=Paper=
{{Paper
|id=None
|storemode=property
|title=Construction of Enzyme Network of Arabidopsis Thaliana Using Graph Theory
|pdfUrl=https://ceur-ws.org/Vol-758/paper_15.pdf
|volume=Vol-758
}}
==Construction of Enzyme Network of Arabidopsis Thaliana Using Graph Theory==
https://ceur-ws.org/Vol-758/paper_15.pdf
Construction and Analysis of Enzyme Centric Network
of A. thaliana using Graph Theory
Kasthuribai Viswanathan1, Nita Parekh 1
1Center for Computational Natural Science and Bioinformatics,
International Institute of Information Technology, Hyderabad - 500032, India
kasthuribai.vpg08@research.iiit.ac.in, nita@iiit.ac.in
Abstract. Graph comparisons, quantitative characterizations, computation of
topological indices, clustering and partitioning are some of the major computations of
graph that have yielded valuable results in various disciplines. Motivated by the
potential benefits of graph theory application on biological data, we discuss the
reconstruction and analysis of enzyme centric network of Arabidopsis thaliana using
graph theory concepts. We had earlier constructed the metabolite network of
Arabidopsis thaliana and witnessed the scale free and small world nature of the
network. Compared to metabolites, the enzymes are more conserved in and across
many pathways. So the aim of constructing the enzyme centric network is to see if the
network follows similar network properties of the metabolite network and to look for
additional details that a metabolite network cannot reveal. The enzyme flat file from
KEGG FTP is used as the data set for the reconstruction of the enzyme centric
network. We examined the network to find the relationship between topological
connections among enzymes and their functions during evolution. The enzyme
sequences of high degree and high betweenness enzymes belonged to ancient fold
class and ancestry value showing evidence that they evolved very slowly.
Keywords: metabolic pathways; graph theory; enzyme network; modularity;
centrality measures.
1 Introduction
Metabolism is one of the most complex cellular processes. Connections between the
biochemical reactions are represented as series of metabolic reactions which
constitute the metabolic pathways. These pathways are used by researchers for the
molecular evolution studies. Most studies of molecular evolution are focused on
individual genes and proteins. The most interesting challenge in systems biology is
constructing such biological networks and trying to interpret the hidden evolutionary
details. The correlations that the researchers draw out in linear pathways are not
highly visible and can emerge when analyzed as a whole network. We had previously
developed a metabolite network from Arabidopsis thaliana pathway data using
reaction files from the KEGG FTP. The metabolite network exhibited the small
world, scale free nature and showed hierarchical organization. But the metabolite
network is not very suitable for evolutionary analysis due to reasons like the
metabolites are less conserved compared to the enzymes in pathways. Also, the
number of enzymes is smaller compared to the number of metabolites enabling a
closer look of the interactions.
The enzyme centric network is constructed with enzymes catalyzing the reactions as
the vertices of the graph and the edge drawn between them if they one or more
metabolites. Thus, an edge is drawn from an enzyme E1 to an enzyme E2 if E1
catalyzes a reaction in which compound A is the product and E2 consumes A, that is,
it is a reactant in the second reaction [1]. For simplification of the network analysis,
we assume that reactions are reversible and therefore each link or enzyme-enzyme
relation in the network is undirected (bidirectional). For reconstruction of the enzyme
centric network, the Enzyme flat file in the KEGG FTP is used as raw data. In order to
include only functional relationships in the calculation of the enzyme connectivity, we
excluded the 18 highly connected metabolites and co-factors. The enzyme network is
then analyzed using Pajek, the network analysis tool, and various network properties
such as degree, betweenness, etc. have been computed using this tool [2].
The degree of a node in a network is the number of connections or edges the node
has with other nodes. The degree distribution of the A.thaliana enzyme network
construction shows that a few nodes have high degree and most of the nodes have
low degree revealing the scale free nature. It would be interesting to investigate role
of high-degree nodes in the evolution of the organism. The enzyme centric network
exhibits modular architecture suggesting clusters of interacting enzymes. The
enzymes having high betweenness values are observed to be relating different
pathways and an analysis of the corresponding gene/protein sequences can help in
assessing its age and conservation across species.
2 Materials and Methods
2.1 Dataset
The KEGG database is designed in a way to facilitate understanding of higher-order
protein and cellular functions using genomic and molecular information. The main
reason for choosing the pathways information from KEGG is because it is open
source and free to academic users and the enzyme data is available as a single flat file
format for easy processing. The enzyme flat file used for the analysis has been
downloaded from KEGG FTP [3]. Each enzyme has details on the genes, organisms,
reactants, products, references, etc.
