J. Biomedical Science and Engineering, 2010, 3, 931-941 JBiSE
doi:10.4236/jbise.2010.310124 Published Online October 2010 (http://www.SciRP.org/journal/jbise/).
Published Online October 20 10 in SciRes. http://www.scirp.org/journal/jbise
Comparative analysis of various modularization algorithms
and species specific study of VEGF signaling pathways
Namrata Tomar, Losiana Nayak, Rajat K. De
Machine Intelligence Unit, Indian Statistical Institute, Kolkata, India.
Email: namrata_t@isical.ac.in; losiana_t@isical.ac.in; rajat@isical.ac.in
Received 24 August 2009; received 9 September 2009; accepted 30 August 2010.
In biology, signal transduction refers to a process
by which a cell converts one kind of signal or sti-
mulus into another. It involves ordered sequences of
biochemical reactions inside the cell. These cas-
cades of reactions are carried out by enzymes and
activated by second messengers. Signal transduc-
tion pathways are complex in nature. Each pathway
is responsible for tuning one or more biological
functions in the intracellular environment as well as
more than one pathway interact among themselves
to carry forward a single biological function. Such
kind of behavior of these pathways makes under-
standing difficult. Hence, for the sake of simplicity,
they need to be partitioned into smaller modules
and then analyzed. We took VEGF signaling path-
way, which is responsible for angiogenesis for this
kind of modularized study. Modules were obtained
by applying the algorithm of Nayak and De (Nayak
and De, 2007) for different complexity values. These
sets of modules were compared among themselves
to get the best set of modules for an optimal com-
plexity value. The best set of modules compared
with four different partitioning algorithms namely,
Farhat’s (Farhat, 1998), Greedy (Chartrand and
Oellermann, 1993), Kernighan-Lin’s (Kernighan
and Lin, 1970) and Newman’s community finding
algorithm (Newman, 2006). These comparisons en-
abled us to decide which of the aforementioned al-
gorithms was the best one to create partitions from
human VEGF signaling pathway. The optimal com-
plexity value, on which the best set of modules was
obtained, was used to get modules from different
species for comparative study. Comparison among
these modules would shed light on the trend of de-
velopment of VEGF signaling pathway over these
Keywords: Signal Transduction Pathway, VEGF Path-
way, Complexity Value, KEGG Database, Modulariza-
tion, Newman’s Community Finding Algorithm, Ker-
nighan-Lin’s Algorithm, Farhat’s Algorithm, and Greedy
The ability of cells to receive and act on signals from
beyond the plasma membrane is fundamental to life.
This ability of cells to respond correctly to their micro-
environment is the basis of development, tissue repair,
immunity and normal tissue homeostasis. Cells respond
to their environment by recognizing their structure, re-
gulating the activity of proteins and finally by altered
gene expression. The stimulus for such type of responses
is known as signal. Signals interact with the responding
cell through molecules, called receptors [1]. For example,
cells receive constant input from membrane proteins that
act as information receptors, sampling the surrounding
medium for pH, osmotic strength, and the availability of
food, oxygen and light and the presence of noxious
chemicals, predators or competitors for food. These sig-
nals elicit appropriate responses like motion towards
food or away from toxic substances [2]. In multi-cellular
organisms, cells with different functions, exchange a
wide variety of signals. For example, plant cells respond
to growth hormones and to variations in sunlight. Ani-
mal cells exchange information through the concentra-
tions of ions and glucose in extra-cellular fluids, the in-
terdependent metabolic activities, taking part in different
tissues, and in an embryo, the correct placement of cells
during development. So, we can get the concept that in
all the cases, signal represents information that is de-
tected by specific receptors and converted to a chemical
process. This conversion of information into a chemical
change or signal transduction is a universal property of
living cells. Errors in cellular information processing are
responsible for diseases such as cancer, autoimmunity
and diabetes. By understanding cell signaling, diseases
may be treated effectively. Systems biology research
helps us to understand the underlying structure of cell
N. Tomar et al. / J. Biomedical Science and Engineering 3 (2010) 931-941
Copyright © 2010 SciRes. JBiSE
signaling networks and how changes in these networks
may affect the transmission and flow of information.
