Volume 10 Supplement 1

## Selected papers from the Seventh Asia-Pacific Bioinformatics Conference (APBC 2009)

# Analysis on relationship between extreme pathways and correlated reaction sets

- Yanping Xi
^{1}, - Yi-Ping Phoebe Chen
^{2}, - Ming Cao
^{1}, - Weirong Wang
^{3}and - Fei Wang
^{1}Email author

**10(Suppl 1)**:S58

https://doi.org/10.1186/1471-2105-10-S1-S58

© Xi et al; licensee BioMed Central Ltd. 2009

**Published: **30 January 2009

## Abstract

### Background

Constraint-based modeling of reconstructed genome-scale metabolic networks has been successfully applied on several microorganisms. In constraint-based modeling, in order to characterize all allowable phenotypes, network-based pathways, such as extreme pathways and elementary flux modes, are defined. However, as the scale of metabolic network rises, the number of extreme pathways and elementary flux modes increases exponentially. Uniform random sampling solves this problem to some extent to study the contents of the available phenotypes. After uniform random sampling, correlated reaction sets can be identified by the dependencies between reactions derived from sample phenotypes. In this paper, we study the relationship between extreme pathways and correlated reaction sets.

### Results

Correlated reaction sets are identified for *E. coli* core, red blood cell and *Saccharomyces cerevisiae* metabolic networks respectively. All extreme pathways are enumerated for the former two metabolic networks. As for *Saccharomyces cerevisiae* metabolic network, because of the large scale, we get a set of extreme pathways by sampling the whole extreme pathway space. In most cases, an extreme pathway covers a correlated reaction set in an 'all or none' manner, which means either all reactions in a correlated reaction set or none is used by some extreme pathway. In rare cases, besides the 'all or none' manner, a correlated reaction set may be fully covered by combination of a few extreme pathways with related function, which may bring redundancy and flexibility to improve the survivability of a cell. In a word, extreme pathways show strong complementary relationship on usage of reactions in the same correlated reaction set.

### Conclusion

Both extreme pathways and correlated reaction sets are derived from the topology information of metabolic networks. The strong relationship between correlated reaction sets and extreme pathways suggests a possible mechanism: as a controllable unit, an extreme pathway is regulated by its corresponding correlated reaction sets, and a correlated reaction set is further regulated by the organism's regulatory network.

## Keywords

## Background

In the past decades, genome-scale metabolic networks capable of simulating growth have been reconstructed for about twenty organisms [1]. A framework for co *nstraint*-b *ased* r *econstruction and* a *nalysis* (COBRA) has been developed to model and simulate the steady states of metabolic networks [2–4]. As reviewed in the literature [5], COBRA has been successfully applied to studying the possible phenotypes. Thus, it has attracted many attentions and gets rapid progress.

**S**. With the homeostatic-steady-state hypothesis and fluxes boundaries, all allowable steady-state flux distributions are limited in a space which can be represented as

where **S**_{m × n}is the stoichiometric matrix for a network consisting of *m* metabolites and *n* fluxes and **v**_{n × 1}is a vector of the flux levels through each reaction in the system [6].

*treme*pa

*thways*(ExPa), (

**p**

^{ i },

*i*= 1, ...,

*k*) [8, 9]. Every possible steady-state flux distribution in the solution space may therefore be represented as a non-negative combination of ex

*treme*pa

*thways*(ExPa):

*treme*pa

*thways*(ExPa) have the following properties which make them biologically meaningful [10, 11]:

- 1.
The ExPa set of a given network is unique.

- 2.
Each ExPa uses least reactions to be a functional unit.

- 3.
The ExPa set is systemically independent which means an ExPa can't be decomposed into a non-negative combination of the remaining ExPas.

A similar network-based pathway definition as ExPa is e *lementary flux* m *odes* (EM) [12–14]. The algorithm for e *lementary flux* m *odes* (EM) treats internal reversible reactions differently from that for ExPas. Actually, ExPa set is a systemically independent subset of e *lementary flux* m *odes* (EM) and each EM can be represented by a non-negative combination of ExPas. The relationship and difference between ExPa and EM have been studied and articulated in literatures [10, 15].

