A simple model for alanine metabolism in isolated rat hepatocytes

A simple model for alanine metabolism in isolated rat hepatocytes

Biochimica et Biophysica Acta, 1175(1993) 161-173 161 © 1993 Elsevier Science Publishers B.V. All rights reserved 0167-4889/93/$06.00 BBAMCR 13299 ...

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Biochimica et Biophysica Acta, 1175(1993) 161-173

161

© 1993 Elsevier Science Publishers B.V. All rights reserved 0167-4889/93/$06.00

BBAMCR 13299

A simple model for alanine metabolism in isolated rat hepatocytes Guy Martin, Nadine Vincent, Jacqueline Combet and Gabriel Baverel Centre National de la Recherche Scientifique (E.P. 18), Physiopathologie M~tabolique et R~nale et Spectroscopie RMN, Facult~ de M#decine Alexis Carrel, Lyon (France)

(Received 3 April 1992) (Revised manuscript received3 August 1992)

Key words: Alanine; Metabolism;Hepatocyte; Model A simple model describing reactions of alanine metabolism in isolated hepatocytes from fasted rats is proposed and applied to radioactive data obtained in experiments in which L-[1-14C]-, L-[2-14C] -, L-[3-14C] -, and L-[U-14C]alanine as well as L-alanine plus NaH14CO3 were used as substrates in parallel. Measurements of the rates of incorporation of the label into glucose and CO 2 and of accumulation of [1-14C]pyruvate, [1-14C]lactate, [1-14C]alanine and [1-14C]glutamate plus [1-14C]glutamine from the different substrates used allows to calculate flux of alanine carbon through the various metabolic steps taken into account in the model. The validity of this model is indicated by the agreement found between calculations and measurement of the 14CO2 released from [1-14C]alanine as well as between the values of flux through pyruvate carboxylase calculated in two different ways. It is shown that the oxaloacetate synthesized by pyruvate carboxylase enters into the Krebs cycle and into the pathway of phosphoenolpyruvate synthesis in about equal proportions and that about 40% of the oxaloacetate synthesized as a result of alanine metabolism is derived from the Krebs cycle operation. These results, together with the conclusion that flux of alanine carbon through pyruvate dehydrogenase is negligible, are in agreement with known characteristics of hepatic alanine metabolism in the fasted state and, therefore, provide further evidence for the validity of the model proposed in the present study.

Introduction

Because alanine plays an important role as a gluconeogenic and ureogenic precursor in the liver (see Refs. 1 and 2 for reviews), considerable interest and research have been focused on its metabolism in isolated rat liver cells [3-6], the most widely used experimental model for studying hepatic metabolism. Several authors have proposed models for quantifying the importance of the various products and pathways of hepatic alanine metabolism by using either 14C- or 13C-labelled alanine [4,7-9]. In these models and in models with other substrates [10-16], attempts were made to quantify total fluxes through the various pathways because, despite the presence of alanine as exogenous substrate, endogenous substrates were also metabolized at significant rates and therefore contributed to decrease the specific activity of the various intermediates formed from alanine. In theory, this approach requires to use a system which is in steady-state, a condition difficult to obtain experimentally in vitro.

Correspondence to: Pr. G. Baverel, Facult6 de M6decine Alexis Carrel, rue Guillaume Paradin, 69372 Lyon cedex 08, France.

In this work, we describe a method for measuring the rates through the various pathways of the metabolism of only alanine in isolated rat hepatocytes by using laC-labelled precursors. This "method can be used whether or not endogenous substrates are simultaneously metabolized and does not require to use hepatocytes metabolizing alanine under steady-state conditions. The mathematical model, glossary of symbols and calculation strategy are detailed in the Appendix. Materials and Methods Reagents

L-Alanine, glutaminase (grade V), glutamic decarboxylase (grade V) and urease were from Sigma Chemical Co. (St Louis, MO, USA). Other enzymes and coenzymes were purchased from Boehringer (Meylan, France) and all other chemicals were reagent grade. L-[1-t4C]Alanine (52 m C i / m m o l ) was from Amersham (Amersham, Bucks., UK) and [14C]bicarbonate (30-50 m C i / m m o l ) was from the C.E.A. (Gif-sur-Yvette, France). Both [2-14C]pyruvate (31.7 m C i / m m o l ) and [3-14C]pyruvate (30 m C i / m m o l ) were supplied by New England Nuclear (Boston, MA, USA). e-[2-14C]Alanine and L-[3-14C]alanine were synthesized from the corre-

162 sponding labelled pyruvate thanks to the action of alanine dehydrogenase in the presence of stoichiometric amounts of NH4CI and an excess of N A D H and then purified by column chromatography [17,18].

Preparations of liver cells and incubations Isolated rat liver cells were prepared from male Wistar rats (200-250 g) obtained from Iffa-Credo (St Germain-sur-l'Arbresle, France) on a conventional diet (U.A.R., Villemoisson-sur-Orge, France). All food was removed 48 h before the experiments, but the animals had free access to water. The cells were isolated by the method of Seglen [19], with the perfusion apparatus used by Krebs et al. [20], as described previously [5]. Incubation was carried out at 37°C in a shaking water bath in 25 ml Erlenmeyer flasks, each with a center well, with a mixture of 95% 0 2 and 5% CO 2 as gas phase. Cell viability was assessed by Trypan blue exclusion, refractility on examination under a light microscope and measurement of the rates of glucose synthesis from 5 mM L-lactate (180 _+ 15 t z m o l / h per g dry wt. of cells). Hepatocytes were incubated in 4 ml of Krebs-Henseleit buffer (pH 7.4) [21] containing as substrates either 5 mM L-[1-~4C]alanine or 5 mM L-[2J4C]alanine or 5 mM L-[3-J4C]alanine, or 5 mM unlabelied L-alanine in the presence of 25 mM Nail 14CO 3. In all experiments, each experimental condition was carried out in duplicate. Incubations were terminated by adding perchloric acid (final concn. 2%, v / v ) to each flask. Then collection and measurement of the 14CO, released from [14C]alanine or from [~4C]bicarbonate were carried out as described by Baverel and Lund [22]. In all experiments, zero-time flasks with and without substrates, were prepared by adding perchloric acid before the hepatocytes when [14C]alanine was the substrate or immediately after the hepatocytes when [HC]bicarbonate was present. After removal of the denaturated protein by centrifugation, the supernatant was neutralized with 20% (w/v) KOH for metabolite determination, measurement of bicarbonate fixation and of isotope incorporation into non volatile carbon products.