Signal transduction is specific and exquisitely sensi-
tive [2]. In unicellular organisms, signals are of envi-
ronmental origin and diffusible in nature. Signals, in
metazoans, are paracrine (e.g. neurotransmitters); they
release from the nearby cells and diffuse over short dis-
tances. In the case of endocrine signals (e.g. hormones),
they may be released from distant cells and vascular
system sends them to their targets. Macromolecular sig-
nals are associated with the extra-cellular matrix or on
the surface of the neighboring cells, and they are called
juxtacrine signals. It requires two adjacent cells to make
physical contact in order to communicate. Some cells
require direct cell-cell contact; others form gap junctions
to connect to the cytoplasm of other cells’ cytoplasm for
communication. A molecular signal that binds to a re-
ceptor is a ligand. As signaling pathway is made up of
many different input and output nodes that make it,
complex network, it is difficult to study and analysis. So
the idea to divide it into small bio-significant modules,
through the process called modularization came into
light. A module is a subset of the original pathway,
which has minimal dependency on the rest part of the
network [3]. Here, the idea is to divide a pathway in
such a way that the complexity of resulting modules is
much less than that of the entire pathway, which pro-
vides an easier way to study the entire pathway. Many
methods are developed to divide a network into smaller
Here, we considered Vascular Endothelial Growth
Factor (VEGF) pathway for applying different partition-
ing algorithms. It has a receptor, i.e., VEGFR, which is
activated by ligand. Ligand binding to the receptor leads
to receptor homodimerization or heterodimerization.
Dimerization of receptors leads to their activation and
subsequent autophosphorylation on certain tyrosine re-
sidues. It has many types of receptors. The receptors for
vascular epithelial growth factor (VEGF) and related
ligands are VEGFR-1 (Flt-1), VEGFR-2 (KDR/Flk-1),
VEGFR-3 (Flt-4), neuropilin-1 and neuropilin-2. The
interaction of VEGFR with either neuropilin-1 (NRP-1)
or heparan sulfate proteoglycan helps in binding VEGF
to its receptor. These receptors have multiple immu-
noglobulin G-like extra-cellular domains and intracellu-
lar tyrosine kinase activity. The human gene for VEGF
resides on chromosome 6p21. The coding region spans
14 kb and contains eight exons. Alternative splicing of a
single pre-mRNA generates several distinct VEGF spe-
cies. There are several splice variants of VEGF, like
VEGF 121, 145, 165, 189, and 206. Among them, VEGF
165 is the predominant form [4]. VEGF family has other
members also. These are VEGF-B, -C, and -D, and Pla-
cental Growth Factor (PlGF). VEGF binds to VEGFR-1
and 2, and triggers angiogenesis.
PlGF is localized to the placenta and binds only to
VEGFR-1. VEGF-B also binds only to VEGFR-1, and
has function in coronary vascularization and growth.
VEGF-C and VEGF-D activate VEGFR-2 and -3 but not
VEGF-1. VEGF-C is involved in lymphangiogenesis.
The function of VEGF-D is unknown [5]. For activation
of the signaling pathway, VEGF binds to at least two
transmembrane Flt-1 (VEGF receptor-1) and Flk-1/KDR
(VEGF receptor-2). Both these are tyrosine kinase re-
ceptors. This results in tyrosine phosphorylation, and
activation of phosphatidylinositol 3-kinase (PI3K) and
phospholipase Ca2+ (PLC-γ). PLC-γ forms two mole-
cules, Diacylgylcerol (DAG) and Inositol (1, 4,
5)-trisphosphate (IP3). These two further activate PKC
and release Ca2+. PI3K activates Akt. PKC, calcium and
Akt activate endothelial Nitric Oxide Synthase (eNOS).
It releases NO that is responsible for vasodilation and
increased vascular permeability. The role for PLC-γ,
PKC, calcium and NO in VEGF-induced hyper perme-
ability has been confirmed in isolated coronary venules,
and the involvement of PI3K/Akt and NO was demon-
strated in human umbilical vein endothelial cell (HU-
VEC) monolayer [6]. Further, it also triggers intracellu-
lar signaling cascade that are able to recognize and dock
at phosphorylated tyrosine residues of the activated re-
ceptors. These interactions are mediated by Src, phos-
phatidylinositol 3-kinase (PI3K), Shc, Grb2, and the
phosphates SHP-1 and SHP-2 and other domains of the
signaling proteins.
