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Bioinformatics Advance Access originally published online on May 8, 2006
Bioinformatics 2006 22(14):1767-1774; doi:10.1093/bioinformatics/btl181
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© The Author 2006. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Observing local and global properties of metabolic pathways: ‘load points’ and ‘choke points’ in the metabolic networks

Syed Asad Rahman 1 and Dietmar Schomburg 1,2,*

1 Cologne University Bioinformatics Center, CUBIC Zülpicher Strasse 47, 50674 Koeln, Germany
2 Institute for Biochemistry Zülpicher Strasse 47, 50674 Koeln, Germany

*To whom correspondence should be addressed.


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 SYSTEM AND METHODS
 ALGORITHM
 IMPLEMENTATION
 RESULTS AND DISCUSSION
 CONCLUSION
 REFERENCES
 

Motivation: The local and global aspects of metabolic network analyses allow us to identify enzymes or reactions that are crucial for the survival of the organism(s), therefore directing us towards the discovery of potential drug targets.

Results: We demonstrate a new method (‘load points’) to rank the enzymes/metabolites in the metabolic network and propose a model to determine and rank the biochemical lethality in metabolic networks (enzymes/metabolites) through ‘choke points’. Based on an extended form of the graph theory model of metabolic networks, metabolite structural information was used to calculate the k-shortest paths between metabolites (the presence of more than one competing path between substrate and product). On the basis of these paths and connectivity information, load points were calculated and used to empirically rank the importance of metabolites/enzymes in the metabolic network. The load point analysis emphasizes the role that the biochemical structure of a metabolite, rather than its connectivity (hubs), plays in the conversion pathway.

In order to identify potential drug targets (based on the biochemical lethality of metabolic networks), the concept of choke points and load points was used to find enzymes (edges) which uniquely consume or produce a particular metabolite (nodes). A non-pathogenic bacterial strain Bacillus subtilis 168 (lactic acid producing bacteria) and a related pathogenic bacterial strain Bacillus anthracis Sterne (avirulent but toxigenic strain, producing the toxin Anthrax) were selected as model organisms. The choke point strategy was implemented on the pathogen bacterial network of B.anthracis Sterne. Potential drug targets are proposed based on the analysis of the top 10 choke points in the bacterial network. A comparative study between the reported top 10 bacterial choke points and the human metabolic network was performed. Further biological inferences were made on results obtained by performing a homology search against the human genome.

Availability: The load and choke point modules are introduced in the Pathway Hunter Tool (PHT), the basic version of which is available on http://www.pht.uni-koeln.de

Contact: d.schomburg{at}uni-koeln.de

Supplementary information: Supplementary data are available on Bioinformatics online.


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
SYSTEM AND METHODS
 ALGORITHM
 IMPLEMENTATION
 RESULTS AND DISCUSSION
 CONCLUSION
 REFERENCES
 
In the present ‘omics’ era, it becomes increasingly more obvious that network analysis is essential for the analysis of genetic, proteomics and metabolomics data (Grigorov 2005; Hartwell et al., 1999). Large-scale, graph-based mathematical models have been developed to demonstrate the intrinsic hierarchical modularity of metabolic networks (Ravasz et al., 2002) and their robustness based on the shortest path analysis of the metabolic networks (Arita, 2004; Barabasi and Oltvai, 2004; Papin et al., 2004).

A typical metabolic network consists of reactions, metabolites and enzymes, which can be modelled using graph theory (Girvan and Newman, 2002; Jeong et al., 2000; Ma and Zeng, 2003; Oltvai and Barabasi, 2002; Schuster et al., 2000). These representations lead from a simple graph consisting of edges (reactions) and nodes (metabolites) or vice versa to a complex bipartite graph where two nodes (metabolites) share a common node (reaction/enzymes) (Rahman et al., 2005). Enzyme-centric networks can be created by joining enzymes that share a common metabolite in a path. The enzyme-centric view (Horne et al., 2004; Rahman et al., 2005) simplifies the representation of the metabolic network by removing loose ends in the network (metabolites at the periphery of the network) and forming clusters of interacting enzymes. The gene-centric view has been successfully used in determining co-regulated genes in the metabolic and regulatory networks (Barrett et al., 2005; Covert et al., 2004; Levchenko 2003; Luscombe et al., 2004; Ozbudak et al., 2004).

