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www.scichina.com | csb.scichina.com | www.springerlink.com Chinese Science Bulletin | March 2009 | vol. 54 | no. 5 | 776-782

Relationship between topology and functions in metabolic network evolution

WANG Zhuo1,3†, CHEN Qi1 & LIU Lei2,3†

1 College of Life Science & Biotechnology, Shanghai Jiao Tong University, Shanghai 200240, China; 2 Bioinformatics Center, Key Lab of Systems Biology, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences, Shanghai 200031, China;

3 Shanghai Center for Bioinformation Technology, Shanghai 200235, China

What is the relationship between the topological connections among enzymes and their functions during metabolic network evolution? Does this relationship show similarity among closely related or-ganisms? Here we investigated the relationship between enzyme connectivity and functions in meta-bolic networks of chloroplast and its endosymbiotic ancestor, cyanobacteria (Synechococcus sp. WH8102). Also several other species, including E. coli, Arabidopsis thaliana and Cyanidioschyzon merolae, were used for the comparison. We found that the average connectivity among different func-tional pathways and enzyme classifications (EC) was different in all the species examined. However, the average connectivity of enzymes in the same functional classification was quite similar between chloroplast and one representative of cyanobacteria, syw. In addition, the enzymes in the highly con-served modules between chloroplast and syw, such as amino acid metabolism, were highly connected compared with other modules. We also discovered that the isozymes of chloroplast and syw often had higher connectivity, corresponded to primary metabolism and also existed in conserved module. In conclusion, despite the drastic re-organization of metabolism in chloroplast during endosymbiosis, the relationship between network topology and functions is very similar between chloroplast and its pre-cursor cyanobacteria, which demonstrates that the relationship may be used as an indicator of the closeness in evolution.

metabolic network, evolution, topology, chloroplast, cyanobacteria

The combination of various high-throughput technolo- gies and the development of metabolic pathway data-bases makes it possible to reconstruct and analyze metabolic networks of many organisms. This greatly facilitates the study on evolution of metabolic networks, which has not been clearly elucidated until now. Previ-ous work on the in silico analysis of metabolic[1], sig-naling[2,3], biochemical[4,5] and regulatory[6] networks has revealed how network properties, such as hubness, scal-ing, mutational robustness, short path length, emerge. One of the main contributors to the robustness and evolvement of biological networks is believed to be their modularity. The modules are defined as sets of genes/ enzymes that are strongly interconnected, whose func-tion is separable from those of other modules[7]. From

simple networks with only 5 genes, to large metabolic networks having many hundreds of nodes with over a thousand edges are in silico evolved[8]. In addition, some studies explored the mechanisms during metabolic net-work evolution by comparison of topological structures among multiple organisms. Zhu and Qin found that metabolic networks in archaeal species are different from those in S. cerevisiae and the 6 bacterial species in almost all measured topological properties, including network indices, degree distribution and motif profile[9]. Received October 22, 2008; accepted December 11, 2008 doi: 10.1007/s11434-009-0072-z †Corresponding authors (email: zhuowang@sjtu.edu.cn; leiliu@sibs.ac.cn) Supported by National Key Basic Research and Development Program of China (Grant Nos. 2006CB0D1203, 2006CB0D1205 and 2006CB910700), and National Natural Science Fundation of China (Grant No. 30800199)

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Zhang et al.[10] reported that the topology of different metabolic pathways provides different phylogenetic in-formation, and reconstructed a phylogenetic tree by merging multiple single pathways, which showed con-siderably higher similarity to the corresponding 16S rRNA-based tree than any other tree based on a single pathway.

It is conceivable that structural features of the bio-logical network may provide a quantitative insight into the biological function. For example, Maslov and Snep-pen[11] analyzed the stability of interaction networks by comparing patterns of average connectivity in interac-tion and regulatory networks. Topological characteriza-tions on protein-protein interaction networks also illu-minate some evolutionary issues. Fraser et al.[12] ob-served that the effect of an individual protein on cell fitness correlates with the number of its interaction partners. Jeong et al.[13] suggested that most highly con-nected proteins are crucial to cell viability. However, few studies explore the relationship between topology and function in metabolic networks, which is rather im-portant for deeply understanding the network evolution. In this study, we ask such questions as “what is the rela-tionship between the topological connections among enzymes and their functions? Does this relationship ex-hibit similarity between evolutionarily closely related organisms?” Metabolic network is a representation of all biochemical reactions; therefore its topology reflects enzyme functions. For example, do enzymes involved in different metabolic pathways have different connec-tivity?