VEGF receptor activation can induce activation of the
MAPK cascade via Raf stimulation. It leads to gene ex-
pression and cell proliferation. Activation of PI3K leads
to PKB activation and cell survival; activation of PLC-γ
leads to cell proliferation, vasopermeability and angio-
genesis. VEGF regulates several endothelial cell func-
tions, including proliferation, differentiation, permeabil-
ity, vascular tone and the production of vasoactive mo-
lecules [5]. H. sapiens VEGF pathway taken from
KEGG database is given in Figure 1.
The organization of this article is as follows. The next
section describes the methodology of algorithm of
Nayak and De in detail, and then introductory descrip-
tion of Kernighan-Lin’s, Farhat’s, Greedy and Commu-
nity finding algorithms has been given. After that, we
provide results in which we analyzed output got through
implementing different partitioning algorithms. Species’
evolution based comparison has also been done over the
modules got through applying the algorithm of Nayak
and De.
N. Tomar et al. / J. Biomedical Science and Engineering 3 (2010) 931-941
Copyright © 2010 SciRes. JBiSE
Figure 1. VEGF signaling pathway of H. sapiens present in KEGG pathway database.
Many algorithms are proposed for the partition of a net-
work. We compared the algorithm of Nayak and De [3]
with community finding algorithm of Newman, Farhat’s,
Greedy and Kernighan-Lin’s algorithms. Farhat’s, Greedy
and Kernighan-Lin’s algorithms are graph partitioning
algorithms and they need cut size and cut number for
partitioning a network. Newman’s community finding
algorithm has been applied to one category of bioche-
mical networks (metabolic pathways). The chosen set
provided a good mix of algorithms that belong to atleast
three categories. They provide a uniform platform for the
comparative study. But by no means, this set of chosen
algorithms is an exhaustive one.
Algorithm of Nayak and De works on a biochemical
pathway which has gene products and chemical com-
pounds. Here, the pathway is considered as a graph, gene
products and chemical compounds are nodes. Edges
show protein-protein interaction, protein-compound in-
teraction or link to another map. The total number of
relations with n as either a preceding or succeeding node
is given by Tn = Rnp+Rns, where Rnp and Rns are out-
degree and indegree, respectively, of a node n. The term
Tn is the total degree of the node. According to algo-
rithm, a node is detected which has maximum number of
relations in the node pool E for a given network. This
detected node is considered as a “starting node”. This is
always considered as a “permanent member”. Permanent
member is removed from the pool E. By defining the
starting node, an initial module is created for relation r.
Here, n may be a predecessor or a successor. After ini-
tialization of the module, the total number of relations of
every individual member is considered.
Now, a node is checked for its permanency. If the
number of relation lying inside the module is equal to
the total number of relation associated with the node,
then, it is permanent member. If a node in a module has
more than c relations lying outside the module, it is ex-
cluded from the module with decreasing the previous
non permanent nodes’ total relation by one. This certain
number of relations is known as complexity level c
which can be set by the user. This process is continued
until we have no new immediate neighboring node to be
included or no node is left to be declared permanent.
One important fact is that if a member X is present four
times in a network, it will be considered four times like
X1, X2, X3 and X4. After formation of a module, it
searches for another starting point and repeat all above
mentioned steps. This process will terminate when all
the nodes of node pool E are exhausted.
This algorithm had been applied for different c-values
N. Tomar et al. / J. Biomedical Science and Engineering 3 (2010) 931-941
Copyright © 2010 SciRes. JBiSE
for VEGF KEGG pathway database http://www.ge-
nome.jp/kegg/pathway.html#environmental. Then, ap-
propriate c-value had been selected for comparative
analysis of different species present in KEGG. KEGG
has KGML layout which has XML files. These XML
files’ coding was used to give input for the algorithm.
Species of which KGML layout and XML coding were
present in KEGG were considered for the comparative
study of VEGF pathway. The species were H. sapiens
(human), P. troglodytes (Chimpanzee), M. musculus
(mouse), R. norvegicus (rat), C. familiaris (dog), B. tau-
rus (cow), S. scrofa (pig).
Kernighan-Lin’s algorithm is a heuristic algorithm
applied for graph partitioning problems. It has important
applications in the layout of digital circuits and compo-
nents in VLSI. B. W. Kernighan and S. Lin has proposed
an heuristic method in paper [7] to partition of the graph
in such a way that it would be effective in finding opti-
mal partitions. They deal with a combinatorial problem
and partition of a graph G into subsets those would be no
larger than a given maximum size. In this way, total cost
of the edge cut is minimized.
