Examination of the relationship between essential genes in PPI network and hub proteins in reverse nearest neighbor topology

Abstract

Abstract Background In many protein-protein interaction (PPI) networks, densely connected hub proteins are more likely to be essential proteins. This is referred to as the "centrality-lethality rule", which indicates that the topological placement of a protein in PPI network is connected with its biological essentiality. Though such connections are observed in many PPI networks, the underlying topological properties for these connections are not yet clearly understood. Some suggested putative connections are the involvement of essential proteins in the maintenance of overall network connections, or that they play a role in essential protein clusters. In this work, we have attempted to examine the placement of essential proteins and the network topology from a different perspective by determining the correlation of protein essentiality and reverse nearest neighbor topology (RNN). Results The RNN topology is a weighted directed graph derived from PPI network, and it is a natural representation of the topological dependences between proteins within the PPI network. Similar to the original PPI network, we have observed that essential proteins tend to be hub proteins in RNN topology. Additionally, essential genes are enriched in clusters containing many hub proteins in RNN topology (RNN protein clusters). Based on these two properties of essential genes in RNN topology, we have proposed a new measure; the RNN cluster centrality. Results from a variety of PPI networks demonstrate that RNN cluster centrality outperforms other centrality measures with regard to the proportion of selected proteins that are essential proteins. We also investigated the biological importance of RNN clusters. Conclusions This study reveals that RNN cluster centrality provides the best correlation of protein essentiality and placement of proteins in PPI network. Additionally, merged RNN clusters were found to be topologically important in that essential proteins are significantly enriched in RNN clusters, and biologically important because they play an important role in many Gene Ontology (GO) processes.

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RESEARCH ARTICLEOpen Access
Examination of the relationship between essential
genes in PPI network and hub proteins in reverse
nearest neighbor topology
Kang Ning1, Hoong Kee Ng3, Sriganesh Srihari3, Hon Wai Leong3, Alexey I Nesvizhskii1,2*
Abstract
Background: In many protein-protein interaction (PPI) networks, densely connected hub proteins are more likely
to be essential proteins. This is referred to as the “centrality-lethality rule”, which indicates that the topological
placement of a protein in PPI network is connected with its biological essentiality. Though such connections are
observed in many PPI networks, the underlying topological properties for these connections are not yet clearly
understood. Some suggested putative connections are the involvement of essential proteins in the maintenance of
overall network connections, or that they play a role in essential protein clusters. In this work, we have attempted
to examine the placement of essential proteins and the network topology from a different perspective by
determining the correlation of protein essentiality and reverse nearest neighbor topology (RNN).
Results: The RNN topology is a weighted directed graph derived from PPI network, and it is a natural
representation of the topological dependences between proteins within the PPI network. Similar to the original PPI
network, we have observed that essential proteins tend to be hub proteins in RNN topology. Additionally, essential
genes are enriched in clusters containing many hub proteins in RNN topology (RNN protein clusters). Based on
these two properties of essential genes in RNN topology, we have proposed a new measure; the RNN cluster
centrality. Results from a variety of PPI networks demonstrate that RNN cluster centrality outperforms other centrality
measures with regard to the proportion of selected proteins that are essential proteins. We also investigated the
biological importance of RNN clusters.
Conclusions: This study reveals that RNN cluster centrality provides the best correlation of protein essentiality and
placement of proteins in PPI network. Additionally, merged RNN clusters were found to be topologically important
in that essential proteins are significantly enriched in RNN clusters, and biologically important because they play an
important role in many Gene Ontology (GO) processes.
Background
Essential genes may cause the death of an organism if
they are not properly expressed or malfunction due to
events such as sequence mutation. Essential genes are
vital for the growth of an organism under a variety of
conditions and are frequently identified experimentally
through deletion experiments (by the analysis of haploid
deletion mutant strain growth rates)[1-3].
Recent high-throughput proteomic experiments, such
as yeast-two hybrid [4] and affinity capture-MS [5,6],
have enabled the systematic mapping of protein-protein
interaction (PPI) for organisms such as Saccharomyces
cerevisiae [4-6] and Escherichia coli [7]. Though the PPI
networks constructed from these experiments are not
yet complete, they nonetheless have revealed interesting
topological properties of PPI networks [8,9] with respect
to gene essentiality.
Specifically, several studies have already investigated
the connection of the topological properties of PPI net-
works and essential genes [10-13]. The PPI network is
represented as an unweighted, undirected graph, in
which each node represents a protein and each edge
(between two nodes) represents an interaction between
these two proteins. In many PPI networks, essentiality is
* Correspondence: nesvi@umich.edu
1Department of Pathology, University of Michigan, 4237 Medical Science
Building I, Ann Arbor, MI, 48109, USA
Full list of author information is available at the end of the article
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© 2010 Ning et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons
Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in
any medium, provided the original work is properly cited.

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correlated with topological placement of the proteins in
the network. That is, hubs that are “highly connected”
in a PPI network tend to correspond to essential genes
[10-17]. This is called the “centrality-lethality rule” [10].
Though the centrality-lethality rule has been observed
in many PPI networks, the underlying topological prop-
erties of essential proteins are not yet fully understood.
