Effectiveness of model-based clustering in analyzing Plasmodium falciparum RNA-seq time-course data

Abstract

Background: The genomics and microarray technology played tremendous roles in the amount of biologically useful information on gene expression of thousands of genes to be simultaneously observed. This required various computational methods of analyzing these amounts of data in order to discover information about gene function and regulatory mechanisms.
Methods: In this research, we investigated the usefulness of hidden markov models (HMM) as a method of clustering Plasmodium falciparum genes that show similar expression patterns. The Baum-Welch algorithm was used to train the dataset to determine the maximum likelihood estimate of the Model parameters. Cluster validation was conducted by performing a likelihood ratio test.
Results: The fitted HMM was able to identify 3 clusters from the dataset and sixteen functional enrichment in the cluster set were found. This method efficiently clustered the genes based on their expression pattern while identifying erythrocyte membrane protein 1 as a prominent and diverse protein in P. falciparum.
Conclusion: The ability of HMM to identify 3 clusters with sixteen functional enrichment from the 2000 genes makes this a useful method in functional cluster analysis for P. falciparum

Full text


Open Peer Review
Discuss this article
(0)Comments
RESEARCHARTICLE
Effectiveness of model-based clustering in analyzing
RNA-seq time-course dataPlasmodium falciparum [version 1;
referees: awaiting peer review]
JeliliOyelade ,   ItunuoluwaIsewon , DamilareOlaniyan , SolomonORotimi ,
JumokeSoyemi1,4
CovenantUniversityBioinformaticsResearch(CUBRE),CovenantUniversity,Ota,Nigeria
DepartmentofComputerandInformationSciences,CovenantUniversity,Ota,Nigeria
DepartmentofBiologicalSciences,CovenantUniversity,Ota,Nigeria
DepartmentofComputerScience,FederalPolytechnic,Ilaro,Nigeria
Abstract
ThegenomicsandmicroarraytechnologyplayedtremendousBackground:
rolesintheamountofbiologicallyusefulinformationongeneexpressionof
thousandsofgenestobesimultaneouslyobserved.Thisrequiredvarious
computationalmethodsofanalyzingtheseamountsofdatainordertodiscover
informationaboutgenefunctionandregulatorymechanisms.
Inthisresearch,weinvestigatedtheusefulnessofhiddenmarkovMethods:
models(HMM)asamethodofclustering genesthatPlasmodium falciparum
showsimilarexpressionpatterns.TheBaum-Welchalgorithmwasusedtotrain
thedatasettodeterminethemaximumlikelihoodestimateoftheModel
parameters.Clustervalidationwasconductedbyperformingalikelihoodratio
test.
ThefittedHMMwasabletoidentify3clustersfromthedatasetandResults:
sixteenfunctionalenrichmentintheclustersetwerefound.Thismethod
efficientlyclusteredthegenesbasedontheirexpressionpatternwhile
identifyingerythrocytemembraneprotein1asaprominentanddiverseprotein
in .P. falciparum
TheabilityofHMMtoidentify3clusterswithsixteenfunctionalConclusion:
enrichmentfromthe2000genesmakesthisausefulmethodinfunctional
clusteranalysisforP. falciparum
1,2 1,2 2 1,3
1,4
1
2
3
4

Referee Status: AWAITING PEER
REVIEW
19Sep2017, :1706(doi: )First published: 6 10.12688/f1000research.12360.1
19Sep2017, :1706(doi: )Latest published: 6 10.12688/f1000research.12360.1
v1
Page 1 of 12
F1000Research 2017, 6:1706 Last updated: 19 SEP 2017


JeliliOyelade( )Corresponding author: ola.oyelade@covenantuniversity.edu.ng
 :Conceptualization,Methodology,ProjectAdministration,Resources,Supervision,Validation,Writing–OriginalDraftAuthor roles: Oyelade J
Preparation,Writing–Review&Editing; :Methodology,Resources,Writing–OriginalDraftPreparation,Writing–Review&Editing;Isewon I
:FormalAnalysis,Investigation,Methodology,Software; :DataCuration,Investigation,Validation,Writing–Review&Olaniyan D Rotimi SO
Editing; :FormalAnalysis,Validation,Writing–Review&EditingSoyemi J
Competing interests: Thereisnocompetinginterestsdeclared.
OyeladeJ,IsewonI,OlaniyanD How to cite this article: et al. Effectiveness of model-based clustering in analyzing Plasmodium
 2017, :1706(doi:RNA-seq time-course data [version 1; referees: awaiting peer review]falciparum F1000Research 6
)10.12688/f1000research.12360.1
©2017OyeladeJ .Thisisanopenaccessarticledistributedunderthetermsofthe ,whichCopyright: et al CreativeCommonsAttributionLicence
permitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.
Theauthor(s)declaredthatnograntswereinvolvedinsupportingthiswork.Grant information:
19Sep2017, :1706(doi: )First published: 6 10.12688/f1000research.12360.1
Page 2 of 12
F1000Research 2017, 6:1706 Last updated: 19 SEP 2017