Greedy algorithm [8] works well when a problem has
greedy choice property and optimal substructure. It
makes local optimal choice at each stage and tries to find
global optimum. Farhat in 1988 has presented an algo-
rithm which is an efficient non-numerical algorithm for
the automatic decomposition of an arbitrary finite ele-
ment domain into a specified number of balanced sub-
domains [9]. It is found to be effective for the imple-
mentation of concurrent solution strategies on high per-
formance architectures.
Community structure detection is used for social net-
works, internet and web data, biochemical networks or
gene network. Here, it is assumed that the network of
interest divides naturally into subgroups, and the re-
searchers find those groups. So, we can say that the
number and size of the subgroups are determined by the
network itself and not by the researcher. It has been ap-
plied to metabolic pathways. It divides a network in
which good modules are not present. So, we can say that
it is based on the properties of the network. Modularity
score is directly dependent on the network architecture,
adjacency matrix and eigenvalues of a symmetric matrix
calculated from the adjacency matrix. Positive value of
modularity means there is presence of modules in a net-
work and a negative value shows that division is not
possible [10].
Species those were available in KEGG database had
been considered for the comparative study. They are H.
sapiens (human), P. troglodytes (Chimpanzee), M. mus-
culus (mouse), R. norvegicus (rat), C. familiaris (dog), B.
taurus (cow), S. scrofa (pig). The gradual development
of this pathway in some species had been studied with
respect to VEGF pathway of H. sapiens using the algo-
rithm of Nayak and De. We applied all selected algo-
rithms to VEGF signaling pathway of H. sapiens as ob-
tained from KEGG database and compared their per-
3.1. Modularization of VEGF Signaling Pathway
of H. Sapiens using Different Algorithms
We took different c-values and studied various modules
obtained by the algorithm of Nayak and De. Then, by
analyzing all the modules for different c-values, we
chose a particular c-value for the comparative study of
organisms. VEGF signaling pathway of H. sapiens has
40 nodes and 34 relations. Modules were created for c =
1, 2, 3, 4 and 5.
For c = 1, we had 12 modules shown in Table 1.
Number of modules was reduced, as complexity level
was increased. For c = 2, node MAK1 merged with cen-
tral node (PLCG1, PLC1) as shown in Table 2. Now,
this node had function of cell survival and migration of
vesicular endothelial cell [11]. For the same complexity
value, another central node, MAPK14 merged into cen-
tral node KDR. KDR has role in cell proliferation and
growth function along with previous function of focal
adhesion turnover and cell migration. It had paxillin and
FAK as node members. Paxillin acts as a focal adhesion
adaptor in focal adhesion dynamics and cell migration.
Paxillin-FAK interaction is involved in Erk activation
[12]. For c = 2, we had 6, and for c = 3, we had 4 mod-
ules as shown in Ta b l e 3 . The node AKT3 was present
as central node for c = 2 but it combined with PIK3R5 as
we changed complexity to c = 3. It resulted in having
multiple functions for the node AKT3. For c = 3,
PIK3R5 functioned for permeability, vasodilatation as
well as for cell survival and nitric oxide release [13]. For
c = 2, there was a central node called CHP that had
members (NFAT5), (PTGS2). But for c = 3, it merged
with central node (PLCG1, PLC1). CHP, a central node
for c = 2, had NFAT as a member, which is a family of
transcription factors. It has at least four structurally sim-
ilar members, e.g., NFATp (NFAT1), NFATc (NFAT2),
NFAT3 and NFAT4. NFATc is present in endocardium,
and is involved in morphogenesis of cardiac valves,
septum and also in heart organization during develop-
ment [14]. It regulates the properties of reserve cells.
SMC uses NFAT signaling for adaptation. Calcineurin
(CHP) is a Ca2+/CAM dependent phosphatase that regu-
lates the process of dephosphorylation and nuclear im-
N. Tomar et al. / J. Biomedical Science and Engineering 3 (2010) 931-941
Copyright © 2010 SciRes. JBiSE
port of NFAT. Another member PTGS2 is a target of
NFAT and is involved in prostaglandin synthesis during
angiogenesis. It is necessary for the migration of endo-
thelial cells to allow the proper formation of endothelial
tubes and postnatal angiogenesis in vivo [15]. For c = 2,
(PRKCA) was a central node which had members (RAF1),
(SPHK 2) and (HRAS, HRAS1), but for c = 3, the same
central node had no members and as complexity was
increased, it became a single node. For c = 4 and c = 5,
the number of modules created were the same but this
number was less as many central nodes merged. These
modules were large enough to study and analysis.
