Adenine and adenosine salvage pathways in erythrocytes and the role of S-adenosylhomocysteine hydrolase
A theoretical study using elementary flux modes
Stefan Schuster and Dimitar Kenanov
Department of Bioinformatics, Friedrich Schiller University, Jena, Germany
Keywords elementary flux modes; enzyme deficiencies; erythrocytes; nucleotide metabolism; salvage pathways
Correspondence S. Schuster, Department of Bioinformatics, Friedrich Schiller University, Ernst-Abbe- Platz 2, 07743 Jena, Germany Fax: +49 3641 946452 Tel: +49 3641 949580 E-mail: schuster@minet.uni-jena.de
(Received 6 June 2005, revised 5 August 2005, accepted 19 August 2005)
This article is devoted to the study of redundancy and yield of salvage pathways in human erythrocytes. These cells are not able to synthesize ATP de novo. However, the salvage (recycling) of certain nucleosides or bases to give nucleotide triphosphates is operative. As the salvage pathways use enzymes consuming ATP as well as enzymes producing ATP, it is not easy to see whether a net synthesis of ATP is possible. As for pathways using adenosine, a straightforward assumption is that these pathways start with adenosine kinase. However, a pathway bypassing this enzyme and using S-adenosylhomocysteine hydrolase instead was reported. So far, this route has not been analysed in detail. Using the concept of elementary flux modes, we investigate theoretically which salvage pathways exist in erythro- cytes, which enzymes belong to each of these and what relative fluxes these enzymes carry. Here, we compute the net overall stoichiometry of ATP build-up from the recycled substrates and show that the network has con- siderable redundancy. For example, four different pathways of adenine sal- vage and 12 different pathways of adenosine salvage are obtained. They give different ATP ⁄ glucose yields, the highest being 3 : 10 for adenine sal- vage and 2 : 3 for adenosine salvage provided that adenosine is not used as an energy source. Implications for enzyme deficiencies are discussed.
it is not straightforward to see
as pyruvate kinase, whether a net production of ATP can be realized.
The human erythrocyte has been a subject not only of intense experimental research but also of many model- ling studies [1–6] because this cell is of high medical relevance, is readily accessible and its metabolism is relatively simple. Human red blood cells are not able to synthesize ATP de novo. However, they involve sal- vage pathways, that is, routes by which nucleosides or bases can be recycled to give nucleotide triphosphates [7]. The exact structure of salvage pathways (for exam- ple, starting from adenine or adenosine) has not yet been analysed in much detail. Because the salvage pathways involve enzymes consuming ATP, such as phosphoribosylpyrophosphate synthetase and adeno- sine kinase, as well as enzymes producing ATP, such
Besides adenine and adenosine, hypoxanthine is usu- ally considered a major substrate of salvage pathways [7]. However, in mature erythrocytes, hypoxanthine cannot be recycled to give ATP because of the lack of adenylosuccinate synthetase, which is necessary for transforming inosine 5¢-monophosphate (IMP) into AMP [8]. Here, we analyse theoretically how many sal- vage pathways exist, which enzymes each of these involves and in what flux proportions (i.e. relative fluxes) the enzymes operate. Moreover, we compute the net overall stoichiometry of ATP anabolism. (Throughout the paper, by ATP anabolism or buildup,
doi:10.1111/j.1742-4658.2005.04924.x
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Abbreviations ADPRT, adenine phosphoribosyltransferase; IMP, inosine 5¢-monophosphate; SAHH, S-adenosylhomocysteine hydrolase; SAM, S-adenosylmethionine.
we mean the production of ATP from salvaged sub- strates rather than de novo synthesis.)
applied to various systems (e.g [3,16–19]). C¸ akiy´ r et al. [6] applied this method to energy metabolism in erythro- cytes. A concept related to that of elementary modes is that of extreme pathways [20]. A comparison of the two concepts was made by Klamt and Stelling in [21].
immunodeficiency,
respectively [22]. However,
Many biochemically relevant products are synthesized or degraded on multiple routes. Elementary modes pro- vide a powerful tool for determining the degree of multi- plicity and, thus, of redundancy [18,19]. This is of particular interest for the study of diseases based on enzyme deficiencies [3,6]. There are several diseases caused by enzyme deficiencies in nucleotide metabolism. Examples are provided by the following diseases: severe combined 2,8-dihydroxyadenine urolithiasis, and Lesch–Nyhan syndrome, caused by deficiencies in the adenosine deaminase (ADA), ADP- RT, and hypoxanthine guanine phosphoribosyltrans- ferase (HGPRT), these diseases are related mainly to cells other than erythro- cytes, such as lymphocytes.
In the case of severe deficiencies, a possible model- ling strategy is to consider the enzyme to be fully inhibited and examine which elementary modes are still present in the system. This allows us to detect bypas- ses, if any, or in other words to estimate the redund- ancy of the system. In this way one can predict which final products are still being produced and assess the impact of the deficiency on the patient’s metabolism. This, in turn, helps us decide which enzyme deficiencies can be considered as not harmful for the cell. Here, we specifically perform this analysis for ATP anabolism in erythrocytes.
Results and Discussion
As for pathways involving adenosine, a plausible assumption is that adenosine kinase would be used. However, Simmonds and coworkers [8–11] found that an elevation of ATP can occur in the absence of adenosine kinase, as long as adenine phosphoribosyl transferase (ADPR transferase, or ADPRT) is present. This is indicative of an alternative salvage pathway in human erythrocytes, and evidence was presented [8–11] that S-adenosylhomocysteine hydrolase (SAHH, EC 3.3.1.1), which is difficult to assess in vivo, is involved in these pathways. Since adenine is a substrate of ADPRT, the elevation of ATP in the absence of adenosine kinase shows that adenine must be released in the process before being incorporated into ATP. Indeed, studies on purified SAHH showed that several purine nucleosides and analogues can release adenine resulting from interaction with this enzyme [12]. One of these analogues is S-adenosylmethionine (SAM) [11] which can be taken up through the erythrocyte mem- brane and is abundant in all living cells [9,11]. Sim- monds and coworkers [8–11] investigated the pathway of ATP buildup from SAM, though not by a detailed stoichiometric analysis. SAM is converted into S-adenosylhomocysteine (the substrate of SAHH) by enzymes from the class of methyltransferases (EC 2.1.1.x). In the catalytic process of SAHH, addition- ally a spontaneous decomposition of the metabolite leading to free adenine and 3¢-ketoadenosine occurs, 3¢-ketoribose [13]. The adenine moiety can then be processed through ADPRT. Although under normal circumstances this pathway is not expected to produce significant amounts of adenine, it is important to men- tion the possibility this pathway offers not only for ATP generation (in erythrocytes or other types of cells harbouring SAHH) but also for the conversion of nucleoside analogues ⁄ derivatives to nucleotides. This is very important from the medical point of view because these analogues are used in chemotherapy, where one is interested in preventing an undesired transformation of these analogues [10]. Also in our present theoretical study, we include the enzyme SAHH and a methyl- transferase.
As outlined in the Introduction, we compute element- ary flux modes in nucleotide metabolism. The reaction scheme is shown in Fig. 1. The scheme is explained in more detail in the Experimental procedures. The goal is to analyse the redundancy and molar yields of sal- vage pathways. This analysis is carried out consecu- tively for different substrates. For the simulation of include adenine and adenosine salvage, we do not methyltransferase and SAHH.