Introduction
Technological advancement in bioinformatics such as the high
through put sequencing technology has resulted in the availability
of a very large amount of informative data1. Expressions of thou-
sands of genes are now being measured concurrently under various
experimental conditions using microarray technology. Microarray
consists of many thousands of short, single stranded sequences,
each immobilized as individual elements on a solid support, that
are complementary to the cDNA strand representing a single gene.
Gene expression measurements can be obtained for thousands
of genes simultaneously using microarray technology. In a cell,
genes are transcribed into mRNA molecules which in turn can
be translated into proteins, and it is these proteins that perform
biological functions, give cellular structure and in turn regulate
gene expression2.
Various researches had been carried out on the analysis and
extraction of useful biological information such as detection of
differential expression, clustering and predicting sample character-
istics3. One of the important of gene expression data is the abil-
ity to infer biological function from genes with similar expression
patterns4. Due to large number of genes and complexity of the
data and networks, research has suggested clustering to be a
very useful and appropriate technique for the analysis of gene
expression data which can be used to determine gene coregulation5,
subpopulation6, cellular processes, gene function7 and understand-
ing disease processes8.
Clustering algorithms as described by9 can either be distance
based or model based. Distance-based clustering such as the
k means10 does not consider dependencies between time points
while the model based approach embeds time dependencies
and uses statistical models to cluster data. Other approaches
include Self Organizing Maps11, Principal Component Analysis,
hierarchical clustering4, graph theory approach12, genetic algo-
rithms and the Support Vector Machine13. These algorithms has
been successfully applied to various time series data but still have
various shortcoming such as determining the optimal number of
clusters and choosing the best algorithm for clustering since
most of them are based on heuristics. The algorithms are also not
very effective especially when a particular gene is associated with
different clusters and performs multiple functions.
This research focuses on clustering of genes with similar expres-
sion patterns using Hidden Markov Models (HMM) for time course
data because they are able to model the temporal and stochastic
nature of the data. A Markov process is a stochastic process such
that the state at every time belongs to a finite set, the evolu-
tion occurs in a discrete time and the probability distribution of
a state at a given time is explicitly dependent only on the last state
and not on all the others. This refers to as first-order Markov proc-
ess (Markov chain) for which the probability distribution of a
state at a given time is explicitly dependent only on the previous
state and not on all the others. That is, the probability of the next
(“future”) state is directly dependent only on the present state
and the preceding (“past”) states are irrelevant once the present
state is given14. Fonzo et al.14 defined HMM as a generalization
of a Markov chain in which each (“internal”) state is not directly
observable (hidden) but produces (“emits”) an observable random
output (“external”) state, also called “emission” state. Schliep
et al.9 proposed a partially supervised clustering method to account
for horizontal dependencies along the time axis and to cope with
the missing values and noise in time course data. This approach
used k means algorithm and the Baum welch algorithm for param-
eter estimation. Further analysis on the cluster was done with the
Viterbi algorithm which gives a fine grain, homogeneous decom-
position of the clusters. The partial supervised learning was
done by adding labeled data to the initial collection of clusters.
Ji et al.15 developed an application to cluster and mine useful bio-
logical information from gene expression data. The dataset was
first normalized to a mean of zero and variance of one and then
discretized into expression fluctuation symbol with each sym-
bol representing either an increase, decrease or no change in the
expression measurement. A simple HMM was constructed for
these fluctuation sequences. The model was trained using the
Baum-Welch EM algorithm and the probability of a sequence given
a HMM was calculated using the forward-backward algorithm.
Several copies of the HMM was made so that each copy repre-
sent a single cluster. These clusters were made to specialize by
using a weighted Baum-Welch algorithm where the weight is
proportional to the probability of the sequence given the model.
The Rand Index and Figure of Merit was used to validate the
optimal number of cluster results.
Geng et al.16 developed a gene function prediction tool based on
HMM where they studied yeast function classes who had suffi-
cient number of open reading frame (ORF) in Munich Information
Center for Protein Sequences (MIPS). Each class was labeled as
a distinct HMM. The process was performed on three stages; the
discretization, training and inference stages and data used for this
analysis was the yeast time series expression data. Lees et al.17 pro-
posed another methodology to cluster gene expression data using
HMM and transcription factor information to remove noise and
reduce bias clustering. A single HMM was designed for the entire
data set to see if it would affect clustering results. Each path in the
HMM represents a cluster, transition between states in a path is
set to a probability of 1 and transition between states on different
path is set to a probability of 0. Genes were allocated to clusters
by calculating the probability of each sequence produced by the
HMM. Clusters were validated using the likelihood ratio test which
computes the difference in the log-likelihood of a complex model
to that of a simpler model. Zeng and Garcia-Frias18 implemented
the profile HMM as a self-organizing map, this profile HMM is
a special case of the left to right inhomogeneous HMM which is
able to model the temporal nature of the data. This makes it very
useful for real life applications. The profile HMM is trained
using the Baum-Welch algorithm19 and clustering was done using
the Viterbi algorithm and the algorithm was implemented on the
fibroblast and the sporulation datasets. Beal et al.20 implemented
the Hierarchical Dirichlet Process Hidden Markov Model (HDP-
HMM) for clustering gene expression data with countably infinite
HMM. Gibbs sampling method was used to reduce the time com-
plexity of the inference. The data used for the implementation was
derived from Lyer et al.21 and Cho et al.22 which was normalized and
standardized to a log ratio of 1 at time t = 1. Baum Welch algorithm
was used for Estimation Maximization. In this work, we adopted the
Page 3 of 12
F1000Research 2017, 6:1706 Last updated: 19 SEP 2017

