©1995 by The American Society for Biochemistry and Molecular Biology, Inc.
Limitations of the Mass Isotopomer Distribution Analysis of Glucose to Study Gluconeogenesis
SUBSTRATE CYCLING BETWEEN GLYCEROL AND TRIOSE PHOSPHATES IN LIVER (*)

(Received for publication, February 17, 1995; and in revised form, June 7, 1995 )

Stephen F. Previs (1) Charles A. Fernandez (2) Dawei Yang (1) Maxim V. Soloviev (1) France David (1) Henri Brunengraber (1)(§)

From the  (1)Departments of Nutrition and (2)Biomedical Engineering, Case Western Reserve University, Cleveland, Ohio 44106

ABSTRACT
INTRODUCTION
EXPERIMENTAL PROCEDURES
RESULTS
DISCUSSION
FOOTNOTES
ACKNOWLEDGEMENTS
REFERENCES

ABSTRACT

Mass isotopomer distribution analysis allows studying the synthesis of polymeric biomolecules from N, C-, or ^2H-labeled monomeric units in the presence of unlabeled polymer. The mass isotopomer distribution of the polymer allows calculation of (i) the enrichment of the monomer and (ii) the dilution of the newly synthesized polymer by unlabeled polymer. We tested the conditions of validity of mass isotopomer distribution analysis of glucose labeled from [U-C(3)]lactate, [U-C(3)]glycerol, and [2-C]glycerol to calculate the fraction of glucose production derived from gluconeogenesis. Experiments were conducted in perfused rat livers, live rats, and live monkeys. In all cases, [C]glycerol yielded labeling patterns of glucose that are incompatible with glucose being formed from a single pool of triose phosphates of constant enrichment. We show evidence that variations in the enrichment of triose phosphates result from (i) the large fractional decrease in physiological glycerol concentration in a single pass through the liver and (ii) the release of unlabeled glycerol by the liver, presumably via lipase activity. This zonation of glycerol metabolism in liver results in the calculation of artifactually low contributions of gluconeogenesis to glucose production when the latter is labeled from [C]glycerol. In contrast, [U-C(3)]lactate appears to be a suitable tracer for mass isotopomer distribution analysis of gluconeogenesis in vivo, but not in the perfused liver.

In other perfusion experiments with [^2H(5)]glycerol, we showed that the rat liver releases glycerol molecules containing one to four ^2H atoms. This indicates the operation of a substrate cycle between extracellular glycerol and liver triose phosphates, where ^2H is lost in the reversible reactions catalyzed by alpha-glycerophosphate dehydrogenase, triose-phosphate isomerase, and glycolytic enzymes. This substrate cycle presumably involves alpha-glycerophosphate hydrolysis.


INTRODUCTION

Mass isotopomer distribution analysis (MIDA) (^1)is a powerful tool to study the synthesis of polymeric molecules from the condensation of identical N-, C-, or ^2H-labeled subunits (1, 2, 3, 4, 5, 6, 7, 8, 9) . The polymer is characterized by a mass isotopomer distribution (MID), which can be predicted from the isotopic enrichment of the precursor subunit (p), using probability analysis and multinomial expansion. Conversely, the pattern of excess isotopomer (^2)frequencies in a polymer allows calculation of p and of the fraction of polymer molecules that are newly synthesized (f) from the labeled precursor. Then, 1 - f represents unlabeled polymer molecules which entered the sampling site, thus diluting the labeling of the newly synthesized pool. MIDA, originally conceived by Strong et al.(1) , has been extensively developed by the groups of Hellerstein(2, 3, 4, 5) , Kelleher(6, 7) , and Lee (8, 9) to study fatty acid and cholesterol synthesis from C substrates and ^2H(2)O.

MIDA can, in principle, be applied to very long polymers such as proteins or to simple dimers. Glucose can be considered as a dimer formed from the condensation of two triose subunits whose labeling patterns should be, under most conditions, identical because of extensive equilibration via triose-phosphate (TP) isomerase(10) . Investigation of gluconeogenesis (GNG) by MIDA is an attractive possibility since it should not be subjected to artifacts of isotope exchange, which lead to underestimations of rates of glucose production (11, 12, 13) .

The main substrates of in vivo GNG are the gluconeogenic amino acids of proteins and glycerol derived from lipolysis. The Cori cycle uses the GNG pathway but does not contribute new glucose to the body's economy. GNG from proteins and the Cori cycle pass through three C(3) interconverted intermediates, i.e. lactate, pyruvate, and alanine.

We recently (14) infused [U-C(3)]glycerol to 60-h fasted humans and assayed the MID of plasma glucose. The contribution of GNG to glucose production, calculated from the MID of glucose, was much lower than what could be expected to occur in 60-h starved humans. In these subjects, glycogenolysis could contribute only a minuscule fraction of glucose production. It was hypothesized (14) that this apparent dilution results from variations in the MPE of triose phosphates (TP) across the liver lobule. Such variation could result from a large decrease in the glycerol concentration across the lobule. In the present study, we investigated in perfused rat livers and in live rats and monkeys, the mechanism that results in this unexpected labeling of glucose from [U-C(3)]glycerol. We also tested the validity of [U-C(3)]lactate as a tracer of GNG. Our data show that physiological zonation of glycerol metabolism in liver results from a major decrease in substrate concentration across the lobule. Zonation of glycerol metabolism results in gradients of enrichment of TP, which explain the observed MID of glucose. In addition, we found evidence for the operation of a substrate cycle between extracellular glycerol and liver TP.