In our previous work, an algorithm was developed to identify bio-chemically correct connectivity in the metabolic network by pruning the network based on metabolic structural similarity (Rahman et al., 2005). The output of the k-shortest path (the algorithm is described in the Supplementary Data) or alternate paths query depends on the chosen source (substrate) and destination (product) in the pathway. The network connectivity is therefore context-dependant. The concept of ‘Global’ and ‘Local’ similarity was used to find a valid connectivity in the network. The effect of metabolic structural similarity on the reported path and connectivity is very significant as this determines the abstraction level of the sub-network (Hattori et al., 2003).

In the present work we extend our analysis to the identification of ‘load points’. The ‘load points’ analysis of metabolites in a metabolic network depends on the ratio of the number of valid k-shortest path passing through the metabolites and its nearest neighbour connectivity. We believe ‘load points’ can complement other existing methods of metabolic network analysis (Croes et al., 2005; Klamt and Gilles, 2004; Ma and Zeng, 2003; Schilling et al., 1999). It provides a global view to the metabolic network activity and such information might help in the analysis of metabolic concentration data obtained from high-throughput methods like GC/MS (Fiehn et al., 2000; Strelkov et al., 2004). A global perspective reveals that certain pathways such as the citrate cycle are highly used in the cell. Most of the enzymes/metabolites in the citrate cycle of glycolysis have high ‘load’ values. The load point(s) analysis might help interpret concentration data, or flux data obtained by flux balance analysis or metabolic control analysis. Hence the importance of a metabolite in a metabolic network can be represented and ranked by this method.

Choke points are critical points in metabolic networks. Inactivation of choke points may lead to an organism's failure to produce or consume particular metabolites which could cause serious problems for fitness or survival of the organism (Yeh et al., 2004). We propose a new method to analyse choke points by screening the entire metabolic network of pathogens and report the probable choke points in the network. This extended graph theory model ranks the choke points according to the k-shortest path passing through it and the load (in/out) on it. This ranking has a major advantage as this measure may help determine the biochemical essentiality of a metabolite/enzyme (when a chokepoint enzyme is removed from the network). For example, in Plasmodium falciparum—a parasite causing malaria in humans—a host cell enzyme 4.2.1.24 [EC] (d-aminolevulinate dehydratase; ALAD) involved in heme biosynthesis was suggested as an antimalarial target (Bonday et al., 2000). This enzyme is also a choke point enzyme and identifying such potential targets in the pathogens can accelerate the drug discovery. Also all three clinically validated drug targets for malaria are chokepoint enzymes. A total of 87.5% of proposed drug targets with biological evidence in the literature are chokepoint reactions (Yeh et al., 2004).

Here we provide a generic framework and model for an automated analysis of metabolic networks by ranking the metabolites on the basis of their load point property. Load points help determine the importance of enzymes and metabolites in the biochemical network. The concept of choke points was used in our study to find potential drug targets in the metabolic network of Bacillus anthracis Sterne. The metabolites and enzymes are further ranked on the basis of their loads in the given network. A comparative study was performed between the human metabolic network and pathogen choke points to discriminate human choke points from the pathogenic bacterial choke points. A homology search was performed against human genome to find non-homologus potential drug targets from the pathogen choke points.

For building the biochemical network we used the LIGAND (Goto et al., 2002) database from KEGG (Kanehisa et al., 2004) as this data model is the backbone for the Pathway Hunter Tool (Rahman et al., 2005) in addition to BRENDA (Schomburg et al., 2004). For the predicted choke points in the pathogen we performed a homology search against the human genome using BLAST (Altschul et al., 1997).


   SYSTEM AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 SYSTEM AND METHODS
ALGORITHM
 IMPLEMENTATION
 RESULTS AND DISCUSSION
 CONCLUSION
 REFERENCES
 
Data and System
In order to demonstrate the efficiency of our algorithm we chose two microbial organisms, namely Bacillus subtilis 168 (Kunst et al., 1997) and B.anthracis Sterne (Read et al., 2002) from the KEGG database. B.subtilis is totally innocuous to man and has been widely used in scientific and industrial applications in the past. B.anthracis is a pathogen that causes anthrax, which in its pulmonary or digestive form is often lethal to humans. A comparative study of the metabolic networks of these two organisms highlights the analogies and differences between their respective pathways.