Adenine salvage
Our analysis is based on the concept of ‘elementary flux mode’. This term refers to a minimal group of enzymes that can operate at steady state with all the irreversible reactions used in the right direction [14,15]. If only the enzymes belonging to one elementary mode are operative and, thereafter, one of the enzymes is inhibited, then the remaining enzymes can no longer be operational because the system cannot any longer main- tain a steady state. Elementary mode analysis has been
In the first simulation, we consider, in addition to the external metabolites mentioned in Experimental proce- dures, adenine as external, to find out how ATP can be synthesized starting from adenine. Running meta- tool on this network gives 153 elementary modes (supplementary Table S1). Four of them produce ATP
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S. Schuster and D. Kenanov A theoretical study using elementary flux modes
S. Schuster and D. Kenanov A theoretical study using elementary flux modes
enarbmem
GPD3,2
PD MG
PD G esa
DLA
HDPAG
IGP
miCLG
KH
FP K
KGP
eCLG
tx
AG P3
GPD3,1
CLG
P6G
F P6
GP3
IPT
PDA
HDAN
PTA
DAN
PTA
PDA
PTA
PDA
MGP
PAHD
P6G DH
PDAN
HSG2
GP2
P6LG
esaLGP
PDA
G
RGSS
xoH
SG
OG P6
NE PEP KP
snartRYP
txeRYP
RYP
HDP6LG
G GSS
PTA HDAN
HPDAN
HDL
tra sn
CAL
DAN
IP5R
CAL
e tx
P6F
CAL
AG P3
OC 2
P7S
P5R
KT I
TA
UR P5
KT II
EP5uX
P5X
AG P3
P4E
P5R
MRP
+ aN
kael
n
ysPPRP
aN +
aN +
PTA
P1R
PPRP
TRPGH
PDA
XH art ns
XPYH
e tx
XPYH
PMI
PPRP
KaN
aPTA
se
es
obiRoteK'3
TRPDA
CUN
PMA
DA
PTA
NEDA
I EN
PMA
ONI
esaPNP
YCH
ADA
CUN
K+
K+
ODA
+ K
kael
PMA
PTA
2HHAS
YCH
KA
pA K
odA-S
H yc
ccAteM
PDA
PDA
PMA
TM
cA c
1HHAS
MAS
txeMAS
(modes 136–139, supplementary Table S1). They are listed in Table 2. Note that in Tables 2–5, the numbers in the brackets denote relative fluxes carried by the corresponding enzymes. + and – indicate whether the elementary mode remains intact if the enzyme in the column heading is deficient.
TPI in addition but not PGI (Table 2). As for mode II.4, it is worth noting that it does not comprise the oxi- dative pentose phosphate pathway. Fructose-diphos- phate aldolase, TPI as well as PGI are involved in that mode. Importantly, none of these pathways involves adenosine kinase (AK), nor do they run via adenosine. Part of the pentose phosphate pathway is needed to pro- vide the R5P necessary for the ribose moiety in the nucleotides.
formation) and that
It can be seen that mode II.1 (here and in the follow- ing, mode x,y means mode y in Table x) uses glycolysis, the oxidative pentose phosphate pathway, and the enzymes d-ribose-5P-isomerase (R5PI), phosphoribosyl- pyrophosphate (PRPP) synthase, ADPRT and adenyl- ate kinase (ApK). Mode II.2 involves glycolysis, both the oxidative and nonoxidative parts of the pentose phosphate pathway, and the enzymes R5PI, PRPP syn- thase, ADPRT and ApK, yet in proportions different from mode II.1. It is worth noting that glucose-6P-iso- merase (PGI) is used backwards (in the direction of fructose- glucose-6-phosphate diphosphate aldolase and triosephosphate isomerase (TPI) are not involved. Mode II.3 involves ALD and
As mentioned in the Introduction, due to the exist- ence of both ATP consuming reactions and ATP pro- ducing reactions in the salvage pathways, it is not easy to see whether a net production of ATP is possible. Note that only a certain fraction of the ATP produced in the lower part of glycolysis is obtained in the net balance because the remaining fraction is needed to ‘upgrade’ adenine. Let us analyse, for example, mode II.1. Two moles of adenine are converted into two AMP by ADPRT. The supply of two PRPP for this two ATP in PRPP synthase. conversion requires
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Fig. 1. Model representing glycolysis, the pentose phosphate pathway and purine metabolism in red blood cells, including a methyltrans- ferase and two possible ways of operation of S-adenosylhomocysteine hydrolase (SAHH1 and SAHH2) (extended from [10]). Transport reac- tions of adenine and adenosine across the cell membrane are not shown for simplicity’s sake. For abbreviations of enzymes and metabolites, see Table 1.
S. Schuster and D. Kenanov A theoretical study using elementary flux modes
Table 1. List of all enzymes and metabolites included in the model. Table 1. Continued.
Abbreviation Full name EC number Abbreviation Full name EC number
Enzyme ADA ADPRT AK ALD1 AMPDA Adenosine deaminase Adenine phosphoribosyltransferase Adenosine kinase Fructose-diphosphate aldolase Adenosine monophosphate 3.5.4.4 2.4.2.7 2.7.1.20 4.1.2.13 3.5.4.6 deaminase
GA3P GL6P GLC GO6P GSH GSSG HCY HYPX IMP INO K+ LAC MetAcc Na+ NAD NADH Glyceraldehyde 3-phosphate D-Glucono-1,5-lactone 6-phosphate Glucose 6-Phospho-D-gluconate Reduced glutathione Oxidized glutathione L-Homocysteine Hypoxanthine Inosine 5¢-monophosphate Inosine Potassium L-Lactate Methylated acceptor Sodium Nicotinamide adenine dinucleotide Nicotinamide adenine dinucleotide reduced APK C5MT DPGase DPGM EN G6PDH GAPDH GL6PDH GSHox GSSGR HGPRT Adenylate kinase Cytosine-5-methyltransferase Diphosphoglycerate phosphatase 2,3-Diphosphoglycerate mutase Enolase Glucose-6P dehydrogenase Glyceraldehyde-3P dehydrogenase 6P-Gluconate dehydrogenase Glutathioneperoxidase Glutathione reductase Hypoxanthine guanine 2.7.4.3 2.1.1.37 3.1.3.13 5.4.2.4 4.2.1.11 1.1.1.49 1.2.1.12 1.1.1.49 1.11.1.9 1.8.1.7 2.4.2.8 NADP Nicotinamide adenine dinucleotide phosphoribosyltransferase phosphate NADPH Nicotinamide adenine dinucleotide
PEP PRPP phosphate reduced Phosphoenolpyruvate 5-Phospho-alpha-D-ribose 1-diphosphate
D-Ribose-5P-isomerase S-Adenosylhomocysteine hydrolase Transaldolase Transketolase Triosephosphate isomerase 1 D-Xylulose-5P-3-epimerase
HK LDH NUC PFK1 PGI PGK1 PGLase PGM PK PNPase PRM PRPP Hexokinase Lactate dehydrogenase AMP phosphatase Phosphofructokinase Glucose-6P-isomerase Phosphoglycerate kinase 1 6P-Gluconolactonase Phosphoglycerate mutase 1 Pyruvate kinase Purine nucleoside phosphorylase Phosphoribomutase Phosphoribosylpyrophosphate 2.7.1.1 1.1.1.27 3.1.3.5 2.7.1.11 5.3.1.9 2.7.2.3 3.1.1.31 5.4.2.1 2.7.1.40 2.4.2.1 5.4.2.7 2.7.6.1 synthase synthetase PYR R5P RIP RU5P S-AdoHcy S7P SAM X5P Pyruvate D-Ribulose 5-phosphate D-Ribose 1-phosphate D-Ribulose 5-phosphate S-Adenosyl-L-homocysteine D-Sedoheptulose 7-phosphate S-Adenosyl-L-methionine D-Xylulose 5-phosphate
5.3.1.6 3.3.1.1 2.2.1.2 2.2.1.1 5.3.1.1 5.1.3.1
ADPR transferase and PRPP synthase together form four AMP. Using another four ATP, these are trans- formed into eight ADP in ApK. Due to the special flux distribution, seven ATP are consumed in hexo- kinase and five ATP in phosphofructokinase. In glyco- lysis, 20 mol ATP are produced; 10 in each of phosphoglycerate kinase and pyruvate kinase. This gives an ATP balance of )2–4)7–5+10+10 ¼ 2. Note that the lower part of glycolysis has to run five times as fast as ADPR transferase to make this positive bal- ance possible. The ATP ⁄ glucose yields (that is, the ratios of ATP production over glucose consumption fluxes) of modes II.1-II.4 are 2 : 7, 1 : 6, 1 : 4 and 3 : 10, respectively. Note that these are the yields for the buildup of ATP from adenine rather than from ADP as usually indicated for glycolysis. Mode II.4 has the highest yield. It can be shown that the flux distri- bution realizing the highest yield always coincides with an elementary mode or a linear combination of two modes with the same maximum yield [14]. Thus, there
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R5PI SAHH TA TK TPI XU5PE Metabolites 1,3 DPG 2,3 DPG 2PG 3¢-keto ribose 3PG Acc Adenine Ado ADP AMP ATP CO2 DHAP E4P F6P FDP G6P 1,3-Diphospho-D-glycerate 2,3-Diphospho-D-glycerate 2-Phospho-D-glycerate 3¢-Keto ribose 3-Phospho-D-glycerate Acceptor for methyl group Adenine Adenosine Adenosine 5¢-diphosphate Adenosine 5¢-monophosphate Adenosine 5¢-triphosphate Carbon dioxide Dihydroxyacetone phosphate D-Erythrose 4-phosphate Fructose 6-phosphate Fructose 1,6-diphosphate Glucose 6-phosphate
S. Schuster and D. Kenanov A theoretical study using elementary flux modes
Table 2. Elementary modes producing ATP from adenine.
