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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptNIH Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
Bioinformatics. Author manuscript; available in PMC Dec 20, 2007.
Published in final edited form as:
PMCID: PMC2149892
NIHMSID: NIHMS34152

A network-based method for target selection in metabolic networks

Abstract

Motivation

The lack of new antimicrobials, combined with increasing microbial resistance to old ones, poses a serious threat to public health. With hundreds of genomes sequenced, systems biology promises to help in solving this problem by uncovering new drug targets.

Results

Here, we propose an approach that is based on the mapping of the interactions between biochemical agents, such as proteins and metabolites, onto complex networks. We report that nodes and links in complex biochemical networks can be grouped into a small number of classes, based on their role in connecting different functional modules. Specifically, for metabolic networks, in which nodes represent metabolites and links represent enzymes, we demonstrate that some enzyme classes are more likely to be essential, some are more likely to be species-specific and some are likely to be both essential and specific. Our network-based enzyme classification scheme is thus a promising tool for the identification of drug targets.

1 INTRODUCTION

Several groups have stressed the threat that the lack of development of new antimicrobial drugs poses to public health (Bax et al., 2000; Norrby et al., 2005; Spellberg et al., 2004). With the ever-increasing amount of biological data available, the promise of systems biology is to help in alleviating this problem by uncovering new drug targets (Nikolsky et al., 2005). A promising approach in this regard is to map the interactions between biochemical agents—such as proteins and metabolites—onto complex networks (Amaral and Ottino, 2004; Newman, 2003), and then study the properties of these networks to gain insight into key biological processes.

In spite of some efforts to uncover new drug targets using this approach (Jeong et al., 2001; Klamt and Gilles, 2004; Palumbo et al., 2005; Rahman and Schomburg, 2006), one may argue that the results have, so far, been modest. A potentially important reason for this is that the structure of complex biochemical networks is typically characterized in terms of global properties (Jeong et al., 2000, 2001; Ma and Zeng, 2003; Tanaka, 2005; Wagner and Fell, 2001). In particular, a lot of attention has been paid to the degree distribution of the nodes in these networks, i.e. the distribution of number of protein interactions per protein in the proteome (Jeong et al., 2001) and the distribution of the number of other metabolites into which a certain metabolite can be transformed through metabolic reactions in the metabolome (Jeong et al., 2000; Ma and Zeng, 2003; Ravasz et al., 2002; Tanaka, 2005; Wagner and Fell, 2001). The caveat is that global quantities are appropriate only when one of two very strict conditions is fulfilled: (i) the network lacks a modular structure (Guimerà and Amaral, 2005b; Han et al., 2004; Hartwell et al., 1999; Holme et al., 2003; Ravasz et al., 2002), or (ii) the network has a modular structure but (a) all functional modules were formed according to the same mechanisms, (b) all functional modules have similar properties and (c) the interface between functional modules is statistically similar to the bulk of the modules, except for the density of links.

To our knowledge, no real biochemical network fulfills either of the two conditions above, which implies that global properties are unlikely to provide insight into the mechanisms responsible for the formation and evolution of these networks (Guimerà et al., 2007), or to facilitate the discovery promising therapeutic targets. Alternative approaches that take into consideration the modular structure (Danon et al., 2005; Girvan and Newman, 2002; Guimerà and Amaral, 2005a; Newman and Girvan, 2004) of real-world complex networks are, thus, necessary. One such approach is the cartographic approach (Guimerà and Amaral, 2005a, b), which enables one to group nodes into a small number of roles according to their pattern of intra- and inter-module connections.

Recently, we demonstrated that the role of a node conveys significant information about the importance of the node, and about the evolutionary pressures on it (Guimerà and Amaral, 2005a, b). Here, we report that in metabolic networks—in which nodes represent metabolites and links represent enzymes—some link types, i.e. some enzyme classes, are more likely to be essential, some are more likely to be species-specific and some are likely to be both essential and specific. Our network-based enzyme classification scheme is thus a promising tool for the identification of drug targets. Intriguingly, we also find that some crucial enzymes are not backed up by alternative pathways.