3.2. Changes Found with the Increased
Complexity Values
We found that different c-values gave different number
and complexity of modules. Number of modules was
decreased as we increased the c-value. This resulted in
over splitting. Many different modules were combined
Table 1. Modularization for c = 1 for H. sapiens VEGF sig-
naling pathway.
S. No. Central Node Other Nodes
(PTK2), (PXN)
2 (PLCG1, PLC1) (SH2D2A)
3 (AKT3) (NOS3), (CASP9), (BAD)
4 (PRKCA) -
5 (CHP) -
6 (PIK3R5) (RAC1),(SRC)
7 (RAF1) -
8 (MAPK1) (PLA2G2D), (MAP2K1)
9 (MAPK14) (CDC42)
10 (HRAS, HRAS1) (SPHK2)
12 (NFAT5) ( PTGS2)
Table 2. Modularization for c = 2 for H. sapiens VEGF sig-
naling pathway.
S. No. Central
Node Other Nodes
1 (KDR)
(VEGFA, VEGF), (SH2D2A), (SHC2),
(PTK2), (PXN), (CDC42), (SRC),
2 (PLCG1,
PLC1) (PLA2G2D), (NOS3), (MAPK1), (MAP2K1)
3 (PRKCA) (RAF1), (SPHK2), (HRAS, HRAS1)
4 (PIK3R5) (RAC1)
5 (CHP) (NFAT5), (PTGS2)
6 (AKT3) (CASP9), (BAD)
Table 3. Modularization for c = 3 for H. sapiens VEGF sig-
naling pathway.
S. No.Central
Node Other Nodes
1 (KDR)
(VEGFA, VEGF), (SH2D2A), (SHC2),
(PTK2), (PXN),
(CDC42), (SRC), (MAPK14), (MAP-
2 (PLCG1,
(CHP), (PLA2G2D), (NOS3), (NFAT5),
(MAPK1), (PTGS2),
(MAP2K1), (RAF1), (HRAS,HRAS1),
3 (PRKCA) -
4 (PIK3R5) (RAC1), (AKT3), (CASP9), (BAD)
and increased in size with increase in c-value. With in-
crease in c-value, new members were inserted in a cer-
tain module or changed its earlier central node. As we
took the case of VEGF signaling pathway of H. sapiens,
we found just half number of modules with decrease in
c-value by one, i.e., for c-value of two, we had six mod-
ules whereas, the number was 12 for c = 1. But, for c = 4
and 5, size and number of modules, and the number of
their members became static (in Ta b le s 4 and 5 respec-
tively). The names of central nodes and their members
for different c-values are given in Tables 1-5.
3.3. Fixing the Complexity Values
Now, by assigning different c-values, we had different
sets of modules. So, by analyzing all the modules thor-
oughly, we understood that for c = 5, we should have
Table 4. Modularization for c = 4 for H. sapiens VEGF sig-
naling pathway.
S. No.Central
Node Other Nodes
1 (KDR)
(VEGFA, VEGF), (SH2D2A), (SHC2),
(PTK2), (PXN),
(CDC42), (PIK3R5), (SRC),(MAPK14),
(RAC1), (AKT3), (MAPKAPK3), (NOS3),
(CASP9), (BAD), (HSPB1)
2 (PLCG1,
(CHP), (PRKCA), (PLA2G2D), (NFAT5),
(SPHK2), (MAPK1), (PTGS2),
Table 5. Modularization for c = 5 for H. sapiens VEGF sig-
naling pathway.