Elementary modes –ADA –AK –PNPase –ADPRT
+ + + –
+ + + –
+ + + –
+ + + –
can be no flux distribution of adenine salvage enabling an ATP ⁄ glucose yield higher than 0.3.
the
adenosine per 3 mol of glucose. Modes III.2 and III.3 involve different combinations of glycolysis and the pentose phosphate pathway as well as AK and ApK. The involvement of the pentose phosphate pathway is not, however, essential for ATP build up in these modes. It merely lowers the ATP ⁄ glucose yield.
Modes III.4-III.9 do not start
Interestingly, none of the ATP producing modes involves phosphatase 2,3-diphosphoglycerate (DPG) bypass. As this would circumvent the enzyme phosphoglycerate kinase, the ATP yield of glycolysis would be decreased, to such an extent that no ATP buildup from adenine would be possible.
intermediates. Modes
Most of the remaining elementary modes of the first simulation can be interpreted as degradation of ATP to hypoxanthine. One elementary mode describes the 2,3DPG bypass of glycolysis, with a zero ATP balance. As we consider ADP as internal, normal glycolysis implying a transformation of ADP into ATP is not computed.
Adenosine salvage
In the second simulation, we analysed ATP buildup from adenosine. Therefore, we consider adenosine (but not adenine) to be external. This gives rise to 97 ele- mentary modes (Supplementary Table S2). Twelve modes (numbers 10, 15, 20, 54–59, 77, 85, and 92 in Table S2) produce ATP from adenosine (Table 3). All of these involve AK and ApK.
from glucose but solely from adenosine. This is used not only as the source for ATP buildup but also as an energy source. Adenosine is degraded into hypoxanthine (which is trans- excreted) and ribose-1-phosphate, which is formed, by the pentose phosphate pathway, into glyco- lytic III.10-III.12 use both glucose and adenosine as energy sources, in different proportions. Modes III.4, III.7 and III.11 involve the 2,3DPG bypass. Again, there is no mode involving the 2,3DPG bypass when glucose is used as the only energy source (modes III.1-III.3) because the ATP ⁄ glu- cose yield would then be so low that no ATP buildup would be possible. The ATP ⁄ adenosine yields of the ATP-producing modes are 1 for modes III.1-III.3, 1 : 4, 2 : 5, 1 : 4, 1 : 4, 8 : 17, 5 : 14, 2 : 3, 1 : 4 and 5 : 8 for modes III.4-III.12, respectively. Thus, modes starting from glucose and adenosine transform the lat- ter completely into ATP, which implies that glucose is the only energy source. By contrast, in the modes starting solely from adenosine, part of this substrate is used as an energy source, so that the yield is lower.
Inclusion of SAHH
Mode III.1 is made up of glycolysis, AK and ApK and does not involve any pentose phosphate pathway enzyme. The flux ratio between the upper and lower parts of glycolysis is, as in pure glycolysis, 1 : 2. The flux ratio between AK as well as ApK and the upper part of glycolysis is 2 : 3. Thus, 2 out of six ATP pro- duced from ADP in glycolysis are used to convert adenosine into AMP. The latter is ‘upgraded’ by ApK to give ADP. In total, 2 mol of ATP are built up from
As mentioned in the Introduction, there is experimen- tal evidence that S-adenosylmethionine can be used by erythrocytes for ATP buildup [8–11]. To analyse this
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1. (5 PGI) (5 ALD) (5 TPI) (10 GAPDH) (10 PGM) (10 EN) (10 LACex) (– 4 ApK) (2 PGLase) (4 GSSGR) (2 R5PI) (7 HK) (5 PFK) (10 PGK) (10 PK) (10 LDH) (2 ADPRT) (4 GSHox) (2 PRPPsyn) (2 G6PD) (2 GL6PDH) 7 GLC + 2 Adenine ¼ 2 CO2 + 10 LACext + 2 ATP 2. ()10 PGI) (5 GAPDH) (5 PGM) (5 EN) (5 LACex) () 2 ApK) (16 PGLase) (32 GSSGR) (6 R5PI) (10 Xu5PE) (5 TKI) (5 TKII) (5 TA) (6 HK) (5 PGK) (5 PK) (5 LDH) ADPRT (32 GSHox) PRPPsyn (16 G6PD) (16 GL6PDH) 6 GLC + Adenine ¼ 16 CO2 + 5 LACext + ATP 3. (2 ALD) (2 TPI) (5 GAPDH) (5 PGM) (5 EN) (5 LACex) () 2 ApK) (4 PGLase) (8 GSSGR) (2 R5PI) (2 Xu5PE) TKI TKII TA (4 HK) (2 PFK) (5 PGK) (5 PK) (5 LDH) ADPRT (8 GSHox) PRPPsyn (4 G6PD) (4 GL6PDH) 4 GLC + Adenine ¼ 4 CO2 + 5 LACext + ATP 4. (10 PGI) (8 ALD) (8 TPI) (15 GAPDH) (15 PGM) (15 EN) (15 LACex) (– 6 ApK) (2 R5PI) (– 2 Xu5PE) -TKI -TKII -TA (10 HK) (8 PFK) (15 PGK) (15 PK) (15 LDH) (3 ADPRT) (3 PRPPsyn) 10 GLC + 3 Adenine ¼ 15 LACext + 3 ATP
S. Schuster and D. Kenanov A theoretical study using elementary flux modes
Table 3. Elementary modes producing ATP from adenosine.
Elementary modes –ADA –AK –PNPase –ADPRT
+ – + +
+ – + +
+ – + +
– – – +
– – – +
+ – – +
– – – +
– – – +
+ – – +
– – – +
– – – +
+ – – +
of S-adenosylmethionine
consumption)
in detail, we performed a simulation with the complete scheme shown in Fig. 1; that is, including at least one methyltransferase (considered irreversible in the direc- tion and SAHH. In that simulation, adenine and adenosine were considered internal, while S-adenosylmethionine was treated as external. This gave rise to 214 element- ary modes (Supplementary Table S3). Twenty-three
modes produce ATP (Table 4). Some of them involve the modes starting from adenine obtained in the first simulation and include methyltransferase and SAHH2 in addition. Some others involve the modes starting from adenosine obtained in the second simulation and include methyltransferases and SAHH1 in addition. Interestingly, some modes involve both SAHH1 and SAHH2.