Jeong and colleagues argued that essential proteins are
important in PPI network for maintaining the overall
network connectivity, [10], while He and colleagues sug-
gested that the majority of essential proteins are corre-
lated with essential protein-protein interactions [11] in
the PPI network. A recent study by Zotenko and collea-
gues utilizing a yeast PPI network, however, rejected
these two suggestions, and proposed that proteins are
essential due to their involvement in densely connected
clusters of proteins with same GO term annotation [12].
Other works have shown high correlations between pro-
tein essentiality and their placement in protein com-
plexes [18-20].
RNN topology was a weighted directed graph that
could be generated from PPI network. In RNN topology,
each of the nodes represented a protein, and each edge
pointed to a protein from its RNN (with that protein as
it nearest neighbor) [21,22]. RNN topology is different
from nearest neighbor (NN) topology, since for each
protein, its NN proteins and RNN proteins comprised
two different protein sets. Since edges in RNN topology
are both weighted and directed, they are useful for the
identification of hub proteins that are important to the
entire network. As with other topology modeling appli-
cations, the RNN topology can elucidate the topological,
but not necessarily the true biological, dependencies
between proteins. Nevertheless, there is an intricate cor-
relation between topological dependencies and biological
dependencies in PPI networks, as discussed in [10].
Therefore, the investigation of correlations between hub
proteins in RNN topology and their essentiality could
provide additional interesting insights such as whether
these hub proteins play an important role in GO
processes.
In this study, we explored the connection between
topological properties of proteins and essential genes
from a different perspective. Namely, we generated
reverse nearest neighbor (RNN) topology [21,22] from
the PPI network, and subsequently examined the con-
nection of essential proteins and their placement in
RNN topology, as well as the topological context in
which essential proteins were enriched in RNN topology
using different types of PPI networks. Our results show
that essential proteins are more likely to be proteins
with many RNNs. Additionally, essential proteins are
enriched in clusters (RNN clusters) of proteins in RNN
topology (referred to as the “clustering property” of
essential proteins). Based on these observations, we pro-
pose the RNN cluster centrality measure, which is super-
ior to other centrality measures in correlating hub
proteins and essential proteins. Furthermore, we have
observed that the RNN clusters play an important role
in many GO processes.
Methods
Experimental data
The computational analysis was performed using PPI
networks from two organisms, E. Coli K12 and budding
yeast. For E. Coli, “DIP core” protein-protein interac-
tions were retrieved from the DIP database [23] (http://
dip.doe-mbi.ucla.edu/dip, accessed on 01/26/2009). The
“DIP core” network was derived from “DIP full”, with
evolutionary information used to filter out unreliable
interactions. Essential genes used in this study were
identified based on a genome-wide targeted mutagenesis
project [1] (http://ecogene.org, accessed on 07/01/2009).
The “DIP core” network for yeast was also obtained as
described above. Several additional yeast PPI networks
from different experiments were retrieved from Bio-
GRID [24] (http://www.thebiogrid.org, version 2.0.52).
These networks included two PPI networks generated
by affinity capture-MS experiments: Krogan et al. [5]
and Gavin et al. networks [25]; Collins et al. network
[26], generated by the application of a statistical scoring
scheme and filtering of low confidence score interac-
tions from Krogan and Gavin’s networks; and high con-
fidence network (HC network) [27], which was
generated by the intersection of small-scale datasets
(including affinity capture-MS, yeast two-hybrid, etc.)
with high throughput datasets [28]. The list of essential
genes for yeast was obtained from Saccharomyces Gen-
ome Deletion Project [2,3] (http://www-sequence.stan-
ford.edu/group/yeast_deletion_project/deletions3.html,
accessed on 07/01/2009).
Known protein complexes were also used for compari-
son. The list of protein complexes was retrieved from a
recent study of protein complexes in yeast [18] (http://
dags.stanford.edu/Complex/reference.txt, accessed on
09/14/2009.)
Methodologies of data analysis
RNN topology generation
RNN topology was a weighted directed graph generated
from the PPI network. The directions of edges in RNN
topology indicated that one node (edge destination) was
another node’s (edge origin) nearest neighbor, with the
edge origin referred to as the RNN of the edge destina-
tion. The weights of edges indicated the topological
importance of one protein to the other: that is, the
lighter the edge weight, the closer (topologically) the
edge origin is to the edge of destination.
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RNN topology was generated from the original PPI
network as follows. As the first step, the CMC algorithm
[29] was applied to compute edge weights in the PPI
network based on the connectivity of proteins in the
PPI network. We have then transformed every edge
weight in this weighted graph so that the closer the two
proteins in RNN topology, the lower edge weight in the
RNN topology. By this means, the more reliable the
interaction, the closer the interaction in the RNN topol-
ogy. Therefore, low edge weight in RNN topology after
transformation actually indicates reliable interaction.
Then RNN topology was generated based on this
weighted PPI network by an efficient metric space
search scheme [22] that identified the RNNs for every
protein in the weighted PPI network. For each protein
in RNN topology, other proteins with this protein
among their top k nearest neighbors were referred to as
the RkNN of this protein. The RkNN topology consisted
of all proteins and the edges to every protein from their
RkNNs. The generation of RNN topologies on a toy
weighted PPI network is shown in Figure 1. For exam-
ple, in Figure 1, Node 2 has no R1NN, and its R2NNs
are Node 1 and Node 3. Note that some interactions in
PPI network may not be present in RNN topology, since
they represent weak dependencies of RNNs to the corre-
sponding protein. It was found that there were special
properties for RkNN with different k: Given any protein
q, R1NN(q) is a subset of R2NN(q), R2NN(q) is a subset
of R3NN(q), and so on. If k ≥ n-1 (where n is the num-
ber of all proteins in the PPI network), then RkNN
includes every interaction in the original PPI network.