EXPERIMENTAL PROCEDURES

Materials

Enzymes and coenzymes were purchased from Boehringer Mannheim. Other chemicals were from Sigma-Aldrich. [U-C(3)]Lactate (99%), [U-C(3)]pyruvate (99%), [U-C(3)]glycerol (99%), [2-C]glycerol (99%), and [^2H(8)]glycerol (98%) were from Isotec.

Liver Perfusion Experiments

Livers from 48-h starved Sprague-Dawley rats (150-160 g, Charles River) were perfused (15) with non-recirculating Krebs Ringer bicarbonate buffer (20 ml/min) containing glucose (0 or 4 mM), octanoate (0 or 0.2 mM), lactate (1 mM), and glycerol (0.1 mM). After 10 min of equilibration, unlabeled lactate or glycerol was replaced by [U-C(3)]lactate, [U-C(3)]glycerol, or [2-C]glycerol. Other perfusions were conducted with 1 mM [U-C(3)]pyruvate. At 30 min, the livers were freeze-clamped and stored in liquid N(2) until analysis.

To measure the kinetics of hepatic glycerol uptake, eight rat livers were perfused each with four sequential 10-min plateaus of increasing [^2H(5)]glycerol concentration, to cover the range 0.1-3.5 mM. The perfusate also contained 1 mM lactate. The concentration and MID of glycerol were measured in effluent perfusate sampled at the end of each plateau. In some experiments, the concentration of pyruvate was assayed at 10 min, before switching to labeled tracers.

To measure the loss of ^2H from [^2H(5)]glycerol, we perfused six livers with 300 ml of recirculating perfusate containing 1 mM lactate and [^2H(5)]glycerol at initial concentrations of 0.2, 0.4, and 0.8 mM. Perfusate was sampled every 30 s for 10 min to measure the concentration and the MID of glycerol.

In Vivo Experiments

Two-day starved rats (170-180 g), prefitted with permanent catheters in the jugular vein and carotid artery, were infused with lactate (10 µmol min kg) and glycerol (5 µmol min kg). In the first series, lactate was [U-C(3)]lactate (99%); in the second series, glycerol was [U-C(3)]glycerol (99%). Arterial blood samples (0.8 ml) were taken at 3, 4, and 5 h. The animals were then quick-killed and the liver freeze-clamped.

Female Maccaca mulatta monkeys were anesthetized with halothane and infused with [U-C(3)]lactate (7 and 10 µmol min kg) or [U-C(3)]glycerol (2 µmol min kg). Arterial blood samples were taken at 3, 4, and 5 h. Samples of liver were then freeze-clamped.

Analytical Procedures

Glucose and glycerol were isolated from the effluent perfusate and from neutralized perchloric acid extracts of plasma, using mixed-bed ion exchange resins. Part of the glucose was permethylated (16) and assayed by ammonia positive chemical ionization GC-MS to get the MID of the whole molecule(17) . Ions monitored were m/z 268-274. The MID of glycerol was measured by ammonia chemical ionization GC-MS of the triacetyl derivative (m/z 236-241). The MID of lactate was measured by electron ionization GC-MS of the TBDMS derivative (m/z 261-264). The concentration of unlabeled pyruvate in the 10-min effluent perfusate was assayed by isotope dilution GC-MS as a hydroxamate di-TBDMS derivative, using [U-C(3)]pyruvate as internal standard. The MID of PEP was assayed (^3)in neutralized perchloric acid extracts of livers. Briefly, the analysis involves reducing pyruvate in the extract to lactate with NaBH(4), enzymatic conversion of PEP to pyruvate, and assay of the latter as hydroxamate di-TBDMS derivative. All GC-MS analyses were run with 3 injections/sample. Areas under all peaks were determined by computer integration and corrected for naturally occurring heavy isotopes, taking into account (i) the variability of measured natural MID compared to theoretical values (18) and (ii) the skew of natural C enrichment in multiply labeled compounds(18) . This skew has been originally described by Rosenblatt et al.(19) .

Calculation of the MID and Dilution of TP

Assume the existence of a single hepatic pool of DHAP/GAP labeled from either [U-C(3)]glycerol or [U-C(3)]lactate. [C]Glucose made by GNG is diluted by unlabeled glucose derived from either glycogenolysis, or GNG from an unlabeled pool of DHAP/GAP. The steady-state MID of glucose leaving the liver, corrected for natural enrichment(18) , can be written in terms of the steady-state MID of the TP pool and the fractional inflow of unlabeled glucose:

where M represents the mol fraction of the nth mass isotopomer of the subscripted compound, and f is the fraction of glucose produced by GNG. For n > 0, M = 0. The parameter n ranges from 0 to 6 since up to six C atoms are incorporated in glucose molecules. Note that M and M = 0 for i > 3. Isotopic equilibrium between DHAP and GAP is assumed. We used non-linear parameter estimation techniques (20) to determine the MID of TP and f values that best fit the measured MID of glucose.

Hellerstein et al.(2, 3) calculate f for a polymer, labeled from an M(1) monomeric precursor, by monitoring the excess labeling of the polymer at two masses, M(1) and M(2). A similar calculation can be derived from a simplification of . When [U-C(3)]glycerol is infused, the MID of glucose includes mostly M(0), M(3), and M(6). Thus, the TP are mostly M(0) and M(3). The explicit expressions for M(3) and M(6) of glucose are given by and .

Assuming isotopic equilibrium of GAP and DHAP, i.e.M = M = M, and become and .

Using the approximation M(0) = (1 - M(3)), the ratio of excess mass isotopomer in the product is shown by ,

or using the notation of Hellerstein and Neese (p = M(3); (5) ), by .