Chloroplasts evolve as a result of endosymbiosis, i.e. engulfment of ancient free-living cyanobacteria by early eukaryotes. Under the sophisticated mechanism of pro-tein translocation, nucleus-encoded plastid-targeted en-zymes are transported into chloroplast to form the chloroplast metabolic network[14,15]. In a previous study, we reconstructed metabolic networks of chloroplast and cyanobacteria, and compared their overall topological properties and modular structures. Our study demon-strated that all cyanobacteria exhibit very similar prop-erties, while chloroplast network is overall less dense and more modular[16]. Given the change of topological properties in the chloroplast metabolic network com-pared with its progenitor, will the relationship between topology and functions vary a lot? Here, we analyzed the enzyme connectivity and its relationships with pathways, enzyme classifications, functional modules

and isozymes. Based on the previous results[16], we only chose one cyanobacterium Synechococcus sp. WH8102 (syw) as a representative for comparing chloroplast. In addition, we included E. coli, Arabidopsis thaliana and Cyanidioschyzon merolae in the comparison, in order to detect the changing trend of the relationship between topology and functions across different species. Our study may shed some light on the evolution of the chloroplast metabolic network.

1 Materials and methods 1.1 Dataset

We collected all biochemical reactions in chloroplast to reconstruct the metabolic network, for detail see ref. [16]. The metabolic pathways of other species, including cyanobacteria Synechococcus sp. WH8102 (syw), E. coli, Arabidopsis thaliana and Cyanidioschyzon merolae were extracted from KEGG database (Kyoto Encyclo-pedia of Genes and Genomes). We represent enzymes and compounds by the corresponding EC number and compound ID number in KEGG database, respectively. The direction of reactions is obtained based on the rules provided by Ma and Zeng[17].

1.2 Modularization of enzyme-centric network

The problem of identifying modules in a complex net-work is closely related to the graph partitioning problem, i.e. the separation of sparsely connected dense subgraphs from each other. Much effort has been devoted to study the decomposition of biological network into modules, among which the simulated annealing module-detection algorithm[18,19] has been successfully applied for meta-bolic network. Therefore we used this method to find modules in the metabolic networks of species examined here. Deviating from Guimerà and Amaral[18,19], we used an enzyme-centric graph representation of the metabolic network where vertices represent enzymes and edges represent compounds. A directed edge from enzyme E1 to enzyme E2 exists if E1 catalyzes a reaction generating a product A which is used as substrate in the reaction of E2. Reversible reactions are considered as two separate reactions. The connectivity of an enzyme is the number of its neighbors in the whole network.

1.3 Highly dense subnetwork — core

For large scale network, it is very important to discover the highly dense parts, which may reflect global prop-erty and be the important factor to compare different

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networks. Here we detect the k-core in enzyme network using Pajek[20], which is defined as a subnetwork of a given network where each vertex has at least k neighbors in the same core[21]. The largest core is the subnetwork with maximum k value, which is the densest center in whole network.

1.4 Isozymes determination

We here designated a pair of enzymes as isozymes if they catalyze the same reaction but are coded for by dif-ferent genes, which are not part of the same enzyme complex. We identified isozymes in all the 5 species examined here and compared their average connectivity with non-isozymes. As shown in Table 4, the amount of isozymes in E. coli, Arabidopsis thaliana and Cyanidio-schyzon merolae are much higher. In contrast, chloro-plast and syw have similar number of isozymes, which are 12 and 18, respectively.

2 Results 2.1 Global topology of enzyme-centric networks

The composition and topological properties of enzyme

networks in chloroplast, syw, E. coli, Arabidopsis thaliana and Cyanidioschyzon merolae are shown in Table 1. It is evident that chloroplast network is less dense for its longer average path length and larger di-ameter. The average connectivity of all enzymes in chloroplast and syw is 14.77 and 17.61, respectively. Two hundred and ten enzymes are common in both chloroplast and syw. The average connectivity of those enzymes is 17 in chloroplast and 20 in syw. The enzymes that only exist in chloroplast but not in syw have the average connectivity of 12, while the enzymes that only exist in syw but not in chloroplast have the average connectivity of 14.