2.2 Construction of Enzyme Centric Network
The flowchart in Figure 1 explains the steps in the reconstruction of enzyme network
starting with the enzyme flat file obtained from KEGG FTP. The enzyme flat file is a
complete listing of all the known enzymes with an enzyme commission name (EC) and
is delimited with “///” (Fig. 1). A total of 5391 enzymes are listed in this file. It is not an
organism specific file, hence A. thaliana specific enzymes need to be extracted by
parsing this file. This was done by first splitting this single file into 5391 separate files
with enzyme name as the file name. Each of these files consisted of all the relevant
information such as the enzyme name, synonyms, class, reactants, products, organisms
and gene for each enzyme and references. This format was chosen to simplify
computational processing and to minimize data duplication and extract only A. thaliana
specific enzymes. Next only those enzyme files which have “ath” in the organism names
list were extracted; a total of 3277 enzymes were identified to be A. thaliana specific and
used for constructing the network.
Fig. 1. Flow chart for the construction of enzyme-centric network.
The next step was to extract reactant and product information corresponding to every
reaction catalyzed by an enzyme. Scripts were developed to automate the extraction
process from each file, and a number of problems were addressed, such as removing
incomplete and redundant reactants and products. The metabolite name had many
synonyms, for example, NADH-glyoxylate reductase, glyoxylic acid reductase, and
NADH-dependent glyoxylate reductase are all synonyms of glyoxylate reductase. So we
replaced all the metabolite names with the KEGG metabolite ID and so the synonyms of
the metabolite are not considered as a new metabolite to the list Fig. 1). Removing the
most abundant substrates, called “currency metabolites” was the second processing step
in the resonstruction of the network. Differentiating the currency metabolite from the
primary metabolite is troublesome. For example, Glutamate (GLU) is a current
metabolite for transferring amino groups in many reactions, but in the following reaction
it is defined as a primary metabolite:
AKG + NH3 + NADPH = GLU + NADP+ + H2O
Fig. 2. The enzyme centric network of Arabidopsis thaliana visualized in Pajek. The circular balls
represent the nodes (enzymes) and the lines represent the edges (metabolites catalyzed by the
enzyme). The distribution of the connection is heterogeneous with few nodes very densely
connected and few with only a single connection.
Jeong et al. (2000) ranked the metabolites according to their connection degree. Based
on their analysis, the metabolites C00001 to C00018 (ATP, H, H20, ADP, H202,
pyrophosphate, orthophosphate, CO2, NAD, glutamate, NADP, NADH, NADPH,
AMP, NH3, and CoA) were labelled as currency metabolites that occurred multiple
times in most of the reactions [4]. We removed these metabolites during our
construction of the enzyme network. To compare enzymes that catalyze the reactants
with the enzymes that catalyze products they share, we wrote perl scripts that split each
enzyme file into two files, listing reactants and products respectively. and enzyme
product. For example, 1.1.1.1_reactant file contains all the reactants that take part in the
reaction catalyzed by enzyme 1.1.1.1. The file 1.1.1.1_product contains the products of
the reaction catalyzed by 1.1.1.1. Now each enzyme product file is compared with all the
enzyme reactant files to find the number of reactants and products that exactly matched.
A file containing the pair of enzymes and the number of shared reactants and products
between them is listed and those that never shared any reactants or products were
removed because product in the enzyme product file, say, EPi, is present in the enzyme
reactant file as product, ERj, then a link is formed between the enzymes catalyzing the
two reactions, Ei and Ej [5]. The edge list of the interacting enzymes is thus constructed.
Each node is labeled with an EC number. The enzyme network of Arabidopsis thaliana
thus constructed is shown in Fig. 2. From the 5391 enzyme files, the number of files
drops to 507 Arabidopsis thaliana specific enzyme files. The enzyme network has 502
enzyme nodes. There are 4950 metabolites that utilize these enzymes in the network.
3 Results and Discussion
The analysis of the enzyme centric network constructed as discussed in the
above section was carried out. It is clear from Fig. 2 that the enzyme network of A.
thaliana is not a random network and a clear clustering of nodes is observed. In Table 1
is summarized the global properties of the network. The diameter of the network,
which is the largest distance between two nodes, is 8. The low diameter reveals that
the information flow between the enzymes is faster which means that the reactions
are very closely connected. The average path length is 2.9. The low value of average
path length means every node is close to all of the others in the network, they can
reach others quickly without going through too many intermediaries.
Table 1. Global Properties of Enzyme Network
Number of Nodes 502
Number of Edges 4950
Clustering Coefficient 0.47
Diameter 8
Average path length 2.9
3.1 Scale free Nature of Arabidopsis thaliana Enzyme Centric Network
The degree distribution P(k) gives the fraction of nodes that have degree k and is
obtained by counting the number of nodes N (k) that have k = 1, 2, 3,… edges and
dividing it by the total number of nodes N. From the degree distribution graph in Fig.