ExPas and EMs lead to a systems view of network properties [16] and they also provide a promising way to understand network functionality, robustness as well as regulation [17, 18]. However, the number of ExPas for a reaction network grows exponentially with network size which makes the use of ExPas for large-scale networks computationally difficult [19, 20].

A rapid and scalable method to quantitatively characterize all allowable phenotypes of genome-scale networks is uniform random sampling [21]. It studies the contents of the available phenotypes by sampling the points in the solution space. The set of flux distributions obtained from sampling can be analyzed to measure the pairwise correlation coefficients between all reaction fluxes and can be further used to define co *rrelated reaction* set *s* (CoSet). Co *rrelated reaction* set *s* (CoSet) are unbiased, condition-dependent definitions of modules in metabolic networks in which all the reactions have to be co-utilized in precise stoichiometric ratios [22]. It means the fluxes of the reactions in the same co *rrelated reaction* set *s* (CoSet) go up or down together in fixed ratios. We may think about whether CoSets provide clues about regulated procedures of a metabolic network.

Both ExPas and CoSets are determined by the topology of a metabolic network. Although lots of analyses were done on them separately [23–25], few attention has been paid to the relationship between them. Here, our aim is to reveal the relationship between ExPas and CoSets. We select *Escherichia coli* core metabolic network, human red blood cell metabolic network and *Saccharomyces cerevisiae* metabolic network as examples to start our research.

## Results and discussion

### Escherichia coli core metabolic network

We use the *E. coli* core model published on the web site of UCSD's systems biology research group. It is "a condensed version of the genome-scale E. coli reconstruction and contains central metabolism reactions" [26]. Details of this model can also be found in a published book [27]. The network contains 62 internal reactions, 14 exchange reactions and a biomass objective function.

CoSets of E. coli core model.

CoSet ID | CoSet Size | Reactions |
---|---|---|

1 | 4 | ACKr, ACt2r, EX_ac(e), PTAr |

2 | 3 | G6PDH2r, GND, PGL |

3 | 3 | EX_for(e), FORt, PFL |

4 | 3 | D_LACt2, EX_lac_D(e), LDH_D |

5 | 3 | CYTBD, EX_o2(e), O2t |

6 | 3 | ADHEr, ETOHt2r, EX_etoh(e) |

7 | 2 | TALA, TKT1 |

8 | 2 | ICL, MALS |

9 | 2 | GAPD, PGK |

10 | 2 | FUM, SUCD4 |

11 | 2 | FBA, TPI |

12 | 2 | EX_pyr(e), PYRt2r |

13 | 2 | EX_h2o(e), H2Ot |

14 | 2 | EX_glc(e), GLCpts |

15 | 2 | ENO, PGM |

16 | 2 | CO2t, EX_co2(e) |

17 | 2 | AKGt2r, EX_akg(e) |

18 | 2 | AKGDH, SUCOAS |

19 | 2 | ADK1, PPS |

20 | 2 | ACONT, CS |

**C**

_{ j }, we check how many type I and II ExPas use

*k*reactions in

**C**

_{ j }, where

*k*ranges from zero to the size of

**C**

_{ j }. The result is shown in table 2. Taking CoSet 3 as an example, from table 1 and 2, we can find that 3 reactions ('EX_for(e), FORt, PFL') belong to CoSet 3. Among all the type I and II ExPas, 5026 of them use all of these 3 reactions and 2722 use none of them. No ExPa uses one or two reactions. It is clear that each ExPa of

*E. coli*core model covers in each CoSet in an 'all or none' manner. We also calculate, for each ExPa

**p**

^{ i }, the ratio of reactions in any CoSet which is fully covered by

**p**

^{ i }to all reactions in

**p**

^{ i }. The distribution of the ratios is shown in Figure 1. Each ExPa of

*E. coli*core model covers at least one CoSet. The coverage rates are higher than 40% which implies that ExPas are under well control of CoSets.

Relationship between ExPas and CoSets for E. coli core metabolic network.