Analytical methods and calculations Aspartate, alanine, glutamate, glutamine, ammonia, urea, pyruvate, lactate, glucose, glycogen, intermediates of the tricarboxylic acid cycle as well as the dry weight of the amount of hepatocytes added to the flasks were determined as previouly described [5]. The specific activity of L-[1-~4C]glutamine + L-[1-14C]glutamate was measured by the combined action of glutaminase and glutamic decarboxylase as described by Squires and Brosnan [23]. Fixation of 14CO2 from [14C]bicarbonate was calculated by dividing the acidstable radioactivity by the specific radioactivity of the total "bicarbonate + CO2" pool measured in the zero-

time flask. Net incorporation of labelled bicarbonate into the products accumulated from alanine was taken as the difference between the labelled bicarbonate fixed in the presence and in the absence of alanine. The radiolabelled alanine or bicarbonate carbon incorporation into carbon 1 of pyruvate, lactate or alanine was measured by decarboxylating with H 2 0 2 [24] the pyruvate found in the flasks and the pyruvate formed from the lactate and alanine present at the end of the incubation due to the action of lactate dehydrogenase and alanine dehydrogenase, respectively. Incorporation of radiolabelled alanine and bicarbonate carbon into glucose was measured after separation of glucose by a double ion exchange chromatographic method described by Palacin et al. [17] and Reilly [18]. Substrate utilization and product formation were calculated as the difference between the total contents of the flask (tissue + medium) at the start (zero-time flasks) and after the period of incubation. Metabolite production from alanine was taken as the difference between the metabolite production in the presence and that in the absence of alanine. The metabolic rates, reported as means + S.E. are expressed as izmol of substance removed or produced per g dry wt. of hepatocytes per h. The rates of release of 14CO2 from radioactive alanine molecules were calculated by dividing the radioactivity found in CO 2 by the specific radioactivity of the labelled alanine carbons determined in the zerotime samples for each experiment. Results

Linearity of alanine metabolism in rat hepatocytes When expressed as a function of alanine utilization (X), the release of labelled CO 2 from [1-~4C]alanine ([*CO2] c'ALA = - 0 . 4 3 + 0.518X; r e = 0.981) and the production of labelled glucose from alanine plus labelled bicarbonate ( [ * G L C ] ALA+*c°: = - 0 . 0 6 + 0.118X; r 2 = 0 . 9 5 1 ) were found to be linear for an alanine removal of at least up to 15/zmol out of the 20 /xmol originally present in the incubation flasks. In all experiments, the lag phase was less than 5 min and the specific activity of [1-14C]alanine did not significantly change during the incubation.

Metabolism of 5 mM 1- 14C-, 2-14C-, 3-14C-, U- ]4C-~4LA, and 5 m M A I ~ t + 25 mM NaH14CO~ Tables I and II show the results obtained with specifically or uniformly labelled alanine and with unlabelled alanine plus labelled bicarbonate; in these experiments, the rate of alanine removal (11.4_+0.5 #tool) was chosen in the range of linearity mentioned above indicating that our ceils metabolized alanine under virtual steady-state conditions.

163 TABLE I

Accumulation of non-volatile products from 5 mM L-alanine in isolated rat hepatocytes Isolated hepatocytes (25.1_+ 1.3 mg dry wt. per flask) were incubated as described in the Methods section. Results ( l z m o i / g dry wt. per h for metabolite removal ( - ) or production are reported as means _+S.E. for four experiments. The radioactivity data corresponding to these experiments are reported in Table II. The value of alanine utilization is used in the equations of the model. Experimental condition

5 m M alanine

Metabolite utilisation ( - ) or production alanine

glucose

pyruvate + lactate

glutamate + glutamine

urea

ammonia

-455.5_+18.2

110.9_+4.7

139.3_+ 16.0

33.8-+4.6

194.7-+4.3

11.9_+9.1

1.2_+ 0.3

21.3+0.7

-3.7_+ 2.7

6.4_+2.5

33.7+7.0

0.4+ 1.5

No added substrate

T A B L E II

Accumulation of labelled products from U14C -, 3 t4C-, 214C-, 114C-alanine and alanine plus 14C-bicarbonate in isolated rat hepatocytes Isolated hepatocytes (25.1 _+ 1.3 mg dry wt. per flask) were incubated as described in the Methods section. Results (izmol o r / z a t o m per g. dry wt. per hour) for labelled product accumulation are reported as means_+ S.E. for four experiments performed in duplicate. Substrate utilization and product formation, measured enzymatically, are reported in Table I. Net incorporation of labelled bicarbonate into the products accumulated from alanine was taken as the difference between the labelled bicarbonate fixed in the presence and in the absence of alanine. Substrate

14CO2

Labelled carbons incorporated into glucose

[1-14C]glutamate + [1-14C]glutamine

[1-14C]lactate + [1-14C]pyruvate

[1-14C]alanine

5 m M [UN4C]alanine 5mM[3-14C]alanine 5 m M [2-14C]alanine 5 mM [lN4C]alanine 5 m M alanine + 2 5 m M NaH~4CO3 No added alanine + 2 5 m M NaHI4CO3

365.9_+ 66.1_+ 56.4_+ 227.6_+

377.8_+ 154.4_+ 148.2_+ 65.4-+

15.4 6.5 13.4 0.8

10.3_+2.0 2.1_+0.5 2.5_+0.4 5.1 4-_1.4

137.2_+ 2.2_+ 4.2_+ 123.6_+

-

-

51.7-+ 3.5

17.1 -+0.5

14.1 -+ 0.2

3.9_+ 1.1

-

7.9_+ 0.3

1.3_+0.1

1.8_+ 0.1

0.5_+0.1

9.4 1.2 2.8 11.8

6.9 0.1 1.4 11.7

T A B L E III

Various proportions and fluxes through pathways of alanine metabolism in isolated rat hepatocytes Values, given as means_+ S.E. for four experiments, were calculated from those of Tables I and II; proportions and fluxes are defined in the Appendix. Fluxes are expressed in /~mol per g dry weight of hepatocytes per h. PYR = pyruvate; L A C = lactate; small letter symbols (or numbers) indicate the proportion of a given intermediate metabolized at a given step. Capital letter symbols indicate the amounts of alanine converted into various intermediates or products; a subscript "zero" accompanying these letters m e a n s that the products or intermediates have been formed before completion of the first Krebs cycle turn, whereas without subscript, they represent the total a m o u n t s of products or intermediates formed as a result of alanine metabolism. * corresponds to the alanine (Po + Lo) accumulated as pyruvate plus lactate directly from pyruvate, without passing through the stage of phosphoenolpyruvate; ** corresponds to the sum of the oxaloacetate (C) synthesized by pyruvate carboxylase and by recycling via the Krebs cycle; G represents the Krebs cycle turnover or oxaloacetate recycling via the Krebs cycle. The symbols of the various proportions, defined in the Appendix, are shown in Fig. 2; c = C o / X , where X is alanine utilization (455.5_+ 18.2 ~ m o l / g dry wt. per h); b = Bo / Co; a = A o / Co; s = G o / A o ; g = Go~Co; j = Jo / B o. Proportions