The use of [U-C]glycerol greatly simplifies the technique of Hellerstein et al. because of the low natural abundance at M(3) and M(6) glucose. All MIDs here are corrected for natural abundance(18) . For this case, the construction of a theoretical standard curve (2, 3) for the particular glucose derivative used is unnecessary. Therefore, the enrichment of the triose phosphate pool can be calculated directly by solving for p in terms of M(6)/M(3). Using the calculated value of p, the fraction of glucose production derived from GNG, i.e.f, is calculated by solving or for f.

Assuming there are two pools of labeled TP, the relative abundances of M(3) and M(6) mass isotopomers of glucose assuming isotopic equilibrium between DHAP and GAP are given by and ,

where the subscripts 1 and 2 refer to the fractional glucose contributions from labeled TP pools 1 and 2. Then, has four unknowns, f(1) and f(2) (the fractional contributions of each pool of TP to GNG) and M(3) and M(3) (their enrichments).

The TP enrichment calculated using MIDA under the assumption of one labeled pool does not reflect the arithmetic average of the enrichments of the two pools (f(1) + f(2)). With no further information, one cannot determine the enrichments of these two pools and thus the fractional contribution of GNG to glucose. This holds true whenever there are more than two labeled TP pools or, more likely, when a gradient of enrichment exists between the periportal and perivenous regions of the liver lobule.

The total amount (µg atom) of C in a population of glucose molecules with a given MID is given by .

Simulation of Substrate Concentrations across the Liver Lobule

The liver lobule is simulated as a plug-flow reactor(21) , i.e. a tube of length L, cross-section A, and inside surface/length S. A substrate, e.g. glycerol, flows through this tube with inlet and outlet concentrations of C and C, respectively (C < C), and perfusion rate Q. The steady-state rate of change of glycerol concentration at position z, C(z), along the length of the tube can be obtained from a one-dimensional mass balance that accounts for flow and metabolism.

The right side of this equation represents the loss of substrate by metabolism expressed as a Michaelis-Menten reaction rate, as shown by ,

where K is a constant. J(max)(z), the maximum rate, may vary with position. In the following analysis, let us assume steady-state conditions and that J(max) decreases linearly with length along the lobule, as shown by ,

where J(max)^0 is the initial rate. When the constant alpha is zero, the reaction rate does not change along the lobule. Using the dimensionless terms: = C(z)/C, = z/L, beta = K/C, = J(0)LS(L)/QC, we can express the model as shown by .

Upon solution using separation of variables, we find

where 0 leq leq1 and 0leq leq 1. If we consider (), for alpha > 0, then is quadratic and its solution is given by .

The solution for alpha = 0 is given by .

We can solve for using measured outlet concentrations ( = 1) by rearrangement of , as shown by .

We can calculate the relative flux along the lobule using the dimensionless form of , which is shown in .


RESULTS

Fig. 1A (solidsymbols) shows the kinetics of [^2H(5)]glycerol uptake by perfused livers from 2-day starved rats. A Lineweaver-Burk plot of the data, for influent concentrations ranging from 0.1 to 1.2 mM (r = 0.99), yields K and V(max) of 0.78 mM and 2.1 µmol min (g, wet weight), respectively. The V(max) is similar to that reported in (22) and (23) . The K, which is in the range of the K of glycerol uptake from dog plasma (1.7 mM; (24) ), is much greater than the K of glycerol kinase in rat liver (3-10 µM; Refs. 22, 25, and 26). This confirms that glycerol uptake by the liver is diffusion-limited(23) . Fig. 1A also shows (opensymbols) the fractional uptake of glycerol; 85-90% of physiological influent concentrations (0.05-0.2 mM) was taken up in a single passage through the liver.


Figure 1: Kinetics of [^2H(5)]glycerol uptake by the perfused rat liver. PanelA, rate of uptake (solid circles) and percent uptake in a single passage through the liver (opentriangles). The continuousline is the Michaelis-Menten curve calculated from the Lineweaver-Burk plot of the uptake for influent concentrations of 0.1-1.2 mM. V(max) = 2.1 µmol min (g, wet weight) and K = 0.78 mM. PanelB, production of unlabeled glycerol (solidsquares) and MPE of M(5) glycerol isotopomer in effluent perfusate (versus 94% in influent perfusate).



In the same experiments, we found that the MPE of [^2H(5)]glycerol decreased in a single passage through the liver. Fig. 1B (opensymbols) shows the M(5) MPE of effluent glycerol. Note that this decrease in MPE occurs mostly in the physiological range of plasma glycerol concentrations. Fig. 1B (closedsymbols) also shows the absolute release of unlabeled glycerol. This release was erratic and independent of inflowing glycerol concentration. At high inflowing [^2H(5)]glycerol concentrations, the release of unlabeled glycerol was not measurable with precision. Similar decreases in total MPE were observed in experiments with [2-C] and [U-C(3)]glycerol (not shown).

In addition, for influent concentrations of [^2H(5)]glycerol of 0.4-1.0 mM, effluent glycerol contained a greater MPE of M(1) to M(4) isotopomers than the influent perfusate. This could not be accounted for by the natural enrichment of released unlabeled glycerol. The production of M(1) to M(4) isotopomers could not be detected in experiments with influent [^2H(5)]glycerol concentrations lower than 0.4 mM and higher than 1.0 mM because of (i) the near complete exhaustion of the labeled substrate, and (ii) its low isotopic dilution, respectively. The release of M(1) to M(4) glycerol isotopomers corresponds to 7-10% of the uptake of M(5) glycerol. The relative proportions of the M(1) to M(4) isotopomers were 3 (M(1)), 5 (M(2)), 32 (M(3)), and 100 (M(4)).