S. No.Central
Node Other Nodes
1 (KDR)
(PTK2), (PXN), (CDC42), (PIK3R5),
(SRC), (MAPK14), (RAC1), (AKT3),
(MAPKAPK3), (NOS3), (CASP9), (BAD),
2 (PLCG1,
(CHP), (PRKCA), (PLA2G2D), (NFAT5),
(RAF1), (SPHK2), (MAPK1), (PTGS2),
N. Tomar et al. / J. Biomedical Science and Engineering 3 (2010) 931-941
Copyright © 2010 SciRes. JBiSE
stopped modularization process. Because for c = 4 and c
= 5, we had the same set of modules. Even for c = 3,
number of modules were less and they were merged, and
thereby, it was unworthy to proceed. As per above anal-
ysis, it was clear that for higher c-values, number of
nodes and relations were greater than that we got for c = 1
as nodes started merging with other nodes. For c = 1, we
had sufficient nodes, and relations for most of the nodes
of this pathway. By analysis of all the modules for dif-
ferent c-values, we assumed that increase in c-value
gave almost similar output as nodes got merged. Module
names, their number of nodes and relations for different
c-values for H. sapiens VEGF signaling pathway are
shown in Table 6. We were getting a simplified and bio-
logically significant network for c = 1. We found c = 1 to
be an optimal one, because for this c-value, network was
modularized properly and not too much over splitting
was occurred. This made us to fix c-value to 1 for VEGF
signaling pathway of H. sapiens .
3.4. Comparison of Algorithm of Nayak and De
with Newman’s Community Finding
For the algorithm of Nayak and De, we got modules
where central nodes were defined but it was not the case
with Newman’s algorithm. By applying Newman’s algo-
rithm, we got four modules while it was 12 for the algo-
rithm of Nayak and De for c = 1. Thus, we found less
number of modules by Newman’s algorithm. Hence, the
complexity of the modules obtained by Newman’s algo-
rithm was quite high compared to those generated by the
algorithm of Nayak and De. This may defeat the objec-
tive of modularizing a signal transduction pathway.
Nodes of a created module obtained by Newman’s algo-
Table 6. Module names and their number of nodes and rela-
tions for H. sapiens VEGF signaling pathway. `N’ represents
number of nodes and `R’ stands for number of relations.
S.No Module
Name c = 1c = 2 c = 3 c = 4c = 5
1 (KDR) 541110 11 10 17 161716
2 (PLCG1,
PLC1) 2154 11 11 11 101110
3 (AKT3) 4332 1 0 1 010
4 (PRKCA) 1344 1 0 0 000
5 (CHP) 1232 1 0 0 000
6 (PIK3R5) 3221 5 4 0 000
7 (RAF1) 1310 0 0 0 000
8 (MAPK1)3210 0 0 0 000
9 (MAPK14)2110 0 0 0 000
10 (HRAS,
HRAS1) 2110 0 0 0 000
11 (MAP-
KAPK3) 2110 0 0 0 000
12(NFAT5) 2110 0 0 0 000
Figure 2. Modules of human VEGF signaling pathway created by the algorithm of Nayak and De for c-value of 1.
N. Tomar et al. / J. Biomedical Science and Engineering 3 (2010) 931-941
Copyright © 2010 SciRes. JBiSE
Figure 3. Modules of human VEGF signaling pathway created by Newman’s algorithm.
Figure 4. Modules created by Farhat’s algorithm of H. sapiens VEGF signaling pathway.
rithm were placed at very much distance, so assigning
functions for these types of modules, was difficult.
Moreover, as we know that signaling networks work on
the basis of interaction between the input signaling node
and output signaling node, most of the nodes present in
the modules created by Newman’s community finding
algorithm had no such interaction. So, we can say that
function and behavior of a modules generated by New-
man’s community finding algorithm were not clearly
revealed as shown in Figure 3.
N. Tomar et al. / J. Biomedical Science and Engineering 3 (2010) 931-941
Copyright © 2010 SciRes. JBiSE
By analyzing the modules obtained by both the algo-
rithms, we found that MAPK1 includes MAP2K1, RAF1
and HRAS by implementing Newman’s algorithm while
in algorithm of Nayak and De; MAPK1 had PLA2G2
instead of RAF1 and HRAS. Here, RAF1 and HRAS
formed a separate module. The module MAPK1, as gen-
erated by the algorithm of Nayak and De, had 2 func-
tions regarding cell proliferation and PGI2 production.