c 0.77_+0.04

b 0.53_+0.04

a 0.47_+0.04

s 0.87_+0.01

g 0.41_+0.02

j 0.21_+0.02

i' 0.40_+0.02

i 0.43_+0.02

Fluxes

PYR + L A C accumulation from PEP

PYR + L A C accumulation

pyruvate carboxylase

a-ketoglutarate dehydrogenase

citrate synthase

alanine accumulation from PEP

phospho enolpyruvate carboxykinase

glucose formation

First Krebs cycleturn All Krebs cycle turns

Po + L" 30.8_+1.7 P ' + L' 52.0_+1.8

Po + Lo * 105.1_+13.1

Co 350.4_+27.6 C ** 591.3_+30.8

Go 142.4_+ 7.0 G 240.9_+17.6

Ao 163.3_+ 8.7 A 276.2_+21.0

Ro 8.4_+2.0 R 14.3_+3.6

Bo 187.1_+24.1 B 299.2_+50.3

Jo 109.2_+ 4.6 J 184.9_+15.1

-

164 As expected, alanine utilization was not significantly different with the various species of labelled alanine. The rates of alanine removal and product formation were in the same range as those previously found by Cornell et al. [6], who employed the same substrate concentration (5 mM) as in our study. Considering that one alanine was needed for each pyruvate, lactate, glutamate, glutamine and glucose (in C3units) found, carbon balance calculations indicate that 107.2 + 7.1 /~mol of the alanine removed were not accounted for by the accumulated products (see Table I), while alanine complete oxidation, which can be estimated by the 14CO2 released from the C-2 of alanine, was only 56.4 + 2.8/~mol (see Table II). Table II shows that, as expected, the sum of the releases of L4C02 from [1-14C]-, [2-14C]-, and [314C]alanine was virtually equal to the release of ~4CO2 from [U-14C]alanine; similarly, the amount of labelled alanine carbon incorporated into glucose from [U14C]alanine on the one hand, and on the other hand from [1-14C]alanine + [2-14C]alanine + [3-14C]alanine were almost identical. It is also apparent from Table II that about twothirds of the CO 2 released from alanine arose from C-1 of alanine. Table II also shows that much more pyruvate plus lactate labelled on their C-1 accumulated from [1lnC]alanine than from alanine plus NaH14CO 3 which means that more pyruvate plus lactate accumulated immediately after alanine transamination than after the operation of pyruvate kinase. It can also be seen from Table II that most of the C-1 of glutamate plus glutamine arose from bicarbonate.

Parameters of alanine metabolism The various proportions and fluxes through pathways of alanine metabolism, calculated from the results given in part in Table I and especially in Table II as explained in the appendix, are shown in Table III. It appears from calculation of c that only 77 + 4% of the pyruvate derived from alanine was converted into oxaloacetate by the pyruvate carboxylase reaction (see the c value in Table III), the remainder being accumulated as pyruvate and lactate. Of the oxaloacetate synthesized by pyruvate carboxylase, about half was converted into citrate (a = 0.47 + 0.04) and the other half (b = 0.53 + 0.04) was directed to the synthesis of phosphoenolpyruvate (Table III). Of the citrate synthesized, 87% was recycled to give oxaloacetate, and only 13% (= 1 - s ) was converted into glutamate plus glutamine. As shown in Table III, 21 _+ 2% ( = j = (Po +L'o + Ro)/B o) of the phosphoenolpyruvate synthesized from the alanine-derived oxaloacetate, was found mainly as pyruvate and lactate and to a negligible extent as alanine; it can also be seen in Table III that the

inversion i' resulting from the equilibration of oxaloacetate with fumarate in the mitochondria or the cytosol, is in the same range as the calculated mitoehondrial inversion i. Using the alanine utilization presented in Table I and the various proportions given in Table III, it has been possible to calculate fluxes through the different pathways of alanine metabolism during the first Krebs cycle turn and finally total fluxes (for infinite Krebs cycle turns) through these pathways (see Table III). Using Eqn. 18 and the data from Table II, it can be calculated that 411.8 _+22.8 ~atom (per g dry wt. and per h) of alanine carbons plus bicarbonate carbon were incorporated into glucose. It can also be calculated from Eqn. 26 and the data of Table I that a total of 537.3 _+26.1 p.atom of glucose carbons were synthesized. Therefore, although there was no net glucose synthesis from endogenous fatty acids, 125.4+4.8 /~atom of glucose carbons originated from sources other than alanine or bicarbonate, namely acetyl-CoA synthesized from endogenous fatty acids and incorporated into the Krebs cycle as citrate. Thus, 23.4_+ 1.6% of the glucose carbons came from acetyl-CoA. This value is very close to the relative amount (25.6 + 2.2%) of glucose carbons derived from acetyl-CoA calculated from Eqn. 31 with the g value of 0.41 given in Table III. These results indicate that almost all the acetyl-CoA needed for citrate synthesis was of endogenous origin and therefore that flux through pyruvate dehydrogenase was very small. It can be deduced that only 8.3 + 5.5% of the acetyl-CoA entering the Krebs cycle (at the rate of citrate synthesis) was formed by the action of pyruvate dehydrogenase. Thus, in our experiments, flux through pyruvate dehydrogenase which was equal to 23.3 + 15.2 p~mol/g dry wt. per h, represented only 5.3 _+3.3% of the alanine removed. It should be emphasized here that, in the presence of alanine as substrate, the rate of entry of acetyl-CoA into the Krebs cycle, which is in agreement with the rate of citrate synthesis calculated in Table III, is also in agreement with the rate of ketone body production (266 + 13 ~ m o l / g dry wt. per h; calculated in C 2 units) observed in the absence of exogenous substrate. The fact that addition of alanine inhibited the synthesis of ketone bodies by 96% indicates that the alanine-derived oxaloacetate directed the endogenous acetyl-CoA to citrate synthesis rather than to ketone body synthesis. Table III shows that, during alanine metabolism, there was a very large oxaloacetate synthesis resulting not only from the operation of pyruvate carboxylase but also from recycling via the Krebs cycle. This raises the question of how many Krebs cycle turns were needed to synthesize the products. The model used allows to calculate that, for n complete Krebs cycle

165 By contrast, in our model, only the total radioactivity transferred from added substrate to intermediates or end products is taken into account; therefore, our model allows to calculate only fluxes related to the utilization of the added substrate through its various metabolic pathways. This limitation is compensated by the major advantage which is that our model can be applied irrespective of whether or not the experiments are performed under steady-state conditions. The simultaneous use of [1-14C] -, [2-14C]- and [314C]alanine as well as of alanine plus NaHI4CO3 represents a novel experimental approach for studying the metabolism of alanine, which was made possible due to the synthesis in our laboratory of [2-14C] - and [314C]alanine, two labelled molecules not commercially available. This approach permitted to obtain in each experiment a complete picture of the metabolic fate

turns, the proportions of products synthesized was equal to 1 - g ' . From this formula, it can be calculated that 97 + 1% of the products was formed after four Krebs cycle turns. Discussion

To our knowledge, the model presented in this paper is the first representation of alanine metabolism which is simple and in which all steps of calculations are completely described. The previous models of hepatic alanine metabolism presented by Cohen [4,7] and Kelleher [8,13], are much more complicated; they are based on the use of specific activities of intermediates and allow one to calculate total fluxes (flux of the added substrate + flux of the endogenous substrates) through the enzymatic steps studied.

tf PYR + LAC "~ it

ALA

I ~'ccumu'*t~'J/ :: (inC3units)J

ALA

.It

/

/

PYR

CIT

~a PYR+ LAC+ALA "~ ccumulated (in C3unitslJ

GLC

s)

Ac-CoA

PYR - -

..