2 METHODS

2.1 Description of the datasets

To build the 18 metabolic networks (Table 1 and Figs 1 and and3)3) from the Kyoto Encyclopedia of Genes and Genomes (KEGG) (Goto et al., 1998), we use the data compiled in the LIGAND section (Kanehisa and Goto, 2000) of the database (as of March–April 2006). To remove carrier metabolites (such as water or ATP), we determine the main reactant pairs in each reaction (Kanehisa et al., 2006). Reactant pairs are pairs of metabolites that have atoms or atom groups in common on both sides of a chemical reaction formula. In contrast with cofactor pairs and leave pairs, main reactant pairs correspond to the most relevant biochemical transformations in a reaction. Main substrates and products are listed in the reaction_main. lst file. We connect all the main substrates to all the main products in a reaction, but not substrates to substrates or products to products.

Fig. 1
Modularity and roles in the studied metabolic networks. In Table 1, we show the number of nodes and links in each network, the modularity M of the best partition obtained using simulated annealing, and the 95% confidence interval for the modularity M ...
Fig. 3
Role-to-role connectivity profiles. For each network, we calculate the number rij of links between nodes belonging to roles i and j, and compare this number to the number Rij of such links in a properly randomized network (see Methods Section). Rij is ...

For each organism, we only take into account reactions that are catalyzed by an enzyme that the organism is able to synthesize, and reactions that are explicitly classified as spontaneous. We obtain the enzymes necessary for each reaction from the reaction file, and the enzymes synthesized by each organism from the organism databases in KEGG.

For our analysis of Escherichia coli and Helicobacter pylori (Figs 2 and and4),4), we use the set of reactions compiled by B. Ø. Palsson’s Systems Biology Research Group, at UCSD (Reed et al., 2003; Thiele et al., 2005). To obtain the modules and the roles of each metabolite in the flux balance analysis (FBA) reconstruction of these metabolic network, we need to remove carrier metabolites from the metabolic network. To this end, we automatically match each reaction in the FBA database to a reaction in the KEGG database, and use the LIGAND section of the KEGG (as of November 2005) to identify the main reactant pairs in the reaction. We find such a match for ~80% of the reactions listed in the FBA databases. For the remaining reactions, we remove carrier metabolites manually.

Fig. 2
Link type indispensability and conservation for E.coli (left) and H.pylori (right). (A) Distribution of link types. The higher the number of links of a certain type, the more reliable the estimation of the corresponding indispensability. Link types represented ...
Fig. 4
In silico analysis of gene indispensability. We plot the distribution of growth rates for mutant (gray) and wild type (black line) E.coli, obtained with FBA from an ensemble of 10 000 random media (see Methods Section). (A) Mutant Δicd in very ...

2.2 Module identification

For a given partition of the nodes of a network into modules, the modularity M of this partition is (Guimerà et al., 2004; Newman and Girvan, 2004)

Ms=1NM[lsL(ds2L)2],
(1)

where NM is the number of modules, L is the number of links in the network, ls is the number of links between nodes in module s, and ds is the sum of the connectivities (degrees) of the nodes in module s. The modularity of a partition is high if the number of within-module links is much larger than expected from chance alone.

The objective of a module identification algorithm is thus to find the partition with the largest modularity. We use simulated annealing to find the partition with the largest modularity (Guimerà and Amaral, 2005a, b; Guimerà et al., 2004). Danon et al. (2005) have recently shown that this method is the most accurate method in the literature to date.

2.3 Role definition

Nodes with similar roles are expected to have similar relative within-module connectivity (Guimerà and Amaral, 2005a, b). If κi is the number of links of node i to other nodes in its module si, [kappa]si is the average of κ over all the nodes in si and σκsi is the standard deviation of κ in si, then we define the within-module degree z-score as

zi=κiκ¯siσκsi.
(2)

The within-module degree z-score measures how ‘well-connected’ node i is to other nodes in the module.