But in Newman’s algorithm, function of this module had
been changed as this module was merged with RAF1
and HRAS. Now, PLA2G2 was involved only in PGI2
production. Another functionally important node PLC-γ
was with SH2D2 through the algorithm of Nayak and De,
while by Newman’s algorithm, it was included in module
3 and had SPHK2 as a different member. In Newman’s
algorithm, KDR emerged as a singleton node in module
4 (Figure 3), while through the algorithm of Nayak and
De, it was with VEGF and three other members. So we
can say that KDR acts as a receptor for VEGF and func-
tions in focal adhesion, as it has PTK2 and PXN as its
members. In Newman’s algorithm, node RAC was with
NOS and other apoptotic signaling pathway components,
functions for cell permeability as well as cell survival.
But for this, the algorithm of Nayak and De, it was with
PI3K and SRC having only one function, i.e., of cell
3.5. Comparison of Algorithm of Nayak and De
with Farhat’s and Greedy Algorithms
Applying Farhat’s and Greedy algorithms to this prob-
lem, we got two partitions. AKT3 appeared as a central
node and had 3 other members by the algorithm of
Nayak and De but both Farhat’s and Greedy algorithms
had divisions in members of AKT3. These members
were present in 2 different partitions. The node KDR had
different members obtained by Farhat’s and Greedy al-
gorithms. Even the members of MAPK signaling path-
way were present in different modules created by the
algorithm of Nayak and De but through implementation
of Greedy and Farhat’s algorithms all the members were
in the same partition. The modularized diagram through
Farhat’s algorithm and Greedy algorithm are shown in
Figures 4 and 5 respectively.
3.6. Comparison of the algorithm of Nayak and
De with the combined Farhat’s, Greedy and
Kernighan-Lin’s algorithms
Kernighan-Lin’s algorithm had been implemented in two
ways. It was implemented by taking output of Farhat’s
and Greedy algorithms as its input. These outputs are
shown in Figures 6 and 7 respectively. It also gave two
partitions that were different from the algorithm of
Nayak and De. Module AKT3 had four members ob-
tained by the algorithm of Nayak and De, while this par-
ticular module had two different partitions through Far-
hat’s and Greedy algorithms. AKT3 and NOS3 were
present in one partition, and CASP9 and BAD were
found in different partitions as shown in Figures 6 and 7
Figure 5. Modules created by Greedy algorithm of H. sapiens VEGF signaling pathway.
N. Tomar et al. / J. Biomedical Science and Engineering 3 (2010) 931-941
Copyright © 2010 SciRes. JBiSE
Figure 6. Modules created by combined Kernighan-Lin’s and Farhat’s algorithms for H. sapiens VEGF signaling pathway.
3.7. Comparative Study of the Modules of VEGF
Signaling Pathways for Different Species for
c = 1
For c = 1, we had applied the algorithm to seven different
species present in KEGG database. In the case of H. sa-
piens, 12 modules were created which were the same for
M. musculus (mouse) where all the modules were same
in number and characteristics. Figure 2 shows a modu-
larized pathway for c = 1 of H. sapiens. As we further
compared these two species with R. norvegicus (rat), we
found difference in only one module and it was Plc –1.
This module appeared as a single node in R. norvegicus
(rat) whereas in H. sapiens (human being) and M. mus-
culus (mouse), it had one member SH2D2A. So this kind
of comparison gives an idea that the VEGF pathway of
these three species is developed almost in a similar
For B. taurus (cow), we had 10 modules. The module
MAPK was fully developed and had other members.
MAPKAP and MAP14 were present as two different
modules in H. sapiens, which were combined in B. tau-
rus(cow). The module LOC534LOC511224 and had a
member COX which was absent in H. sapiens. Here the
module AKT3, named as AKT1, had a member MGC
127164 that made it different from others because in
other species, it had all the three members. Even,
PRKCA was present as a single node. For P. troglodytes
(Chimpanzee), we had 8 modules. As in the previous
species’ modules, MAPK, PI3K were fully developed
and even node RAF1 was a central node and had two
members. It was not present as a single node as we had
seen earlier. In C. familiaris (dog), we found 7 modules.
The modules KDR, MAPK and AKT3 were fully devel-
oped but PLC-γ, PRKCA and PIP3K were absent. In H.
sapiens, the node Src was included in module PIK3R5
but it was in module KDR in C. familiaris (dog). But for
S. scrofa (pig), it was the least developed and had only
one module for NFAT [13]. Table 7 provides the details
of the modules obtained, for c = 1, from VEGF path-
ways of these species. So, from this comparison, we can
say that, KDR and MAPK are said to be consistent in
most of the studied species.
