Abstract
Detecting associations between an input gene set and annotated gene
sets (e.g., pathways) is an important problem in modern molecular
biology. In this paper, we propose two algorithms, termed NetPEA and
NetPEA’, for conducting network-based pathway enrichment analysis. Our
algorithms consider not only shared genes but also gene–gene
interactions. Both algorithms utilize a protein–protein interaction
network and a random walk with a restart procedure to identify hidden
relationships between an input gene set and pathways, but both use
different randomization strategies to evaluate statistical significance
and as a result emphasize different pathway properties. Compared to an
over representation-based method, our algorithms can identify more
statistically significant pathways. Compared to an existing
network-based algorithm, EnrichNet, our algorithms have a higher
sensitivity in revealing the true causal pathways while at the same
time achieving a higher specificity. A literature review of selected
results indicates that some of the novel pathways reported by our
algorithms are biologically relevant and important. While the
evaluations are performed only with KEGG pathways, we believe the
algorithms can be valuable for general functional discovery from
high-throughput experiments.
Keywords: pathway, protein–protein interaction network, enrichment
analysis, gene sets, random walk with restart
1. Introduction
Modern molecular biology has been revolutionized with the emergence of
high-throughput experimental technologies such as microarrays and
next-generation DNA sequencing. While many exciting discoveries have
been made by data-driven analysis of such whole-genome data sets, an
important problem that many biologists face everyday is how to
interpret such large-scale data sets. A typical output from such a
high-throughput experiment is a list of genes that are observed to be
associated with a certain phenotype, such as those differentially
expressed in tumors compared to normal tissues. In contrast to the
easiness in obtaining the gene list, the bottleneck usually lies in
understanding the meaning of the genes and generating new testable
hypotheses with the hope to reveal the underlying molecular cause of
the phenotype.
Biologists are knowledge-driven. A principled way to interpret such
gene lists is to compare them with a database of well-annotated gene
sets, such as biological pathways. For example, one of the most widely
used approach, Over Representation Analysis (ORA) [[28]1], counts the
number of common genes shared by an input gene set and each annotated
gene set and applies a statistical test, such as the cumulative
hyper-geometric test, to calculate the statistical significance of the
overlap. A p-value cutoff, e.g., 0.05, is then applied to select the
annotated gene sets that share a statistically significant overlap with
the input gene set. ORA is very easy to implement, and the idea behind
it is straightforward to biologists. A popular extension of ORA, known
as the Gene Set Enrichment Analysis (GSEA) [[29]2], tries to eliminate
the need for an ad hoc cutoff (e.g., expression fold change), which is
often used in defining the input gene set. GSEA works by ranking all
genes in the genome according to, say, level of differential
expression, and tests whether any annotated gene set is ranked
unexpectedly high or low through a running-sum statistic. While GSEA is
becoming more popular, it is sensitive to noise and may report too many
pathways that are conceptually hard to comprehend by biologists. In
addition, GSEA is not applicable in cases where a completely ranked
gene list is unavailable. As a result, ORA is still widely used by
biologists.
Both ORA and GSEA depend on the availability of trusted gene
annotations, such as gene ontology (GO) or metabolic pathways, which
limits their applicability to only well annotated species. In addition,
gene annotations in databases such as GO or Kyoto Encyclopedia of Genes
and Genomes (KEGG) pathway may be strongly biased by some classes of
genes or phenotypes that are popular targets, such as cancer. More
importantly, it is becoming more and more well known that such
enrichment-based analyses, including both ORA and GSEA, have very low
discriminative power, as they treat genes as independent functional
units. In reality, genes function in a highly coordinated way. For
example, two gene sets may share few genes but can be involved in
similar functional pathways, or they can represent two sub-modules of
the same pathway. Common enrichment-based analysis may not be able to
detect the relationship between gene sets.
To address the aforementioned issues, several studies have proposed the
use of biological networks, such as protein–protein interaction (PPI)
networks, as a more unbiased tool to investigate the biological meaning
of gene sets [[30]3,[31]4,[32]5,[33]6]. The rationale is that genes
that are located within a short distance in the same network are likely
involved in similar biological processes. As such networks are
typically obtained from high-throughput experiments, they are less
likely to be biased by existing knowledge and can probably provide
better coverage to different classes of genes and phenotypes.