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1. (3 PGI) (3 ALD) (3 TPI) (6 GAPDH) (6 PGM) (6 EN) (6 LACex) ()2 ApK) (3 HK) (3 PFK) (6 PGK) (6 PK) (6 LDH) (2 AK) 3 GLC +2 ADO ¼ 6 LACext + 2 ATP 2. ()6 PGI) (3 GAPDH) (3 PGM) (3 EN) (3 LACex) –ApK (9 PGLase) (18 GSSGR) (3 R5PI) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (3 HK) (3 PGK) (3 PK) (3 LDH) (18 GSHox) (9 G6PD) (9 GL6PDH) AK 3 GLC + ADO ¼ 9 CO2 + 3 LACext + ATP 3. (6 ALD) (6 TPI) (15 GAPDH) (15 PGM) (15 EN) (15 LACex) (–ApK) (9 PGLase) (18 GSSGR) (3 R5PI) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (9 HK) (6 PFK) (15 PGK) (15 PK) (15 LDH) (18 GSHox) (9 G6PD) (9 GL6PDH) (5 AK) 9 GLC +5 ADO ¼ 9 CO2 + 15 LACext + 5 ATP 4. (– 6 PGI) (3 GAPDH) (3 DPGM) (3 PGM) (3 EN) (3 LACex) –ApK (6 PGLase) (12 GSSGR) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (3PNPase) (3 PRM) (3 HXtrans) (3 DPGase) (3 PK) (3 LDH) (12 GSHox) (3 ADA) (6 G6PD) (6 GL6PDH) AK 4 ADO ¼ 3 HYPXext + 6 CO2 + 3LACext + ATP 5. ()6 PGI) (3 GAPDH) (3 PGM) (3 EN) (3 LACex) ()2 ApK) (6 PGLase) (12 GSSGR) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (3 PNPase) (3 PRM) (3 HXtrans) (3 PGK) (3 PK) (3 LDH) (12 GSHox) (3 ADA) (6 G6PD) (6 GL6PDH) (2 AK) 5 ADO ¼ 3 HYPXext + 6 CO2 + 3 LACext + 2 ATP 6. ()6 PGI) (3 GAPDH) (3 PGM) (3 EN) (3 LACex) –ApK (6 PGLase) (12 GSSGR) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (3 PNPase) (3 PRM) (3 HXtrans) (3 PGK) (3 PK) (3 LDH) (3 AMPDA) (12 GSHox) (3 IMPase) (6 G6PD) (6 GL6PDH) (4 AK) 4 ADO ¼ 3 HYPXext + 6 CO2 + 3 LACext + ATP 7. (2 ALD) (2 TPI) (5 GAPDH) (5 DPGM) (5 PGM) (5 EN) (5 LACex) –ApK ()2 R5PI) (2 Xu5PE) TKI TKII TA (3 PNPase) (3 PRM) (3 HXtrans) (2 PFK) (5 DPGase) (5 PK) (5 LDH) (3 ADA) AK 4 ADO ¼ 3 HYPXext +5 LACext + ATP 8. (6 ALD) (6 TPI) (15 GAPDH) (15 PGM) (15 EN) (15 LACex) ()8 ApK) ()6 R5PI) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (9 PNPase) (9 PRM) (9 HXtrans) (6 PFK) (15 PGK) (15 PK) (15 LDH) (9 ADA) (8 AK) 17 ADO ¼ 9 HYPXext + 15 LACext + 8 ATP 9. (6 ALD) (6 TPI) (15 GAPDH) (15 PGM) (15 EN) (15 LACex) ()5 ApK) ()6 R5PI) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (9 PNPase) (9 PRM) (9 HXtrans) (6 PFK) (15 PGK) (15 PK) (15 LDH) (9 AMPDA) (9 IMPase) (14 AK) 14 ADO ¼ 9 HYPXext + 15 LACext + 5 ATP 10. (2 ALD) (2 TPI) (5 GAPDH) (5 PGM) (5 EN) (5 LACex) ()2 ApK) (2 PGLase) (4 GSSGR) (2 Xu5PE) TKI TKII TA PNPase PRM HXtrans (2 HK) (2 PFK) (5 PGK) (5 PK) (5 LDH) (4 GSHox) ADA (2 G6PD) (2 GL6PDH) (2 AK) 2 GLC + 3 ADO ¼ HYPXext + 2 CO2 + 5 LACext + 2 ATP 11. (6 ALD) (6 TPI) (15 GAPDH) (15 DPGM) (15 PGM) (15 EN) (15 LACex) –ApK (6 PGLase) (12 GSSGR) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (3 PNPase) (3 PRM) (3 HXtrans) (6 HK) (6 PFK) (15 DPGase) (15 PK) (15 LDH) (12 GSHox) (3 ADA) (6 G6PD) (6 GL6PDH) AK 6 GLC + 4 ADO ¼ 3 HYPXext + 6 CO2 + 15 LACext + ATP 12. (6 ALD) (6 TPI) (15 GAPDH) (15 PGM) (15 EN) (15 LACex) (–ApK) (6 PGLase) (12 GSSGR) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (3 PNPase) (3 PRM) (3 HXtrans) (6 HK) (6 PFK) (15 PGK) (15 PK) (15 LDH) (3 AMPDA) (12 GSHox) (3 IMPase) (6 G6PD) (6 GL6PDH) (8 AK) 6 GLC + 8 ADO ¼ 3 HYPXext + 6 CO2 + 15 LACext + 5 ATP
S. Schuster and D. Kenanov A theoretical study using elementary flux modes
Table 4. ATP producing modes in the extended system including SAHH and methyltransferase.