We then compared the highly dense core of the two networks using Pajek (see Materials and methods). As illustrated in Figure 1, the largest core in chloroplast and syw network includes 34 and 38 enzymes respectively, among which 27 enzymes are shared by the two cores. For chloroplast, each enzyme in the largest core has at least 28 neighbors in the same core. Correspondingly each enzyme has at least 31 neighbors in the largest core of syw network. The average connectivity of enzymes in

Table 1 The scale and topological property of enzyme network

Species Enzyme number Average connectivity Average path length Diameter

Chloroplast 376 14.77 4.56888 16

syw 371 17.61 3.81601 12

E. coli 587 24.52 3.70899 11

Cyanidioschyzon merolae 359 18.19 3.66545 14

Arabidopsis 457 22.70 3.74563 12

Figure 1 The largest core in enzyme network of chloroplast and syw. There are 34 enzymes in 28-core and 38 enzymes in 31-core respec-tively in chloroplast and syw network. The 27 enzymes with magenta color are shared by these two cores; Light-green and light-orange nodes represent enzymes specific for chloroplast and syw respectively.

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these two cores is 42.03 and 47.87 respectively, which are more highly connected than the other parts. Among the 27 common enzymes, 22 enzymes are related to amino-acid metabolism, and the rest are involved in nu-cleotide metabolism and carbohydrate metabolism. Consequently the common parts between chloroplast and syw are highly conserved and connected. In addition, 81.48% of the shared enzymes are synthetases.

2.2 Connectivity of enzymes belonging to different functional pathways is very similar between chloro-plast and syw

According to KEGG database, the biochemical path-ways can be mainly classified to 9 parts: carbohydrate metabolism, energy metabolism, lipid metabolism, nu-cleotide metabolism, amino-acid metabolism, glycan biosynthesis and metabolism, metabolism of cofactors and vitamins, biosynthesis of secondary metabolites and biodegradation of xenobiotics. For each species exam-ined here, we determined which pathways each enzyme belongs to and then calculated the mean connectivity of enzymes in different functional pathways. As shown in Table 2, the mean connectivity for the enzymes involved in amino acid metabolism, nucleotide metabolism and energy metabolism is higher in all these species. In con-trast, the mean connectivity for enzymes involved in lipid and glycan metabolism are lower. Interestingly, glycan biosynthesis and metabolism, and biodegradation

of xenobiotics were absent from chloroplast[16]. Among all the pathways existed in chloroplast, we found that the average connectivity is very similar between chloroplast and syw, but very different from other species.

2.3 Connection of different enzyme classification is similar between chloroplast and syw

We examined the association between enzyme classifi-cation and connectivity in the metabolic network. As shown in Table 3, the average connectivity of syntheta-ses is the highest in all species in this study. Transferases and lyases have second highest connectivity. The two least connected enzyme classes are hydrolases and isomerases. Across species, we found again that the av-erage connectivity of each enzyme classification is very similar between chloroplast and syw, but different from the other species.

2.4 Rank of modules by average connectivity is similar between chloroplast and syw

We used the simulated annealing module-detection algo-rithm to detect 11 and 7 modules in the enzyme net-works of chloroplast and syw respectively, those en-zymes having no any links with others were excluded here. We found 5 pairs of modules with very similar en-zyme contents[16], which are regarded as conserved modules, as illustrated in Figure 2. There are three pairs of modules mainly corresponding to amino-acid me-

Table 2 The mean connectivity of enzymes in different functional pathways

KEGG pathway classification syw Chloroplast E. coli Arabidopsis Cyanidioschyzon merolae

Carbohydrate metabolism 14.19 13.45 20.1 18.99 17.67

Energy metabolism 21.37 20.46 32.6 26.86 15.35

Lipid metabolism 12.23 7.54 21.38 19.29 14.07

Nucleotide metabolism 19.86 17.9 27.77 25.36 20.91

Amino-acid metabolism 23.41 21.93 33.6 30.54 28.06

Glycan biosynthesis and metabolism 5.69 17.16 13.78 11.54

Metabolism of cofactors and vitamins 18.49 8.18 23.99 20.23 13.81

Biosynthesis of secondary metabolites 10.17 9.52 22.36 32.71 15.59

Biodegradation of xenobiotics 11 26.5 27.79 18.13

Table 3 The average connectivity of different enzyme class and their ranks (in parenthesis)