Naturally, there is sometimes more than one reaction for an enzyme in KEGG ligand database. Some of the potential reactions may be irrelevant to the organism as not all the reactions coded by an enzyme are necessarily used by the organism.

Data representation in graph theory
Using graph theory we can define the system in terms of a bipartite graph (Fig. 1), which can be reduced to an enzyme-centric graph and a metabolic-centric graph (Fig. 1). In a bipartite view, two nodes share a common enzyme and the edges define the biological relationship between a set of metabolites and enzymes. In the metabolic-centric view metabolites are nodes and reactions/enzymes are edges, whereas in the enzyme-centric view, enzymes are nodes and metabolites are edges.


Figure 1
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  		Figure 1 Bipartite view of one of the shortest paths between pyruvate and citrate in B.subtilis 168 (left). Metabolic-centric view (top-right) and enzyme-centric view (bottom-right) of the above mentioned path.

 

   ALGORITHM
TOP
 ABSTRACT
 INTRODUCTION
 SYSTEM AND METHODS
 ALGORITHM
IMPLEMENTATION
 RESULTS AND DISCUSSION
 CONCLUSION
 REFERENCES
 
Load points

Load points are defined as hot spots in the metabolic network (enzymes/metabolites) based on the ratio of number of k-shortest paths passing through a metabolite/enzyme (in/out) and number of nearest neighbour links (in/out) attached to it, compared to the average load value in the network.

For a given metabolic network, the load L on metabolite m can be defined as

Formula
where –{infty} < Lm(in/out) < {infty}, p is the number of shortest paths (in/out) passing through a metabolite m; k is the number of nearest neighbour links (in/out) for m in the network; P is the total number of shortest paths and K is the sum of links in the metabolic network of M metabolites (where M is the number of metabolites in the network). Use of the logarithm makes the relevant values more distinguishable.

 

The network model emphasizes metabolites participating in the shortest path connectivity, thus minimizing the number of less important links. Since the connectivity is based on the metabolite structural similarity, only metabolites satisfying the similarity constraints are included in the pathway (e.g. false links via ATP, ADP, etc. are excluded by the algorithm). A higher load value will result if a greater number of shortest paths pass through a node (e.g. maximum number of paths) having a minimum number of nearest neighbour connectivity (e.g. minimum number of edges). In the bio-chemical context, load points can suggest the importance of an enzyme or metabolite in a given static metabolic network of various organisms.

Choke points

Choke points are those enzymes which uniquely consume and/or produce a certain metabolite. Choke points are ranked by the number of k-shortest paths (in/out) passing through it and the load point (in/out) on it. Since it is a reasonable assumption that a large number of the biochemical reactions follow the shortest path, we assume that the shortest path count can be a good indicator of the biochemical activity.

In our graph model (Fig. 2), node 6 (metabolite) and the unique edges (enzymes) attached to it, all represent choke points. Choke points are bio-chemically essential points in the network. Thus removing a single choke point enzyme (edge between nodes 5 and 6 or 6 and 7) from the network affects the consumption or production of the metabolite(s) (e.g. node 5 or 7) attached to it.

 


Figure 2
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  		Figure 2 Metabolic-centric view of a graph model. Grey colour node (6) is a choke point (metabolite) and thinner edges adjacent to this node (enzymes) are also choke points. This figure is generated by yEd (http://www.yworks.com/).

 
In order to confer biological meaning to the graph-based approach of finding choke points, we proceeded in three steps.

Calculation of the top choke points (ranked by number incoming shortest paths) which were reported in the metabolic network of B.anthracis.

A network based comparative study of the top 10 choke points between B.anthracis and Homo sapiens was performed using Pathway Hunter Tool (PHT). ‘+’ implies that a particular enzyme acts as a choke point in the human biochemical network as well as in the pathogen whereas ‘–’ indicates that this enzyme is only a choke point in the pathogen and not in the human biochemical network.

A homology search was performed between the human and B.anthracis choke point enzymes using BLAST and chokepoints with a closest homologue with e-values <1.0e–02 were removed.