Different roles can also arise because of the connections of a node to modules other than its own (Guimerà and Amaral, 2005a, b). We define the participation coefficient Pi of node i as

Pi=1s=1NM(κiski)2
(3)

where κis is the number of links of node i to nodes in module s, and ki is the total number of links of node i. The participation coefficient of a node is therefore close to one if its links are uniformly distributed among all the modules and zero if all its links are within its own module.

We classify as non-hubs those nodes that have low within-module degree (z < 2.5). Depending on the amount of connections they have on other modules, non-hubs are further subdivided into (Guimerà and Amaral, 2005a, b): (R1) ultra-peripheral nodes, i.e. nodes with all their links within their own module (P ≤ 0.05); (R2) peripheral nodes, i.e. nodes with most links within their module (0.05 < P ≤ 0.62); (R3) satellite connectors, i.e. nodes with a high fraction of their links to other modules (0.62 < P ≤ 0.80) and (R4) kinless nodes, i.e. nodes with links homogeneously distributed among all modules (P > 0.80). We classify as hubs those nodes that have high within-module degree (z ≥ 2.5). Similar to non-hubs, hubs are divided according to their participation coefficient into: (R5) provincial hubs, i.e. hubs with the vast majority of links within their module (P ≤ 0.30); (R6) connector hubs, i.e. hubs with many links to most of the other modules (0.30 < P ≤ 0.75) and (R7) global hubs, i.e. hubs with links homogeneously distributed among all modules (P > 0.75).

Note that, since we use a stochastic module identification algorithm, small differences do exist between different partitions of the network. Nevertheless, results are highly consistent (Guimerà and Amaral, 2005a, b), so that by obtaining 100 quasi-optimal partitions, we can estimate the likelihood that a link is of a certain type.

2.4 Network randomization and statistical models

We use two different network randomization schemes. To assess the significance of the modular structure of a network (Fig. 1), we randomize all the links in the network while preserving the degree of each node. To uniformly sample all possible networks, we use the Markov-chain Monte Carlo switching algorithm (Maslov and Sneppen, 2002; Itzkovitz et al., 2004). In this algorithm, one repeatedly selects pairs of links and swaps one of the ends of the links.

For the analysis of the over- and under-representation of links between pairs of roles, it is crucial to preserve not only the degree of each node, but also the modular structure of the network and the role of each node. Therefore, we restrict the Markov-chain Monte Carlo switching algorithm to pairs of links that connect nodes in the same pair of modules. In other words, we apply the Markov-chain Monte Carlo switching algorithm independently to links whose ends are in modules 1 and 1, 1 and 2 and so forth for all pairs of modules. This method guarantees that, with the same partition as the original network, the modularity of the randomized network is the same as that of the original network (since the number of links between each pair of modules is unchanged) and that the role of each node is also preserved.

2.5 Flux balance analysis and link indispensability

Flux balance analysis (FBA) (Edwards and Palsson, 2000a) enables us to computationally estimate metabolic fluxes in an organism. FBA is based on the idea that metabolic fluxes producing and consuming a certain metabolite must, in the steady state, balance each other. Additionally, some amounts of certain metabolites can be obtained from or excreted to the extracellular medium. These considerations impose a set of linear constraints on the metabolic fluxes. One can further assume that, among all possible flux solutions satisfying all the constraints, the one realized in nature is the one that maximizes the growth rate of the organism. With these assumptions, the problem of finding the flux distribution becomes a linear programming problem, which can be solved using standard numerical techniques (Winston and Venkataramanan, 2002).

For our analysis, we use the set of reactions compiled for E.coli (Reed et al., 2003) and H.pylori (Thiele et al., 2005). In our simulations of gene deletions, we use ensembles of random media that are built as follows. A minimal medium is defined for each species (Reed et al., 2003; Thiele et al., 2005) (the E.coli minimal medium contains oxygen to simulate aerobic conditions). To the minimal medium, we add a randomly selected fraction f of all possible uptake fluxes, which are set to a maximum of 10 mmol/g h. Each random medium is evaluated 200 times, each time with a different selection of the uptake fluxes. Additionally, for E.coli we simulate a glucose medium, which consists of the minimal medium plus a glucose uptake rate of up to 10 mmol/g h.