In real applications, it is of interest to analyze RkNN
primarily for small k values.
RNN cluster generation
Based on RNN topology, we analyzed two types of clus-
ters; simple and merged clusters. To generate simple
clusters, all proteins in RNN topology were ranked by
the number of their RNNs. The clusters were then gen-
erated by iteration. In each iteration, both the top-rank-
ing protein and its RNNs (which were still present in
the ranked list) formed a simple cluster, and all of these
proteins were removed from the ranked list. This pro-
cess was continued until there was no remaining protein
in the ranked list.
For a cluster I in RNN topology, the RNN cluster con-
nectivity(I), was defined as the ratio of the number of
RNN edges from proteins outside of RNN cluster to
proteins inside the cluster, divided by the total number
of edges pointing to proteins in this RNN cluster. The
RNN cluster connectivity measure indicated the topologi-
cal importance of RNN clusters (see RESULTS for dis-
cussion). Higher RNN cluster connectivity indicates
higher connectivity of corresponding RNN cluster in the
whole RNN topology. Therefore, the RNN cluster con-
nectivity indicates connectivity of RNN clusters at the
level of clusters of proteins rather than individual pro-
teins. Using the RNN cluster connectivity measure,
merged RNN clusters were then created by iteratively
merging simple clusters and previously merged clusters.
In each iteration, two simple (or merged) RNN clusters
with the highest RNN cluster connectivity were merged
if the resulting merged RNN cluster had a RNN cluster
Figure 1 An example of R1NN and R2NN topology generated from a toy weighted PPI network. Numbers beside edges represent edge
weights. The direction of the edges indicates that on node (edge destination) is another node (edge origin)’s nearest neighbor. The R1NN and
R2NN from the PPI network were given.
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connectivity greater than a certain threshold. In this
study, the threshold was set to be 0.5 for the balance
between the quality and the number of merged clusters.
This process was continued until there were no remain-
ing proteins (clusters) that could be merged. All RNN
clusters with RNN cluster connectivity smaller than 0.5
were subsequently filtered out.
Centrality measures for proteins
In this work, hub proteins were defined as proteins with
high centrality values. Here, we introduce several cen-
trality measures that are based either on RNN topology
or the original PPI network. First, suppose the number
of RNNs for each of the protein i is RNN(i). The RNN
centrality for a protein i is defined as the number of
RNNs for this protein.
RNN centrality (i) RNN (i)
=
(1)
RNN centrality may be important for distinguishing
essential and non-essential proteins. Note that this RNN
centrality is also dependent on the types of RkNN used.
For the same protein, when k value increases, the RNN
centrality value also increases.
Second, we define RNN cluster centrality, which takes
into consideration both RNN centrality and the enrich-
ment of essential proteins in RNN clusters (clustering
property). The enrichment of essential proteins in RNN
clusters is represented by the RNN cluster connectivity
measure described above. The RNN cluster centrality for
each protein i in RNN cluster I is defined as
RNN cluster centrality (i)RNN (i) RNN cluster connectivit
∗=
y y(I)|(iI)
∈
(2)
For clustering methods other than RNN clustering,
the clustering centralities are defined in a similar way.
Suppose the number of interactions for protein i is
degree(i) in the PPI network. The cluster connectivity(I)
for cluster I is thus defined as the ratio of the number
of interactions between one protein inside and another
outside of this cluster, divided by the total number of
interactions connecting proteins in the cluster. The clus-
tering centrality is defined as:
Clustering centrality (i)degree(i) cluster connectivity(I
∗=
) )|(iI)
∈
(3)
Measures for comparison
To compare the performance of different centrality mea-
sures in terms of their ability to identify essential pro-
teins, two metrics are used. One metric is the
“proportion of essential proteins in selected proteins”
(Precision):
Precision = #/ # essential proteins selectedproteins selected
(4)
The proteins are selected by their centrality measures
(formula (1)-(3)). “# Essential proteins selected” is the
number of proteins in the selected set of proteins. Note
that the precision value is directly related to the central-
ity-lethality rule: the higher the proportion, the better
the discrimination between essential and non-essential
proteins provided by the centrality measure.
Another measure is the “proportion of essential pro-
teins selected”, Recall, which is the number of essential
proteins selected in proportion to the total number of
essential proteins in the dataset.
Recall = # / #essential proteins selectedall essential proteins s
(5)
Results and discussion
We have analyzed the connection between the place-
ment of proteins in RNN topology and essential proteins
based on different PPI networks. These include five net-
works for yeast: HC, Krogan, Gavin, Collins and DIP
core, as well as DIP core network for E. Coli (see Meth-
ods). Among these PPI networks, the yeast HC network
is presented here as a model network for most of the
experimentation. Detailed statistics of these PPI net-
works are shown in Table 1.
The RNN topology is a scale free network [30], in
which the distribution of the number of RNN connec-
tions follows a power law. In RNN topology, there are
only a few proteins (hub proteins) that are the nearest
neighbors for a large number of proteins (Additional file
1, Figure S1 and Additional file 1, Figure S2). These pro-
teins are especially interesting since, having a large
number (>6) of RNNs, there are more essential proteins
than non-essential proteins (Additional file 1, Figure S2).