CoSet ID | CoSet Size | Number of ExPas using k reactions of a CoSet | ||||
---|---|---|---|---|---|---|

0 | 1 | 2 | 3 | 4 | ||

1 | 4 | 6652 | 0 | 0 | 0 | 1096 |

2 | 3 | 3556 | 0 | 0 | 4192 | - |

3 | 3 | 2722 | 0 | 0 | 5026 | - |

4 | 3 | 7151 | 0 | 0 | 597 | - |

5 | 3 | 1306 | 0 | 0 | 6442 | - |

6 | 3 | 3984 | 0 | 0 | 3764 | - |

7 | 2 | 3556 | 0 | 4192 | - | - |

8 | 2 | 5223 | 0 | 2525 | - | - |

9 | 2 | 928 | 0 | 6820 | - | - |

10 | 2 | 2240 | 0 | 5508 | - | - |

11 | 2 | 1352 | 0 | 6396 | - | - |

12 | 2 | 7106 | 0 | 642 | - | - |

13 | 2 | 1983 | 0 | 5765 | - | - |

14 | 2 | 904 | 0 | 6844 | - | - |

15 | 2 | 928 | 0 | 6820 | - | - |

16 | 2 | 1697 | 0 | 6051 | - | - |

17 | 2 | 6499 | 0 | 1249 | - | - |

18 | 2 | 5671 | 0 | 2077 | - | - |

19 | 2 | 5181 | 0 | 2567 | - | - |

20 | 2 | 2193 | 0 | 5555 | - | - |

### Human red blood cell metabolic network

*ed*b

*lood*c

*ell*(RBC) metabolic network has been well reconstructed and simulated [28–31]. The RBC model consists 39 metabolites, 32 internal metabolic reactions (See additional file 2) as well as 19 exchange fluxes (Figure 2) [25].

CoSets of RBC metabolic network.

CoSet ID | CoSets Size | Reactions |
---|---|---|

1 | 7 | PDGH, Ex_CO2, Ex_NADPH, PGI, PGL, G6PDH, Ex_NADP |

2 | 4 | Xu5PE, TKI, TKII, TA |

3 | 4 | PFK, ALD, TPI, R5PI |

4 | 3 | PGM, EN, PK |

5 | 2 | Ex_NAD, Ex_NADH |

6 | 2 | PNPase, PRM |

7 | 2 | AdPRT, Ex_ADE |

8 | 2 | LDH, Ex_LAC |

Relationship between ExPas and CoSets for RBC metabolic network.

CoSet ID | CoSets Size | Number of ExPas using k reactions of a CoSet | |||||||
---|---|---|---|---|---|---|---|---|---|

0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||

1 | 7 | 18 | 6 | 0 | 0 | 0 | 0 | 9 | 6 |

2 | 4 | 21 | 0 | 0 | 0 | 18 | - | - | - |

3 | 4 | 18 | 6 | 0 | 6 | 9 | - | - | - |

4 | 3 | 27 | 0 | 0 | 12 | - | - | - | - |

5 | 2 | 19 | 0 | 20 | - | - | - | - | - |

6 | 2 | 24 | 0 | 15 | - | - | - | - | - |

7 | 2 | 30 | 0 | 9 | - | - | - | - | - |

8 | 2 | 37 | 0 | 2 | - | - | - | - | - |

The reasons for the complementary relationship on usage of reactions in CoSet 1 and CoSet 3 are as follows. 'PGI' belongs to one of 'historical' metabolic pathways named *Embden-Meyerhof-Parnas pathway* (EMP), while all other internal reactions in CoSet 1 are in pathway *Pentose Phosphate Pathway* (PPP). As for CoSet 3, 'R5PI' belongs to pathway PPP and all other reactions are in EMP. Since EMP provides the metabolite 'G6P' to PPP and inversely, PPP offers the metabolite 'GA3P' to EMP, the two pathways should cooperate with each other to fulfill the functions of the metabolic network. In order to work normally, the metabolic network may either utilize an ExPa using all the reactions in CoSet 1 (CoSet 3) or combine two (or more) ExPas together to fully cover CoSet1 (CoSet 3). By splitting some CoSet on different ExPas, it may bring redundancy and flexibility which are important properties for a cell to survive in various environments.