3, it is clear that the A. thaliana enzyme network exhibits power law behavior
(Fig. 3(a)), revealed by the straight line on a logarithmic plot (Fig. 3(b)). This
indicates the ‘scale free nature’ of the enzyme network [6]. That is, a high
heterogeneity in the degree of the nodes is observed, critically influencing the
topological properties of the network. Following Barabasi-Albert algorithm of
preferential growth model, the power-law behavior of enzyme network proposes that,
during evolution, new nodes tend to attach preferentially to well connect
network nodes. As a consequence, the nodes having high degree are likely to be
ancient enzymes.
Fig. 3. Degree distribution of the enzyme network plotted both on linear and logarithmic scale.
The degree distribution of the scale-free network follows the power law P (k) = Ak-1.26, which
appears as a straight line on a logarithmic plot.
3.2 Analysis of High Betweenness Enzymes
The betweenness of a node v is defined as the number of shortest paths going through
that node:
1
CB ( v ) = ∑ g st ( v ) / g st
( V − 1)( V − 2) s ≠ v ≠ t∈V
where V is the set of nodes and |V| represents the number of nodes in V; gst is the
number of shortest paths from node s to node t; gst (v) is the number of shortest paths
from node s to node t lying on node v. The nodes connecting pathways are critical
and their removal can have a deleterious effect on the stability of the network. Such
nodes can be identified by an analysis of their betweenness value. Enzymes that
connect pathways do have relatively high betweenness value. This reflects the central
role that such enzymes play in relaying metabolites from one enzymatic reaction to
another. The differences in the amino acids of the encoded protein (nonsynonymous
changes) and some, because of the degeneracy of the genetic code, leave the amino
acid unchanged (synonymous or silent changes). Counting up the number of each
gives us a measure of the amount of change of the sequence. Chiaoquan Qi has
shown that a negative correlation between Ka/Ks (non-synonymous/synonymous
substitutions) and betweenness of an enzyme, providing clear evidence that high-
betweenness enzymes evolve slowly [7] .
In Table 2 are listed top 10 enzymes with high betweenness values. These are highly
central in the network as most of the reactions are catalyzed by these enzymes. These
high betweenness enzymes belong to transferases that help in transfer of a functional
group, oxidoreductases that catalyzes the transfer of electrons from one molecule,
and hydrolases which hydrolysis a chemical bond. Theoretically these enzymes are
more important as all the pathways involve reactions that help in transferring
functional groups by breaking bonds.
Table 2. Top Ten Enzymes with High Betweeness values in the Network
Betweenness
Enzyme Enzyme Name Enzyme Class
Values
2.3.3.8 ATP citrate synthase 48571.2 Transferase
2.4.2.17 ATP phosphoribosyltransferase 47192.5 Transferase
2.3.3.8 ATP citrate synthase 46350.1 Transferase
Glutamate-5-semialdehyde
1.2.1.41 34695.7 Oxidoreductases
dehydrogenase
3.6.1.1 Hydrolases 22370 Hydrolases
3.3.1.1 Adenosylhomocysteinase 18708.4 Hydrolases
3.1.3.16 Phosphoprotein phosphatase 18333.2 Hydrolases
1.11.1.6 Catalase 18316.4 Oxidoreductases
1.7.7.1 Oxidoreductases 16426.6 Oxidoreductases
3.3 Enzymes with degree one
In the enzyme centric network of A. thaliana, there are 136 nodes with degree one.
These enzymes are catalysis just a single reaction. These are referred to as choke
points. A “chokepoint reaction” is a reaction that either uniquely consumes a specific
substrate or uniquely produces a specific product. Enzymes associated with high
damage are involved in the production of compounds of small connectivity that
connect important parts of the metabolism. 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. We listed ten degree one
enzymes in the Arabidopsis enzyme network is shown in Table 3. We show only top
ten of them for convenience and comprehensiveness.
Table 3. List of Degree One Enzymes in Arabidopsis thaliana Enzyme Network
Enzyme ID Enzyme Name
1.10.2.2 ubiquinol---cytochrome-c reductase
1.1.1.1 alcohol dehydrogenase
1.15.1.1 superoxide dismutase
1.1.5.3 glycerol-3-phosphate dehydrogenase
methylmalonate-semialdehyde
1.2.1.27
dehydrogenase
1.2.4.1 Pyruvate dehydrogenase
1.2.4.4 3-methyl-2-oxobutanoate dehydrogenase
1.3.3.3 coproporphyrinogen oxidase
phytochromobilin:ferredoxin
1.3.7.4
Oxidoreductases
1.3.99.3 acyl-CoA dehydrogenase
3.4 Enzyme Evolution
The earliest enzymes were probably weakly catalytic and multifunctional and
specific new enzymes should have evolved through gene duplication, mutation and
divergence. As enzymatic pathways became more complicated, new enzymatic
function could have been generated by recruitment of individual enzymes from the
same or different pathways. The age of metabolic enzymes and the evolution of their
metabolism with phylogenetic analysis are interesting. Since the network is scale
free, it follows preferential attachment of nodes. The preferential attachment means
that new nodes attach to a growing network by connecting to nodes with existing
high connectivity. Nodes with high connectivity are therefore often those that have
been in the network for a very long time [8]. Thus, enzymes appearing in the early
stages of evolution tend to be found more frequently in different organisms (e.g.
those involved in glycolysis) and that much of the metabolism of current species is
based on the products of those enzymes.