ICT

ASP

II II II II II II II

~ 1 , , . CO 2 cc-KG

\ ~,~:02~MA L (OAA

-

"

,,~CYCLEJ _

-

FUM~

~

SUC CO 2

I1~ NH4+

~

GLX

CO 2

CYTOSOL) Fig. 1. Alanine pathways in isolated hepatocytes from fasted rats. Alanine is converted into pyruvate by alanine aminotransferase either in the cytosol or in the mitochondria and subsequently accumulates as pyruvate and lactate or is converted either into oxaloacetate by pyruvate carboxylase or into acetyl-CoA by pyruvate dehydrogenase. The mitochondrial oxaloacetate partially equilibrates with fumarate resulting in a randomization of oxaloacetate and malate carbons. Oxaloacetate is transferred into the cytosoi as aspartate which enters the urea cycle from which it is released as fumarate, a symmetrical molecule. This fumarate gives cytosolic oxaloacetate (50% of which is inverted) and phosphoenolpyruvate. The malate transported into the cytosol partially equilibrates with cytosolic fumarate and gives cytosolic oxaloacetate, and then phosphoenolpyruvate thanks to the phosphoenolpyruvate carboxykinase reaction which releases the C-4 of oxaloacetate as CO 2. Phosphoenolpyruvate either enters the gluconeogenic pathway or is converted by pyruvate kinase into pyruvate which accumulates as pyruvate, lactate or alanine. A fraction of the oxaloacetate formed by pyruvate carboxylase condenses with acetyl-CoA (formed mainly from endogenous fatty acids) to yield citrate. T h e C-6 of isocitrate is released as CO 2 by isocitrate dehydrogenase which gives a-ketoglutarate. Alpha-ketoglutarate accumulates as glutamate plus glutamine (GLX) or is tranformed by a-ketoglutarate dehydrogenase into succinyl-CoA and subsequently into oxaloacetate. This oxaloacetate represents the beginning of the second Krebs cycle turn. Both mitochondrial bicarbonate, and the a m m o n i a released by glutamate dehydrogenase (to provide the second nitrogen' atom of the urea molecule) are incorporated into the urea cycle. Abbreviations: A L A = alanine;. P Y R = pyruvate; L A C = lactate; A c C o A = acetyl coenzyme A; CIT = citrate; ICT = isocitrate; a - K G = alphaketoglutarate; G L X = glutamate plus glutamine; SUC = succinate; F U M = fumarate; M A L = malate; O A A = oxaloacetate; ASP = aspartate; PEP = phosphoenolpyruvate; G L C = glucose.

166 and pathway of each alanine carbon, which in turn provided the numerous items of information necessary for applying the simple model developed in this study. It should be stressed that, with this simple model, a conclusion similar to that of Cohen [4] was reached about the small involvement of pyruvate dehydrogenase in hepatic alanine metabolism. The fact that flux through pyruvate dehydrogenase was very small compared with alan~ne utilization (see Results section) justified neglecting it in our model. That this was indeed justified is indicated by the agreement found between the calculated amount of CO 2 released from the C-1 of alanine (Eqn. 2) and the corresponding experimental value obtained with [1-]4C]alanine as substrate (see Table II). It should be mentioned that, if

needed, it would be possible to include flux through pyruvate dehydrogenase in our model but this would make equations somewhat more complicated. It appears that most of the pyruvate derived from alanine was converted into oxaloacetate which was directed in approximately equal proportions to citrate and phosphoenolpyruvate synthesis. It is important to emphasize that our model allows to calculate that 41% ( = g ) of the total oxaloacetate synthesized was derived from the Krebs cycle operation (see Table III) and that four Krebs cycle turns were sufficient to explain almost all (97 _+ 1%) the products found. In addition, it should be underlined that, thanks to this model, it was possible to distinguish between the

C 1 ALA PYR LAC ALA ~ (p')

GLC

c 1 LAC ~

0)

~ (t)

ClPYR ~

(p)~c1PYR

I I (1') (r)

lX

PYR LAC ALA GLC

/ 4 *CO2 -- -- (d)/

--=,-AcCoA

IP')

I ,/J1- j)

\ 1(j)~ /

(r)

PEP

~

/

/

(C)~

(l-j)

PEP

/ ~ ' - *c02

"CO2 C40AA ~

(t)

(r)

\1/ (J) \

~-- C4OAA

(1- i")

(i") (b)

(C, MAL.

" C1OAA~

(C4OAA.

" C4MAL'~--(b)~.

(i") C 10AA

C 1 PEP

(a)

/\

*

C6 CIT

'

C1PYR C1LAc ClALA °GLC

,-

(s)

GLX

OAA

'CO2 ~l'j

IJ)

(1- J)

(13

(r)

/\\

,L

(l_s)

PEP

/\

C 1 CIT

<

/1\ \ '

C1

(a)

(p')

Is)

(l-s)

OAA

C1GLX

(t)

C1PYR CILA C C1ALA "GLC

Fig. 2. Metabolid fate of the C-1 of alanine in isolated hepatocytes from fasted rats. The amount (in izmol/g dry wt. per h) of labelled alanine (C1-ALA) utilized to form pyruvate is represented by X. Small letter symbols (or numbers) indicate the proportion of a given intermediate metabolized at a given step. The proportions p and l of Cl-pyruvate accumulates as pyruvate and lactate, respectively, while the proportions c and d of Cl-pyruvate are converted into Cl-oxaloacetate or acetyl-CoA+labelled CO2, respectively. In hepatocytes from fasted rats, d is very low and, therefore, it is assumed that d = 0. A proportion, i, of mitochondrial Cl-oxaloacetate is inverted into C4-oxaloacetate. A proportion, b, of mitochondrial oxaloacetate and malate gives cytosolic oxaloacetate. A proportion, i", of this oxaloacetate undergoes inversion as a result of partial equilibration with fumarate, i', which does not appear in Fig. 2, is the proportion of the oxaloacetate synthetized by pyruvate carboxylase in the mitochondria that is found inverted in the cytosol as a result of a single inversion having occurred in the mitochondria or in the cytosol. Oxaloacetate is then converted into phosphoenolpyruvate which either leads (with a proportion j) to pyruvate, lactate and alanine accumulation (with the respective proportions p ' , l' and r) or enters the gluconeogenic pathway at the end of which a proportion t accumulates as glucose. A proportion a of oxaloacetate forms citrate. The proportion ( 1 - s ) of a-ketoglutarate accumulates as glutamate and glutamine, while the proportion s is recycled to give oxaloacetate. A proportion represents the relative amount of a given intermediate that is converted into the next one. The relative amount of substrate (Cl-alanine) transformed into any labelled intermediate or end-product is obtained by multiplying the successive proportions found on the pathway from the substrate to the intermediate or end-product of interest. The amount (named flux) of intermediate formed or of end-product accumulated is obtained by multiplying the corresponding relative amount by the amount ( X ) of labelled alanine utilized; with Cl-alanine as substrate, these labelled intermediates or end-products can be formed only during the first Krebs cycle turn.