Both 'Ex_NADP' and 'Ex_NADPH' belong to CoSet 1, indicating the need of RBC cell to balance the NADPH/NADP ratio. According to "historically" partition of metabolic pathways, when pathway PPP is up-regulated, the quantity of NADP increases. When metabolic pathway EMP is up-regulated, the quantity of NADPH comes up. From the point of view of ExPa, 'Ex_NADP', 'Ex_NADPH' are used together in opposite direction by ExPas. It means that the fluxes through these reactions increase or decrease together. As a result, the quantity of NADP increases when that of NADPH decreases and vice versa. Situation is similar for reactions 'Ex_NAD' and 'Ex_NADH' in CoSet 5.

*E. coli*core metabolic network, nearly 1/3 ExPas of RBC model has a CoSets coverage rate higher than 20%. There are 7 ExPas whose CoSets coverage rate is 0. All these 7 ExPas utilize relatively few reactions (1–3 internal reactions as well as the corresponding exchange reactions), among which, ExPas 10 and 11 utilize the regulated reaction 'IMPase', ExPas 12 and 13 are type II ExPas which serve to dissipate excess ATP, and ExPas 14, 15, 16 which participate in nucleotide metabolism may be regulated by the quantity of inosine and adenosine. In short, ExPas are in control of the regulatory structure of the metabolic network and our study suggests that the regulatory command usually spread from the regulated reactions to CoSets and finally to the related ExPas.

### Saccharomyces cerevisiae metabolic network

*S. cerevisiae*, iND750, has been reconstructed and validated in 2004 [33]. We use this model to represent the metabolism of

*S. cerevisiae*. Model iND750 accounts for 646 metabolites, 1149 internal reactions as well as 116 exchange fluxes excluding the objective reaction. Since the scale of iND750 is too large, enumerating all the ExPas of the model is computational intractable. Thus we samples a subset of ExPas to represent the whole ExPas (See Methods Section). The sampling procedure has executed 1000 times with 250–300 internal reactions being randomly removed out every time and finally resulted a sample set of 56496 unique ExPas. The lengths of sample ExPas range from 20 to 80 (Figure 4). It is difficult to sample the ExPas containing more than 80 reactions within acceptable cost of time.

One hundred and thirty five CoSets have been identified for this model. Some CoSets, especially the CoSets containing more than 5 reactions, have no sample ExPa passing through as if they are forgotten by the metabolic network. We name them *CoSets of solitary island*. We have tried different methods, such as removing all reactions which cannot be reached from a certain *CoSet of solitary island*, to sample some ExPas passing through the 'solitary island' but in vain because the sampling procedures take too much time. It seems that, the reactions in a *CoSet of solitary island* together with the reactions related to them form a complex network, and ExPas usually have to take a long way to go from some exchange reactions to a *CoSet of solitary island* and finally reach other exchange reactions. Because of the network's complexity, there are many bypaths along the road which causes a combinatorial explosion. So a *CoSet of solitary island* is not really solitary, and it is not too few but too many ExPas passing through these CoSets that prevent the ExPas computation algorithm, one step of which is enumerating all possible combinatorial paths, from catching them.

*CoSets of solitary island*, almost all the CoSets are covered by ExPas in an 'all or none' manner except CoSet 30 which is covered by ExPas in a complemental mode. CoSet 30 has three reaction members, 'AKGMAL', 'AKGt2r' and 'MALt2r'. Reaction 'AKGMAL' transports alpha ketoglutarate (AKG) and malate (MAL) across the epicyte in opposite directions. Reaction 'AKGt2r' transports AKG and hydrogen ion (H) across the epicyte in the same directions. And 'MALt2r' transports MAL and H across the epicyte in the same directions as well. If the quantity of AKG rises, the fluxes through 'AKGMAL' will grow up taking AKG and H out of the cell and bringing MAL into the cell. As a result, the quantity of H rises causing an increase on the flux of 'MALt2r'. Vice versa. These three reactions work together to balance the AKG/MAL ratio inside the cell and thus form a CoSet. Among the sample ExPas, we find that some of them utilize 'AKGMAL' and 'AKGt2r' while others use 'MALt2r' only. But, there are also some ExPas utilizing 'AKGt2r' while we don't find any sample ExPas that use the other two reactions in the CoSet. However, according to the above analysis, there should be some complemental ExPas utilizing reactions in the CoSet other than 'AKGt2r'. Otherwise, the cell will die due to the insupportable internal environment. Since the whole ExPa set is extremely large, the available ExPa sample set can only give a glance at the tremendous ExPa set and will certainly lose some information.