Generation of RNN topology and assessment of RNN
centrality measures
The connection of RNN centrality and essential proteins
was first analyzed based on the yeast HC PPI network.
In the RkNN topology network, each protein has
weighted edges pointing to it from other proteins, which
in turn consider this protein to be among their top k
nearest neighbors (see details in Methods). Based on
RkNN topologies with different k values, it was observed
that for RkNN with k > 5, increasing precision is
observed in protein categories with increasing RNN cen-
trality. However, this is not obvious for RkNN with
smaller k values (see Figure 2). This may be due to a fil-
tering effect: RkNN topologies with small k values may
have filtered out so many edges from original PPI net-
work, that the correlation of essential proteins and hub
proteins could not be established. On the other hand,
higher precision could be obtained from R5NN rather
than from other RkNN (k>5) for protein categories with
RNN centrality ≥ 6 (Figure 2). The underlying reason is
that RkNN with k>5 would include most edges in
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weighted PPI network, therefore rendering RNN topol-
ogy less advantageous to the original PPI network. To
determine this, we have computed the RNN centrality
values based on RnNN (n = # of proteins), which would
be exactly the same as degree centrality values (calcu-
lated as the degrees of proteins in the PPI network)
computed on the original PPI network for every protein.
We also observed that RNN centrality values based on
R10NN are not significantly different from those based
on RnNN (Figure 2). Therefore, the best RNN centrality
values were obtained based on RkNN with k value not
too large (>10) or too small (<5). Based on this analysis,
we selected R5NN to represent RNN topology, and used
it to perform all analyses described in the remainder of
this manuscript.
Comparing RNN centrality with other centrality measures
RNN centrality was compared with simple centrality
measures based on the original PPI network. These cen-
trality measures included the following: degree centrality
(DC), which is calculated as the degree of the specific
protein in the PPI network; closeness centrality (CC),
which is calculated as the sum of the lengths of shortest
paths from all other proteins to the specific protein in
the PPI network; and betweenness centrality (BC) [16],
which is the number of all-to-all shortest paths that go
through the specific protein in the PPI network. A ran-
dom selection method, based on the average result from
ten runs of random sampling of proteins in PPI net-
work, was also used for comparison of these centrality
measures. Results show that all of these centrality mea-
sures were much better than random selection (Figure
3). Additionally, RNN centrality was superior to other
centrality measures with regard to precision values.
Assessment of RNN cluster centrality
Since PPI networks are incomplete and noisy, it is not
sufficient to distinguish essential and non-essential pro-
teins based solely on a single protein’s property, such as
the RNN centrality. Alternatively, previous research has
shown that essential proteins are more likely to be in
densely connected clusters [31]. Here, we also analyzed
the enrichment of essential proteins in RNN clusters
Table 1 Statistics of the tested PPI networks.
Organism PPI network name Number of proteins Number of interactions Average degree Number (Proportion) of essential proteins
E Coli
DIP Core1,223993 1.62 113 (0.09)
Yeast
DIP Core
Krogan
Gavin
Collins
HC
3,645
2,674
1,430
1,958
2,998
4,553
7,079
7,592
23,486
9,258
2.50
5.29
10.62
23.99
6.18
690 (0.19)
712 (0.27)
576 (0.40)
622 (0.31)
871 (0.29)
Proportion of essential proteins was computed as the number of essential proteins, divided by the total number of proteins in the PPI network.
Figure 2 The proportion of essential proteins (precision) (y-axis) in proteins categorized by values of centrality (x-axis). Results are
based on RkNN with different k values generated from yeast HC PPI network. The higher the centrality values, the higher proportion of essential
proteins could be observed.
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(clustering property). Proteins with a higher proportion
of their RNNs as essential proteins were more likely to
be essential proteins, indicating that essential proteins
tend to cluster together in RNN topology (see example
Figure 4, also Additional file 1, Figure S3),. More specifi-
cally, in Figure 4, all of the 9 proteins in the RNN clus-
ter were essential, and out of their 97 R1NNs, 63
(64.9%) were also essential proteins. This illustrates the
importance of analyzing the connection of essential pro-
teins and protein clusters (RNN clusters) in RNN
topology.
First, we analyzed the enrichment of essential proteins
in RNN clusters (see Methods for details of the cluster-
ing procedure). We compared the “proportion of
essential proteins identified” (recall) values based on all
merged RNN clusters (defined in Methods) with that
based on random selection of the same number of pro-
teins in PPI network. In the HC yeast PPI network, 87%
of the essential proteins in the whole PPI network were
within merged RNN clusters, as compared to 29% from
random selection of proteins (Table 2). For other PPI
networks, similar results were also observed: more than
70% of the essential proteins in the whole PPI network
were within merged RNN clusters (recall = 70% ~ 90%),
compared to only recall = 20~40% from random selec-
tion of proteins (Table 2).
The topological importance of RNN clusters was
examined by analyzing the effect of removing merged
Figure 3 The proportion of essential proteins (precision) in proteins ranked by different centrality measures. RNN centrality is compared
with DC (degree centrality), CC (closeness centrality), BC (betweenness centrality) and centrality based on random selection. Results were based
on yeast HC PPI network. In each category, the top % of proteins with highest centrality values were computed by different methods and
compared.