167 two origins of the lactate plus pyruvate found (see Fig. 1 and Table III); this allowed to calculate the minimal flux through pyruvate kinase (66.3/xmol/g dry wt. per h) which is probably close to the real flux of alanine carbons through this enzyme because it has been demonstrated by Rognstad that, with pyruvate as substrate, only 30-40% of the pyruvate recycled via pyruvate kinase was further metabolized in hepatocytes from fasted rats [15]. It should be pointed out that the agreement between the experimental value (227.6) given in Table II and the calculated value (230.2) obtained from Eqn. 2 and data in Table III represents a strong argument in favor of the validity of our model; further evidence for this validity is obtained by comparing the values of flux through pyruvate carboxylase calculated in two different ways, from Eqns. 1 and 20 (347.3) on one hand, and Eqn. 16 (350.4) on the other hand. In conclusion, this study proposes a simple model useful for characterizing and quantifying precisely the routes of alanine metabolism in isolated hepatocytes from fasted rats. Application of this model to the experimental values obtained almost exclusively by radioactive measurements, leads to conclusions in accordance with known characteristics of hepatic alanine metabolism, providing further support for its validity. This model may prove very useful for studying alanine metabolism under various experimental conditions not only in liver, but also in other organ preparations with either radioactive or non-radioactive labelled carbons, such as carbon 13.

References 1 Meiier, A.J., Lamers, W.H. and Chalumeau, R.A.F.M. (1990) Physiol. Rev. 70, 701-749. 2 Felig, P. (1973) Metabolism 22, 179-207. 3 Krebs, H.A., Hems, R. and Lund, P. (1978) Biochem. J. 176, 733-737. 4 Cohen, S.M., Glynn, P. and Shulman, R.G. (1981) Proc. Natl. Acad. Sci. USA 78, 60-64. 5 Martin, G. and Baverel, G. (1983) Biochim. Biophys. Acta 760, 230-237. 6 Cornell, N.W., Zuurendonk, P.F., Kerich, M.J. and Straight, C.B. (1984) Biochem. J. 220, 707-716. 7 Cohen, S.M. (1987) Biochemistry 26, 573-580. 8 Kelleher, J.K. (1986) Am. J. Physiol. 250, E296-E305. 9 Garfinkel, D. (1971) Comput. Biomed. Res. 4, 1-17. 10 Goebel, R., Berman M. and Foster D. (1982) Fed. Proc. 41, 96-103. 11 Hetenyi, G. (1982) Fed. Proc. 41, 104-109. 12 Janssens, P., Hems R. and Ross B. (1980) Biochem. J. 190, 27-37. 13 Kelleher, J.K. (1985) Am. J. Physiol. 248, E252-E260. 14 Malloy, C.G., Sherry, A.D. and Jeffrey F.M.H. (1990) Am. J. Physiol. 259, H987-H995. 15 Rognstad, R., and Katz J. (1972) J. Biol. Chem. 247, 6047-6054. 16 Weinman, E.O., Strisower, E.H. and Chaikoff I.L. (1957) Physiol. Rev. 37, 252-272. 17 Palacin, M., Lasuncion, M.A., Martin Del Rio, R. and Herrera, E. (1985) Biochim. Biophys. Acta 841, 90-96.

18 Reilly, P.E.B. (1975) Anal. Biochem. 64, 37-44. 19 Seglen, P.O. (1973) Exp. Cell Res. 82, 391-398. 20 Krebs, H.A., Cornell, N.W., Lund, P. and Hems, R. (1974) in Regulation of Hepatic Metabolism (Lundquist, F. and Tygstrup, N. eds.), Vol. 6, pp. 726-750, Munskgaard, Copenhagen. 21 Krebs, H.A. and Henseleit, K. (1932) Hoppe-Seyler's Z. Physiol. Chem. 210, 33-66. 22 Baverel, G. and Lund, P. (1979) Biochem. J. 184,599-606. 23 Squires, E.J. and Brosnan, J.T. (1978) Anal. Biochem. 84, 473478. 24 Odessey, R. and Goldberg, A.L. (1979) Biochem. J. 178, 475-489.

Appendix

Mathematical model of alanine metabolism in isolated rat hepatocytes Fig. 1 gives a schematic representation of alanine metabolism in the rat liver and Fig. 2 shows the metabolic fate of labelled C-1 of alanine. It can be seen in Fig. 2 that, if oxaloacetate does not equilibrate with fumarate, the C-1 of oxaloacetate gives the C-1 of malate (or of aspartate) or the C-6 of citrate which is released as ~4CO2 by the isocitrate dehydrogenase reaction (see the left part of the figure). If oxaloacetate equilibrates with fumarate, half the C-1 of this oxaloacetate gives rise to the C-4 of oxaloacetate and then to the C-4 of malate (or of aspartate), or the C-1 of citrate which gives either the C-1 of glutamate plus glutamine (GLX), or is released as 14C02 by the a-ketoglutarate dehydrogenase reaction. When the aspartate carbon skeleton incorporated into the urea cycle to form argininosuccinate is released as fumarate by the argininosuccinate lyase reaction, it gives equal amounts of C-1 and C-4 of oxaloacetate irrespective of whether it arises from the C-4 or the C-1 of oxaloacetate because fumarate is a symmetrical molecule, and therefore C-1 and C-4 are indistinguishable. The C-4 of oxaloacetate is released as ~4CO2 by the phosphoenolpyruvate carboxykinase reaction whereas the C-1 of oxaloacetate (and also the C-1 of malate) gives the C-3 and C-4 of glucose or the C-1 of pyruvate, lactate or alanine if this amino acid is re-synthesized by the alanine aminotransferase reaction.

Metabolism of C l-alanine The amount (expressed in txmol/g dry wt. per h) of any given intermediate or end-product formed from C IALA can be calculated by multiplying the amount of C1ALA removed by the successive proportions of intermediates passing through the different pathways leading to the intermediate or end-product of interest. Let[*CO2] CIALA = the amount of 14CO2 released from CIALA.

Assuming that (d) = 0, i.e., that flux of C1PYR through pyruvate dehydrogenase does not occur (that this assumption is correct will be proved later), and taking into account that 14CO2 is released by the phospho-

168 enolpyruvate carboxykinase, isocitrate dehydrogenase and a-ketoglutarate dehydrogenase reactions,

Then, [* G L C ] C'ALA = (1 - j ) . t . ( 1 - i ' ) . B o = (1 - i ' ) . T o

[ * C O 2 ] clALA

=

(4)

X . c . [ ( 1 - i ) . i ' . b + i.(1 - i " ) . b + (1 - i ) . a + (i.a.s)],

where where X is the amount of labelled alanine removed during the incubation time (60 min), i and i" are the proportions of oxaloacetate carbons inverted as a result of equilibration~with fumarate in the mitochondria and the cytosol, respectively. The latter equation can be simplified as follows:

TO = (1 - j ) . t . B o

Let [CIGLX]c'ALA = the amount of C1GLU + CIGLN synthesized from CIALA. It can be seen from Fig. 2, that: [ C 1 G L X ] cIALA = X . c . i . a ( 1 -

[ * C O 2 ] CIALA

=

s)= X.c.i.(a-a.s)

X . c . [ ( i ' . b ) + (1 - i ) . a + (i.a.s)] = X.c.i.(a-g)

where i' = (1 - i).i" + i.(1 - i"), i' being the proportion of oxaloacetate (formed by pyruvate carboxylase) having exchanged its symmetrical carbons only once either in the mitochondria or in the cytosol, as a result of equilibration with fumarate. Let a.s=g