To better characterize the loss of ^2H from [^2H(5)]glycerol, we perfused livers with a large volume (300 ml) of recirculating perfusate containing 1 mM lactate and various concentrations of [^2H(5)]glycerol. Fig. 2shows the accumulation of M(1) to M(4) glycerol isotopomers (M(3) > M(4) > M(2) > M(1)) when the recirculating perfusate contained initially 0.8 mM [^2H(5)]glycerol. Similar MIDs of perfusate glycerol were obtained when the initial [^2H(5)]glycerol concentration was 0.4 and 0.2 mM (not shown). Total glycerol concentration decreased from 0.6 to 0.4 mM and from 0.2 to 0.05 mM, respectively.


Figure 2: Loss of ^2H from [^2H(5)]glycerol in the perfused rat liver. A liver was perfused with 300 ml of recirculating perfusate containing [^2H(5)]glycerol at an initial concentration of 0.8 mM. The decrease in total glycerol concentration is shown by the brokenline. Perfusate glycerol was progressively enriched with M(1) to M(4) isotopomers identified in the caption.



Table 1shows the MID of glucose isolated from non-recirculating effluent liver perfusates, rat plasma, and monkey plasma. Glucose was labeled from [U-C(3)]lactate, [U-C(3)]pyruvate, [U-C(3)]glycerol, or [2-C]glycerol. In many cases, lactate and glycerol were infused together (with alternate labeling) to simulate the physiological supply of gluconeogenic substrates. All data of Table 1are corrected for natural C enrichment by a technique that takes into account the skew of natural enrichment in multiply C-labeled molecules(18) .



In livers perfused with [U-C(3)]glycerol (Table 1, rows 2, 4, 8, and 9), the main labeled glucose isotopomers were M(3) and M(6), with much lower abundances of the other labeled isotopomers. This was expected since glycerol is a very direct precursor of glucose. Only a small fraction of [U-C(3)]glycerol was processed in the CAC, with loss of C, before generating M(1), M(2), M(4), and M(5) glucose. In contrast, with [U-C(3)]lactate (rows 1 and 3), the MID of glucose was more evenly distributed since all the label from the substrate passes through oxaloacetate and PEP. This results in losses of label in the CAC and in the PEP pyruvate oxaloacetate cycle. In livers perfused with unlabeled lactate and [2-C]glycerol (rows 10, 11), only M(1)- and M(2)-labeled glucose isotopomers were detected, as expected.

Since the isolated livers were taken from 2-day starved rats, they were essentially glycogen-depleted(27) , and all glucose production must have been derived from GNG. Parameter f, which quantitates the contribution of GNG to glucose production ( and ), should have been 100% in all cases (Table 1, rows 1-11). In fact, f ranged from 36 to 92%. When the influent concentration of [U-C(3)]glycerol was increased from 0.1 to 0.5 and to 1.5 mM, f increased from 75 to 85 and to 92%, respectively (Table 1, rows 2, 8, and 9). When glucose was labeled from [U-C(3)]lactate, f was 54% and 36%, in the absence and presence of 0.2 mM octanoate, respectively (rows 1 and 3). Also, when uniform labeling of lactate and glycerol was alternated, substantially different values of f were calculated (compare f in rows 1 and 2 and in rows 3 and 4). In similar perfusions conducted with 4 mM glucose in addition to 1 mM lactate and 0.1 mM [U-C(3)]glycerol, M(3) and M(6) glucose isotopomers were the only two for which MPE could be precisely measured (rows 9 and 10) corresponding to f of 3% and 1%. This was expected since unlabeled glucose was added to the perfusate to simulate the production of glucose from unlabeled precursors.

In 2-day fasted rats infused with lactate and glycerol (Table 1, rows 14 and 15), f was 97% and 75% when lactate or glycerol were uniformly labeled, respectively. When [U-C(3)]lactate was infused, no label was detected in plasma glycerol, and the final MID of plasma lactate was 0.41 ± 0.06 (M(1)), 0.67 ± 0.10 (M(2)), and 9.69 ± 1.14% (M(3), n = 6). When [U-C(3)]glycerol was infused, the MPE of plasma glycerol was stable between 3 and 5 h, with final level of 15.3 ± 1.8% (n = 6). In the same rats, lactate became labeled with final MID of 0.82 ± 0.10 (M(1)), 0.53 ± 0.08 (M(2)), and 1.82 ± 0.21% (M(3)).

So, of all the above cases where f should have been 100% (rows 1-11, 14, and 15), only in 2-day starved rats infused with [U-C(3)]lactate did f approach this value (row 14). In overnight-fasted monkeys (rows 13 and 14), f was also greater when [U-C(3)]lactate versus [U-C(3)]glycerol was infused (80% and 48%, respectively). So, for in vivo experiments in rats and monkeys, f for [U-C(3)]glycerol was 3/4 and 3/5 that for [U-C(3)]lactate.

In perfused livers, the MID of glucose labeled from [U-C(3)]glycerol or [2-C]glycerol yielded similar values for f (Table 1, rows 2 and 10) when the substrates were used at their maximal MPE. However, when [2-C]glycerol was used at 30% MPE, which is closer to what would occur in in vivo experiments, values of f were erratic (not shown). This is ascribed to the sensitivity of the M(2)/M(1) ratio when the M(2) enrichment is low (about 1.6%) compared to natural enrichment at M(2) (2%). This was the case, although permethylglucose has the lowest natural enrichment MID of all common glucose derivatives. For M(4) to M(6) glucose isotopomers, natural enrichment is practically zero, which increases the precision of measurements. So, to optimize the measurement of f, using the MID of glucose, we recommend (i) using uniformly labeled rather than singly labeled substrates and (ii) conducting GC-MS analysis of permethylglucose under ammonia chemical ionization(17) .