   IMPLEMENTATION
TOP
 ABSTRACT
 INTRODUCTION
 SYSTEM AND METHODS
 ALGORITHM
 IMPLEMENTATION
RESULTS AND DISCUSSION
 CONCLUSION
 REFERENCES
 
The similarity measure between the two metabolites used in our approach is based on the similarity of their molecular structures as measured by the agreement of their respective 2D molecular fingerprints (Steinbeck et al., 2003). The chosen metabolite similarity criteria (for calculating the shortest pathways) determine the range of network sizes and average degrees of the nodes for the various metabolic networks (Hattori et al., 2003; Le et al., 2004). Thus the higher the global similarity (structural similarity between substrate or source and product or sink in a pathway over a series of intermediate metabolites) and local similarity (the metabolite structural similarity between a pair of consecutive metabolites) cut-off score (Rahman et al., 2005), the smaller is the network diameter and the average degree of the nodes. In the discussed example the local similarity score was chosen as 20% and global similarity score was chosen as 10%.

A comparative study of metabolic network topology between a pathogenic and a non-pathogenic bacterium
For conducting a comparative study between B.subtilis 168 and B.anthracis Sterne metabolic network (Table 4 in Supplementary Data), we calculated shortest path distribution (Fig. 3), the average path length and average alternate paths (Fig. 5 in supplementary data). It is important to keep track of alternate paths in the metabolic network because this indicates the ability of the organism to survive in adverse conditions. Thus, blocking a path may not be lethal as organisms can switch to an alternate path performing similar conversions. Alternate paths can be bio-energetically costlier or longer than the native pathway. Hence organisms may slow down their metabolic activity, yet can survive.


Figure 3
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  		Figure 3 Shortest path distribution in B.subtilis 168 and B.anthracis Sterne.

 

   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 SYSTEM AND METHODS
 ALGORITHM
 IMPLEMENTATION
 RESULTS AND DISCUSSION
CONCLUSION
 REFERENCES
 
A comparative study of metabolic pathways based on shortest path analysis reveals the metabolic network topology of B.subtilis and B.anthracis. In our opinion, analysing the metabolic network based on shortest path is preferable to a full path analysis as on average, shorter paths should be used more often than longer paths. (This is not always true as the free-energy changes on the different paths have to be taken into account. However in the absence of that information it is a sound assumption.)

B.subtilis and B.anthracis have the same network diameter and the same average degree distribution of ~3.0 (average connectivity) and also approximately the same number of reactions. However, their average path lengths are different, suggesting that the underlying topology in both the bacterial networks must be different.

The key for an organism to survive under extreme conditions is characterized by the ability to change and adapt its metabolic activity accordingly. Hence organisms may activate alternate pathways which may be either longer in terms of reaction steps or bio-energetically costlier. Thus alternate paths are representative of the pathway stability and bio-chemical activity. A contrast in the topological behaviour between the selected model organisms is presented in Figure 5 (Supplementary Data) where a shift in the average alternate path in both the organism is observed. B.subtilis has a greater number of alternate paths between path lengths 18 and 25 whereas B.anthracis has more alternate paths at path lengths between 10 and 15. This may have biological significance/implications and further research is warranted on such behaviour (alternate paths) and topological patterns occurring in metabolic networks.

Load point analysis of metabolic networks between a pathogenic and a non-pathogenic bacterium
We identified the top 10 metabolite load points (the top ‘10’ load points were chosen purely for convenience—both of presentation and of comprehensibility) in both organisms. The loads on the metabolites differ between the two bacterial networks (Tables 1 and 2). Most of the metabolites that occur in the list of top 10 load points in pathogenic bacteria B.anthracis Sterne (bat) do not match with the load points in non-pathogenic bacteria B.subtilis 168 (bsu).