(which corresponds to the proportion of OAA regenerated at each Krebs cycle turn). Substituting for a.s;[*CO2] TM

= X . c . [ i ' . b + (1 - i ) . a + i.g]

Let X.c.b =Bo, X.c.a =Ao, X.c.g = G O and X.c = Co, where the subscript "zero" is indicative of the first Krebs cycle turn. It c a n b e d e d u c e d that C o = G o / g

(1)

Substituting for X.c.b, X.c.a and X.c.g:

= i.(Ao-Go)

(5)

It is important to note that: (1) Fig. 2 can also be used to study the fate of the 14CO2 fixed by pyruvate carboxylase when unlabelled alanine plus labelled bicarbonate are used as substrates; (2) under this condition, the oxaloacetate synthesized by the pyruvate carboxylase reaction is labelled on its C-4 instead of on its C-1 when C1ALA is the substrate (see Fig. 2); therefore, all the equations presented above can be used to measure the amount of labelled 14CO2 incorporated into the various intermediates or end-products of interest provided i and ( 1 - i), as well as i' and ( 1 - i'), replace each other in these equations as follows: [ C 1 P E P ] ALA + * c ° 2

=

i'.B o

(6)

[ * G L C ] A L A + * c ° 2 = (1 - j ) . t . i ' . B o = i ' . T o

(7)

[ C I P Y R + C I L A C + C I A L A ] ALA+*cO2 = i ' . B o , j

(8)

[ C I A L A ] A L A + *CO2 = i , . B o.j.r = i ' . R o

(9)

where [ * C O 2 ] clALA

=

i ' . B o + (1 - i ) . A o + i . G o

(2)

R o = j.r.B o

Let [CIPEP] c~ALA= the amount of CIALA that has passed through the stage of C1PEP. As can be seen in Fig. 2, [ C I P E P ] CIALA = X . c . ( 1 - i ' ) . b

Therefore, [ C I P E P I CIALA = (1 - i ' ) . B o

(3)

(10)

Let [*GLC] c'aLa+*c°2 = the amount of labelled carbon incorporated into glucose from C~ALA plus labelled bicarbonate. Given the Eqns. 4 and 7, [ * G L C ] c ' A L A + * c ° 2 = B o . ( 1 - j ) . t = To

Let [*GLC] CIALA= the amount of CIALA incorporated into glucose, which is equal to the amount of C1ALA that has passed through the stage of C1PEP multiplied by the proportion [(1 - j ) . t ] of PEP directed to glucose. Therefore: [ * G L C ] clALA = (1 - J ) . t . [ C I P E P ] CIALA

[C1GLX] aLA+*c°2 = (1- i).(Ao-Go)

(11)

Let [C1GLX] C~ALA+*C°2= the amount of labelled carbon incorporated into carbon 1 of glutamate + glutamine from C~ALA plus labelled bicarbonate. Given the Eqns. 5 and 10, [ C1GLX]C~AL.4 +*co2 = A o _ Go

(12)

From Eqns. 7 and 11, it is also possible to calculate i' as the labelled glucose (in C-3 units) arising from the oxaloacetate synthesized by pyruvate carboxylase when

169

incubation occurs in the presence of alanine plus NaH14CO3 divided by that when incubation occurs in the presence of CIALA + NaH14CO3: [, GLc]ALA + *CO2 i ' = [, GLc]C,ALA+,CO 2

(13)

As i' can be calculated from glucose labelling (Eqn. 13), Po + L'o can also be calculated. Let [CaPYR + C1LAC] clgLg = the amount of alanine incorporated into pyruvate plus lactate that did not exchange its carbon 1 with the carbon of bicarbonate (see Fig. 2):

Calculation of P" + L o and Po + Lo: The CIPYR + C1LAC accumulated results either from C1PYR synthesized directly by alanine aminotransferase (Po +Lo) or from CIPYR synthesized by pyruvate kinase (P" + L'o). Thanks to the measurement of C~PYR + CtLAC accumulated in the presence of A L A + NaH14CO3, and given the value of i' is known, one can calculate the PYR + LAC accumulated secondary to the operation of pyruvate kinase. Let [C]PYR + C z L A C ] ALA+*c°2 = the amount of alanine incorporated into pyruvate plus lactate after having exchanged its carbon 1 with the carbon of bicarbonate (see Fig. 2),

[CzPYR + CILAC] CIALA= S . ( p q- l) "t- X.c.(1

-

i').b.j.(p' + l')

Substituting (X.p) by Po, (X.l) by L o, (X.c.b.j.p ') by P', and (X.c.b.j.l') by L'o, [CIPYR+ C1LAC]C]ALA = (eo + Lo) + (1 - i').(P o + L'o)

(15)

Substituting (X.c.b.j.p') by Po and (X.c.b.j.l') by Lo,

Calculation of flux through pyruvate carboxylase (= Co): Since no significant decrease in the specific activity of alanine was found, the alanine utilization enzymatically measured corresponded to labelled alanine utilization (X) by alanine aminotransferase. Flux through pyruvate carboxylase is given by (X.c), where (c + p + / ) = 1 (see Fig. 2); then, it can be rewritten that:

[C~PYR+ C1LAC] ALA+*C02 = i'.( Po + Lo)

Co=X.[1-(p+l)]=X-(Po+Lo)

[ClPYR + C1LAC] ALA+ *c°2

X.c.i'.b.j. ( p ' + l')

=

(14)

(16)

C 2ALA C2PYR C2LAC C2ALA "GLC

ttt

t (j)

c2,Ac.,,_.__.- (i) C2PYR ~

1x

(P)

C2PYR . . . . .

~ C1 AcCoA

t

(p')

/

(i"l~

c30AA-~------(1.,..)~ (b)~\

(c3.AL.

(i)

" C30AA)

1

/\

(1- j)

(t)

(j)~

..~"

tJ)

~(1-

i")

~ C20AA

~- C30AA

c2 G~ -~---0.s)

C2iIT C2~-KG

(r)

It)

(c, o,,.

C3PEP

/\

C3CIT

/\

t

(r)

C2 PEP

(1- i)

(a)

C3PEP

111

"GLC

(c)~

C20AA ~

(r)

(d) . . . .

(1- j)

C2 PEP

(p')

C2PYR C2LAC C2ALA

It)

I

CI OAA"~--- (1/2) ~

(s)

SUC C3PYR C3 LAC C3ALA "GLC

C4OAA ,.ql---(1/2) " / C l

!

~,-~KG/(i-s)---,-c3a~ C3 I

(s) j~ /(I/2)--.-i~ C20A A

/P\ (J)

(p')

(1')

(I. i)

(r)

(t)

c3suc~ x(I/2) ---I~ C 30AA

C3PYR C3LAC C3ALA "GLC

Fig. 3. Metabolic fate of C2-alanine during the first Krebs cycle turn in isolated hepatocytes from fasted rats. Proportions are the same as those presented in Fig. 2, but oxaloacetate recycled after one complete Krebs cycle turn remains labelled indicating that the fate of the C-2 of alanine, in contrast with the fate of the C-1 of alanine, requires more than one Krebs cycle turn to be defined. The synthesis of oxaloacetate resulting from the first Krebs cycle turn is considered to represent the beginning of the second turn.