CoSets of S. cerevisiae metabolic network.

CoSet ID | CoSet Size | Reactions |
---|---|---|

11 | 5 | HETZK, HMPK1, PMPK, TMN, TMPPP |

13 | 5 | ACGKm, ACOTAim, AGPRim, ORNTACim, ORNt3m |

20 | 3 | PGCD, PSERT, PSP_L |

22 | 3 | GCCam, GCCbim, GCCcm |

25 | 3 | CYTK2, DCTPD, NDPK7 |

27 | 3 | CYOOm, CYOR_u6m, O2tm |

29 | 3 | ARGSL, ARGSSr, OCBTi |

30 | 3 | AKGMAL, AKGt2r, MALt2r |

31 | 3 | AKGDam, AKGDbm, SUCOASm |

33 | 3 | ACSm, ADK1m, PPAm |

34 | 3 | ACLSm, DHAD1m, KARA1im |

35 | 3 | ABTA, GLUDC, SSALy |

38 | 3 | 34HPPt2m, TYRTAm, TYRt2m |

Relationship between ExPas and CoSets for S. cerevisiae model.

CoSet ID | CoSet Size | Number of ExPas using k reactions of a CoSet | |||||
---|---|---|---|---|---|---|---|

0 | 1 | 2 | 3 | 4 | 5 | ||

11 | 5 | 56445 | 0 | 0 | 0 | 0 | 51 |

13 | 5 | 49250 | 0 | 0 | 0 | 0 | 7246 |

20 | 3 | 39967 | 0 | 0 | 16529 | - | - |

22 | 3 | 54670 | 0 | 0 | 1826 | - | - |

25 | 3 | 56393 | 0 | 0 | 103 | - | - |

27 | 3 | 9983 | 0 | 0 | 46513 | - | - |

29 | 3 | 56454 | 0 | 0 | 42 | - | - |

30 | 3 | 47180 | 8900 | 416 | 0 | - | - |

31 | 3 | 56132 | 0 | 0 | 364 | - | - |

33 | 3 | 53692 | 0 | 0 | 2804 | - | - |

34 | 3 | 47600 | 0 | 0 | 8896 | - | - |

35 | 3 | 41082 | 0 | 0 | 15414 | - | - |

38 | 3 | 39550 | 0 | 0 | 16946 | - | - |

The scale of *S. cerevisia* metabolic network is much larger. However, complementary relationship on usage of reactions in a CoSet is repeated as that in *E. coli* core metabolic network and RBC metabolic network.

## Conclusion

In this study, we investigated the relationship between CoSets and ExPas on the *in-silicon* representations of three metabolic networks. These models are different in species and scale. However, the experiment on each model leads to similar results that ExPas show strong complementary relationship on the usage of reactions in the same CoSet. It implies that this kind of relationship may exist in most of organisms. Since both CoSets and ExPas are generated from the topology information of metabolic networks, this phenomenon may reflect some inherent properties resulting from the topology constraints composed on the networks.

Moreover, our study not only reveals the interesting relationship between CoSets and ExPas but also provides a new sight of how the metabolic network works and how it is adjusted. The strong relationship between CoSets and ExPas provides clues about regulated procedure of a metabolic network, thus suggests a possible mechanism of how a metabolic network transferring its phenotype from one steady state to another. As functional units, ExPas are in control of the regulatory structure of the metabolic network, and the regulatory command usually spreads from regulated reactions to CoSets and finally to the related ExPas. As fluxes through each ExPa change according to the regulatory orders from its corresponding CoSets, the flux distribution of the whole metabolic network transfers towards a new steady state. By interrogating the relationship between CoSets and ExPas, we can tell which ExPas are possible to be up (down) regulated caused by an increasing (decreasing) flux in a given CoSet. This result may help predict the function of regulatory factors acting on metabolism. However, in order to answer the question which ExPas are really regulated, more information should be considered, such as regulatory structure of the metabolic networks as well as kinetic and thermodynamic constraints, which will be our future work.