Figure 4 A graphical representation of a sub-network of RNN topology derived from yeast HC PPI network. Large green nodes
represent a RNN cluster, small nodes represent the R1NNs of it members, circles represent essential proteins, and rectangle nodes (all in small
nodes) represent non-essential proteins. All of the proteins in this RNN cluster are essential, and out of their 97 R1NNs, 63 (64.9%) are also
essential proteins.
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RNN clusters (including protein members and corre-
sponding edges) on the change of topological properties
of the PPI network. By comparing the average degree,
betweenness, and closeness per protein in the original
PPI network and those after removing all (100%) merged
RNN clusters, we observed that these topological prop-
erties decreased to nearly half of their original values
(Table 3). Furthermore, the removal of merged RNN
cluster significantly deteriorated the network properties
as compared to removal of the same number of ran-
domly selected proteins (Table 3).
Analysis of properties of RNN clusters
Next, we performed the analysis of various properties of
simple and merged clusters. Out of 1,677 proteins, there
were 565 simple clusters with average size of 2.87, out
of which more than 70% were of size less than 4. There
were 309 merged clusters with average size of 5.01, out
of which less than 30% were of size less than 4. Then
we have analyzed the properties that could accurately
represent the enrichment of essential proteins in RNN
clusters (clustering property). We have examined three
properties: (1) Num-RNN-total measured as the average
number of edges pointing to a protein in RNN cluster;
(2) Num-RNN-inside measured as the average number
of edges pointing from one protein in RNN cluster to
another protein in RNN cluster; and (3) Num-RNN-out-
side which was similarly defined. As shown in Figure 5,
as the Num-RNN-outside increases, on merged RNN
clusters, there is a corresponding linear increase of the
precision value. However, both Num-RNN-total and
Num-RNN-inside do not have such a linear correlation
with precision. The same phenomenon was observed
when the basis was simple RNN clusters (details not
shown). Therefore, among these three properties, Num-
RNN-outside reflects the enrichment of essential pro-
teins in RNN cluster. This is also the underlying princi-
pal defining RNN cluster connectivity (refer to
METHODS section).
Additionally, the cluster density on merged RNN clus-
ters was also analyzed. The cluster density is defined as
the number of edges in a cluster, divided by the number
of all possible edges between proteins in the cluster.
However, it was discovered that increasing the threshold
of density of RNN clusters did not result in increased
precision in RNN clusters (see Additional file 1, Figure
S4 (a)). This indicated that cluster density was not good
at discriminating between essential and non-essential
proteins.
The simple RNN clusters and merged RNN clusters
were compared by computing the RNN cluster centrality
based on single RNN clusters, with those that based on
merged RNN clusters. The RNN cluster centrality based
on merged RNN clusters as consistently better than that
based on simple RNN clusters, with regard to precision
values (Figure 6 (a)s). For simplicity, hereafter, “RNN
cluster centrality“ is referred to that computed for a
merged RNN cluster.
Comparison of RNN cluster centrality with other centralities
By comparing RNN cluster centrality with RNN central-
ity, precision values were consistently much higher when
based on RNN cluster centrality rather than RNN cen-
trality (see Figure 6 (a)). This indicated that essential
proteins were more likely to be hub proteins inside
RNN clusters than hub proteins outside of the RNN
cluster.
RNN cluster centrality was then compared with clus-
tering centrality measures based on several clustering
methods applied to PPI networks. The clustering
Table 2 Comparison of “proportion of essential proteins identified” (recall) based on merged RNN cluster and that
based on random selection of the same number of proteins in PPI network.
OrganismPPI network
Recall (merged RNN cluster)
Recall (random selection)p-value
E Coli
DIP Core0.890.090.0002
Yeast
DIP Core
Krogan
Gavin
Collins
HC
0.73
0.81
0.85
0.79
0.87
0.19
0.27
0.40
0.31
0.29
0.0116
0.0183
0.0036
0.0110
0.0014
Results were based on different PPI networks. p-value indicates the probability that the recall value is obtained based on random selection of proteins.
Table 3 The effect of removal of RNN clusters on the change of topological properties of yeast HC PPI network.
Remove top % RNN clusters 0%10% 20%50%100%p-value
Average Degree per protein
6.185.61 (5.94)4.94 (5.83) 4.15 (5.39)3.55 (4.79)0.021
Average Betweenness per protein
0.1900.073 (0.210)0.0069 (0.207)0.063 (0.196)0.057 (0.192) 0.002
Average Closeness per protein
0.103 0.084 (0.088) 0.080 (0.084)0.065 (0.081) 0.059 (0.074) 0.023
Values in brackets were based on random removal of the same number of proteins as in top % RNN clusters. p-values were associated with observing changes
by random removal in PPI network.
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methods that we compared included the following:
MCODE, which is based on network density [32]; the
MCL method, based on random walk [33]; the COACH
method, based on core-attachment structure [34]; and
clustering by cliques [31]. A clique in PPI network is a
subgraph in which each of the proteins is connected
with all other proteins in the same subgraph. Recently, a
research study was conducted on clustering proteins in
PPI network based on GO function annotation [12], in
which densely connected proteins with same GO term
annotations were considered to be in the same cluster.