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  		Table 1 Top 10 Metabolite load points based on incoming load value in Bacillus subtilis 168 (bsu) and Bacillus anthracis Sterne (bat)

 

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  		Table 2 Top 10 Metabolite load points based on outgoing load value in Bacillus subtilis 168 (bsu) and Bacillus anthracis Sterne (bat)

 
For example, there is no reaction which can produce Cystathionine in B.anthracis Sterne whereas this metabolite seems to be a hot spot in B.subtilis 168 (Table 1). Cystathionine is involved in the ‘sulphur and methionine metabolic pathway’ of the non-pathogenic bacteria B.subtilis. Cystathionine is a product of the enzyme cystathionine gamma-synthase (2.5.1.48 [EC] ) whose substrate is O-Succinyl-L-homoserine and it is a substrate for the enzyme cystathionine beta-lyase (4.4.1.8 [EC] ) whose product is L-Homocysteine. Since the enzyme cystathionine gamma-synthase (2.5.1.48 [EC] ) according to the annotated pathway is not present in pathogenic bacteria Bacillus anthracis there is no way to produce this metabolite. There is an alternate path to convert O-Succinyl-L-homoserine into L-Homocysteine in Bacillus anthracis.

Analysing the degree (connectivity) of metabolites and its load in both bacterial organisms (Fig. 4) suggests that their network has a more or less similar degree distribution but the load points vary in the networks. As shortest paths are calculated on the basis of metabolite structural similarity, load values also suggest the demand for certain metabolic structures in the network. The distribution of mean load (incoming) of metabolites versus the degree (incoming links) suggests that some highly connected metabolites have high load in the network. Our calculations show that the load (determined by global network properties) and the connectivity (representing a local property of the network) are positively (though weakly) correlated [rbsu (706) = 0.49, p < 0.0001; rbat (704) = 0.47, p < 0.0001). However the graph in Fig. 4 suggests that even non-hub metabolites can have high load values (high variance as seen in Table 5 of the Supplementary Data) and they can be bio-chemically as important or even more important in the network, as compared with the hubs. It can thus be inferred that greater connectivity may lead to robustness in the network but does not support the functionality assignment (Guimera and Nunes Amaral, 2005; Mahadevan and Palsson, 2005).


Figure 4
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  		Figure 4 Average load (IN) on metabolites versus connectivity (IN) of metabolites in the metabolic network of the selected bacterial genome.

 
As an illustration, In B.anthracis, Formamidopyrimidine nucleoside triphosphate (C10H18N5O15P3), which is a non-hub metabolite has an incoming load value of 2.02 (high) and incoming connectivity as 1 (low) whereas pyruvate—a hub—has an incoming load value of 1.45 (high) and incoming connectivity of 15 (high). Thus, though metabolite connectivity defines the network robustness, this information is not sufficient to rank the importance of metabolites in the network. In this respect ‘load points’ provide a more global biochemical measure of metabolic activity than the ‘local’ connectivity analysis. The load on metabolites/enzymes can differ from organism to organism and this can be a sound measure for deciphering the underlying metabolic topology of various organisms.

Load point analysis and metabolic concentration data
The experimental parallel determination of 100–500 metabolite concentrations has recently become possible and provides a highly sensitive phenotype characterization (Fiehn, 2002; Schauer et al., 2005; Strelkov et al., 2004). We rank the activity of different metabolites based on the load points. First, the incoming and outgoing path for a participating metabolite in an organism can differ within itself and consequently, so can their ranking (Tables 1 and 2).Second, the incoming load (Table 1) and outgoing load (Table 2) for metabolites between pathogenic (B.anthracis) and non-pathogenic (B. subtilis) bacterial systems is different. Higher load value may hint towards an active or hot spot reaction, whose optimization (minimization/maximization) may lead to a change in solution space implying a change in biochemical activity. This indeed could be seen in the case of the citrate cycle where most of the enzymes/metabolites have high load values. This phenomenon could be very helpful for interpreting metabolic concentration data and results obtained from other metabolic engineering methods. Load point analysis can complement the analysis of metabolic networks at the level of connectivity and metabolic concentration data

The importance of enzymes with a high load as determined by our method was verified experimentally. The enzyme shikimate dehydrogenase (EC 1.1.1.25 [EC] ) in Corynebacterium glutamicum was calculated to have the sixth-highest load and at the same time represented a choke-point. A knock out of this enzyme in the mutant resulted in severe repression of growth (Suma Choorapoikayil, Sebastian Buchinger, Jan Schoepe, Dietmar Schomburg, Unpublished data)