Following the work of Edwards and Palsson, (2000b), we define the indispensability of a link as the ratio between the growth rate gΔ of the mutant and the growth rate g of the wild type organism. In particular, the indispensability I is defined as

I=1gg.
(4)

3 RESULTS

3.1 Functional modules and metabolite roles in metabolic networks

In a metabolic network, each node represents a metabolite, and two metabolites are connected if there is a biochemical reaction that transforms one into the other, so that, in general, links represent reactions and the enzymes catalyzing them. However, a single link may correspond to several parallel reactions and/or enzymes (if distinct reactions transform one metabolite into the other and/or if different enzymes are involved in such transformation). Moreover, a single reaction may correspond to different links (if there is more than one reactant or product), while a few reactions occur spontaneously and therefore have no associated enzymes.

We start by quantifying the modular structure of the metabolic network for 18 different organisms obtained from the KEGG database (Goto et al., 1998; Kanehisa and Goto, 2000) (see Methods Section). We use simulated annealing to find the partition of the network into modules that maximizes the modularity (Guimerà and Amaral, 2005b; Guimerà et al., 2004) (see Methods Section), and assess the significance of the modular structure of each network by comparing it to a large number of randomizations of the same network (Guimerà et al., 2004) (Fig. 1). We find that all networks have a significant modular structure.

Next, we determine the role of each node (see Methods Section). In our cartography, we classify nodes into seven roles according to their pattern of inter- and intra-module connections (Guimerà and Amaral, 2005a, b) (Fig. 1): (R1) ultra-peripheral nodes, (R2) peripheral nodes, (R3) satellite connectors, (R4) kinless nodes, (R5) provincial hubs, (R6) connector hubs and (R7) global hubs. Similarly, links can be classified in several types according to the roles of the nodes they connect. For example, R3–R5 links connect satellite connectors to provincial hubs. For simplicity, and because roles R4 and R7 rarely occur in real complex networks (Guimerà and Amaral, 2005a, b), we focus on roles R1, R2, R3, R5 and R6, and on the links connecting nodes with these roles.

We surmise that links of different types in the network correspond to enzymes with different functions and importance in the metabolism. Additionally, because metabolites with certain roles are significantly conserved across species (especially satellite connectors and connector hubs) while others are not (Guimerà and Amaral, 2005b), links of certain types are more likely to be species-specific.

3.2 Reactions with the highest median indispensability involve satellite connector metabolites

These considerations suggest a novel approach to identify promising drug targets. Indeed, by considering links of certain types, we should be able to identify enzymes that are indispensable for an organism but not needed by other organisms. Given that nodes with roles R3 and R6 are highly conserved across organisms, we hypothesize that links of types R3–R3, R3–R6 and R6–R6 will be, in general, essential to an organism. These links are, however, likely to be non-specific. In contrast, links connecting highly conserved metabolites (R3 or R6) to less conserved metabolites (e.g. R2) may still be essential because of the conserved end, and specific because of the non-conserved end. These link types thus appear to be natural candidates for drug targets.

To investigate this possibility, we analyze in depth the metabolic network of two bacteria: E.coli and H.pylori (the human pathogen responsible for gastritis and peptic ulcer disease). We select these two organisms because one can use FBA to estimate the fluxes of each of the reactions in their metabolism (Edwards and Palsson, 2000a; Reed et al., 2003; Thiele et al., 2005). Importantly, FBA also enables us to computationally test the effect of gene deletions that result in a specific reaction not taking place (Edwards and Palsson, 2000a; Thiele et al., 2005).