Since essential proteins tend to be enriched in cliques
[31] and in clusters with the same GO term annotations
[12], we introduced the “GO term cliques” where essen-
tial proteins were expected to be highly enriched. The
“GO term cliques” were created as follows: proteins
with the same GO function annotation [35] from the
PPI network were clustered, and then cliques (with
number of proteins > 2) from these clusters were
extracted as GO term cliques. Note that “GO term cli-
ques” was a stringent term, since all proteins in the cli-
que should have the same GO function annotation and
also connect to all other proteins in the same clique.
Formula (3) was used to compute clustering centralities
based on these clustering methods.
Results on the yeast HC PPI network show that RNN
cluster centrality had superior precision values relative
to other clustering centralities (Figure 6 (b)). Among all
of these centrality measures, the RNN cluster centrality
was more effectively discriminated between essential
and non-essential proteins. It is worth noting that the
superior results of RNN centrality were obtained with-
out utilizing functional annotation information as is the
case for GO term clique. Additionally, though similarly
high precision values could be obtained from GO term
clique centrality (Figure 6 (b)), higher recall values were
obtained from all RNN clusters than from those
obtained from GO term cliques. Based on the yeast HC
PPI network, 754 essential proteins (out of all 871
essential proteins, recall = 0.87) were identified from all
RNN clusters, while only 172 essential proteins (recall =
0.20) were identified from all GO term cliques. The
main reason for low recall values based on GO term cli-
ques is that GO term cliques contained only a small
fraction of proteins in the PPI network; out of all 2,998
proteins in yeast HC PPI network, only 311 were mem-
bers of GO term cliques. On the other hand, 1,192 pro-
teins in the yeast HC PPI network were members of
merged RNN clusters.
We also compared different cluster centrality mea-
sures on other yeast PPI networks, as well as an E.Coli
PPI network. Results from these PPI networks indicated
that RNN cluster centrality and GO term clique central-
ity gave consistently higher precision values (Additional
file 1, Figure S5). Additionally, in the E. Coli PPI net-
work, RNN cluster centrality yielded superior precision
values as compared to other centrality measures (Addi-
tional file 1, Figure S5). This also indicated that RNN
cluster centrality was superior for examination of corre-
lations of network topology with essential proteins, and
Figure 5 The correlation of proportion of essential proteins (precision) and the average number of RNNs (of different types) per
protein in merged RNN clusters. Results are based on yeast HC PPI network. For the same proteins, the results are categorized by the number
of total RNNs for this protein, the number of RNNs outside RNN clusters for this protein, and the number of RNNs inside RNN cluster for this
protein.
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this was independent of the organisms on which the PPI
network was established.
Assessment of biological importance of RNN cluster
centrality
Comparison of merged RNN clusters with known protein
complexes
Previous studies [20] suggest that proteins were essential
due to their involvement in densely connected and
biologically meaningful clusters of proteins, such as pro-
tein clusters sharing the same GO term annotation [12]
and protein complexes [20]. As we have related here,
merged RNN clusters were comparable to GO term cli-
ques with regard to the enrichment of essential proteins.
Here, we compared merged RNN clusters with known
protein complexes [18].
Results based on the yeast HC PPI network show that
there were significant overlaps between RNN clusters
Figure 6 Comparison of RNN cluster centrality with other centrality measures in proteins ranked by different centrality measures. (a)
Shows the comparison of precision based on RNN cluster centrality with precision based on RNN centrality. (b) Shows the comparison of precision
by RNN cluster centrality with precision based on other centrality measures based on clustering methods. Results are based on yeast HC PPI
network.
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and protein complexes: out of the 309 merged RNN
clusters, 115 (37.2%) had higher than 20% protein over-
laps (computed as the # of overlapping proteins/# pro-
teins in complex) with 126 (29.8%) out of 423 reference
protein complexes, and 81 (26.2%) with least 50% pro-
tein overlaps with 81 (19.1%) reference protein com-
plexes. The amount of overlap was high, which is even
comparable to the results of some of the most recent
work on protein complex prediction [36].
An example of a merged RNN cluster in a yeast HC
PPI network consisted of 8 proteins, all these 8 proteins
belonged to a protein complex for rRNA processing that
consisted of 12 proteins (complex SG_0000176 from
SGD [37]) (Figure 7). All of these 8 proteins and their
connections composed of a big clique, while adding the
other 4 proteins outside of the merged RNN cluster
would result in a non-clique. This indicated that pro-
teins are very densely connected. From these 8 proteins,
6 were found to be essential proteins, as identified by
gene deletion experiments [2]. The other two proteins
(YDL111C for gene RRP42 and YGR195W for gene
SKI6) were also essential (refer to http://www.yeastgen-
ome.org), but they were not identified by the gene dele-
tion experiments. Additionally, except for protein
YGR095C, 7 out of 8 proteins in this RNN cluster are
exosome complex exonuclease proteins. While in the
other 4 proteins that are members of protein complex
SG_0000176 but not members of this RNN cluster, only
two proteins are exosome complex exonuclease proteins.