## Methods

### ExPas computation and classification

ExPas are computed by an open source tool, 'expa', developed by Steven L. Bell and Bernhard O. Palsson [34]. The exchange fluxes can be separated into two groups: primary exchange fluxes and currency exchange fluxes. Primary exchange fluxes are external fluxes and currency exchange fluxes are fluxes external to metabolism but internal to the cell [27]. ExPas can be divided into three categories according to their use of exchange fluxes [35]. Type I ExPas utilize primary exchange fluxes as well as currency exchange fluxes. Type II ExPas involve currency exchange fluxes only. Type III ExPas are solely internal cycles without any exchange fluxes. Since type III ExPas are thermodynamically infeasible [36], we neglect type III ExPas and only focus on those of type I and II.

### CoSets computation

The CoSets of each metabolic model is generated by COBRA toolbox, an integrated toolbox of functions which are useful for analysis and simulation of organism's metabolic behavior [22]. For each model, uniform random sampling has been done first in the condition of optimum growth and results in 100,000 unique sample flux distributions that are available to the network. Then, 10,000 samples have been randomly selected and used to measure the pairwise correlation coefficients between reactions. We set the threshold of square pairwise correlation coefficient to 1 - 1*e*^{-8}while identifying CoSets of each metabolic network assuring that reactions in the same CoSets have strong correlation with each other. The procedure of CoSets identification has been carried out 20 times for each model and the results are quite stable.

### Sampling for ExPa subset

We randomly delete a few reactions in *S. cerevisiae*'s iND750 model, and enumerate all the ExPas of the sub network. Then, the dimensions of deleted reactions are inserted back with zeros to these ExPas. As proved in Theorem 1, the ExPa set derived from sampling is a subset of the whole ExPa set of iND750. One thousand ExPa sets of different sub networks of iND750 model have been generated and merged together without redundancy. The union of all these ExPas constitute the sample set of ExPas used in the analysis on *Saccharomyces cerevisiae* metabolic network.

**Theorem 1**. *Suppose G is a metabolic network and* ℙ *is the ExPa set of G, then for any sub network G', its ExPa set* ℙ' *is a subset of* ℙ.

*Proof*. We assume that the available steady state flux distribution (**v**) of *G* lies in the convex cone $\mathcal{C}$:

**Sv** = **0**, *v*_{
i
}≥ 0, *i* = 1, ..., *n*

*G'*is generated from

*G*by deleting reactions

*v*

_{ k },

*v*

_{k+1}, ...,

*v*

_{ n }, then the steady state flux distribution of

*G'*lies in the convex cone ${c}^{\prime}$:

Assuming that $\mathbb{A}$ = {**a**^{
i
}| **a**^{
i
}∈ $\mathcal{C}$ and ${a}_{j}^{i}$ = 0, *j* = *k*, ..., *n*}. Obviously, $\mathbb{A}={c}^{\prime}$.

**a**

^{ i }∈ $\mathbb{A}$, $\exists {\mathbb{P}}^{\u2033}\subseteq \mathbb{P}$, that

Since ${a}_{j}^{i}$ = 0, *j* = *k*, ..., *n*, then ∀**p**^{
i
}∈ ℙ", ${p}_{j}^{i}$ = 0, *j* = *k*, ..., *n*, where **p**^{
i
}is the *i* th ExPa in ℙ and ${p}_{j}^{i}$ is the *j* th component of **p**^{
i
}.

Assuming that ℙ' = {**p**^{
i
}| **p**^{
i
}∈ ℙ and ${p}_{j}^{i}$ = 0, *j* = *k*, ..., *n*}. Thus, ${\mathbb{P}}^{\u2033}\subseteq {\mathbb{P}}^{\prime}$.

Because ${\mathbb{P}}^{\prime}\subseteq \mathbb{A}$ and ℙ' is a systematically independent set, ${\mathbb{P}}^{\prime}\subseteq {\mathbb{P}}^{\u2033}$. Thus ℙ' = ℙ". Since the ExPa set of *G'* is unique, ℙ' is the ExPa set of *G'*, and ${\mathbb{P}}^{\prime}\subseteq \mathbb{P}$. □

## List of abbreviations used

List of abbreviations used in this study.