Choke point analysis in B.anthracis—a pathogen
Drug target identification based on ‘omics’ networks (di Bernardo et al., 2005; Giaever et al., 2004; Holzhutter and Holzhutter, 2004; Yeh et al., 2004) is a very promising approach that has only recently become possible. The concept of choke points (Dawson and Elliott, 1980) in a given network contributes effectively in identification of the lethality/bottleneck (here potential drug targets) in a network. Since a high load on a certain enzyme means that a large number of shortest paths go through it and therefore indicates a position in the central metabolism, we assume that ranking choke points on the basis of load will move enzymes with a higher probability of biochemical lethality to the top of the candidate list. A comparative study of choke points with the human metabolic network is essential to identify possible interference of the drugs with the human metabolism which might lead to side effects. It has to be kept in mind though that presently a large number of genes have unidentified functions which could affect erroneous prediction of choke points.

Often drug targets are identified by a unique pathogen-specific metabolic activity, as in the case of reverse transcriptase in the case of HIV (Imamichi, 2004). However, the screening of the entire metabolic network of the pathogen to find choke point-based potential drug candidates followed by a comparative study with human metabolic network provides additional targets. Examples are the anti-malarial drugs (Sixsmith et al., 1984) pyrimethamine and cycloguanil targeting a choke point enzyme dihydrofolate reductase (1.5.1.3 [EC] ) (also a human homologue) in P.falciparum with some side effects on humans but lethal to the parasite.

An analysis of the top 10 choke points (the top ‘10’ choke points were chosen purely for convenience—both of presentation and pomprehensibility) in B.anthracis, a pathogen, is presented (Table 3). In Table 3 a number of possible drug targets against infection of B.anthracis are identified. We found that the enzymes tryptophan synthase (EC: 4.2.1.20 [EC] ) and anthranilate phosphoribosyltransferase (EC: 2.4.2.18 [EC] ) could be effective potential drug targets. Neither of these enzymes are choke points in the human metabolic network nor do they share a significant homology with the human genome (Table 3). This means that blocking these enzymes might affect the pathogen but not the human as there exists an alternate pathway.


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  		Table 3 A comparative study of top 10 choke points in Bacillus anthracis Sterne against the Homo sapiens metabolic network

 
The approach presented in this article may contribute to the first identification of potential target enzymes for rational drug design. However, it must be noted that the absence of complete pathway information may lead to false identification of choke points. Additional computational, biological and/or experimental methods or data will further narrow down the list of potential drug targets.


   CONCLUSION
TOP
 ABSTRACT
 INTRODUCTION
 SYSTEM AND METHODS
 ALGORITHM
 IMPLEMENTATION
 RESULTS AND DISCUSSION
 CONCLUSION
REFERENCES
 
Our results highlight the local and global properties of complex biological metabolic networks. Thus the load (in/out) of metabolites is a more global indicator of their importance, as compared with mere connectivity information. The network model and algorithm presented can process the information contained in the topology of the metabolic network and extract knowledge about the function, role and importance of the metabolites in a network. The extended graph-based choke point concept can facilitate drug discovery and ranking choke points based on their load values may be a likely pointer to the lethality level of such potential drug targets in the network. Further study and comparative analysis of various metabolic networks based on our network model can be beneficial for in vivo and in vitro studies. As a note of caution we would like to add that presently such an analysis is limited by the limited accuracy and completeness of pathway annotations and by the lack of knowledge of the proteins actually present in a certain state of the cell.

The algorithm described has been implemented in the Pathway Hunter Tool (PHT) with the aim of identifying enzymes for potential drug targets and designing synthetic networks with highly specialized metabolic functions.


   Acknowledgments
 
S.A.R. would like to acknowledge Professor Rainer Schrader (ZAIK, Cologne, Germany) for his encouragement and fruitful discussions. The authors are grateful for the financial support from the German Federal Ministry for Education and Research (BMBF).

Conflict of Interest: none declared.


   FOOTNOTES
 
Associate Editor: Alfonso Valencia

Received on August 9, 2005; revised on May 3, 2006; accepted on May 4, 2006

   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 SYSTEM AND METHODS
 ALGORITHM
 IMPLEMENTATION
 RESULTS AND DISCUSSION
 CONCLUSION
 REFERENCES
 

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