Elementary modes –ADA –AK –PNPase –ADPRT
– – – +
– – – +
+ – – +
– – – +
– – – +
+ – – +
+ – + +
– – – +
+ – + +
+ – + +
– – – +
+ – – +
Through SAHH1 but not SAHH2 1. (3 DPGase) (3 PK) (3 LDH) (4 MT) (12 GSHox) (3 ADA) (6 G6PD) (6 GL6PDH) AK (– 6 PGI) (3 GAPDH) (3 DPGM) (3 PGM) (3 EN) (3 LACex) -ApK (6 PGLase) (12 GSSGR) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (3 PNPase) (3 PRM) (3 HXtrans) (4 SAHH1) 4 SAM + 4 H2O +4 Acc ¼ 3 HYPXext + 6 CO2 + 4 HCY + ATP + 3 LACext + 4 MetAcc 2. (3 PGK) (3 PK) (3 LDH) (5 MT) (12 GSHox) (3 ADA) (6 G6PD) (6 GL6PDH) (2 AK) ()6 PGI) (3 GAPDH) (3 PGM) (3 EN) (3 LACex) ()2 ApK) (6 PGLase) (12 GSSGR) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (3 PNPase) (3 PRM) (3 HXtrans) (5 SAHH1) 5 SAM + 5 H2O + 5 Acc ¼ 3 HYPXext + 6 CO2 +5 HCY + 2 ATP + 3 LACext + 5 AccMet 3. (3 PGK) (3 PK) (3 LDH) (3 AMPDA) (4 MT) (12 GSHox) (3 IMPase) (6 G6PD) (6 GL6PDH) (4 AK) ()6 PGI) (3 GAPDH) (3 PGM) (3 EN) (3 LACex) –ApK (6 PGLase) (12 GSSGR) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (3 PNPase) (3 PRM) (3 HXtrans) (4 SAHH1) 4 SAM + 4 H2O + 4 Acc ¼ 3 HYPXext + 6 CO2 + 4 HCY + ATP + 3 LACext + 4 AccMet 4. (2 PFK) (5 DPGase) (5 PK) (5 LDH) (4 MT) (3 ADA) AK (2 ALD) (2 TPI) (5 GAPDH) (5 DPGM) (5 PGM) (5 EN) (5 LACex) –ApK ()2 R5PI) (2 Xu5PE) TKI TKII TA (3 PNPase) (3 PRM) (3 HXtrans) (4 SAHH1) 4 SAM +4 H2O +4 Acc ¼ 3 HYPXext + 4 HCY + ATP + 5 LACext + 4 AccMet 5. (6 PFK) (15 PGK) (15 PK) (15 LDH) (17 MT) (9 ADA) (8 AK) (6 ALD) (6 TPI) (15 GAPDH) (15 PGM) (15 EN) (15 LACex) ()8 ApK) ()6 R5PI) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (9 PNPase) (9 PRM) (9 HXtrans) (17 SAHH1) 17 SAM +17 H2O +17 Acc ¼ 9 HYPXext + 17 HCY + 8 ATP + 15 LACext +17 AccMet 6. (6 PFK) (15 PGK) (15 PK) (15 LDH) (9 AMPDA) (14 MT) (9 IMPase) (14 AK) (6 ALD) (6 TPI) (15 GAPDH) (15 PGM) (15 EN) (15 LACex) ()5 ApK) ()6 R5PI) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (9 PNPase) (9 PRM) (9 HXtrans) (14 SAHH1) 14 SAM +14 H2O + 14 Acc ¼ 9 HYPXext +14 HCY + 5 ATP + 15 LACext + 14 AccMet 7. (3 HK) (3 PGK) (3 PK) (3 LDH) MT (18 GSHox) (9 G6PD) (9 GL6PDH) AK ()6 PGI) (3 GAPDH) (3 PGM) (3 EN) (3 LACex) –ApK (9 PGLase) (18 GSSGR) (3 R5PI) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) SAHH1 SAM + H2O + Acc +3 GLC ¼ 9 CO2 + HCY + ATP +3 LACext + AccMet 8. (6 HK) (6 PFK) (15 DPGase) (15 PK) (15 LDH) (4 MT) (12 GSHox) (3 ADA) (6 G6PD) (6 GL6PDH) AK (6 ALD) (6 TPI) (15 GAPDH) (15 DPGM) (15 PGM) (15 EN) (15 LACex) –ApK (6 PGLase) (12 GSSGR) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (3 PNPase) (3 PRM) (3 HXtrans) (4 SAHH1) 4 SAM + 4 H2O + 4 Acc + 6 GLC ¼ 3 HYPXext + 6 CO2 + 4 HCY + ATP + 15 LACext + 4 AccMet 9. (3 HK) (3 PFK) (6 PGK) (6 PK) (6 LDH) (2 MT) (2 AK) (3 PGI) (3 ALD) (3 TPI) (6 GAPDH) (6 PGM) (6 EN) (6 LACex) ()2 ApK) (2 SAHH1) 2 SAM +2 H2O + 2 Acc + 3 GLC ¼ 2 HCY + 2 ATP + 6 LACext + 2 AccMet 10. (9 HK) (6 PFK) (15 PGK) (15 PK) (15 LDH) (5 MT) (18 GSHox) (9 G6PD) (9 GL6PDH) (5 AK) (6 ALD) (6 TPI) (15 GAPDH) (15 PGM) (15 EN) (15 LACex) (– 5 ApK) (9 PGLase) (18 GSSGR) (3 R5PI) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (5 SAHH1) 5 SAM +5 H2O +5 Acc +9 GLC ¼ 9 CO2 +5 HCY +5 ATP +15 LACext +5 AccMet 11. (2 HK) (2 PFK) (5 PGK) (5 PK) (5 LDH) (3 MT) (4 GSHox) ADA (2 G6PD) (2 GL6PDH) (2 AK) (2 ALD) (2 TPI) (5 GAPDH) (5 PGM) (5 EN) (5 LACex) ()2 ApK) (2 PGLase) (4 GSSGR) (2 Xu5PE) TKI TKII TA PNPase PRM HXtrans (3 SAHH1) 3 SAM +3 H2O + 3 Acc + 2 GLC ¼ HYPXext + 2 CO2 + 3 HCY + 2 ATP + 5 LACext + 3 AccMet 12. (6 HK) (6 PFK) (15 PGK) (15 PK) (15 LDH) (3 AMPDA) (8 MT) (12 GSHox) (3 IMPase) (6 G6PD) (6 GL6PDH) (8 AK) (6 ALD) (6 TPI) (15 GAPDH) (15 PGM) (15 EN) (15 LACex) ()5 ApK) (6 PGLase) (12 GSSGR) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (3 PNPase) (3 PRM) (3 HXtrans) (8 SAHH1) 8 SAM + 8 H2O + 8 Acc + 6 GLC ¼ 3 HYPXext + 6 CO2 + 8 HCY + 5 ATP + 15 LACext + 8 AccMet
– + – –
(8 Xu5PE) (4 TKI) (4 TKII) (4 TA) (5 PNPase) (5 PRM)
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Through SAHH1 & SAHH2 1. (4 DPGase) (4 PK) (4 LDH) (6 MT) ADPRT (16 GSHox) PRPPsyn (5 ADA) (8 G6PD) (8 GL6PDH)()8 PGI) (4 GAPDH) (4 DPGM) (4 PGM) (4 EN) (4 LACex) (– 2 ApK) (8 PGLase) (16 GSSGR) (5 HXtrans) SAHH2 (5 SAHH1) 6 SAM + 6 H2O + 6 Acc ¼ 5 HYPXext + 8 CO2 +6 HCY + ATP + 4 LACext + 6 AccMet + 3KRibose
S. Schuster and D. Kenanov A theoretical study using elementary flux modes
Table 4. Continued.