Péroni et al.(28) reported that, in rat livers perfused with 0.5 mM [2-C]glycerol (15% MPE) and 0.7 mM lactate, the MID of effluent glucose yielded a f of 91 to 100%, which is substantially higher than the 85% value of f we obtained using 99% MPE [2-C]glycerol (Table 1, row 11). Péroni et al. had analyzed the MID of glucose by electron ionization GC-MS of the aldonitrile pentaacetate derivative. To test for differences in analytical techniques, we reanalyzed the MID of glucose in our perfusions with 0.1 and 0.5 mM [2-C]glycerol (Table 1, rows 10 and 11), using the same derivative as Péroni et al.. Whether the assays were conducted under electron ionization (m/z 212-214, 314-316, 225-227) or ammonia chemical ionization (m/z 405-407), we obtained the same values of f as with permethylglucose (84-85%). We cannot fully explain why the data of Péroni et al. differ from ours. This may result from their use of higher than physiological concentrations of glycerol and/or from differences in techniques for correcting the measured MID of glucose for natural enrichment at M(1) and M(2): standard curves with commercial M(1) and M(2) glucoses (28) versus correction for skew of natural enrichment(18) . A small overestimation of the M(2)/M(1) ratio would substantially increase f.

Some investigators correct the measured MID of multiply C-labeled compounds by simple subtraction of the MID of an unlabeled standard(29) . Rosenblatt et al. have shown (19) that the natural MID of compounds is skewed with increasing C labeling. To illustrate the impact of this skew, consider the data shown on row 7 of Table 1(MID of glucose in livers perfused with 1 mM [U-C(3)]pyruvate + 0.1 mM glycerol). Taking the skew of natural MID into consideration(18) , we calculate a f of 72.4 ± 4.6%. If the raw data were corrected for natural MID as in (29) , f would be decreased to 63.7 ± 4.5% (p = 0.1). Thus, a proper correction for natural MID is required for precise calculation of f.

Table 2shows, for most of the same experiments as Table 1, the measured MID of liver PEP and the calculated MID of the TP (). When [U-C(3)]glycerol is the labeled substrate, the MIDs of PEP and of the TP are very different. When [U-C(3)]lactate is the labeled tracer, the distributions are quite similar, but significant differences remain, particularly between the MPEs of M(1) isotopomers. In addition, the total labeling of TP is much higher than that of PEP when [U-C(3)]glycerol (but not [U-C(3)]lactate) is the labeled substrate (Table 2, last column).



Table 3shows the balance of substrates and C in four series of perfused liver experiments where we had reciprocal and uniform labeling of lactate and glycerol (corresponding to rows 1-4 of Table 1). Balances are calculated by combining data from experiments with reciprocal labeling conditions. Note the very different absolute and fractional uptakes of lactate and glycerol. In these perfusions conducted with only lactate and glycerol, only 1/4 of the total uptake of these substrates was converted to glucose (Table 3, row F).




DISCUSSION

Although lipases have been described in liver(30, 31) , to the best of our review of the literature, this is the first report of the release of glycerol by the intact liver. This has implications for in vivo studies of glycerol metabolism, which usually assume that liver is the main site of utilization of glycerol released by lipolysis. In studies to be published elsewhere, we confirmed that the liver of live dogs releases glycerol.

In livers perfused with [^2H(5)]glycerol, the production of glycerol isotopomers with fewer than 5 deuterium atoms (Fig. 2) strongly suggests that a substrate cycle operates between extracellular glycerol and tissue TP. Cycling between [^2H(5)]glycerol and DHAP forms M(4) glycerol. Cycling between [^2H(5)]glycerol and GAP forms M(3) glycerol because the TP isomerase reaction removes specifically the R hydrogen on C-1 of DHAP(31) . Cycling between [^2H(5)]glycerol and glycolytic intermediates between GAP and PEP forms M(2) glycerol. Finally, cycling between [^2H(5)]glycerol and PEP that has gone through the PEP pyruvate oxaloacetate PEP cycle forms M(1) and probably M glycerol. As evidence for cycling between liver TP and oxaloacetate is the production of M(1), M(2), M(4), and M(5) glucose in perfused livers and animals infused with [U-C(3)]glycerol (Table 1, rows 2, 4, 8, and 9).

While alpha-glycerophosphate dehydrogenase and TP isomerase are reversible enzymes, glycerol kinase is irreversible. So alpha-glycerophosphate hydrolysis is probably catalyzed by some phosphatase. The rate of release of M(1) to M(4) glycerol isotopomers, which corresponds to 7-10% of the rate of uptake of M(5) glycerol, probably underestimates what would be the corresponding rate of cycling of non-deuterated glycerol. Since the energy of a carbon-deuterium bond is greater than that of a carbon-protium bond, one can expect sizable isotope effects at the alpha-glycerophosphate dehydrogenase and TP isomerase steps. Indeed a 2.9 kinetic isotope effect has been described for the isomerization of (R)-[1-^2H]DHAP, compared to the non-deuterated compound(32) . Additionally, in vivo studies showed the discrimination of liver TP isomerase against [1-^2H]GAP(33) .

This study points to two mechanisms for glycerol release from liver. The release of unlabeled glycerol in livers perfused with [^2H(5)]-, [U-C(3)]-, or [2-C]glycerol results probably from lipase activity and appears independent of inflowing glycerol concentration (Fig. 1B, solidsymbols). The release of M(1) to M(4) glycerol in livers perfused with [^2H(5)]glycerol (Fig. 2) can only be explained by a substrate cycle operating between extracellular glycerol, tissue TP, and lower glycolytic intermediates. This cycle, which probably involves a phosphatase, may contribute to the regulation of alpha-glycerophosphate concentration in liver cells. The phosphatase may allow production of glycerol via glycolysis or GNG. This question, which is out of the scope of the present study, will be investigated separately.