Furthermore, network-based analysis allows the relationship between
genes to be explicitly modeled, instead of treating them as independent
entities. While conceptually interesting, such methods have had limited
success because high-throughput biological networks are usually very
noisy, and still have many missing edges. Furthermore, the results
obtained by such analyses, often in the form of PPI subnetworks, can be
difficult to interpret because functional connections to biological
processes are missing.
Another strategy, which seems to be more successful in practice, is to
combine both biological networks and pathways in an analysis. For
example, Alexeyenko et al. proposed a network-based method to
investigate the associations between input gene sets and annotated gene
sets by counting the number of network links between members of two
gene sets [[34]7]. Later, Glaab et al. proposed an algorithm called
EnrichNet, which extends the method of [[35]7] to include gene pairs
that are not necessarily direct neighbors but are within close
proximity in the network [[36]8]. These approaches take gene
correlations and interactions into consideration and agree with the
fact that genes function in a coordinated way, which is a meaningful
improvement over ORA. However, EnrichNet only provides scores to
measure the functional associations and does not provide information
about the statistical significance of the scores.
In this paper, we propose two network-based pathway enrichment analysis
algorithms, NetPEA and NetPEA’, for conducting a network-based pathway
enrichment analysis. Our algorithms consider not only shared genes but
also gene–gene interactions. The two algorithms share some common
features to identify hidden relationships between an input gene set and
pathways, but each uses a different randomization strategy to evaluate
statistical significance and, as a result, emphasize different pathway
properties.
The remainder of this paper is organized as follows. We present the
details of the two algorithms and the data sets in [37]Section 2. In
[38]Section 3, we present the test results of our methods on multiple
data sets and discuss the significance of our finding. We conclude with
some remarks for future improvements in [39]Section 4.
2. Methods and Materials
2.1. Overview of Our Algorithms
We propose two network-based pathway enrichment analysis algorithms,
NetPEA and NetPEA’. NetPEA treats gene interactions as important as
shared genes, while NetPEA’ is devised to find hidden causal pathways
that are not enriched within the input gene set.
The two algorithms share their first step to calculate similarity
scores between the input gene set and pathways based on their
“closeness” on a PPI network, measured by a random walk with restart
procedure. The two methods then adopt different randomization
strategies as their background models to evaluate the statistical
significance of the similarity scores. NetPEA uses randomized gene sets
as its background; NetPEA’ employs randomized gene sets and randomized
networks as its background. Both algorithms take gene interactions into
account but focus on different pathways. Considering not only shared
genes but also interacting genes, NetPEA extends the search scope of
ORA, and therefore it reports more significant pathways. On the other
hand, NetPEA’ attempts to de-emphasize pathways that are considered
statistically significant simply because of their overlaps with the
input gene set, and, as a result, it is able to identify pathways that
are within close proximity to the input genes but do not have a
significant overlap with them. As shown in [40]Section 3, these hidden
pathways, which are typically ignored by ORA and similar approaches,
may very likely be the actual causal pathways and can be robust among
experiments.
2.2. Random Walk-Based Similarity Measure
[41]Figure 1 shows the main component of our methods, calculating
similarity scores, which is used to measure the closeness of pathways
to the input gene set. First, we map the genes in the input gene set
and pathways to a relevant biological network (PPI network in this
study). Then all nodes are assigned an initial value of 0, except the
ones in the input gene set which are assigned a value of 1. The Random
Walk with Restart (RWR) procedure [[42]9] is then used to spread the
nonzero initial values to other nodes in the network. RWR is a
well-known machine learning algorithm used to measure the similarities
between nodes by imagining that, starting from each nonzero node, there
is a random walker that, at each step, either moves to a randomly
chosen neighbor or jumps back to the starting node. We formulate the
procedure in Equation ([43]1). V denotes the vector of initial node
values; p represents the restart probability, which indicates the
probability for random walkers to jump back to their starting nodes
(fixed at 0.5 in this study); M is the PPI network transition matrix;
and S[n] is a vector of all nodes in the network, which is used to
measure the similarities between each node in the network and nodes in
the input gene set after n rounds of propagation. At the very
beginning, S[0] is initialized with V. After a period of time of
propagation, S[n] reaches some dynamic balance and the node values
converge and become stable. For each pathway, we take the average of
its member gene values as its similarity score to the input gene set.
[MATH:
Sn=(
1−p)∗M
∗Sn−1+p∗V :MATH]
(1)
Figure 1.