Elementary modes –ADA –AK –PNPase –ADPRT
– + – –
– + – –
– + – –
– + – –
– + – –
– + – –
2. (2 PGK) (2 PK) (2 LDH) (4 MT) ADPRT (8 GSHox) PRPPsyn (3 ADA) (4 G6PD) (4 GL6PDH) (– 4 PGI) (2 GAPDH) (2 PGM) (2 EN) (2 LACex) (– 2 ApK) (4 PGLase) (8 GSSGR) (4 Xu5PE) (2 TKI) (2 TKII) (2 TA) (3 PNPase) (3 PRM) (3 HXtrans) SAHH2 (3 SAHH1) 4 SAM + 4 H2O + 4 Acc ¼ 3 HYPXext + 4 CO2 +4 HCY + ATP + 2 LACext + 4 AccMet + 3KRibose 3. (8 PFK) (20 DPGase) (20 PK) (20 LDH) (18 MT) (3 ADPRT) (3 PRPPsyn) (15 ADA) (8 ALD) (8 TPI) (20 GAPDH) (20 DPGM) (20 PGM) (20 EN) (20 LACex) ()6 ApK) ()8 R5PI) (8 Xu5PE) (4 TKI) (4 TKII) (4 TA) (15 PNPase) (15 PRM) (15 HXtrans) (3 SAHH2) (15 SAHH1) 18 SAM + 18 H2O + 18 Acc ¼ 15 HYPXext + 18 HCY + 3 ATP + 20 LACext + 18 AccMet + 3 3KRibose 4. (2 PFK) (5 PGK) (5 PK) (5 LDH) (7 MT) (2 ADPRT) (2 PRPPsyn) (5 ADA) (2 ALD) (2 TPI) (5 GAPDH) (5 PGM) (5 EN) (5 LACex) ()4 ApK) ()2 R5PI) (2 Xu5PE) TKI TKII TA (5 PNPase) (5 PRM) (5 HXtrans) (2 SAHH2) (5 SAHH1) 7 SAM + 7 H2O + 7 Acc ¼ 5 HYPXext + 7 HCY + 2 ATP + 5 LACext + 7 AccMet + 2 3KRibose 5. (8 HK) (8 PFK) (20 DPGase) (20 PK) (20 LDH) (6 MT) ADPRT (16 GSHox) PRPPsyn (5 ADA) (8 G6PD) (8 GL6PDH) (8 ALD) (8 TPI) (20 GAPDH) (20 DPGM) (20 PGM) (20 EN) (20 LACex) (– 2 ApK) (8 PGLase) (16 GSSGR) (8 Xu5PE) (4 TKI) (4 TKII) (4 TA) (5 PNPase) (5 PRM) (5 HXtrans) SAHH2 (5 SAHH1) 6 SAM + 6 H2O + 6 Acc + 8 GLC ¼ 5 HYPXext + 8 CO2 + 6 HCY + ATP + 20 LACext + 6 AccMet + 3KRibose 6. (2 HK) (2 PFK) (4 PGK) (4 PK) (4 LDH) (2 MT) ADPRT PRPPsyn ADA (2 PGI) (2 ALD) (2 TPI) (4 GAPDH) (4 PGM) (4 EN) (4 LACex) ()2 ApK) PNPase PRM HXtrans SAHH2 SAHH1 2 SAM + 2 H2O + 2 Acc + 2 GLC ¼ HYPXext + 2 HCY + ATP + 4 LACext + 2 AccMet + 3KRibose 7. (4 HK) (4 PFK) (10 PGK) (10 PK) (10 LDH) (8 MT) (3 ADPRT) (8 GSHox) (3 PRPPsyn) (5 ADA) (4 G6PD) (4 GL6PDH) (4 ALD) (4 TPI) (10 GAPDH) (10 PGM) (10 EN) (10 LACex) ()6 ApK) (4 PGLase) (8 GSSGR) (4 Xu5PE) (2 TKI) (2 TKII) (2 TA) (5 PNPase) (5 PRM) (5 HXtrans) (3 SAHH2) (5 SAHH1) 8 SAM + 8 H2O + 8 Acc + 4 GLC ¼ 5 HYPXext + 4 CO2 + 8 HCY + 3 ATP + 10 LACext + 8 AccMet + 3 3KRibose
+ + + –
+ + + –
+ + + –
+ + + –
Note that operation of ATP-producing pathways starting from S-adenosylmethionine permanently util- izes a methyl acceptor and produces the corresponding methylated form. In our simulation, we consider both substances to be external. A more detailed model may include a regeneration of the methyl acceptor from the methylated form or from other sources. Another possi- bility is to consider the following reaction mechanism. As SAHH1 is reversible, adenosine may react with
homocysteine halfway and then (via the SAHH2 func- tion) back to adenine, ribose and homocysteine. Thus, there is no net consumption of homocysteine in the process, and S-adenosylmethionine is not involved at all. Therefore, we performed a simulation with a model including the two functions of SAHH but excluding the methyltransferase (and, hence, S-adeno- sylmethionine). Adenosine was considered external. This produced 135 elementary modes (Supplementary
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Through SAHH2 only 1. (5 PK) (5 LDH) MT ADPRT (32 GSHox) PRPPsyn (16 G6PD) (16 GL6PDH) ()10 PGI) (5 GAPDH) (5 PGM) (5 EN) (5 LACex) ()2 ApK) (16 PGLase) (32 GSSGR) (6 R5PI) (10 Xu5PE) (5 TKI) (5 TKII) (5 TA) SAHH2 SAM + H2O + Acc + 6 GLC ¼ 16 CO2 + HCY + ATP + 5 LACext + AccMet + 3KRibose 2. (10 HK) (8 PFK) (15 PGK) (15 PK) (15 LDH) (3 MT) (3 ADPRT) (3 PRPPsyn) (10 PGI) (8 ALD) (8 TPI) (15 GAPDH) (15 PGM) (15 EN) (15 LACex) ()6 ApK) (2 R5PI) ()2 Xu5PE) –TKI –TKII –TA (3 SAHH2) 3 SAM + 3 H2O + 3 Acc +10 GLC ¼ 3 HCY + 3 ATP + 15 LACext + 3 AccMet + 3 3KRibose 3. (4 HK) (2 PFK) (5 PGK) (5 PK) (5 LDH) MT ADPRT (8 GSHox) PRPPsyn (4 G6PD) (4 GL6PDH) (2 ALD) (2 TPI) (5 GAPDH) (5 PGM) (5 EN) (5 LACex) ()2 ApK) (4 PGLase) (8 GSSGR) (2 R5PI) (2 Xu5PE) TKI TKII TA SAHH2 SAM + H2O + Acc + 4 GLC ¼ 4 CO2 + HCY + ATP + 5 LACext + AccMet + 3KRibose 4. (7 HK) (5 PFK) (10 PGK) (10 PK) (10 LDH) (2 MT) (2 ADPRT) (4 GSHox) (2 PRPPsyn) (2 G6PD) (2 GL6PDH) (5 PGI) (5 ALD) (5 TPI) (10 GAPDH) (10 PGM) (10 EN) (10 LACex) (– 4 ApK) (2 PGLase) (4 GSSGR) (2 R5PI) (2 SAHH2) 2 SAM + 2 H2O + 2 Acc + 7 GLC ¼ 2 CO2 + 2 HCY + 2 ATP + 10 LACext + 2 AccMet + 2 3KRibose
S. Schuster and D. Kenanov A theoretical study using elementary flux modes
Table 5. Elementary modes producing ATP in the presence of SAHH (but not methyltransferase). There are 14 more modes not including SAHH but producing ATP.
Elementary modes –ADA –AK –PNPase –ADPRT
+ + + –
+ + + –
+ + + –
– + – –
– + – –
– + – –
– + – –
– + – –
– + – –
– + – –
there are 14 more modes not worth noting that including SAHH but producing ATP (Supplementary Table S4).