Table 3shows that in livers perfused with 1 mM lactate and 0.1 mM glycerol, in the absence and presence of 0.2 mM octanoate, only 1/4 of the lactate + glycerol uptake was converted to glucose (row F). Thus, 3/4 of the gluconeogenic substrates taken up must have been used for energy production, even in the presence of octanoate.

In Table 3, the calculations of the loss of label between [U-C(3)]lactate and glucose assume that the percent C from [U-C(3)]glycerol uptake found in glucose equals the percent conversion of glycerol to glucose (row H). This is a legitimate assumption since the conversion of glycerol to glucose is direct without carbon exchange. Rows H and J of Table 3show the percent of the uptake of C of each substrate recovered in glucose. This recovery is much larger for [U-C(3)]glycerol than for [U-C(3)]lactate. This is because (i) a large fraction of lactate uptake is oxidized to generate ATP and (ii) the conversion of [U-C(3)]lactate to glucose involves losses of label in the CAC and pyruvate cycles. The last row of Table 3shows the percentages of C from the glucose-bound [U-C(3)]lactate molecules that were recovered in glucose. The unrecovered percentages (74% and 80%) were lost by isotopic exchanges. Using Hetenyi's nomenclature(34) , these numbers would correspond to dilution factors of 3.8 and 4.9, respectively.

MIDA of glucose formed in the presence of a C-labeled gluconeogenic precursor allows, in principle, calculation of parameter f, i.e. the fraction of glucose production derived from GNG. The (1 - f) unlabeled fraction of glucose production derives presumably from preformed glycogen. In all experiments reported in rows 1-11, 14, and 15 of Table 1, f should have been 100% since the liver donors and the live rats had been starved for 2 days and thus depleted of liver glycogen(27) . Except for the infusion of [U-C(3)]lactate in live rats (row 14), the lower than 100% f values would seem to indicate the production of unlabeled glucose by the livers. Even more incompatible with the MID theory is the variation of f in alternate labeling experiments (compare f in rows 1 and 2 and in rows 3 and 4 of Table 1). Let us now show how these contradictory data can be ascribed to variations in the MPE of TP across the lobule.

The concept of metabolic zonation (35) is based on variations in enzymatic activities in hepatocytes across the liver lobule. Striking examples of enzymatic zonation are the distributions of the enzymes of urea and glutamine metabolism(36) . Although there is no information on the zonation of glycerol kinase, other gluconeogenic enzymes are present at higher activities in periportal compared to pericentral hepatocytes(37) .

Although variations in the activities of many enzymes across the lobule are well established, our data suggest that such variations are not necessary to induce metabolic zonation if (i) a substantial decrease in substrate concentration occurs across the lobule and (ii) the range of substrate concentration is close to or below the Kof the first limiting enzyme metabolizing the substrate. The K of glycerol kinase for glycerol is 3-10 µM in rat liver(22, 25, 26) , which is much lower than the 0.78 mMK for glycerol uptake in the perfused rat liver (Fig. 1A). Therefore glycerol uptake is transport-limited. and allow calculating the simulated profiles of relative glycerol concentrations (C/C) and relative glycerol flux (J/J(max)) across the liver lobule for different inflowing concentrations. When parameter alpha = 0, J(max) is constant across the lobule. Fig. 3(A and B) shows these profiles calculated if one assumes no zonation of glycerol kinase activity. Fig. 4(A and B) shows the corresponding profiles if one assumes a linear decrease to zero of glycerol kinase activity from periportal to pericentral cells (alpha = 1). Note that for the low 0.1 mM initial glycerol concentration, C/C and J/J(max) decrease by the same percentage (80%) across the lobule. This is because the range of glycerol concentration is much lower than the K for glycerol uptake. The curvature of these profiles is greater when one assumes a linear decrease in glycerol kinase activity across the lobule. At physiological influent glycerol concentration (0.1 mM), the decrease in glycerol concentration across the lobule, in a range much lower than the Kfor glycerol uptake, results in marked variations in the simulated relative flux of label into the cells (Fig. 3B and 4B).


Figure 3: Simulation of relative concentration of glycerol (panel A) and relative flux of glycerol (panel B) across the lobule. A constant glycerol kinase kinase activity is assumed. The simulations are run for three initial glycerol concentrations (0.1, 0.5, and 1.5 mM).




Figure 4: Simulation of relative concentration of glycerol (panel A) and relative flux of glycerol (panel B) across the lobule. The activity of glycerol kinase is assumed to decrease linearly to zero from the periportal to the pericentral area of the liver lobule. The simulations are run for three initial glycerol concentrations (0.1, 0.5, and 1.5 mM).



Let us turn to perfusions with [U-C(3)]lactate and unlabeled glycerol (Table 1, rows 1 and 3). The influent and effluent concentrations of [U-C(3)]lactate were 1.0 and 0.70 mM, respectively. The influent pyruvate concentration was zero, while its effluent concentration was about 4 µMi.e. much lower than the 400 µMK of pyruvate carboxylase for pyruvate(38) . We cannot assess the profile of pyruvate concentration across the lobule. Because of the high activity of liver lactate dehydrogenase, it is likely that the intracellular concentration of pyruvate (i) increased from zero to some unknown level in the periportal area and (ii) decreased further down the lobule as lactate concentration decreased by 30%. So the rate of pyruvate carboxylation decreased by at least 30% between some periportal cells and pericentral cells. The decrease in the rate of pyruvate carboxylation might even be greater than 30%, given that the activity of pyruvate carboxylase is greater in periportal than in pericentral cells(37) .