[44]Figure 1
[45]Open in a new tab
The workflow for calculating similarity scores between the input gene
set and pathways. RWR refers to a Random Walk with Restart procedure.
2.3. Network-Based Pathway Enrichment Analysis
To evaluate the statistical significance for pathways to achieve such
similarity scores, we introduce two algorithms based on different
randomization strategies.
2.3.1. Algorithm NetPEA
NetPEA only randomizes the input gene set, in which we randomly choose
the same number of genes as the input gene set to calculate the
similarity score for each pathway. After we repeat this randomization
1000 times, we then get 1000 similarity scores for each pathway as its
background. Equation ([46]2) is used to calculate z-scores for pathway
significance. D is the similarity score using gene set of interest as
input, while R is a set 1000 similarity scores taking randomized gene
sets as inputs.
[MATH:
z-score=D−mean(R)s
td(R)<
/mrow> :MATH]
(2)
We rank the pathways in descending order according to their z-scores.
As the distribution of the z-scores roughly follows a normal
distribution, we also convert the z-scores to p-values under a normal
distribution assumption. We then select pathways with z-scores greater
than 1.65, which corresponds to a p-value 0.05, as statistically
significant pathways.
2.3.2. Algorithm NetPEA’
NetPEA’ randomizes both the input gene set and PPI network to calculate
the statistical significance of the associations between the input gene
set and annotated gene sets. To randomize the network, we rewire the
network connections randomly but ensure all nodes in the network
maintain the same degrees as in the original PPI network. Repeating
this rewiring 10 times, we have 11 networks including the original
human PPI network. For each network, we perform a random walk with a
restart procedure to calculate the similarity scores between the true
input gene set and each of the annotated gene sets. This is also
repeated for 1000 randomized input gene sets.
The z-score of the association between an input gene set and each
annotated gene set is calculated by Equation ([47]3). For each pathway,
DN represents the similarity score taking the real input gene set and
human PPI network as input; DR is a set of 10 similarity scores using
the real input gene set and randomized networks as input; RN represents
a set of 1000 similarity scores taking randomized gene sets and the
human PPI network as input; and RR is 10 sets (each set corresponding
to one randomized network) of 1000 similarity scores taking randomized
gene sets and randomized networks as input. Similarly as in NetPEA, we
rank all pathways according to their z-scores, and use a cutoff 1.65 to
select statistically significant pathways.
[MATH:
z-score=(DN−mean(DR))−mean(RN−mea
n(RR))std(RN−mean(RR
)) :MATH]
(3)
Consider that there is a modest overlap between an input gene set and a
particular pathway, and that none of the genes in the input gene set,
other than those overlapping, are located within close proximity to the
pathway genes in the PPI network. In this case, the expected values in
the vector DR are close to DN. As a result, the z-score for this
particular pathway will be “corrected” and becomes insignificant in
NetPEA’ compared to that in NetPEA. Therefore, we expect NetPEA’ to
report less pathways than NetPEA but, at the same time, be able to
promote the ranking of the true causal pathways, which may not be
ranked high in NetPEA or other overlap-based methods.
2.4. Data Sets
The annotated gene sets used in this study are from KEGG pathways
[[48]10]. We test our algorithms using input gene sets from several
well-cited sources, including a Parkinson’s disease gene set [[49]11],
a lymphoma cancer gene set [[50]12], two breast cancer gene sets
obtained by two groups [[51]13,[52]14], two lung cancer gene sets
[[53]15,[54]16], a diabetes disease gene set [[55]17], a leukemia gene
set [[56]18], and two unpublished gene sets, “gender” and “p53” from
the GSEA website [[57]2]. All gene sets except “Parkinson” are from
high throughput experiments. The Parkinson’s disease gene set is from a
literature search. For four of the data sets, (p53, gender, diabetes,
leukemia), genes are further categorized into “up” and “down” according
to the direction its expression level changes in the experiments. The
human PPI network is downloaded from the Human Protein Reference
Database (HPRD, version 9) [[58]19].
3. Results and Discussion
Validation of associations between genes sets is difficult because of
the lack of ground truth and the biases inherent in different
evaluation standards. To evaluate the performance of our methods and
have a fair comparison with the existing ones, we adopted and designed
multiple evaluation methods.