EC class syw Chloroplast E. coli Arabidopsis Cyanidioschyzon merolae

Oxyreductases 11.87 (4) 15.16 (4) 19.76 (4) 25.77 (3) 13.15 (4)

Transferases 18.48 (3) 15.44 (3) 25.64 (3) 21.63 (4) 18.89 (2)

Hydrolases 7.98 (5) 7.11 (5) 15.51 (5) 11.56 (5) 9.46 (5)

Lyases 19.13 (2) 17.67 (2) 27.72 (2) 26.62 (2) 16.26 (3)

Isomerases 5.9 (6) 3.42 (6) 6.78 (6) 4.08 (6) 4.13 (6)

Synthetases 34.29 (1) 35.92 (1) 51.66 (1) 40.87 (1) 37.76 (1)

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Figure 2 The module composition of metabolic network in chloroplast and syw. Each sector of the pie chart represents a module marked with the number of enzymes in it. The 5 pairs of modules represented with same colors are conserved modules between chloroplast and syw, among which the cyan, yellow and light-purple modules correspond to amino-acid metabolism, the pink and green modules belong to carbo-hydrate metabolism and nucleotide metabolism respectively. The modules with grey and black colors represent specialized modules respec-tively for chloroplast and syw.

tabolism, and the other two pairs belonging to nucleotide metabolism and carbohydrate metabolism respectively. These 5 conserved modules include 69.68% and 80.32% of all enzymes in chloroplast and syw respectively. Among the common 210 enzymes shared by them, ap-proximately 60% exist in these conservative modules.

Here we rank the modules in the two networks by av-erage connectivity, as shown in Figure 3. Remarkably, the top three modules with high connectivity in chloro-plast and syw are just the best matches to each other, which mainly consist of enzymes related to amino-acid metabolism. Moreover, the other two pairs, module 8 in chloroplast and module 7 in syw, and module 1 in chloroplast and module 6 in syw also have relative higher connectivity and respectively have the same ranks among modules in each species. In contrast, the specialized modules with different colors for chloroplast and syw are less connected (Figure 3).

In addition, we ranked the connectivity of enzymes in both chloroplast and syw and found the most highly

Figure 3 The rank of modules in chloroplast and syw by average connectivity. The 5 modules with same colors are conserved mod-ules between chloroplast and syw consistent with Figure 2.

connected nodes existed in those conserved modules with high average connectivity. There are 84 enzymes with connectivity above 20 in chloroplast, which are all involved in the three large and dense modules 7, 2, 10, which correspond to amino acid metabolism. Similarly, in syw, the three best-matched modules (2, 3, 4) to the three modules with high connectivity in chloroplast con-sist of 91 enzymes with connectivity above 30.

2.5 Isozymes show higher connectivity and reside in conserved modules

The hubs (highly connected nodes) are the most impor-tant nodes for the integrity of the network. If a fraction of the hubs are removed, the network is likely to become fragmented into smaller components[22]. Since these en-zymes are very important for the robustness of the net-work, it might be suspected that the enzymes with the highest connectivity could have more than one repre-sentatives in the genome, i.e. that there are two or more isozymes representing these highly connected nodes. We calculated the mean connectivity of the isozymes and non-isozymes in each network, as shown in Table 4. For all the 5 species examined here, isozymes have signifi-cant higher connectivity than non-isozymes verified by t-test.

In chloroplast, the average connectivity of isozymes and non-isozymes is 31.67 and 14.21 respectively (t-test, P = 0.0002). Similarly, in syw, the average connectivity is 26.78 and 17.14 respectively (t-test, P = 0.02) for isozymes and non-isozymes. Furthermore, all of the isozymes exist in conserved modules between chloro-plast and syw (module 1, 2, 7, 10 in chloroplast and module 6, 3, 2, 4 in syw). In addition, 75% of the

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Table 4 The average connectivity of isozymes and non-isozymes Parameters syw Chloroplast E. coli Arabidopsis Cyanidioschyzon merolae

Number of isozymes 18 12 48 44 36

Average connectivity of isozymes 26.78 31.67 42.02 32.95 24.83

Number of non-isozymes 353 364 539 413 323

Average connectivity of non-isozymes 17.14 14.21 22.96 21.61 17.45

t-test, P-value 0.02 0.0002 3.48×10−07 0.0023 0.0187

isozymes in chloroplast correspond to carbohydrate me-tabolism, nucleotide metabolism and amino-acid me-tabolism. Similarly, for syw, 77.78% of the isozymes belong to carbohydrate and amino-acid metabolism.