Concept Abbreviation | |||
---|---|---|---|

COBRA | Constraint-based reconstruction and analysis | EM | Elementary flux mode |

CoSet | Correlated reaction set | RBC | Human Red Blood Cell |

ExPa | Extreme pathway | ||

| |||

AKG | Alpha ketoglutarate | MAL | Malate |

GLC | Glucose | G6P | Glucose-6-phosphate |

F6P | Fructose-6-phosphate | FDP | Fructose-1,6-phosphate |

DHAP | Dihydroxyacetone phosphate | GA3P | Glyceraldehyde-3-phosphate |

13DPG | 1,3-Diphosphoglycerate | 23DPG | 2,3-Diphosphoglycerate |

3PG | 3-Phosphoglycerate | 2PG | 2-Phosphoglycerate |

PEP | Phosphoenolpyruvate | PYR | Pyruvate |

LAC | Lactate | 6PGL | 6-Phosphogluco-lactone |

6PGC | 6-Phosphogluconate | RL5P | Ribulose-5-phosphate |

X5P | Xylulose-5-phosphate | R5P | Ribose-5-phosphate |

S7P | Sedoheptulose-7-phosphate | E4P | Erythrose-4-phosphate |

PRPP | 5-Phosphoribosyl-1-pyrophosphate | IMP | Inosine monophosphate |

R1P | Ribose-1-phosphate | HX | Hypoxanthine |

INO | Inosine | ADE | Adenine |

ADO | Adenosine | AMP | Adenosine monophosphate |

ADP | Adenosine diphosphate | ATP | Adenosine triphosphate |

NAD | Nicotinamide adenine dinucleotide | H | Hydrogen Ion |

NADH | Nicotinamide adenine dinucleotide(R) | NH3 | Ammonia |

NADP | Nicotinamide adenine dinucleotide phosphate | Pi | Inorganic Phosphate |

NADPH | Nicotinamide adenine dinucleotide phosphate(R) | CO2 | Carbon Dioxide |

H2O | Water | ||

| |||

EMP | Embden-Meyerhof-Parnas pathway | PPP | Pentose Phosphate Pathway |

34HPPt2m | 3 4 hydroxyphenyl pyruvate mitochondrial transport via proton symport | ACKr | acetate kinase |

ACOTAim | acteylornithine transaminase irreversible mitochondrial | ACONT | aconitase |

ACt2r | acetate reversible transport via proton symport | ABTA | 4 aminobutyrate transaminase |

AGPRim | N acetyl g glutamyl phosphate reductase irreversible mitochondrial | ACSm | acetyl CoA synthetase |

AKGDbm | oxoglutarate dehydrogenase dihydrolipoamide S succinyltransferase | ADHEr | Acetaldehyde dehydrogenase |

ACGKm | acetylglutamate kinase mitochondrial | ALD | Aldolase |

AKGDam | oxoglutarate dehydrogenase lipoamide | ADK1m | adenylate kinase mitochondrial |

AdPRT | Adenine phosphoribosyl transferase | ADK1 | adenylate kinase |

AKGMAL | alpha ketoglutaratemalate transporter | AKGDH | 2 Oxogluterate dehydrogenase |

AKGt2r | 2 oxoglutarate reversible transport via symport | ARGSL | argininosuccinate lyase |

ARGSSr | argininosuccinate synthase reversible | ACLSm | acetolactate synthase mitochondrial |

CYOR_u6m | ubiquinol 6 cytochrome c reductase | CS | citrate synthase |

CYOOm | cytochrome c oxidase mitochondrial | CO2t | CO2 transporter via diffusion |

CYTBD | cytochrome oxidase bd ubiquinol 8 2 protons | CYTK2 | cytidylate kinase dCMP |

D_LACt2 | D lactate transport via proton symport | DCTPD | dCTP deaminase |

DHAD1m | dihydroxy acid dehydratase 2 3 dihydroxy 3 methylbutanoate mitochondrial | EN | Enolase |