3.1. Validation Using KEGG Pathways as Input Genes
To validate that our algorithms can indeed identify the most relevant
pathways, we first used KEGG pathways as input genes to identify the
most significantly associated KEGG pathway for each pathway. The
rationale is that each pathway should have a closer relationship with
itself. Indeed, NetPEA ranks each pathway itself as the most enriched
pathway with a very significant z-score. Moreover, some between-pathway
associations found by NetPEA are also reasonable. For example, the top
three pathways associated with “DNA replication” are “DNA replication”,
”mismatch repair”, and “nucleotide excision repair”, while the top
three pathways associated with “chemokine signaling” are “hemokine
signaling”, “cytokine–cytokine receptor interaction”, and “gap
junction”.
On the other hand, NetPEA’ ranks the pathway itself as the most
enriched pathway only for 62% pathways, and ranks the pathway itself in
the top 10% for 91% of pathways. The deviation from the ground truth is
because NetPEA’ is intended to explore hidden pathways by
de-emphasizing pathways that are considered significant simply because
of their overlaps with the input gene set. Indeed, for a number of
cases where the input gene set itself is not ranked as the top gene
set, we found evidence of the association between the reported top gene
set and the input gene set, such as “maturity onset diabetes of the
young” and “methane metabolism”. Note also that the association between
the two pathways is not significant according to NetPEA.
3.2. Validation Using GSEA Outputs as Benchmarks
For four data sets that we have access to the coupled microarrays and
ranked gene lists, we applied GSEA to rank the pathways and we use the
rankings as benchmarks. GSEA is a benchmark widely used to validate
gene set rankings, and [[59]8] uses it to check pathway rankings. While
the results may be biased, it provides partial evidence that our
algorithms achieve better performances. Here we calculate Spearman
correlation coefficients between each mentioned method and GSEA.
[60]Table 1 shows that for each input gene set, the largest correlation
coefficient is from NetPEA or NetPEA’, which means that our algorithms
gain more support on pathway rankings and are better than ORA and
EnrichNet.
Table 1.
Spearman correlation coefficient between GSEA and four other
approaches.
Input Gene Set p53 (down) Gender (down) Diabetes (down) Leukemia (down)
NetPEA 0.4653 0.2713 0.2373 0.3253
NetPEA’ 0.3978 0.1265 0.2401 0.182
ORA 0.3968 0.2406 0.1602 0.264
EnrichNet 0.2967 0.219 0.1779 0.2726
Input gene set p53 (up) Gender (up) Diabetes (up) Leukemia (up)
NetPEA 0.3427 0.4349 0.227 0.1195
NetPEA’ 0.2911 0.2756 0.1419 0.1438
ORA 0.2507 0.332 0.1421 0.0583
EnrichNet 0.2167 0.3067 0.0823 0.0599
[61]Open in a new tab
3.3. Evaluation Based on Number of Enriched Pathways
We apply our algorithms, NetPEA and NetPEA’, to each of the data sets
mentioned in [62]Section 2.4. Meanwhile, we run ORA on these input gene
sets and compare the significant pathways found by the three methods.
3.3.1. NetPEA vs. ORA
[63]Table 2 shows significant pathways only reported by NetPEA but not
present in the results for ORA. For most of cases (11/14), ORA does not
identify any pathway that is not found by NetPEA. For common
significant pathways discovered by both methods, we define
[MATH:
NetPEA≪ORA :MATH]
,
[MATH:
NetPEA≫ORA :MATH]
and
[MATH:
NetPEA≈ORA :MATH]
by the ratios of their p-values.
[MATH:
NetPEA≫ORA :MATH]
means the p-value ratio (NetPEA/ORA) is less than 0.001;
[MATH:
NetPEA≪ORA :MATH]
represents the ratio greater than 1000; otherwise it is
[MATH:
NetPEA≈ORA :MATH]
. Strikingly, no pathways fall into the range
[MATH:
NetPEA≪ORA :MATH]
. Overall, NetPEA can successfully identify nearly all significant
pathways reported by ORA. Moreover, NetPEA reports many significant
pathways not found by ORA. The superiority of NetPEA over ORA can be
explained by the fact that NetPEA not only considers the pathway
enrichment caused by common genes but also takes gene interactions into
account. Through the gene interactions, some pathways not enriched in
ORA are elevated to be significant. In [64]Section 3.6, we will show
that these additional pathways are biologically meaningful.
Table 2.
Significant pathways: NetPEA vs. ORA .