We analyze systematically the effect of removing links from the metabolic networks of E.coli and H.pylori, i.e. we simulate the removal of all enzymes catalyzing the reactions connecting a certain pair of metabolites (Fig. 2). We quantify the effect of a link deletion by the indispensability I, which measures the relative difference between the growth rate of the mutant and that of the wild type (see Methods Section): a link with I = 0 can be removed without affecting the growth rate, whereas a link with I = 1 is indispensable for the survival of the organism.

We find that for all types of links there are instances of high indispensability. Our results indicate, however, that certain link types have a significantly higher likelihood of being indispensable than others (Fig. 2B), which confirms that our node and link classification scheme captures important biological information. In particular, we find that the links with the highest indispensability in both E.coli and H.pylori involve satellite connector metabolites (R3). Satellite connectors are metabolites that, despite participating in a relatively small number of biochemical reactions, bridge several different modules. The finding that links involving satellite connectors have high median indispensability may thus account for the high conservation rate of satellite connectors reported earlier (Guimerà and Amaral, 2005b): Since many reactions involving satellite connectors are indispensable, it is unlikely that a mutation causing the loss of the ability to process these metabolites results in a viable organism.

3.3 High indispensability link types are not over-represented in the metabolism

Biological systems are considered mutationally robust if they are able to function even after genetic mutations occur. Mutational robustness through redundancy and the so-called distributed robustness are thought to provide an evolutionary advantage to organisms, which would explain the pervasiveness of robustness in biological systems (Wagner, 2005). Within this context, however, our findings on link indispensability are somewhat puzzling: some links in the metabolism are highly fragile and the these links often involve satellite connector metabolites, which seems to contradict the hypothesis that fragile links are random evolutionary ‘accidents’.

A relevant question is, thus, whether: (i) evolution tries to provide backups for links in link types that are likely to be fragile, however it cannot backup all of these links so that those link types are still more fragile than one would expect, or (ii) fragile link types are fragile and (or because) evolution does not back them up. To address this question quantitatively, we consider the FBA reconstructions for E.coli and H.pylori as well as the KEGG reconstructions for these and other bacteria, archaea and eukaryotes. For each network, we obtain the role-to-role connectivity profiles by computing the number rij of links between nodes belonging to roles i and j, and comparing this number to the number Rij of such links that are expected to appear purely by chance (Fig. 3, see Methods Section and Supplementary Fig. S1).

We find that the role-to-role connectivity profiles are consistent across domains, which indicates that the profiles are a result of the fundamental tasks that all metabolic networks need to carry out, and not of the particularities of each metabolic network. Remarkably, we also find that the most indispensable link types (R2–R3, R3–R3, and R3–R6) are not significantly or consistently over-represented in the 18 organisms we consider (Fig. 3). This result seems to indicate that fragile link types are fragile and (or because) evolution does not back them up.

Although we do not have a definite theory to understand this finding, we put forward two plausible explanations, both of them closely connected to the modular structure of metabolic networks. One possibility is that satellite connectors have chemical properties that make them unique in their ability to bridge two or more modules whose metabolites have, otherwise, little in common. In this case, it would be impossible for organisms to develop alternative pathways. A second hypothesis is that some ‘fragile’ links between modules provide a net evolutionary advantage, even at the price of making the metabolism less robust. This advantage may arise from the fact that fragile links between modules (i.e. those that do not have backups) enable some degree of module independence and can act as system-level regulation points: a small change in the fluxes through these links can reshape the global distribution of the metabolic fluxes, and can switch on and off whole modules (for similar ideas in neuroscience, (Hilgetag and Kaiser, 2004; Sporns et al., 2000)).

3.4 Enzymes connecting peripheral metabolites and satellite connectors are promising drug targets

Besides posing interesting fundamental questions about the evolution of metabolism, our analysis also opens the door for novel approaches to exploit the information hidden in metabolic networks. We have established that, at least in E.coli and H.pylori, biochemical reactions involving satellite-connector metabolites are particularly vulnerable. These reactions could, therefore, be of great importance to metabolic engineering and be natural targets for drugs.

