycling, i.e., PEP → pyruvate → oxaloacetate → PEP (16). For PEP cycled into pyruvate to be included in the estimate of the contribution of GNG, the pyruvate would have to equilibrate with blood lactate. Labeled oxaloacetate and α-ketoglutarate exchanges during equilibrium with circulating unlabeled aspartate, glutamate, and glutamine also result in underestimations (3, 16). Other non-MID analysis methods for estimating GNG by labeled pyruvate using ^{13}C- or ^{14}C-labeled tracers have the same limitations.

Also, the MID values in blood lactate may not reflect adequately those in intrahepatic and intrarenal pyruvate (to the extent that kidney contributes to GNG). Although there is evidence for an adequate reflection, at least under certain conditions (8, 23), there is also evidence to the contrary (2, 3, 13). Similar enrichments in arterial, hepatic vein, and renal vein lactate (Tables 4 and 6) support the enrichment in arterial plasma lactate reflecting that in liver and kidney. However, the enrichments in hepatic vein lactate after an overnight fast appear somewhat less than in arterial lactate, and the enrichment is lower in alanine than in lactate after 60 h of fasting.

If the correct equation is used, estimates might be more reasonable were it not for systematic bias in mass spectral analysis. Thus, when methods for analyzing spectral data are used, there can be errors in estimates of mass isotopomers when enrichments are low (1, 14), as encountered here in*M*
_{1},*M*
_{2},*m*
_{1}, and*m*
_{2}. The optimal approach to eliminating systematic bias is yet to be achieved (1). Despite giving prime and infusing [U-^{13}C]glucose doses for 5 h, labeling from lactate, as reflected in isotopomer*M*
_{3}, still had not reached steady state. That is so even when we consider that the contribution of GNG increases with the duration of fasting (11). The failure to achieve steady state presumably reflects the time needed for [^{13}C]lactate to equilibrate with unlabeled lactate/pyruvate and recycle into glucose (15).

In conclusion, when correctly calculated, estimates of the contributions of GNG to GP and Cori cycling from isotopomer distributions in blood glucose and lactate on [U-^{13}C_{6}]glucose administration are underestimates. The reasons for that are several.

## Acknowledgments

This study was supported by National Institute of Diabetes and Digestive and Kidney Diseases Grants DK-14507 and DK-35543, the Karolinska Institute, and the Nobel Foundation.

## NOTE ADDED IN PROOF

Data were recently reported from experiments in which [U-^{13}C]glucose was infused into fasted piglets {Wykes, L. J., F. Jahoor, and P. J. Reeds. Gluconeogenesis measured with [U-^{13}C]glucose and mass isotopomer analysis of apoB-100 amino acids in pigs. *Am. J. Physiol.* 274 (*Endocrinol. Metab.* 37): E365–E376, 1998}. The authors calculated by several methods the contribution of gluconeogenesis to glucose production 20–22 h into the fast. Values calculated by using the equation of Tayek and Katz (20) were consistently >100%. With the use of the data of Wykes et al. (Table 1 in Wykes et al.) and our*Eq. 6
*, the contribution calculates to 59%.

## Footnotes

Address for reprint requests: B. R. Landau, Dept. of Medicine, Case Western Reserve Univ. School of Medicine, 10900 Euclid Ave., Cleveland, OH 44106-4951.

↵1 Tayek and Katz, who concluded in calculating gluconeogenesis (19) to provide an adequate approximation when recycling is low (20), doubled the product of the fraction of glucose carbon recycled and the dilution by unlabeled carbon. However, the fraction of glucose recycled times the extent of its dilution equals the fraction of glucose production by gluconeogenesis, not one-half that fraction. When this is combined with the use of the “dilution via TCA cycle” factor, a large overestimation of gluconeogenesis results. The overestimation is reduced by

*1*) use of an equation for calculating the recycling of glucose carbon,*Eq. 3*of Ref. 19 and*Eq. 2*of Ref. 20, with weighted isotopomers (so, for example, using that equation, the scheme of Fig. 2 would give a fraction of 0.067 and not 0.100),*2*) the extent blood lactate is not the measure of intrahepatic pyruvate, and*3*) the extent gluconeogenic substrates are converted to glucose without pyruvate as intermediate (see discussion). Estimates of glucose recycling from differences in R_{a}glucose measured with irreversible tracers, e.g., [3-^{3}H]glucose and [6-^{3}H]glucose, and reversible tracers, e.g., [^{14}C]glucose and [^{13}C]glucose, also expressed in*Eq. 3*of Ref. 19 and*Eq. 3*of Ref. 20, suffer again from the failure to exclude exchange and to include unlabeled triose phosphate with labeled triose phosphate as having been cycled.

- Copyright © 1998 the American Physiological Society