This implies that evolutionarily early enzymes tend to have more connectivity to
other enzymes or metabolites. The high degree enzymes in the enzyme network
should therefore be highly conserved and should belong to primitive class of
enzymes. In Molecular Ancestry Network database (MANET) a method the
evolutionary scale of enzymes is computed using information in the Structural
Classification of Proteins (SCOP) database[9]. MANET traces evolution of protein
architecture in bimolecular networks by linking information in the Structural
Classification of Proteins (SCOP), the Kyoto Encyclopedia of Genes and Genomes
(KEGG), and phylogenetic reconstructions depicting the evolution of protein fold
architecture. In MANET, the phylogenetic tree drawn for all the enzymes in KEGG
and the phylogenetic distance is defined as the ancestry value. Table 4 shows the list
of top ten high degree enzymes and their ancestory value predicted by MANET from
a scale of (0-1), where the values closer to zero means they are older enzymes. It also
shows the enzyme fold class and the PDB id of the enzyme structure. Most of the
enzymes with high degree have an ancestory value closer to zero and belong to
ancient fold class, proving that they are highly conserved and are older enzymes.
Table 4. Enzyme Ancestry value for the Top Ten Degree Enzymes in the Enzyme Network
Ancestry
Enzyme Degree Fold class PDB
Value
1.11.1.6 Catalase 113 0.0314 c.23.16.3 1SY7
2.3.3.8 ATP citrate synthase 111 0.0188 c.1.12 NA
3.5.1.5 Urease 106 0.0188 c.1.9.2 4UBP
4.2.1.52 Dihydrodipicolinate
102 0.0188 c.1.10.1 1S5W
synthase
1.2.1.41 Glutamate-5-
101 0.213 c.82.1.1 1VLU
semialdehyde dehydrogenase
4.1.1.31 Phosphoenolpyruvate
101 0.0188 c.1.12.3 1QB4
carboxylase
4.2.1.11 Phosphopyruvate
101 0.0188 c.1.11.1 7ENL
hydratase
1.9.3.1 Cytochrome-c oxidase 101 0.088 a.118.11.1 2OCC
3.1.3.16 Phosphoprotein
101 0.088 a.118.8.1 1A17
phosphatase
4.2.1.9 Dihydroxy-acid
100 0.0188 c.37.1 NA
dehydratase
3.6.1.1 inorganic diphosphatase 93 0.044 b.40.5.1 8PRK
2.4.2.17 ATP
67 0.0125 d.58.5.3 1Q1K
phosphoribosyltransferase
3.3.1.1 Adenosylhomocysteinase 66 0.025 c.2.1.4 1V8B
4 Conclusion
Here we have reconstructed and analyzed the enzyme centric network of Arabidopsis
thaliana using information available in the KEGG metabolic pathway data. The
scale-free behavior of the enzyme network of A. thaliana suggests that suggests that
during evolution new nodes tend to attach preferentially to a few ancient nodes.
This possibly indicates that enzymes (nodes) with very high-degree are likely
to be very ancient, which is further confirmed by the analysis of high degree
nodes. Our preliminary analysis of betweenness centrality measure suggests that
apart from high-degree nodes, nodes having high betweenness values are also very
crucial for the stability of the network, and these are typically enzymes catalyzing
reactions that connect pathways, or are involved in catalyzing important reactions
such as those transferases that help in transfer of a functional group, oxidoreductases
that catalyzes the transfer of electrons from one molecule, etc.
5 References
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biological complexity, BMC Syst Biol, vol. 2, p. 70, (2008).
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York: Cambridge University Press, (2005).
[3] ftp://ftp.genome.jp/pub/kegg/ligand/enzyme/enzyme, Kyoto Encyclopedia
of Genes and Genomes
[4] H. Jeong, et al., The large-scale organization of metabolic networks, Nature,
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[7] Chiaoquan Qi, Genes encoding hub and bottleneck enzymes of the
Arabidopsis metabolic network preferentially retain homeologs through
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[8] B. S. Hartley, Evolution of enzyme structure, Proc R Soc Lond B Biol Sci,
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