In vivo, there is always some pyruvate in plasma. So, to check whether the low f calculated from perfusions with [U-C(3)]lactate (Table 1, rows 1 and 3) resulted from the absence of pyruvate in the influent, we perfused some livers with 1 mM [U-C(3)]lactate + 0.2 mM [U-C(3)]pyruvate + 0.1 mM glycerol in the absence and presence of 0.2 mM octanoate (Table 1, rows 5 and 6). The calculated f was still low (62% and 87%). In these experiments, 86% and 95% of the influent [U-C(3)]pyruvate was taken up in a single passage through the liver. Finally, to insure a large supply of [U-C(3)]pyruvate to all areas of the liver lobule, we perfused livers with 1 mM [U-C(3)]pyruvate + 0.1 mM glycerol (Table 1, row 7). Contrary to our expectations, f was only 72%. Thus, in all liver perfusions with labeled lactate and/or pyruvate, unrealistic low values of f were calculated from the MID of glucose.

The variations of f when octanoate is added to the perfusate (Table 1, rows 3, 4, and 6) are difficult to explain. In the presence of [U-C(3)]lactate, f is decreased by octanoate (compare rows 1 and 3 of Table 1). In contrast, in the presence of unlabeled lactate + [U-C(3)]glycerol or in the presence of [U-C(3)]lactate + [U-C(3)]pyruvate, f is increased by octanoate (compare rows 2 versus 4 and rows 5 versus 6 of Table 1). We have no explanation for these effects of octanoate. Still, somehow octanoate must affect the profile of triose phosphate labeling across the liver lobule.

The above data lead us to conclude that, in livers perfused under the conditions of rows 1-11 of Table 1, the MIDs of TP and of synthesized glucose vary across the lobule. Therefore, the measured MIDs of effluent glucose and of liver PEP are composites, and not necessarily averages, of the MIDs of these compounds in cells across the lobule. Let us illustrate this point by two numerical examples.

Fig. 5shows the theoretical combination of two equal pools of glucose made from two homogeneous pools of TP labeled from [U-C(3)]glycerol. The TP are only labeled in M(3) isotopomers with enrichments p(1) and p(2) of 20% and 5%, respectively. Such conditions reflect the periportal and the pericentral cells of a liver perfused with [U-C(3)]glycerol. Since each pool is homogeneous, f(1) = f(2) = 100%. This condition and impose in each primary pool the M(3) and M(6) MID of glucose shown on Fig. 5. The combination of these two pools results in a measured MID of glucose from which one computes () erroneous values for f (73.5%) and of the M(3) MPE of TP (17%). Although the two pools of glucose were of equal size, the combined M(6)/M(3) ratio was not the average of the individual ratios.


Figure 5: Combination of two pools of glucose of equal size made from triose phosphates labeled from [U-C(3)]glycerol with a M(3) MPE (p) of 20% (pool 1) and 5% (pool 2). Each primary pool is constrained with a f of 100%. The combined pool (which would be actually measured in liver effluent) had a MID of glucose from which an artifactual f of 73.5% is calculated.



Similar calculations can be made (Fig. 6) for 20 equal pools of glucose made from 20 pools of TP whose M(3) MPE decrease exponentially along the lobule. The equation of decay is M(3)(pool i) = 100 exp(-0.095 (i - 1)). The rate constant 0.095 results in a decrease in the MPE of the TP to 15% of its original value between the 1st and the 20th pool. We observed a similar decrease in the [^2H(5)]glycerol MPE in perfused livers (Fig. 1B). For each pool of TP, f = 100%. Fig. 6shows the enrichments of M(3) TP, M(3) glucose, and M(6) glucose along a liver lobule divided into 20 compartments. Again, using , one computes impossible values for f (76% instead of 100%) and of p, the integrated M(3) MPE of TP (60% instead of 45%). Although a 100% M(3) MPE of TP would not occur in vivo, this simulation reflects the consequence of such exponential decrease from any initial MPE. This simulation also shows that the M(6)/M(3) ratio in glucose varies over a large range with p, i.e. the M(3) MPE of TP.


Figure 6: Simulation of the decrease in the M(3) MPE of triose phosphates across the liver lobule. The simulation assumes 20 equal pools of glucose made from 20 pools of TP whose M(3) MPE decreases exponentially from the periportal to the pericentral area. The equation of decay is M(3)(pool i) = 100 exp(-0.095 (i - 1)).



The only experiment where MIDA of glucose yields a plausible f (97%) is in the case of 2-day starved rats infused with unlabeled glycerol and [U-C(3)]lactate (Table 1, row 14). Such high f must result from practically constant enrichment of TP in the gluconeogenic cells. Note that the MID of liver PEP in these experiments (Table 2) is still different from the calculated MID of the TP. This may result from a different MID of PEP in non-gluconeogenic pericentral hepatocytes. Also, the f with [U-C(3)]lactate is much higher in live rats than in perfused rat livers. This may result from the equilibration of the MPEs of plasma lactate and pyruvate, via red cell metabolism, before and during passage through the liver. In contrast, in isolated livers perfused with [U-C(3)]lactate in red cell-free medium, the first periportal cells are probably not in contact with [U-C(3)]pyruvate. Also, the rate of perfusion of red cell-free perfusate (4-5 ml g min) is higher than the rate of blood perfusion in vivo (1 ml g min). The shorter transit time of labeled substrates through isolated livers and the absence of red cells do not allow equilibration of the MPE of lactate and pyruvate when only one of these two substrates is infused in the non-recirculating medium. We realize that, in isolated livers, f is lower than in vivo even when livers are perfused with a mixture of [U-C(3)]lactate + [U-C(3)]pyruvate (Table 1, rows 5 and 6). The marked increase in the [lactate]/[pyruvate] ratio between influent and effluent perfusates (from 5 to 23) reflects the lack of equilibration of lactate and pyruvate concentrations in these perfusions. In contrast, with labeled glycerol where the problem of equilibration of the two partners of a redox couple does not arise, the perfused liver data and the in vivo data are very compatible.