Purine nucleoside phosphorylase, ADA, AK and ADPRT deficiencies
By checking which of the computed elementary modes remain after deleting a given enzyme, it can easily be analysed which salvage pathways can be operative in spite of severe enzyme deficiencies. If ADA is deficient,
Table S4) of which 10 generate ATP from adenosine (Table 5). As expected, all of these use SAHH1 in the backward and SAHH2 in the forward direction. As can be seen in Table 5, both the ATP ⁄ glucose yield and ATP ⁄ adenosine yields are rather diverse. The highest values are 3 : 4 (in the modes really using glu- cose) and 1, respectively. However, they do not occur together, the elementary mode producing 3 mol of ATP from 4 mol of glucose requires 8 mol of adeno- sine. As for the modes allowing an ATP ⁄ adenosine yield of 1, the highest ATP ⁄ glucose yield is 3 : 10. It is
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1. (5 PGI) (5 ALD) (5 TPI) (10 GAPDH) (10 PGM) (10 EN) (10 LACex) ()4 ApK) (2 PGLase) (4 GSSGR) (2 R5PI) ()2 SAHH1) (7 HK) (5 PFK) (10 PGK) (10 PK) (10 LDH) (2 ADPRT) (4 GSHox) (2 PRPPsyn) (2 G6PD) (2 GL6PDH) (2 SAHH2) 7 GLC + 2 ADO ¼ 2 CO2 +10 LACext + 2 3KRibose + 2 ATP 2. (10 PGI) (8 ALD) (8 TPI) (15 GAPDH) (15 PGM) (15 EN) (15 LACex) ()6 ApK) (2 R5PI) (– 2 Xu5PE) -TKI -TKII -TA ()3 SAHH1) (10 HK) (8 PFK) (15 PGK) (15 PK) (15 LDH) (3 ADPRT) (3 PRPPsyn) (3 SAHH2) 10 GLC + 3 ADO ¼ 15 LACext + 3 3KRibose + 3 ATP 3. ()10 PGI) (5 GAPDH) (5 PGM) (5 EN) (5 LACex) ()2 ApK) (16 PGLase) (32 GSSGR) (6 R5PI) (10 Xu5PE) (5 TKI) (5 TKII) (5 TA) -SAHH1 (6 HK) (5 PGK) (5 PK) (5 LDH) ADPRT (32 GSHox) PRPPsyn (16 G6PD) (16 GL6PDH) SAHH2 6 GLC + ADO ¼ 16 CO2 +5 LACext + 3KRibose + ATP 4. ()8 PGI) (4 GAPDH) (4 DPGM) (4 PGM) (4 EN) (4 LACex) ()2 ApK) (8 PGLase) (16 GSSGR) (8 Xu5PE) (4 TKI) (4 TKII) (4 TA) (5 PNPase) (5 PRM) (5 HXtrans) )SAHH1 (4 DPGase) (4 PK) (4 LDH) ADPRT (16 GSHox) PRPPsyn (5 ADA) (8 G6PD) (8 GL6PDH) SAHH2 6 ADO ¼ 5 HYPXext + 8 CO2 + 4 LACext + 3KRibose + ATP 5. ()4 PGI) (2 GAPDH) (2 PGM) (2 EN) (2 LACex) ()2 ApK) (4 PGLase) (8 GSSGR) (4 Xu5PE) (2 TKI) (2 TKII) (2 TA) (3 PNPase) (3 PRM) (3 HXtrans) –SAHH1 (2 PGK) (2 PK) (2 LDH) ADPRT (8 GSHox) PRPPsyn (3 ADA) (4 G6PD) (4 GL6PDH) SAHH2 4 ADO ¼ 3 HYPXext + 4 CO2 + 2 LACext + 3KRibose + ATP 6. (8 ALD) (8 TPI) (20 GAPDH) (20 DPGM) (20 PGM) (20 EN) (20 LACex) ()6 ApK) ()8 R5PI) (8 Xu5PE) (4 TKI) (4 TKII) (4 TA) (15 PNPase) (15 PRM) (15 HXtrans) ()3 SAHH1) (8 PFK) (20 DPGase) (20 PK) (20 LDH) (3 ADPRT) (3 PRPPsyn) (15 ADA) (3 SAHH2) 18 ADO ¼ 15 HYPXext + 20 LACext + 3 3KRibose + 3 ATP 7. (2 ALD) (2 TPI) (5 GAPDH) (5 PGM) (5 EN) (5 LACex) ()4 ApK) ()2 R5PI) (2 Xu5PE) TKI TKII TA (5 PNPase) (5 PRM) (5 HXtrans) ()2 SAHH1) (2 PFK) (5 PGK) (5 PK) (5 LDH) (2 ADPRT) (2 PRPPsyn) (5 ADA) (2 SAHH2) 7 ADO ¼ 5 HYPXext + 5 LACext + 2 3KRibose + 2 ATP 8. (2 PGI) (2 ALD) (2 TPI) (4 GAPDH) (4 PGM) (4 EN) (4 LACex) ()2 ApK) PNPase PRM HXtrans -SAHH1 (2 HK) (2 PFK) (4 PGK) (4 PK) (4 LDH) ADPRT PRPPsyn ADA SAHH2 2 GLC + 2 ADO ¼ HYPXext + 4 LACext + 3KRibose + ATP 9. (4 ALD) (4 TPI) (10 GAPDH) (10 PGM) (10 EN) (10 LACex) (–ApK) (4 PGLase) (8 GSSGR) (4 Xu5PE) (2 TKI) (2 TKII) (2 TA) (5 PNPase) (5 PRM) (5 HXtrans) ()3 SAHH1) (4 HK) (4 PFK) (10 PGK) (10 PK) (10 LDH) (3 ADPRT) (8 GSHox) (3 PRPPsyn) (5 ADA) (4 G6PD) (4 GL6PDH) (3 SAHH2) 4 GLC + 8 ADO ¼ 5 HYPXext + 4 CO2 + 10 LACext + 3 3KRibose + 3 ATP 10. (8 ALD) (8 TPI) (20 GAPDH) (20 DPGM) (20 PGM) (20 EN) (20 LACex) ()2 ApK) (8 PGLase) (16 GSSGR) (8 Xu5PE) (4 TKI) (4 TKII) (4 TA) (5 PNPase) (5 PRM) (5 HXtrans) –SAHH1 (8 HK) (8 PFK) (20 DPGase) (20 PK) (20 LDH) ADPRT (16 GSHox) PRPPsyn (5 ADA) (8 G6PD) (8 GL6PDH) SAHH2 8 GLC + 6 ADO ¼ 5 HYPXext + 8 CO2 + 20 LACext + 3KRibose + ATP
S. Schuster and D. Kenanov A theoretical study using elementary flux modes
Conclusions
the four modes producing ATP from adenine all remain intact because they do not involve ADA (Table 2). Out of the 12 modes producing ATP from adenosine, modes III.1-III.3, III.6, III.9, and III.12 remain intact. It is interesting that the other ATP-pro- ducing modes (which drop out) involve ADA although it is an adenosine-degrading enzyme.
Interestingly, the modes of adenine salvage (Table 2) are not affected at all by ADA, AK or purine nucleoside phosphorylase (PNPase) deficiencies. That is, these modes do not require these enzymes. How- ever, they do require ADPRT, which is in agreement with the experimental observation mentioned in the Introduction that patients deficient in ADPRT are accumulating adenine [8–11]. The modes of adenosine salvage (Table 3) all require AK, so that they are not operative in the case of AK deficiency. This is clear because phosphorylation of adenosine is important in the buildup of ATP from adenosine. Five out of 12 modes require ADA, AK and PNPase, and another three require AK and PNPase but not ADA. None of the 12 modes requires ADPRT.
We have analysed, by mathematical modelling, the ATP buildup via salvage pathways in erythrocytes. Several authors used kinetic modelling to analyse erythrocyte metabolism [1,2,4]. We have used meta- bolic pathway analysis, which is a structural approach not requiring the knowledge of kinetic parameters. Pathway analysis has been applied to various enzyme deficiencies in the energy metabolism of erythrocytes [6] and to glutathione metabolism in a number of cells including erythrocytes [23]. Our results show once again that pathway analysis allows one to derive inter- esting conclusions about biochemical systems from a fairly limited amount of input information. The disad- vantage is that dynamic effects cannot be analysed. When different disease states are to be studied, the metabolite levels at different time scales need to be considered. In that case, a dynamic model is preferable [2]. Earlier, we had calculated the elementary modes in a subnetwork involving the enzymes of nucleotide metabolism only [24]. One of the elementary modes obtained corresponds to part of an adenine salvage pathway. The system studied here is much more exten- ded in that it involves glycolysis and the pentose phos- phate pathway in addition.
The modes of ATP buildup in the presence of SAHH1 (but not SAHH2) and methyltransferase (Table 4) all require AK but not ADPR transferase. Six out of 12 modes require ADA, AK and PNPase and another three require AK and PNPase but not ADA. The modes in the presence of SAHH2 and MT (Table 4) do not require AK, while they do require in agreement with experimental findings ADPRT, [9,10]. Interestingly, the pathways using SAHH2 but not SAHH1 are completely independent of the three enzymes ADA, AK and PNPase.