3 Discussion

We have uncovered the relationship between topology and functions in several representative metabolic net-works and found this relationship is very similar for chloroplast and cyanobacteria.

Firstly, enzymes in different functional pathways have different average connectivity. Those primary metabo-lism pathways, such as amino acid metabolism, nucleo-tide metabolism, and energy metabolism, consist of en-zymes with higher average connectivity in all species examined here. These enzymes have been suggested to be more ancient, i.e. appeared earlier during evolution, than those in other pathways such as lipid metabo-lism[23,24]. The observed correlation between connec-tivity and enzyme age is consistent with the mechanism of preferential attachment which predicts that ancient enzymes should have a higher average connectivity than less ancient enzymes[25,26]. In addition, the average con-nectivity of most functional pathways is very similar between chloroplast and syw, except that glycan bio-synthesis and metabolism, and biodegradation of xeno-biotics were absent from chloroplast. To further validate the relationship between enzyme connection and func-tional classification, we will also match enzymes to other function annotation sources, such as COG and TIGR. Recently, Karimpour-Fard et al.[27] classified the function of proteins in the co-conserved protein network using three annotation sources including KEGG, COG and TIGR, and got consistent results.

Secondly, the tightness of enzymes belonging to dif-ferent enzyme classes is different; the synthetases classes show the highest connectivity in all these net-works. In fact, most (81.48%) of the enzymes shared by the two most densest cores between chloroplast and syw are synthetases (Figure 1), which are very conserved and

important. For example, aminoacyl-tRNA synthetases have been speculated to be among the first proteins to evolve[28]. Logically, the synthetases used for the syn-thesis of amino acid should also be among the earlier enzymes to evolve to supply amino acid for aminoa-cyl-tRNA synthetases. Furthermore, the average connec-tivity of enzymes in each enzyme classification is rather similar between chloroplast and syw.

Thirdly, the modules in chloroplast and syw networks exhibit same rank by average connectivity. These mod-ules are detected based on topological linkage, which has max connection within each module and min con-nection among modules. These modules have been demonstrated well matched with functional path-ways[18,19], so network modules are good representation of relationship between topology and function. The common enzymes shared by chloroplast and cyanobac-teria have higher connectivity than their own specialized enzymes. In addition, the conserved modules are highly connected. Especially, three pairs of modules corre-sponding to amino acid metabolism are all highly con-nected and involving most of the hub enzymes. In addi-tion, the other two modules belonging to carbohydrate metabolism and nuclear acid metabolism are sub-highly dense. Since most enzymes in a module are belonging to same functional pathways, it is efficient to predict func-tion of unclassified proteins or enzymes based on the other nodes in the same topological module.

Another important point, the significant high connec-tivity of isozymes found in all species examined here indicates that isozymes are crucial for the integrity of metabolic network. Furthermore, all isozymes of chloroplast and syw exist in conserved modules between them, and majority of the isozymes correspond to pri-mary metabolism processes such as amino-acid metabo-lism. Consistent with this result, whole system flux analysis suggested that genes coding enzymes with high connectivity and high metabolic flux have higher prob-ability to retain duplicate during evolution[29], which inevitably leads to greater chance to evolve isozymes.

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In metabolic networks, flux balance analysis (FBA) have recently significantly improved our ability to make quantifiable predictions on the relative importance of various reactions, giving rise to experimentally testable hypotheses[30,31]. The flux of a given metabolic reaction represents the amount of substrate that is being con-verted to a product within a unit of time[32]. Under same environment, different reactions may carry different fluxes. Furthermore, knockout different enzymes or re-actions may result in different variations on flux distri-bution. Consequently, detecting the influence of en-

zyme’s position on metabolic flux will further help to elucidate the relationship between network topology and functions.

In conclusion, despite the drastic re-organization of metabolism in chloroplast during endosymbiosis, the relationship between topology and functions is very similar between chloroplast and its precursor cyanobac-teria, which demonstrates that the relationship may be used as an indicator of the closeness in evolution.

We thank Dr. Zhu XinGuang for valuable comments on the manuscript.

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