In 18-h starved monkeys infused with [U-C(3)]lactate, f was 80% (Table 1, row 16). This probably reflects a 20% contribution of preformed liver glycogen to glucose production. Although less than what was reported in 14-h fasted humans (23-42%; (39) ) using the incorporation of ^2H from ^2H(2)O on C-2 and C-6 of glucose, this percentage is reasonable for a small animal with a high metabolic rate. A similar value of f (82%) was reported by Lee et al.(40) in 24-h starved rats infused intragastrically with [2,3-C(2)]lactate.

The calculated total labeling of TP was much higher than the measured total labeling of PEP when [U-C(3)]glycerol (but not [U-C(3)]lactate) was the labeled substrate (Table 2, last column). This, in itself, does not reflect zonation of TP labeling from [U-C(3)]glycerol but different degrees of isotopic equilibrium between TP and PEP. Consider, for example, the pair of alternate labeling experiments whose data are presented in Table 2(rows 1 and 2) and in Table 3(first column of data). Roughly, in these experiments, glycerol and lactate contribute equally to glucose production (Table 3, rows K and L and first data column). The ratio (total C in TP)/(total C in PEP) depends on the degree of reversibility of the steps between TP and PEP. When [U-C(3)]glycerol + [C]lactate are used, the ratio ranges from (no reversibility) to 1.0 (reversibility at infinite velocity). With [C]glycerol + [U-C(3)]lactate, the corresponding range of the ratio is 0.5-1.0. A ratio of 4.7 with unlabeled lactate + [U-C(3)]glycerol (Table 2, row 2) shows reversibility between TP and PEP. A ratio slightly greater than 1.0 with [U-C(3)]lactate + unlabeled glycerol (Table 2, row 1) reflects probably (i) the effect of some errors in the many numbers that make up this ratio and/or (ii) heterogeneity of PEP labeling across the liver lobule (e.g. PEP in pericentral non-gluconeogenic hepatocytes may be less labeled than in periportal gluconeogenic hepatocytes).

In the in vivo experiments with [U-C(3)]glycerol (Table 1, rows 15 and 17), p was 3/4 and 6/10 those of the corresponding experiments with [U-C(3)]lactate (rows 14 and 16). This confirms the unsuitability of labeled glycerol for assessing the contribution of GNG to glucose production(14) . Our data contrast with those of Hellerstein's group(41) , who reported similar values for f (87-90%) in 48-h starved rats infused with [3-C]lactate, [1-C]lactate, and [2-C]glycerol. We found very different f when using lactate versus glycerol tracers (Table 1, rows 14-17). Elsewhere(42) , they report that, in 24-h starved rats infused with [2-C]glycerol, f was 86%. However, the glycogen content of the rats' livers (<5 mg g) could not supply the missing 14% of the glucose turnover (7 mg min kg) for more than 2-3 h.

We draw the following conclusions from our study. First, our data identify and confirm limitations of MIDA for measuring the contribution of GNG to glucose production. In this study conducted in animal models, and in our previous study conducted in humans(14) , [C]glycerol yields artifactually low contributions of GNG to glucose production. This is ascribed to metabolic zonation of glycerol metabolism across the liver lobule. This zonation does not necessarily require variations in glycerol kinase activity, but can be mostly ascribed to (i) the large decrease in glycerol concentration across the lobule and (ii) the low range of glycerol concentrations compared to the K of glycerol uptake by the liver. Second, our data suggest that [U-C(3)]lactate is a suitable substrate for MIDA of GNG in vivo. This is not the case for perfused livers, presumably because of disequilibrium of labeling between lactate and pyruvate across the lobule, resulting in marked variations in the MPE of TP. Third, measurements of the MID of glucose are more precise with uniformly labeled than with singly labeled C substrates. In the latter case, M(2)/M(1) ratios in glucose are very sensitive to a small error in the fairly high background correction at M(2). Fourth and last, correction of measured MID for natural enrichment should take into account (i) the variability of measured natural MID compared to theoretical values (18) and (ii) the skew of natural C enrichment in multiply labeled compounds(18, 19) .


FOOTNOTES

*
This work was supported by Grant DK35543 from the National Institutes of Health and the Nutrition Fund of the Cleveland Mt. Sinai Medical Center. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore by hereby marked ``advertisement'' in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

§
To whom correspondence should be addressed: Dept. of Nutrition, Mt. Sinai Medical Center, Cleveland, OH 44106-4198. Fax: 216-421-6661.

(^1)
The abbreviations used are: MIDA, mass isotopomer distribution analysis; DHAP, dihydroxyacetone phosphate; GAP, glyceraldehyde 3-phosphate; GC-MS, gas chromatography-mass spectrometry; GNG, gluconeogenesis; MID, mass isotopomer distribution; MPE, molar percent enrichment; PEP, phosphoenolpyruvate; TBDMS, tert-butyl dimethylsilyl; TP, triose phosphate(s).

(^2)
In the context of this report, the word ``isotopomer'' refers to ``mass isotopomer.'' Positional isotopomers are not considered here.

(^3)
S. F. Previs, M. Beylot, F. David, and H. Brunengraber, submitted for publication.


ACKNOWLEDGEMENTS

We thank M. Beylot for sharing data (28) with us in advance of publication.


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