Báo cáo khoa học: 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 ppt

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
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
as pyruvate kinase, it is not straightforward to see
whether a net production of ATP can be realized.
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,
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:
(Received 6 June 2005, revised 5 August
2005, accepted 19 August 2005)
doi:10.1111/j.1742-4658.2005.04924.x
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.
Abbreviations
ADPRT, adenine phosphoribosyltransferase; IMP, inosine 5¢-monophosphate; SAHH, S-adenosylhomocysteine hydrolase;
SAM, S-adenosylmethionine.
5278 FEBS Journal 272 (2005) 5278–5290 ª 2005 FEBS
we mean the production of ATP from salvaged sub-
strates rather than de novo synthesis.)
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
3¢-ketoadenosine occurs, leading to free adenine and
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.
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
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].
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 immunodeficiency, 2,8-dihydroxyadenine
urolithiasis, and Lesch–Nyhan syndrome, caused by
deficiencies in the adenosine deaminase (ADA), ADP-
RT, and hypoxanthine guanine phosphoribosyltrans-
ferase (HGPRT), respectively [22]. However, 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 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
adenine and adenosine salvage, we do not include
methyltransferase and SAHH.
Adenine salvage
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
S. Schuster and D. Kenanov A theoretical study using elementary flux modes
FEBS Journal 272 (2005) 5278–5290 ª 2005 FEBS 5279
(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.
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
glucose-6-phosphate formation) and that fructose-
diphosphate aldolase and triosephosphate isomerase
(TPI) are not involved. Mode II.3 involves ALD and
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.
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
conversion requires two ATP in PRPP synthase.
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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.
A theoretical study using elementary flux modes S. Schuster and D. Kenanov
5280 FEBS Journal 272 (2005) 5278–5290 ª 2005 FEBS
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
Table 1. List of all enzymes and metabolites included in the model.
Abbreviation Full name EC number
Enzyme
ADA Adenosine deaminase 3.5.4.4

ADPRT Adenine phosphoribosyltransferase 2.4.2.7
AK Adenosine kinase 2.7.1.20
ALD1 Fructose-diphosphate aldolase 4.1.2.13
AMPDA Adenosine monophosphate
deaminase
3.5.4.6
APK Adenylate kinase 2.7.4.3
C5MT Cytosine-5-methyltransferase 2.1.1.37
DPGase Diphosphoglycerate phosphatase 3.1.3.13
DPGM 2,3-Diphosphoglycerate mutase 5.4.2.4
EN Enolase 4.2.1.11
G6PDH Glucose-6P dehydrogenase 1.1.1.49
GAPDH Glyceraldehyde-3P dehydrogenase 1.2.1.12
GL6PDH 6P-Gluconate dehydrogenase 1.1.1.49
GSHox Glutathioneperoxidase 1.11.1.9
GSSGR Glutathione reductase 1.8.1.7
HGPRT Hypoxanthine guanine
phosphoribosyltransferase
2.4.2.8
HK Hexokinase 2.7.1.1
LDH Lactate dehydrogenase 1.1.1.27
NUC AMP phosphatase 3.1.3.5
PFK1 Phosphofructokinase 2.7.1.11
PGI Glucose-6P-isomerase 5.3.1.9
PGK1 Phosphoglycerate kinase 1 2.7.2.3
PGLase 6P-Gluconolactonase 3.1.1.31
PGM Phosphoglycerate mutase 1 5.4.2.1
PK Pyruvate kinase 2.7.1.40
PNPase Purine nucleoside phosphorylase 2.4.2.1
PRM Phosphoribomutase 5.4.2.7

PRPP
synthase
Phosphoribosylpyrophosphate
synthetase
2.7.6.1
R5PI
D-Ribose-5P-isomerase 5.3.1.6
SAHH S-Adenosylhomocysteine hydrolase 3.3.1.1
TA Transaldolase 2.2.1.2
TK Transketolase 2.2.1.1
TPI Triosephosphate isomerase 1 5.3.1.1
XU5PE
D-Xylulose-5P-3-epimerase 5.1.3.1
Metabolites
1,3 DPG 1,3-Diphospho-
D-glycerate
2,3 DPG 2,3-Diphospho-
D-glycerate
2PG 2-Phospho-
D-glycerate
3¢-keto ribose 3¢-Keto ribose
3PG 3-Phospho-
D-glycerate
Acc Acceptor for methyl group
Adenine Adenine
Ado Adenosine
ADP Adenosine 5¢-diphosphate
AMP Adenosine 5¢-monophosphate
ATP Adenosine 5¢-triphosphate
CO2 Carbon dioxide