Input Gene Set # Unique Pathways # Common Pathways
NetPEA ORA
[MATH: PNetPEA≫PORA :MATH]
[MATH: PNetPEA≪PORA :MATH]
[MATH: PNetPEA≈PORA :MATH]
Parkinson 18 0 19 0 18
Lymphoma 18 0 10 0 5
Breast cancer [[65]13] 13 0 6 0 12
Breast cancer [[66]14] 4 1 4 0 16
Lung cancer [[67]15] 28 0 3 0 12
Lung cancer [[68]16] 25 1 6 0 17
Diabetes (down) 13 0 4 0 2
Diabetes (up) 7 0 0 0 2
Leukemia (down) 22 0 1 0 2
Leukemia (up) 7 0 3 0 7
Gender (down) 7 0 0 0 1
Gender (up) 10 0 1 0 2
p53 (down) 14 0 1 0 5
p53 (up) 24 1 5 0 18
[69]Open in a new tab
3.3.2. NetPEA’ vs. ORA
As NetPEA’ is devised to complement NetPEA, it provides new significant
pathway information that is not present in the results of ORA or
NetPEA. Compared to information in [70]Table 2, the number of common
significant pathways decreases for each input gene set ([71]Table 3).
At the same time, NetPEA’ produces some significant pathways not
present in ORA. This difference is because of the network randomization
in NetPEA’, which eliminates some significant pathways in ORA or NetPEA
with loose gene interactions and lifts insignificant ones in ORA with
close gene interactions. As shown clearly in [72]Section 3.4, these
pathways are often preserved between different experiments for the same
disease, signifying the importance of the pathways for the disease.
Table 3.
Significant pathways: NetPEA’ vs. ORA.
Input Gene Set # Unique Pathways # Common Pathways
NetPEA’ ORA
[MATH: PNetPEA′≫PORA :MATH]
[MATH: PNetPEA′≪PORA :MATH]
[MATH: PNetPEA′≈PORA :MATH]
Parkinson 7 28 3 1 5
Lymphoma 16 5 4 0 6
Breast cancer [[73]13] 11 9 0 0 9
Breast cancer [[74]14] 5 9 1 0 11
Lung cancer [[75]15] 28 12 1 0 2
Lung cancer [[76]16] 27 12 1 0 11
Diabetes (down) 19 4 0 0 2
Diabetes (up) 13 2 0 0 0
Leukemia (down) 16 2 0 0 1
Leukemia (up) 15 6 0 0 4
Gender (down) 5 1 0 0 0
Gender (up) 20 3 0 0 0
p53 (down) 13 5 0 0 1
p53 (up) 27 15 0 0 9
[77]Open in a new tab
3.4. Evaluation Using Cross-Data Stability Analysis
It is well known that the agreement is often poor between different
high throughput experiments concerning the same disease performed by
different groups. Among other reasons, this is because many of the
genes identified by these experiments are caused by downstream effects,
which can vary significantly among experiments. It is reasonable to
assume that if indeed we can find true causal genes/pathways, agreement
between experiments will be improved. Therefore, for the genes
identified from the two breast cancer data sets and the two lung cancer
data sets, we compare the significant pathways from different data sets
reported by NetPEA, NetPEA’ and ORA. We calculate the ratios of common
significant pathways to the total number of unique significant pathways
identified from the two experiments as well as the p-values of the
overlap under the hypergeometric distribution using 208 total KEGG
pathways as background. [78]Table 4 shows that NetPEA can find more
common significant pathways than ORA and NetPEA’ as a result of the
increased number of significant pathways reported by NetPEA, which
partially suggest that the additional pathways reported by NetPEA are
reasonable. Remarkably, while NetPEA’ reports much fewer pathways than
NetPEA, the number of common pathways remains almost unchanged. As
shown in [79]Figure 2, the statistical significance of overlap between
the pathways detected from different data sets is the highest in
NetPEA’, compared to NetPEA and ORA. Therefore, we believe that the
pathways reported by NetPEA’ may have a greater chance of containing
the pathways that are directly associated with the phenotype instead of
downstream effects. In addition, while the overlap of pathways detected
by NetPEA is not as significant as in ORA, this is mainly due to the
increased number of detected pathways and the limited number of
candidate pathways as background. Since almost all pathways reported by
ORA are also reported by NetPEA, we removed the ORA-detected pathways
from NetPEA results and reanalyzed the overlap. As shown in [80]Figure
2 (“NetPEA unique”), the pathways found by NetPEA but not by ORA do
have an increased level of overlap compared to ORA, suggesting that the
additional pathways identified by NetPEA are biologically relevant.