ETOHt2r | ethanol reversible transport via proton symport | ENO | enolase |

EX_ac(e) | Acetate exchange | EX_ADE | ADE exchange |

EX_akg(e) | 2 Oxoglutarate exchange | EX_co2(e) | CO2 exchange |

EX_etoh(e) | Ethanol exchange | EX_for(e) | Formate exchange |

EX_fum(e) | Fumarate exchange | EX_glc(e) | D Glucose exchange |

EX_h2o(e) | H2O exchange | EX_LAC | LAC exchange |

EX_lac_D(e) | D lactate exchange | EX_NAD | NAD exchange |

EX_NADH | NADH exchange | EX_NADP | NADP exchange |

EX_NADPH | NADPH exchange | EX_pyr(e) | Pyruvate exchange |

FBA | fructose bisphosphate aldolase | EX_o2(e) | O2 exchange |

FORt | formate transport via diffusion | G6PDH2r | glucose 6 phosphate dehydrogenase |

GCCam | glycine cleavage complex lipoylprotein mitochondrial | GND | phosphogluconate dehydrogenase |

GCCcm | glycine cleavage complex lipoylprotein mitochondrial | GLCpts | D glucose transport via PEPPyr PTS |

GCCbim | glycine cleavage complex lipoylprotein irreversible mitochondrial | GLUDC | Glutamate Decarboxylase |

GAPD | glyceraldehyde 3 phosphate dehydrogenase | HETZK | hydroxyethylthiazole kinase |

GAPDH | Glyceraldehyde phosphate dehydrogenase | H2Ot | H2O transport via diffusion |

HMPK1 | hydroxymethylpyrimidine kinase ATP | ICL | Isocitrate lyase |

KARA1im | acetohydroxy acid isomeroreductase mitochondrial | LDH | Lactate dehydrogenase |

NDPK7 | nucleoside diphosphate kinase ATPdCDP | MALS | malate synthase |

MALt2r | L malate reversible transport via proton symport | LDH_D | D lactate dehydrogenase |

O2t | o2 transport diffusion | O2tm | O2 transport diffusion |

OCBTi | ornithine carbamoyltransferase irreversible | PFK | Phosphofructokinase |

ORNTACim | ornithine transacetylase irreversible mitochondrial | PGM | Phosphoglyceromutase |

ORNt3m | ornithine mitochondrial transport via proton antiport | PFL | pyruvate formate lyase |

PGCD | phosphoglycerate dehydrogenase | PGI | Phosphoglucoisomerase |

PGK | phosphoglycerate kinase | PGL | 6 phosphogluconolactonase |

PGL | 6-phosphoglyconolactonase | PGM | phosphoglycerate mutase |

PDGH | 6-phosphoglycononate dehydrogenase | PMPK | phosphomethylpyrimidine kinase |

PGPPAm_SC | phosphatidylglycerol phosphate phosphatase A yeast specific mitochondrial | PK | Pyruvate kinase |

PNPase | Purine nucleoside phosphorylase | PPS | phosphoenolpyruvate synthase |

PRM | Phosphoribomutase | PSERT | phosphoserine transaminase |

PSP_L | phosphoserine phosphatase L serine | PTAr | phosphotransacetylase |

PYRt2r | pyruvate reversible transport via proton symport | R5PI | Ribose-5-phosphate isomerase |

SSALy | succinate semialdehyde dehydrogenase NADP | SUCD4 | succinate dehyrdogenase |

SUCOAS | succinyl CoA synthetase ADP forming | TA | Transaldolase |

SUCOASm | Succinate CoA ligase ADP forming | TALA | transaldolase |

TYRt2m | tyrosine mitochondrial transport via proton symport | TKII | Transketolase |

TYRTAm | tyrosine transaminase mitochondrial | TKT1 | transketolase |

TMPPP | thiamine phosphate diphosphorylase | TMN | thiaminase |

TPI | Triose phosphate isomerase | TKI | Transketolase |

Xu5PE | Xylulose-5-phosphate epimerase |

## Declarations

### Acknowledgements

This work is supported by grants 60673016, 60496324 of Chinese National Natural Science Foundation and 863 project (No. 2006AA02Z324).

This article has been published as part of *BMC Bioinformatics* Volume 10 Supplement 1, 2009: Proceedings of The Seventh Asia Pacific Bioinformatics Conference (APBC) 2009. The full contents of the supplement are available online at http://www.biomedcentral.com/1471-2105/10?issue=S1

## Authors’ Affiliations

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