In this paper, different partitioning algorithms were ap-
plied to human VEGF signaling pathway in order to di-
vide it into smaller meaningful modules for analysis
purpose. The applied partitioning algorithms are: modu-
larization algorithm of Nayak and De, Newman’s com-
munity finding algorithm, Graph partitioning algorithm
of Kernighan-Lin’s, Farhat’s and Greedy algorithms.
First of all, algorithm of Nayak and De was applied to
human VEGF signaling pathway for different c-values.
The best set of modules were found for c = 1. The com-
parison of human VEGF signaling pathway modules for
c = 1 was done with those obtained by some other parti-
tioning algorithms. We got four modules by applying
Newman’s algorithm, while it was 12 for the algorithm
of Nayak and De for c = 1. We got only two partitions by
applying Farhat’s, Greedy and Kernighan-Lin’s algo-
rithms. The number of partitions and their members
N. Tomar et al. / J. Biomedical Science and Engineering 3 (2010) 931-941
Copyright © 2010 SciRes. JBiSE
Figure 7. Modules created by combined Kernighan-Lin's and Greedy algorithms for H. sapiens VEGF signaling pathway.
Table 7. Created modules and nodes for VEGF signaling pathway of seven species for c = 1. (M- Modules names; (N) - Number of
Nodes present in a module).
Human and Mouse Rat Cow Chimpanzee Dog Pig
M(N) M(N) M(N) M(N) M(N) M(N)
KDR(5) Kdr(5) PLCG1(1) LOC461315(3) LOC460400(2) NFATC1(3)
PLCG, PLC1(0) Plcg1(1) PIK3CA(2) LOC455085(3) KDR(3) -
AKT3(4) Akt1(4) flk-1(3)
LOC460182(3) LOC484648(3) -
PRKCA(0) Prkca(1) LOC521196(2) LOC453202(3) AKT3(3) -
CHP(0) Ppp3cc(1) LOC454037(3)
LOC477575(3) MAPK3, - -
PIK3R5(3) Pik3ca(3) MAPK1(3) MAPK14(2) MAPK14(3) -
RAF1(0) Raf1(1) LOC534492(3) LOC452821(3) LOC479678(2) -
MAPK1(3) Mapk1(3) PRKCA(1) LOC460400(2) - -
MAPK14(2) Mapk13(2) AKT1(2) - - -
HRAS,HRAS1(2) Kras(2) LOC511224(2) - - -
MAPKAPK3(2) Mapkapk2(2) - - - -
NFAT5(2) Nfatc4(2) - - - -
were kept the same while applying Farhat’s and Greedy
algorithms. So again, our objective was not fulfilled of
getting smaller biological meaningful modules. All the
modules got through applying algorithm of Nayak and
De are self-sufficient and have minimal dependency on
the rest part of the network. This property works behind
the idea of modularization of a biological signaling
pathway. Through the result analysis, we can say that the
algorithm of Nayak and De is superior over considered
existing partitioning algorithms here, and better in re-
ducing the complexity of the signaling pathway.
Moreover, the species specific modules were obtained
for the same optimal c-value through the algorithm of
Nayak and De. Their comparison proved that the trend
of development, in ascending order, was “S. scrofa (pig),
C. familiaris (dog), P. troglodytes (chimpanzee), B. tau-
rus (cow), M. musculus (mouse), R. norvegicus (rat) and
H. sapiens (human being).” This trend shows that sig-
naling pathways become more complex in higher organ-
isms. We found that the modules KDR and PLC-γ were
consistent in H. sapiens for all c-values and were func-
tional in all studied species. So, we can say, as per com-
parative analysis that modules KDR and PLC-γ are con-
served in all the studied species. Even the module AKT3
N. Tomar et al. / J. Biomedical Science and Engineering 3 (2010) 931-941
Copyright © 2010 SciRes. JBiSE
was found in all the studied species except in S. scrofa
(pig) and B. Taurus (cow).
This analysis makes one to study a conserved or con-
sistent module rather than considering the complex sig-
naling pathway as a whole. It is easier to determine un-
derlying mechanism of normal development as well as in
certain disorders or diseased conditions. In a certain dis-
ease, only one molecule or a small group of molecules
gets deregulated, so modularized study makes one to
concentrate over a few modules containing responsible
molecules only. This type of implementation also saves
time and cost for experimental analysis.
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