Collectively, the results suggest that our algorithms have an advantage
in interpreting the results of high throughput experiments performed by
different groups and can potentially discover the key pathways
underlying the diseases.
Table 4.
Common significant pathways analysis.
NetPEA NetPEA’ ORA
Common pathways between two breast cancer data sets ([[81]13,[82]14])
glycolysis/gluconeogenesis, homologous recombination,
oocyte meiosis, p53 signaling, progesterone-mediated
oocyte maturation, base excision repaire, cell cycle lipoic acid
metabolism, progesterone-mediated oocyte maturation, cell cycle,
protesome, ubiquitin mediated proteolysis, oocyte meiosis
glycolysis/gluconeogensis, homologous recombination,
progesterone-mediated oocyte maturation, cell cycle, oocyte meiosis
Common pathways between two lung cancer data sets ([[83]15,[84]16])
DNA replication, ECM -receptor interaction, focal adhesion, mismatch
repair, nucleotide excision repair, pancreatic cancer, pathways in
cancer, prostate cancer, small cell lung cancer, base excision repair,
bladder cancer antigen processing and presentation, base excision
repair, DNA replication, ErBB signaling, FC epsilon RI signaling, FC
gamma r-mediated phagocytosis, lysosome, mismatch repair, nucleotide
excision repair, prostate cancer, vibrio cholerae infection focal
adhesion, mismatch repair, pathways in cancer, small cell lung cancer
[85]Open in a new tab
Figure 2.
[86]Figure 2
[87]Open in a new tab
Common pathways from two different datasets of the same disease. (a)
Overlap between two breast cancer data sets; (b) Overlap between two
lung cancer data sets.
3.5. Pathways Cross Verification Analysis
Checking whether pathways ranked at the top by one method are also
ranked at the top by other methods can provide additional confidence to
biologists and help biologists to narrow down new hypotheses to test.
Here we use two cross verification methods, positive cross verification
and negative cross verification, to compare our algorithms with ORA,
EnrichNet and GSEA. For positive cross verification, we examine how
many pathways out of the top 20 by one method appear in the top 20
pathways determined by all the other methods. For negative cross
verification, we checked how many pathways out of the top 20 by one
method are ranked below the top 100 by the other three methods. We
verify NetPEA and NetPEA’ separately because if we verify them together
they may vote for each other, which would provide biased, favorable
results for our algorithms.
3.5.1. NetPEA
[88]Table 5 shows that ORA receives the most recognition and reports
only one pathway that is not agreed by others, which is understandable
because ORA is the most conservative method and most of its results are
also reported by NetPEA and EnrichNet. For the two network-based
approaches, they receive similar results on positive cross
verification, while NetPEA is better than the counterpart with less
negative results. Moreover, the only pathway of negative verification
result of NetPEA is “taste transduction” for diabetes, which has been
reported previously [[89]20]. The pathways of EnrichNet’s negative
verification result include “thyroid cancer”, “basal cell carcinoma”,
“melanogenesis”, “endometrial cancer” and “hedgehog signaling”. Our
limited literature search does not reveal enough evidence of their
associations with diabetes. GSEA is the one receiving the least
recognition as it exploits whole microarrays and, from a methodology
point of view, it is far away from the other three methods. Its
negative cross verification results include “olfactory transduction”,
“mismatch repair” and “snare interactions in vesicular transport” for
diabetes. These associations claimed by GSEA are hard to understand.
Therefore, NetPEA has an advantage over other methods to rank
meaningful pathways at the top.
Table 5.
Pathways cross verification analysis for NetPEA.
Input Gene Set Positive Negative
NetPEA ORA EnrichNet GSEA NetPEA ORA EnrichNet GSEA
Lung cancer [[90]15] 16 16 16 7 0 0 0 2
Lung cancer [[91]16] 14 16 16 4 0 0 1 8
Diabetes (down) 17 19 16 5 0 0 0 3
Diabetes (up) 15 16 13 5 1 1 5 3
Leukemia (down) 18 18 15 5 0 0 0 7
Leukemia (up) 15 19 15 8 0 0 1 4
Gender (down) 18 19 15 8 0 0 1 2
Gender (up) 17 19 15 7 0 0 0 1
p53 (down) 19 19 13 10 0 0 1 2
p53 (up) 16 15 16 6 0 0 2 3
[92]Open in a new tab
3.5.2. NetPEA’
Compared with [93]Table 5, [94]Table 6 shows that NetPEA’ receives less
support than NetPEA. This is reasonable since NetPEA’ eliminates some
pathways that are an important part of ORA. On the other hand, we
conclude that NetPEA’ shares some similarities with GSEA because the
results of positive verification of GSEA increase while its negative
verification results decrease.
