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

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 kinas

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: schuster@minet.uni-jena.de

(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 salsal-vage are obtained They give different ATP⁄ glucose yields, the highest being 3 : 10 for adenine sal-vage and 2 : 3 for adenosine salsal-vage 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.

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

(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

e

C

L

G x t GLC K

P

A D P

P 6

G PGI F P 6

P 6 L G

P D

F A 3 P

P A D

D L

G P D 3 , 1 I

P N D A H

G P 3

P

D G M 2,3DPG

P

D G e s K

P m

i

C

L

G

P

A D P P

6

G DH

e L G P

O 6 P

O 2

U 5 P

P D

N 2 G S H

G S G H

P D N

S

G H x

G S R

P 5 R

P 5 X

P 7 S

A 3 P

P 6 F

P 4 E

K

T I TA I

P 5 R

E 5 X

K

T II

A 3 P

G P 2 M G P P

D A P

P P N E

K P P D

P A

R

P P Rrans P R e x t

C

L L Ctra sn L C e t x

H L H A

D N

N E

D I E N

P R P

T R P D

P M A

P M I

O A

O I P

M

A DA N C

A A C N

X P Y P R P T R P G

P 1 R

X P

Y e t x

P 5

R PRM y

s P R

P n

P A

P M A

P A

K

P

P M A

p

A K

e P N P P

A

P D a

N + N a+

k

a

l

a

N

K +

K+

k

a

l

K

K

a

N A P a se

e n a b m e m

M A S

t x e M A S

2 H A S o A

-S H y c

T M

Y H

1 H A S

o i R o t e K '

c

A c

Y H

F

P K

H P 6 L G

X t ns r a

c A t e M

+

+

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 abbreviareac-tions of enzymes and metabolites, see Table 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 phosphofructohexo-kinase 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

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 (Suppleele-mentary 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 2 CO 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 4 CO 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

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 (Supplementelement-ary 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 9 CO 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 9 CO 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

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 +4 Acc ¼ 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 H2O + 5 Acc ¼ 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 H2O + 4 Acc ¼ 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 +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 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 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 CO 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 H2O + 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 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 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 H2O + 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 H2O + 6 Acc ¼ 5 HYPXext + 8 CO 2 +6 HCY + ATP + 4 LACext

+ 6 AccMet + 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

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) ( )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 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 H2O + 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 + 6 GLC ¼ 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 + 4 GLC ¼ 4 CO 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 H2O + 2 Acc + 7 GLC ¼ 2 CO 2 + 2 HCY + 2 ATP + 10 LACext + 2 AccMet

+ 2 3KRibose

+ + + –

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 2 CO 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) ( )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 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

– + – –

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,

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