Another example of merged RNN cluster in a yeast
HC PPI network consisted of 8 proteins (Figure 8). All
of these 8 proteins were in the 26S proteasome regula-
tory particle chain. Out of these 8 proteins, only one
was not an essential proteins, and its degree in R5NN
topology was ranked 5th out of 8 proteins. Out of these
8proteins,5belonged
(SG_0008541). This protein complex contained 10
members, and the other 5 members of this protein com-
plex were within the R5NN for proteins in this RNN
cluster. The proportion of essential proteins within the
R5NN was 59.0% (23/39), which was lower than the
enrichment of essential proteins in RNN cluster 87.5%
toa proteincomplex
Figure 7 A graphical representation of the sub-network in yeast HC PPI network. All nodes belong to a protein complex (SG_0000176).
Large nodes represent members of a RNN cluster, small nodes represent non-members of this RNN cluster, circles represent essential proteins
and rectangle nodes represent non-essential proteins.
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(7/8) but higher than the PPI network average (29%).
This indicated that (1) essential proteins tended to be
enriched in R5NN topology and (2) essential proteins
were more enriched in RNN clusters. Additionally, we
have noticed that among all proteins in this RNN clus-
ter and their R5NN, the members of the RNN cluster
did not have high connectivity, indicating that density-
based methods may not work well on clustering essen-
tial proteins.
From “DIP core” E. Coli PPI network, a merged RNN
cluster consisted of 5 proteins: DIP-9704N (FtsL), DIP-
9703N (FtsK), DIP-9706N (FtsQ), DIP-9702N (PBP-3)
and DIP-12117N (YgbQ). Except for the last one, which
was a hypothetical protein, 4 proteins in this merged
RNN cluster were essential proteins. The protein DIP-
9704N, DIP-9703N, DIP-9706N and DIP-12117N were
all cell division protein, and DIP-12117N was also a
Penicillin-binding protein. Together, DIP-9704N, DIP-
9703N and DIP-9706N could be members of different
protein complexes, though sometimes DIP-9704N, DIP-
9706N could both be members of a complex without
DIP-9703N [38]. As respect to structure, the localization
of DIP-9704N was dependent on DIP-9703N and DIP-
9706N, and DIP-9702N’s localization required DIP-
9704N and DIP-9703N [39].
Comparing RNN clusters with protein complexes, it
was also observed that the enrichment of essential pro-
teins is more significant in merged RNN clusters than
in protein complexes; we have defined protein complex
centrality in the same way as clustering centrality, and
discovered that RNN cluster centrality is superior to
protein complex centrality with regard to precision
values (Additional file 1, Figure S6).
Analysis of the connection between merged RNN clusters
and GO processes
The significant overlap between merged RNN clusters
and known protein complexes suggests that merged
RNN clusters have some biological importance. To
further investigate this possibility, we analyzed the con-
nection between merged RNN clusters and GO pro-
cesses. We extracted all GO processes that contain at
least one merged RNN cluster (referred to as “important
Figure 8 A graphical representation of the sub-network in yeast HC PPI network. Large nodes (inner circle) represent members of a RNN
cluster; small nodes (outer circle) represent R5NN of proteins in the RNN cluster. Circles represent essential proteins and rectangle nodes
represent non-essential proteins. Nodes in red represent all 10 members of a protein complex (SG_0008541).
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GO processes” in [12]), and generated GO sub-networks
so that each of these sub-networks contains proteins of
the same GO process. Following these operations, the
proportion of essential proteins in these GO sub-net-
works was computed. It was apparent that the enrich-
ment of essential proteins in proteins that are in GO
sub-network and merged RNN clusters was usually
higher than the enrichment of essential proteins in GO
sub-networks, which indicates that merged RNN clus-
ters play an important role in these GO processes
(Table 4). In GO processes that are highly enriched in
essential proteins, such as RNA metabolic process
(GO:0016070), the essential proteins were also distribu-
ted unevenly (with regard to inside and outside of the
RNN clusters): For RNA metabolic process, 69% of pro-
teins in GO sub-network were essential proteins, while
for proteins that are both in the GO sub-network and in
the merged RNN cluster, 85% are essential proteins.
This property of merged RNN clusters is similar to that
of essential complex biological modules (ECOBIMs) that
are introduced in [12], suggesting that there is a low tol-
eranceof mergedRNN clusterstobiological
perturbation. However, it is worth noting that biological
annotation, such as GO, was not used in creating the
RNN clusters, whereas ECOBIMs were generated based
on such information. From the above results, it was sug-
gested that both the placement of the protein in the
RNN topology and the GO process annotation of the
protein are very good predictors of protein essentiality.
Analysis of putative types of hubs
Some debate has persisted in the literature regarding the
possible distinction between “date” and “party” hubs
([40]) in the PPI network. In this work, we have also
tried to analyze whether any significant difference is
detectable between the two putative hub types using
RNN cluster centrality measure. The date/party distinc-
tion is a biologically meaningful property, and we have
used the intersection of hub proteins derived from our
work and those from [27]. Based on yeast HC PPI net-
work, we deleted either putative date hubs or putative
party hubs in descending order of RNN cluster central-
ity from the PPI network, and computed the average
closeness of the proteins of the remaining part in the
PPI network. It was observed that there was not much
Table 4 The enrichment of essential proteins in merged RNN clusters for GO sub-networks in the yeast HC PPI
network.