DHAP Dihydroxyacetone phosphate
E4P
D-Erythrose 4-phosphate
F6P Fructose 6-phosphate
FDP Fructose 1,6-diphosphate
G6P Glucose 6-phosphate
Table 1. Continued.
Abbreviation Full name EC number
GA3P Glyceraldehyde 3-phosphate
GL6P
D-Glucono-1,5-lactone 6-phosphate
GLC Glucose
GO6P 6-Phospho-
D-gluconate
GSH Reduced glutathione
GSSG Oxidized glutathione
HCY
L-Homocysteine
HYPX Hypoxanthine
IMP Inosine 5¢-monophosphate
INO Inosine
K
+
Potassium
LAC
L-Lactate
MetAcc Methylated acceptor
Na
+
Sodium

NAD Nicotinamide adenine dinucleotide
NADH Nicotinamide adenine dinucleotide
reduced
NADP Nicotinamide adenine dinucleotide
phosphate
NADPH Nicotinamide adenine dinucleotide
phosphate reduced
PEP Phosphoenolpyruvate
PRPP 5-Phospho-alpha-
D-ribose
1-diphosphate
PYR Pyruvate
R5P
D-Ribulose 5-phosphate
RIP
D-Ribose 1-phosphate
RU5P
D-Ribulose 5-phosphate
S-AdoHcy S-Adenosyl-
L-homocysteine
S7P
D-Sedoheptulose 7-phosphate
SAM S-Adenosyl-
L-methionine
X5P
D-Xylulose 5-phosphate
S. Schuster and D. Kenanov A theoretical study using elementary flux modes
FEBS Journal 272 (2005) 5278–5290 ª 2005 FEBS 5281
can be no flux distribution of adenine salvage enabling
an ATP ⁄ glucose yield higher than 0.3.

Interestingly, none of the ATP producing modes
involves the 2,3-diphosphoglycerate phosphatase
(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.
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.
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

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 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
excreted) and ribose-1-phosphate, which is trans-
formed, by the pentose phosphate pathway, into glyco-
lytic intermediates. Modes 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
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
Table 2. Elementary modes producing ATP from adenine.
Elementary modes –ADA –AK –PNPase –ADPRT
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 2CO
2
+ 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 CO
2
+ 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 4CO
2
+ 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
+++ –

A theoretical study using elementary flux modes S. Schuster and D. Kenanov
5282 FEBS Journal 272 (2005) 5278–5290 ª 2005 FEBS
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 of S-adenosylmethionine consumption) 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.
Table 3. Elementary modes producing ATP from adenosine.
Elementary modes –ADA –AK –PNPase –ADPRT
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 9CO
2
+ 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 9CO
2
+ 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 CO
2
+ 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 CO
2
+ 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 CO
2
+ 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 CO
2
+ 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 CO
2
+ 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 CO

2
+ 15 LACext + 5 ATP
+–– +
S. Schuster and D. Kenanov A theoretical study using elementary flux modes
FEBS Journal 272 (2005) 5278–5290 ª 2005 FEBS 5283
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 H
2
O+4Acc¼ 3 HYPXext + 6 CO
2
+ 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 H
2
O+5Acc¼ 3 HYPXext + 6 CO
2
+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 H

2
O+4Acc¼ 3 HYPXext + 6 CO
2
+ 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 H
2
O+4Acc¼ 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 H
2
O +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 H
2
O + 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 + H

2
O + Acc +3 GLC ¼ 9CO
2
+ 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 H
2
O + 4 Acc + 6 GLC ¼ 3 HYPXext + 6 CO
2
+ 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 H
2
O + 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 H
2

O + 3 Acc + 2 GLC ¼ HYPXext + 2 CO
2
+ 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 H
2
O + 8 Acc + 6 GLC ¼ 3 HYPXext + 6 CO
2
+ 8 HCY + 5 ATP
+ 15 LACext + 8 AccMet
+–– +
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) (8 Xu5PE) (4 TKI) (4 TKII) (4 TA) (5 PNPase) (5 PRM)
(5 HXtrans) SAHH2 (5 SAHH1)
6 SAM + 6 H
2
O+6Acc¼ 5 HYPXext + 8 CO
2
+6 HCY + ATP + 4 LACext
+ 6 AccMet + 3KRibose
–+– –
A theoretical study using elementary flux modes S. Schuster and D. Kenanov
5284 FEBS Journal 272 (2005) 5278–5290 ª 2005 FEBS
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
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 H
2
O + 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) ()4ApK)()2 R5PI) (2 Xu5PE)
TKI TKII TA (5 PNPase) (5 PRM) (5 HXtrans) (2 SAHH2) (5 SAHH1)
7 SAM + 7 H
2
O+7Acc¼ 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 H
2
O + 6 Acc + 8 GLC ¼ 5 HYPXext + 8 CO
2
+ 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 H
2
O + 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 H
2