170

Metabolism of C2- and C3-alanine: calculation of g In our model, an important parameter of the Krebs cycle is the proportion of oxaloacetate which is resynthesized (or recycled) at the end of each turn of the Krebs cycle, which is equal to g (see Fig. 2). Since the C-1 of ALA and the CO2 fixed by pyruvate carboxylase are not recycled, the use of C-2 and C-3 of alanine, which can undergo recycling, is very convenient for calculating g. Fig. 3 shows the representation of the conversion of the C-2 of alanine into the different carbons of various intermediates and products during the first Krebs cycle turn, whereas figure 4 is a simplified representation of the conversion of the C,2 of alanine into the different carbons of oxaloacetate during the three first complete Krebs cycle turns. The operation of alanine aminotransferase and pyruvate carboxylase, and the equilibration of oxaloacetate with fumarate give both the C-2 and the C-3 of oxaloacetate from CzALA (see Figs. 3 and 4). As shown in Figs. 3 and 4, recycling of the C-3 of oxaloacetate gives rise to equal proportions (g/2) of C-1 and C-4 of oxaloacetate whose fate has already been studied (see Fig. 2). Fig. 4 also shows that recycling of the C-2 of oxaloacetate yields equal proportions (g/2) of C-2 and C-3 of oxaloacetate and that the latter process is repeated during all the next Krebs cycle turns (al-

though only 3 complete Krebs cycle turns are represented in Fig. 4). It should be stressed that, when using C3-alanine as substrate, both C 2- and C 3- oxaloacetate are synthesized as shown in figure 4; however, under this condition, the proportion i should be replaced by (1 - i) and conversely, and all the equations used with C2-ALA as substrate should be modified accordingly. Calculations of the label incorporated into the various oxaloacetate carbons from C2ALA: In the following calculations, [ C z O A A ] C2ALA m e a n s the label from CzALA found in carbon z of oxaloacetate, where z is equal to 1, 2, 3 or 4. From Fig. 3, it can be deduced that: X.c.i.g/2+ ~ X.c.(l

[CIOAA] C2ALA =

i).(g/2) n,

-

n=2

assuming that g is less than 1, a condition verified experimentally because a proportion of the oxaloacetate formed by the pyruvate carboxylase reaction is not recycled.

[C[OAA]c2AL~= X.c.(g/2).[i + (1- i ) . g / ( 2 - g)] and [C4OAA] c2ALA = [ C , O A A ] c:Ax'A (see Fig. 4)

C2ALA

,lx C2PYR

C3OAA ~ .

.

.

.

.

.

(i) .

.

.

.

.

.

.

.

.

.

.

.

(1-i) .

C1OAA C40AA .............................

.

.

.

.

.

.

.

.

~- C20AA _

_

_

C30AA (g/_2)_~_ _. . . . ~ i CI OAA

.

.

.

.

.

.

.

.

.

.

...... ~~C4OAA / (g

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

1st turn n=0

G b~i

C30AA ~

.....

.

/2)

c4o~

.

.

.

.

.

.

.

.

.

.

C20AA - - - -~)-

/ (g/ - - -G b~i

.

.

.

.

. . . . . . 21n°--flrn

C20AA ~

/2)

3rn0~u~n

- - - - G ~A-A- - 4th turn n=3

Fig. 4. Label incorporation into oxaloacetate from C2-alanine. T h e various proportions of oxaloacetate specifically labelled on one of its carbons are shown on this figure not only for the first (n = 0) and second (n = 1) Krebs cycle turn (as in Fig. 3) but also for the third (n = 2) and fourth (n = 3) Krebs cycle turn. The repetitiveness of this diagram allows to deduce the amount of label incorporated into oxaloacetate for the next Krebs cycle turns. The proportion g/2 represents a.s. 1 / 2 (see Fig. 3).

171 oe [ C 3 O A A ] C2ALA =

X.c.i + ~ X.c.(1- i ) . ( g / 2 ) " n=l

[ C 3 O A A ] C2ALA =

X.c.[i + (1 - i ) . g / ( 2 - g ) ]

[ C 2 O A A ] C2ALA =

X . c . ( 1 - i). ~ ( g / Z ) " n--O

[C2OAA] C2ALA = X.c.(1 - i ) . [ 2 / ( 2 - g)]

Let [*GLC]C2 ALA= the amount of C-2 of alanine incorporated into glucose; this amount can be calculated by multiplying the amount of labelled oxaloacetate carbons arising from CeALA by the proportion of these carbons directly converted to glucose. Hence, 4 [* GLc]C2ALA = E [Cz O A A ] C 2 A L A ' ( C z O A A + * GLC) z=l

Using the latter equations, it can be calculated that: Calculation of the proportion of the labelled OAA converted into the various intermediates or end-products: Fig. 3, which shows the metabolic fate of the C-2 of alanine, allows us to calculate the proportions of C-2 of oxaloacetate and C-3 of oxaloacetate (formed by equilibration with fumarate) giving rise directly (in the absence of recycling) to the different intermediates and end-products formed during the first Krebs cycle turn. Let (C3OAA ~ * GLC) = the proportion of C3OAA directly converted into labelled glucose during any given Krebs cycle turn:

+ Bo.(l - j).t.[1 + (1 - i ) . ( 2 g / ( 2 - g))]

Similarly, the amount of C-3 of alanine incorporated into glucose, which is [*GLC] c3ALA, can be calculated using the latter equation in which i should be replaced by (1 - i) and conversely. Therefore, [*GLC] C3ALA = B o . ( 1 - j ) . t . ( g / 2 ) . [ i . ( g / ( 2 - g))+ ( 1 - i)] + B o . ( 1 - j).t.[1 + i . ( 2 g / ( 2 - g))]

and [*GLC]%ALA+C3ALA, which is the amount of C-2 and C-3 of alanine incorporated into glucose, is equal

( C 3 O A A ~ * G L C ) = b.(1 - j).t Similarly, ( C 2 O A A --* * GLC) = b.(1 -

[* GLC] C2ALA = Bo.(1 - j).t.(g/2).[(1 - i).(g/(2 - g)) + i]

j).t

Because no labelled CO2 is released in the direct conversion of C2OAA into PEP, ( C 2 O A A ~ 14CO2) = 0

and, similarly, ( C 3 O A A ~ 14CO2) = 0

Fig. 3 also shows that no C IGLX can be directly formed, i.e., without recycling, from C-2 or C-3 of oxaloacetate; therefore, (C2OAA ~ C1GLX) = 0 and (C3OAA ~ CIGLX) = 0 Applying the same method of calculation, one can deduce from Fig. 2 that (CIOAA ~ *GLC), which is the proportion of C1OAA giving rise to labelled glucose, is equal to [(1 - i").b.(1 -j).t] Similarly, as can be seen in Fig. 2,

to: Bo.(1 - j ) . t . ( 4 + g ) / ( 2 -

g)

(17)