GO term Name Proportion of essential proteins in
GO sub-
network
GO sub-network and merged RNN
clusters
GO sub-network but not in merged RNN
clusters
GO:0042254 ribosome biogenesis
GO:0016070 RNA metabolic process
GO:0006997 nucleus organization
GO:0007059 chromosome segregation
GO:0070271 protein complex biogenesis
GO:0007049 cell cycle
GO:0044257 cellular protein catabolic process
GO:0006350 transcription
GO:0006259 DNA metabolic process
GO:0006457 protein folding
GO:0051276 chromosome organization
GO:0006810 transport
GO:0016192 vesicle-mediated transport
GO:0006412 translation
GO:0016044 membrane organization
GO:0006464 protein modification process
GO:0006950 response to stress
GO:0000746 conjugation
GO:0007126 meiosis
GO:0044262 cellular carbohydrate metabolic
process
GO:0007165 signal transduction
GO:0019725 cellular homeostasis
GO:0042221 response to chemical stimulus
0.69
0.48
0.47
0.47
0.44
0.36
0.36
0.35
0.33
0.33
0.30
0.29
0.27
0.25
0.24
0.20
0.20
0.19
0.17
0.17
0.85
0.66
0.60
0.50
0.67
0.48
0.81
0.50
0.44
0.13
0.37
0.52
0.55
0.47
0.46
0.38
0.39
0.20
0.35
0.57
0.63
0.41
0.44
0.46
0.39
0.34
0.21
0.30
0.30
0.36
0.28
0.26
0.22
0.21
0.21
0.16
0.16
0.18
0.14
0.14
0.15
0.08
0.07
0.30
0.08
0.17
0.13
0.08
0.06
Each of the GO sub-networks contains at least one merged RNN cluster; the proportion of essential proteins in “proteins in GO sub-network”, “proteins in GO
sub-network and also in merged RNN clusters”, and “proteins in GO sub-network but not in merged RNN clusters”.
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difference between the deletion of putative date hubs
and the deletion of putative party hubs: when 50% of
putative date hubs were deleted, the average closeness
was 0.076, while deletion of 50% of putative party hubs
resulted in the average closeness of 0.073. Therefore,
there was not much topological difference between date
and party hubs in the PPI network as regard to hub
deletion from PPI network based on RNN cluster
centrality.
Conclusions
In this work, we have examined the placement of essen-
tial proteins in RNN topology. The RNN topology is a
weighted directed graph generated from PPI network, in
which the topological dependencies of one protein to
the others are elucidated. Based on different types of
PPI networks, we found that proteins with many RNNs
(high RNN centrality values) are more likely to be essen-
tial proteins. Additionally, it was observed that essential
proteins tend to be enriched in RNN clusters (i.e., clus-
tering property of essential proteins). This finding was
consistent with recent reports, suggesting that essential
proteins tend to be members of densely connected clus-
ters [20]. Moreover, we have shown that RNN clusters
have a higher proportion of essential proteins than
other types of clusters. We have also introduced the
RNN cluster essentiality. And demonstrated that it was
constantly superior to RNN centrality and other cluster-
ing centrality measures, e.g., clustering centrality based
on cliques, with regard to the proportion of selected
proteins that are essential proteins. Furthermore, we
have analyzed the connection between merged RNN
clusters and GO processes, and discovered that enrich-
ment of essential proteins in the intersection of a GO
sub-network and merged RNN clusters is generally
higher than the enrichment of essential proteins in GO
sub-networks alone. This indicated that the placement
of the protein in the RNN topology and the GO process
annotation of the protein are both important predictors
of protein essentiality. Therefore, future work should
include a meta centrality measurement, such as Uni-
Score [13] based on several existing methods, that com-
bines both the RNN cluster centrality and the GO term
for increased power to discriminate between essential
and non-essential proteins.
Appendix
KN’s current address: Qingdao Institute of BioEnergy
and Bioprocess Technology, Chinese Academy of
Sciences. Qingdao, Shandong, China. Email: ningkang@-
qibebt.ac.cn.
Additional material
Additional file 1: Additional figures for the paper. Figure S1. The
weighted yeast HC PPI network. Figure S2. The distribution of the
frequency (number) of essential and non-essential proteins. Figure S3.
Number of proteins and proportion of essential proteins in these
proteins (y-axis) categorized by the proportion of essential proteins as
their RNN (x-axis). Figure S4. The effect of cluster density on essential
protein identification in RNN topology. Figure S5. The proportion of
essential proteins in top proteins on different PPI networks. Figure S6.
The proportion of essential proteins in top proteins ranked by different
centrality measures.
Acknowledgements
We thank Hon Nian Chua from Harvard University for insightful discussions.
This work was supported in part by NIH grants R01-CA-126239 and R01-GM-
094231.
Author details
1Department of Pathology, University of Michigan, 4237 Medical Science
Building I, Ann Arbor, MI, 48109, USA.2Center for Computational Biology
and Medicine, University of Michigan, Ann Arbor, MI, 48109, USA.
3Department of Computer Science, National University of Singapore, 117417,
Singapore.
Authors’ contributions
KN conceived the study, proposed the methods, performed the experiments,
wrote and revised the manuscript. HKN and SS performed the experiments.
HWL and AIN revised the manuscript. All authors have read and approved
this manuscript.
Received: 29 January 2010 Accepted: 12 October 2010
Published: 12 October 2010
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doi:10.1186/1471-2105-11-505
Cite this article as: Ning et al.: Examination of the relationship between
essential genes in PPI network and hub proteins in reverse nearest
neighbor topology. BMC Bioinformatics 2010 11:505.
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