O + 8 Acc + 4 GLC ¼ 5 HYPXext + 4 CO
2
+ 8 HCY + 3 ATP
+ 10 LACext + 8 AccMet + 3 3KRibose
–+– –
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 + H
2
O+Acc+6GLC¼ 16 CO
2
+ 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 H
2
O + 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 + H
2
O+Acc+4GLC¼ 4CO
2
+ 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 H
2
O + 2 Acc + 7 GLC ¼ 2CO
2
+ 2 HCY + 2 ATP + 10 LACext + 2 AccMet
+ 2 3KRibose
+++ –
S. Schuster and D. Kenanov A theoretical study using elementary flux modes
FEBS Journal 272 (2005) 5278–5290 ª 2005 FEBS 5285
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
worth noting that there are 14 more modes not
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 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
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 2CO
2
+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 CO
2
+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 CO
2

+ 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 CO
2
+ 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) ()4ApK)()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 CO
2
+ 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 CO
2
+ 20 LACext + 3KRibose + ATP
–+– –
A theoretical study using elementary flux modes S. Schuster and D. Kenanov
5286 FEBS Journal 272 (2005) 5278–5290 ª 2005 FEBS
all the four modes producing ATP from adenine
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.
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
ADPRT, in agreement with experimental findings
[9,10]. Interestingly, the pathways using SAHH2 but
not SAHH1 are completely independent of the three
enzymes ADA, AK and PNPase.
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.
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.
Conclusions
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.
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].
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
known to be redundant, this is surprising because
erythrocyte metabolism in general has little redundancy
and robustness. Earlier, we compared the structural
S. Schuster and D. Kenanov A theoretical study using elementary flux modes
FEBS Journal 272 (2005) 5278–5290 ª 2005 FEBS 5287
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].
It follows from our calculations that there is no
salvage pathway starting from hypoxanthine. This is in
agreement with experimental evidence for human
erythrocytes because these cells lose, during
development, the enzyme adenylosuccinate synthetase,
which converts the first step leading from IMP to AMP
[8].
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 found here, this 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, 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
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.
Simmonds and coworkers [8–11] proposed a novel
route of ATP synthesis starting from S-adenosyl-
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.
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.
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:
A theoretical study using elementary flux modes S. Schuster and D. Kenanov
5288 FEBS Journal 272 (2005) 5278–5290 ª 2005 FEBS
S-adenosylmethionine þ acceptor ! S-adenosylhomocysteine
þ methylated acceptor
Besides, we include the enzyme SAHH because it is present
in erythrocytes [29]. SAHH usually catalyses the reaction:
S-adenosylhomocysteine ! adenosine þ homocysteine
This function is here referred to as SAHH1 and is, in
accordance with the database ExPASy-ENZYME (
http://
us.expasy.org/enzyme/) assumed to be reversible. Also, it
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:
S-adenosylhomocysteine ! adenine þ 3
0
-ketoribose
þ homocysteine

is here referred to as SAHH2 and is assumed to be irre-
versible because the disintegration occurs spontaneously.
The complete list of enzymes is given in Table 1. Of course,
the considered scheme does not cover the complete erythro-
cyte metabolism. The choice of reactions was motivated
mainly by earlier models, textbook knowledge about sal-
vage pathways and energy metabolism, as well as our aim
to analyse the pathways using S-adenosylmethionine.
Regarding sensitivity of the model results to addition of
enzymes, it is important that elementary modes have the
favourable property that the set of elementary modes in
the extended system contains the elementary modes of the
original system as a subset [24]. A drawback of the method
might be that this structural analysis does not take into
account genetic regulation. However, in mature erythro-
cytes, gene expression does not play any role as erythro-
cytes do not have a nucleus. Thus, all enzymes considered
in our model are indeed expressed and cannot be downreg-
ulated by genetic means, so that this drawback does not
apply to such cells.
In metabolic pathway analysis, usually a distinction is
made between internal and external metabolites. Internal
metabolites are intermediates that have to fulfil a balance
equation at steady state, that is, their production must
equal their consumption. External metabolites are the
sources and sinks of the network and are assumed to
have buffered concentrations ([30], which also gives a
detailed explanation of terms in metabolic pathway analy-
sis). In all simulations throughout the paper, we consider
glucose, lactate, CO

2
and ATP, as well as hypoxanthine,
sodium and potassium outside the cell to be external sub-
stances.
Elementary flux modes are computed by the program
metatool, which was developed by Pfeiffer et al. [15]
and is continuously refined in our group (http://pinguin.
biologie.uni-jena.de/bioinformatik). Alternative programs
for the same task are available, for example, fluxanalyzer
[31] and scrumpy (Poolman, http://161.73.117.95/
ScrumPy/).
Acknowledgements
The authors wish to thank Dr Kutlu U
¨
lgen (Istanbul)
for very helpful discussions on the manuscript and the
Deutsche Forschungsgemeinschaft (SPP 1063) for
financial support.
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Supplementary material
The following supplementary material is available for

this article online:
Appendix S1. Tables S1–S4.
A theoretical study using elementary flux modes S. Schuster and D. Kenanov
5290 FEBS Journal 272 (2005) 5278–5290 ª 2005 FEBS