Enzymes connecting peripheral metabolites and satellite connectors (R2–R3) seem the most promising as drug targets, given that peripheral metabolites (R2) are not highly conserved across species (Guimerà and Amaral, 2005b). This means that it should be possible to find vulnerable and species-specific links of type R2–R3 in pathogens. To investigate this possibility, we study the conservation in humans of the enzymes that correspond to different types of links in E.coli and H.pylori (Fig. 2C). We find that, as hypothesized, the most conserved enzymes correspond to links involving connector hubs (R6), and that enzymes corresponding to R2–R3 links are not significantly more conserved than enzymes of types not involving R6 nodes.

4 CONCLUSION

As we have shown, FBA does predict that enzymes of types R2–R3, R3–R3 and R3–R6 have greater median indispensability than other enzyme types. The true test of our predictions, however, will have to come from new experimental studies. New experiments are necessary because two important aspects reduce the usefulness of existing system-level databases on gene essentiality (Gerdes et al., 2003; Thiele et al., 2005) (Fig. 4).

The first limitation of existing databases is that essentiality is assumed to be a binary variable, i.e. either a gene is considered to be essential or it is considered to be non-essential. This simplification overlooks the fact that the absence of certain genes in a mutant may severely reduce its growth rate, which would render the mutant inviable in selective environments (Fig. 4A). Concretely, a host is a selective environment because of the immune response triggered by the presence of the pathogen. Another selective environment is one in which the mutant competes for limited resources with the wild type or with other organisms.

The second limitation of current databases is that they store experimental results on essentiality obtained for rich media, whereas many genes will be essential only when certain compounds are not available (Fig. 4B). Papp et al. (2004) have predicted that, for Saccharomyces cerevisiae, over 50% of the genes that are non-essential in rich media will be essential in more stringent conditions.

Our results therefore suggest that a more thorough description of essentiality is necessary, and our network-based method to identify and classify enzymes may be a useful guide for further and more exhaustive experiments, specially on enzymes corresponding to links of type R2–R3, which are likely to have fundamental and practical importance.

In the absence of such comprehensive experimental studies, we have nonetheless been able to verify that some enzymes that correspond to R2–R3 links in E.coli have been previously suggested or are being investigated as potential drug targets. The enzymes encoded by genes glmS (EC 2.6.1.16) pfs (EC 3.2.2.16 3.2.2.9) and ptsI (EC 2.7.3.9) catalyze transformations that our method assigns a high probability (>33%) of being of type R2–R3 in E.coli, and are research targets for bacterial infections according to the Therapeutic Target Database (TTD) (Chen et al., 2002). It is important to note that these enzymes also catalyze transformations of types other than R2–R3. This turns out to be a quite general situation for the enzymatic targets listed in the TTD; most target enzymes listed in the database correspond to multiple links in the E.coli metabolic network, often including several R1–R1 and R1–R2 links and sometimes including links that involve connector hubs (R6) and, to a lesser extent, provincial hubs (R5). This suggests that the ‘effectiveness’ of current enzymatic targets might be more related to removing many links in the metabolic network, with the associated lack of specificity and potential side effects, than to their ability to actually interfere with critical species-specific links. We believe that our results will help clarifying these issues, providing justification to why certain enzymes are better targets than others, and will open the door to the guided discovery of new targets.

Acknowledgments

We thank V. Hatzimanikatis, W.M. Miller, A. Mongragón, D.B. Stouffer and L.K. Wing for useful comments and suggestions. We thank J. Reed, I. Thiele and the Systems Biology Research Group at UCSD for their help and for making their FBA reconstructions publicly available. R.G. and M.S.-P. gratefully acknowledge support from the Fulbright Program. L.A.N.A. gratefully acknowledges support from a NIH/NIGMS K-25 award, from the J.S. McDonnell Foundation, and from the W.M. Keck Foundation.

Footnotes

Conflict of Interest: none declared.

Supplementary information: Supplementary data are available at Bioinformatics online.

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