The total amount of alanine carbons and bicarbonate carbon incorporated into glucose, using Eqns. 11 and 17, is: [ . GLc]C1ALA + *CO2 + [ . GLc]C2ALA + C3ALA

= B o . ( 1 - j ) . t . [ 6 / ( 2 - g)]

(18)

The same kind of reasoning allows us to calculate [CIGLX]C2ALA+C3ALA,which is the amount of C-2 and C-3 of alanine converted into the C-1 of glutamate plus glutamine: [CIGLX] C2ALA+C3ALA = ( A o - G o ) . [ g / ( 2 - g)]

(19)

Similarly, it is possible to calculate the release of labelled CO 2 from CzALA plus C3ALA: [ * C O 2 ] C2ALA+CJALA = ( C o q- G o ) . [ g / ( 2 -

g)]

(20)

( C 4 O A A ~ * G L C ) = i".b.(1 - j).t ( C I O A A ~ * C O 2 ) = (i".b)+ a ( C 4 O A A --~ * C O 2 ) = [(1 - i " ) . b ] + g ( C I O A A ~ C1GLX ) = 0 ( C 4 O A A ~ C1GLX ) = ( a - g )

Calculations of the amount of C-2 and C-3 of alanine incorporated into the various end-products of alanine metabolism:

where [*CO2] c2ALA = ( G o / 2 ) . ( 1 + g).[i + ( 1 - i ) . g / ( 2 -

g)]

and, [ * C O 2 ] C3ALA = ( G O / 2 ) . ( 1 + g).[(1 - i ) + i . g / ( 2 - g)]

(21) (22)

The final calculation of g can be obtained by combining Eqns. 11 and 18 as follows: [*GLC]c 2ALA + C3ALA _{_[ ,

GLC]CI ALA + * CO 2

[,GLC]CjALA+,CO 2

= 6/(2-

g)

(23)

172 Calculations of the other parameters of the model Given that the value of g is known, it is now possible to calculate flux through various pathways: Flux through a-ketoglutarate dehydrogenase during the first Krebs cycle turn (G o) can be calculated from Eqns. 1 and 16 and total flux through a-ketoglutarate dehydrogenase is equal to

The PEP arising from the oxaloacetate synthesized by pyruvate carboxylase (B o) can be calculated as follows: Bo = CO- A o

(28)

Total synthesis of PEP is equal to: B = Bo/(1- g)

oo

G= Y~,gn.Go=Go/(1-g )

(24)

n=0

Flux through pyruvate carboxylase (Co), already calculated with Eqn. 16, can also be obtained from Eqn. 20:

Given that g is known, the proportion, i, of oxaloacetate inverted in the mitochondria can be calculated from Eqns. 21 and 22 as follows: [* C o 2 ] C 3 ALA -- [* C o 2 ] C 2 ALA

[. CO2]C3ALA+ [. CO2]C2ALA (t-- g).(1--2i)

(29)

[*Co2]C2ALA+C3ALA= (Co + Go).[g/(2- g)] The proportions characterizing alanine metabolism were calculated as flux ratios as follows:

where Go = g.Co (see Eqn. 1) Flux through citrate synthase during the first Krebs cycle turn (A o) and, then, total flux through citrate synthase (A) can be derived from Eqn. 12: [CIGLx]CIALA+*CO2_ GO= A o

(25)

Therefore, A = A o / ( 1 - g) The rate of glucose synthesis (in C 3 units) from the oxaloacetate synthesized by pyruvate carboxylase (To), given by Eqn. 11, allows to calculate total glucose synthesis (T) with the following equation: T = B o . ( 1 - j ) . t / ( 1 - g) =B.(1-j).t Then, the total amount of individual glucose carbons is: 3.T = 3.B.(1 - j ) . t

(26)

Flux through pyruvate kinase (Jo) during the first Krebs cycle turn, is equal to t (1/i).[CIPYR + CILAC+ C1ALA]ALA +*CO2

=X.c.b.j.(p' +l' +r) Thus, Jo = P" + Lo + Ro, with (p' + l' + r) = 1

Bomin = (Po + L" + Ro)+ TO The minimal value for total PEP synthesized is given

Bmin =

Bomin/(1- g) = (P' + L' + R)+ T

Flux through pyruvate dehydrogenase The assumption that flux through pyruvate dehydrogenase was negligible implies that virtually all the oxaloacetate converted into citrate was condensed with acetyl-CoA formed from endogenous sources, resulting in the incorporation of carbons of the acetyl moiety into glucose. The latter incorporation (0) can be calculated by subtracting from the total amount of glucose carbons found in the presence of alanine and given by Eqn. 26, the amount of glucose carbons derived from alanine plus bicarbonate given by Eqn. 18. Thus, 0 = [3.B.(1 - j).t] - [ Bo.(1 - j).t.6/(2- g)] 0 = B.(1 - j).t.3g/(2- g) = 3.T.g/(2- g)

(30)

where T = B.(1 - j).t The relative amount of glucose carbons originating from acetyl-CoA carbons is obtained by dividing Eqn. 30 by Eqn. 26 as follows: O/3T = g / (2- g)

(27)

Total flux through pyruvate kinase is given by J = P ' + L' + R The minimal amount of PEP arising from the oxaloacetate synthesized by pyruvate carboxylase (B o min) can be calculated as follows:

by:

a= Ao/Co; b= Bo/Co; c = Co/X; j= Jo/Bo

(31)

These calculations allow one to demonstrate that, if the proportion of unlabeUed carbons into glucose is g / ( 2 - g), there is no flux through pyruvate dehydrogenase. Strategy of calculation of various parameters of alanine metabolism The values of the parameters of alanine metabolism during the first Krebs cycle turn were obtained in the following order: X = alanine utilization TO---glucose formation (Eqn. 11) A o - G O= glutamate + glutamine formation (Eqn. 12)

173 i' was calculated using Eqn. 13 R o = alanine formation (Eqn. 9) Po and L o = direct accumulation of pyruvate and lactate (Eqn. 14) Po and L'o = pyruvate and lactate accumulated from phosphoenolpyruvate (Eqn. 15) C o = flux through pyruvate carboxylase (Eqn. 16) g = proportion of oxaloacetate recycled at the end of each Krebs cycle turn (Eqn. 21) Calculation of C O by a second method (Eqn. 20) G O= flux through a-ketoglutarate dehydrogenase (Eqn. 1) A o = flux through citrate synthase (Eqn. 25) Jo = glucose synthesis (Eqn. 27) B o = phosphoenolpyruvate synthesis (Eqn. 28)

The values of the parameters of alanine metabolism during all Krebs cycle turns were obtained by dividing those during the first Krebs cycle turn by (1 - g ) . The other parameters of alanine metabolism were calculated as follows: a = the proportion of oxaloacetate giving citrate ( =

A o/Co) b = the proportion of mitochondrial oxaloacetate and malate giving cytosolic oxaloacetate ( = Bo/C o) c = the proportion of pyruvate converted into oxaloacetate ( = Co~X) j = the proportion of phosphoenolpyruvate giving pyruvate, lactate and alanine ( = Jo/Bo) d = the proportion of pyruvate converted into acetylCoA (see Eqn. 31 and the accompanying comments)