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

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-

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.

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

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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

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

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.

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-

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
+–+ +

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
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

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-

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

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

+ 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
–+– –

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

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

‘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-

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

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