Table 6.
Pathways cross verification analysis for NetPEA’.
Input Gene Set Positive Negative
NetPEA’ ORA EnrichNet GSEA NetPEA’ ORA EnrichNet GSEA
Lung cancer [[95]15] 7 14 16 9 0 0 0 2
Lung cancer [[96]16] 4 15 15 4 4 0 1 7
Diabetes (down) 6 19 16 6 4 0 0 2
Diabetes (up) 8 15 13 5 1 1 4 2
Leukemia (down) 7 15 16 5 1 0 0 6
Leukemia (up) 7 18 15 9 1 0 0 2
Gender (down) 8 17 15 9 2 0 1 2
Gender (up) 9 18 15 10 2 0 0 1
p53 (down) 6 14 14 11 1 0 1 3
p53 (up) 6 13 15 8 0 0 2 2
[97]Open in a new tab
3.6. Novel Pathways
As shown in [98]Section 3.3, our algorithms usually report more
significant pathways than ORA. A careful inspection of these additional
pathways suggests that many of them are biologically relevant and
important. Here we only discuss a few of these pathways.
For the diabetes down-regulated input gene set, NetPEA ranks the
pathway “glycerolipid metabolism”, as 5th with a significant z-score
3.5 (p-value =
[MATH:
2.3×10−
4 :MATH]
), and NetPEA’ ranks it as 1st with a significant z-score 7.9 (p-value
=
[MATH:
1.4×10−
15 :MATH]
). The same pathway has a p-value 0.12 in ORA and is ranked 37th by
EnrichNet. Extensive literature review shows that “glycerolipid
metabolism” plays an important role in the pathogenesis of obesity and
type 2 diabetes [[99]21,[100]22].
Another good example is the Leukemia up-regulated input gene set, where
NetPEA’ ranks the pathway “chronic myeloid leukemia” 4th with a
significant z-score 3.12 (p-value =
[MATH:
9.0×10−
14 :MATH]
). ORA ranks it 63rd with an insignificant p-value, and EnrichNet ranks
it 77th. This pathway is missed by NetPEA (z-score = 0.23). For the
Leukemia down-regulated gene set, both NetPEA and NetPEA’ rank “folate
biosynthesis” as the most significant pathway (z-score = 5.0 and 6.5
respectively), while the same pathway is ranked 22nd in EnrichNet and
has a p-value 0.05 in ORA. A search through the literature confirms
that the relationship between the pathway, “folate biosynthesis”, and
leukemia can be verified [[101]23].
Other verifiable significant associations that are identified by our
methods but missed by both EnrichNet (rank > 30) and ORA (p-value >
0.05) include “pathways in cancer” for the p53 up-regulated gene set,
“steroid hormone biosynthesis” and “sphingolipid metabolism” in
Parkinson’s disease, “natural killer cell mediated cytotoxicity” in
diabetes, as well as “MAPK signaling”, “ERBB signaling”, “PPAR
signaling”, “focal adhesion” and “ECM receptor interaction” for various
cancer gene sets, to mention a few.
4. Conclusions
In this paper, we propose two novel network-based algorithms to analyze
functional associations between input gene sets and annotated gene sets
(e.g., KEGG pathways). The two algorithms apply different randomization
strategies to evaluate the statistical significance of the associations
and often return complementary results. Compared to the well-adopted
over representation analysis (ORA), our methods extend beyond
overlap-based comparison, and as a result they are able to identify
more significant pathways, report more common pathways shared by
different gene sets of the same diseases and gain more GSEA support on
the pathways rankings. Compared to another network-based approach,
EnrichNet, our algorithms usually report fewer false negative pathways,
have a better discriminative power and provide statistical
significance. We demonstrate that novel significant pathways reported
by our algorithms are biologically meaningful and are confirmed by
previous publications. In the future, we plan to extend the methods to
be applied to multiple heterogeneous terms and contexts.
Acknowledgments