We have found four elementary modes producing ATP starting from adenine. They involve parts of glycolysis and the pentose phosphate pathway in dif- ferent proportions. As far as the pentose phosphate pathway is concerned, there is some interrelation to the modes found earlier for that system [14]. In partic- ular, mode 1 (Table 2), which involves the oxidative pentose phosphate pathway and the enzyme R5PI, corresponds to the mode shown in Fig. 2D in Schuster et al. [14]. The modes II 2–4 correspond to the modes depicted in Fig. 2B,C,E, respectively [14]. However, R5PI is more active to provide the ribose necessary for ATP buildup.
Twelve pathways of ATP buildup from adenosine have been found. However, only three of these convert adenosine completely into ATP. The other nine trans- form some of it to hypoxanthine to obtain free energy. Thus, the latter cannot be considered as perfect salvage pathways. They also serve the purpose of purine trans- port by erythrocytes [25].
Out of the 10 modes involving SAHH but not methyl- transferase (Table 5), three modes do not require any of the enzymes ADA, AK and PNPase, the remaining seven require ADA and PNPase. AK is not required in any of the 10 modes. Interestingly, in these modes, it makes no difference whether ADA or PNPase are dele- ted, that is, a single deficiency in either enzyme has the same effect as the double deficiency. By contrast, in the modes of adenine salvage and adenosine salvage, dele- tion of PNPase is, on average, more critical than dele- tion of ADA. From Tables 2–5, it can easily be seen which elementary modes remain in the case of double or multiple deficiencies. For example, elementary mode 1 in Table 2 is still operating if ADA, AK and PNPase are deficient.
Our results predict that there is redundancy both in adenine salvage and in adenosine salvage in that paral- lel pathways producing ATP from each of these sub- strates exist. While the metabolism of many cells is this is surprising because known to be redundant, erythrocyte metabolism in general has little redundancy and robustness. Earlier, we compared the structural
In agreement with biochemical knowledge on human erythrocytes, HGPRT is not involved in any of the computed elementary modes corresponding to salvage pathways. Thus, hypoxanthine is not relevant for ATP salvage in these cells.
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of the salvage pathways are preferably used in vivo and whether they comply with these criteria. This, however, is beyond the scope of the present study, which is aimed at enumerating all potential pathways.
robustness of Escherichia coli and erythrocytes and found that the latter is less robust [19]. In glycolysis, deletion of one enzyme (e.g. hexokinase) may suppress the entire pathway. Therefore, hexokinase or phospho- fructokinase deficiencies have severe consequences [26]. Here, we have shown that the salvage pathways have a relatively high redundancy. This can be seen as a theor- etical explanation of the clinical observation that defici- encies in the nucleotide metabolism of erythrocytes are usually less critical than deficiencies in enzymes of the energy metabolism of these cells and deficiencies in enzymes in the nucleotide metabolism of other cells such as lymphocytes. For example, no disease seems to be caused by PNPase deficiency in erythrocytes. This gives additional support for considering elementary mode analysis as an appropriate tool for metabolic pathways analysis [21].
because
lose,
cells
It follows from our calculations that there is no salvage pathway starting from hypoxanthine. This is in agreement with experimental evidence for human erythrocytes during these development, the enzyme adenylosuccinate synthetase, which converts the first step leading from IMP to AMP [8].
Simmonds and coworkers [8–11] proposed a novel starting from S-adenosyl- route of ATP synthesis methionine or other nucleoside analogues. That route involves SAHH and is independent of AK but depend- ent on ADPRT. We have examined whether this way of ATP buildup is stoichiometrically and thermody- namically feasible. The result is positive. We found that this route is formed by a set of 11 slightly different pathways (Table 4). We found, second and additionally, third parts 12 pathways starting from S-adenosylmethionine involving the standard function- ality of SAHH (here denoted as SAHH1) and another 10 pathways starting from adenosine (rather than S-adenosylmethionine) and involving SAHH1 in the backward direction and SAHH2 in the forward direc- tion. This is a novel result because these pathways do depend on AK (whereas Simmonds and coworkers [8– 11] only spoke about a pathway independent of AK). Interestingly, from Tables 4 and 5, it can be seen that the modes involving SAHH1 and ⁄ or SAHH2 do not depend on ADPR transferase if they involve AK and vice versa.
On the basis of elementary flux modes analysis, it can be said that, even though not easily provable experimentally, the rarely mentioned route via SAHH is rather important. It gives additional opportunities to the cell for generating ATP. Moreover, its analysis can help better understand some diseases affecting nucleo- tide metabolism and, hence, improve the treatment of patients.
S. Schuster and D. Kenanov A theoretical study using elementary flux modes
Experimental procedures
The reaction scheme of human erythrocyte metabolism ana- lysed here is shown in Fig. 1, which is based on schemes analysed earlier [1,3]. Reversible reactions are depicted by bidirectional arrows; all other reactions are assumed to be irreversible. The network essentially involves the enzymes from the glycolytic pathway, pentose phosphate pathway and purine metabolism (Table 1). We take into account that both adenine and adenosine can be taken up by the erythrocyte.
found here,
this
From our theoretical analysis, a hitherto rarely dis- cussed feature of the salvage pathways becomes trans- parent and understandable. This is the high number of ATP molecules degraded in some part of each path- way while the total balance of ATP production is pos- itive. A ‘molar investment ratio’ could be defined to express the number of moles of ATP consumed divi- ded by the difference between moles of ATP produced and moles of ATP consumed. The newly proposed ‘molar investment ratio’ should not be confused with the usual concept of ‘molar yield’; it only refers to one metabolite (ATP) and takes into account the consump- tion and formation of this, while the yield refers to two metabolites. The molar investment ratio quantifies how many ATP are needed to trigger a pathway pro- ducing ATP. In elementary mode 1 of adenine salvage (Table 2), this ratio is 18:(20–18) ¼ 9 : 1. Consider, for comparison, the glycolytic pathway. Two ATP are invested at the upper end of the pathway while four ATP are gained in the process, so that the difference is two. The molar investment ratio is one (2 : 2). In all salvage pathways ratio is much higher. Thus, a considerable effort in terms of enzyme activity is needed to build up ATP by salvage path- ways.
It has sometimes been suggested that,
In addition to items in the previous schemes [1,3], we include enzymes from the class of methyltransferases (EC 2.1.1.x). An example is provided by protein-l-isoaspartate O-methyltransferase (EC 2.1.1.77). This enzyme plays a role in the methylation of haemoglobin [28]. Methyltransferases transfer the methyl group from S-adenosylmethionine to various acceptors:
if parallel pathways exist, living cells use the pathway with the highest yield [27] or obeying a minimum flux criterion [5]. It will be interesting to analyse, in the future, which
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scrumpy
(Poolman,
http://161.73.117.95/
S-adenosylmethionine þ acceptor ! S-adenosylhomocysteine
and [31] ScrumPy/).
þ methylated acceptor
Besides, we include the enzyme SAHH because it is present in erythrocytes [29]. SAHH usually catalyses the reaction:
S. Schuster and D. Kenanov A theoretical study using elementary flux modes
Acknowledgements
S-adenosylhomocysteine ! adenosine þ homocysteine
(SPP 1063)
The authors wish to thank Dr Kutlu U¨ lgen (Istanbul) for very helpful discussions on the manuscript and the Deutsche Forschungsgemeinschaft for financial support.
References
This function is here referred to as SAHH1 and is, in accordance with the database ExPASy-ENZYME (http:// it us.expasy.org/enzyme/) assumed to be reversible. Also, was found that in the SAHH reaction, the unstable inter- mediate 3-ketoadenosine occurs, which can spontaneously disintegrate into adenine and 3¢-ketoribose [11,13]. This alternative reaction:
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S-adenosylhomocysteine ! adenine þ 30-ketoribose
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Supplementary material
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The following supplementary material is available for this article online: Appendix S1. Tables S1–S4.
Schuster S (2003) A method for classifying metabolites
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