work of Lee et al.17 and applied HMM on the Plasmodium falci-
parum RNA-seq dataset.
Materials and methods
In this work, data was extracted and normalized to a mean of 1
and standard deviation of 0. Discretization was done on the data
to improve the clustering results. The HMM forward-backward
algorithm and Baum-Welch training algorithm was implemented
to cluster the gene expression data. Genes were then assigned
to cluster using the forward algorithm and inference was done
by obtaining functionally enriched genes in the cluster set using
FunRich tool. The data used was published by 23, they used the
Illumina based sequencing technology to extract expressions
of 5270 P. falciparum genes at seven different time points every
8hrs for 42hrs. The clustering algorithms was implemented by
first randomly initializing all the HMM parameters, then, forward
algorithm was implemented to calculate the forward probabili-
ties of the observation and Baum-Welch algorithm was used for
data fitting, then the likelihood of each HMM was calculated
iteratively until the optimal likelihood is obtained. This process
is repeated for all the different sized HMMs used.
Definitions and notation
HMMs can be viewed as probabilistic functions of a Markov
chain24 such that each state can produce emissions according to
emission probabilities.
Definition 1. (Hidden Markov Model). Let O = (O1,…) be a
sequence over an alphabet ∈. A Hidden Markov Model λ is deter-
mined by the following parameters:
• Si, the states i = 1, … N
• πi, the probability of starting in state Si,
• αij, the transition probability from state Si to state Sj, and
• bi(ω), the emission probability function of a symbol ω ∈ Σ in
state Si.
Definition 2. (Hidden Markov Cluster Problem). Given
a set O = {O1, O2,…, On} of n sequences, not necessarily of
equal length, and a fixed integer K ≪ n. Compute a partition
C = (C1, C2,…, Ck) of O and HMMs λ1,…, λk as to maximize the
objective function
( )
()
=1
= |
ki
k
k O C
i k
f c L O λ
∏ ∏ ε
(1)
Where L(Oi | λk) denotes the likelihood function for generating
sequence Oi by model λk:
Data preprocessing
The preprocessing was done in two stages. The first stage was the
normalization and the second stage was discretization. The normal-
ization was done with the R statistical package using the normalize
library. Normalization removes static variation in the microarray
experiment which affects the gene expression level. Normalization
also helps in speeding up the learning phase. Missing values are
also removed during normalization. Discretization was done by
converting the time points to symbols depending on whether the
expression value has increased, decreased or not changed. This is
done by using the equation below.
1
1
1
0
1
2
ii
i
i i
i
i
if E E a
S if E E a
if E E a
+
+
+
− <


= − ≥

−≥


(2)
Where:
Si = fluctuation level between time i and i + 1
Ei = expression level at time point i
L = number of time points.
a = threshold value between timepoints.
HMM for clustering gene expression data
In this work, we implemented a model-based HMM clustering
algorithm where a cluster represents a path in the HMM model.
Therefore, as the number of cluster increases, the number of
paths through the model increases and the HMM becomes larger
and larger. The number of hidden state is the number of clus-
ters multiplied by the sequence length. Research has also shown
that HMM that transverse from left to right best models time series
data, therefore HMM moves from only right-to-left. The structure
of the HMM is shown in Figure 1.
Figure 1. HMM design from cluster 2 to w. The number 0, 1, and 2 represents the emmission symbols at each state.
Page 4 of 12
F1000Research 2017, 6:1706 Last updated: 19 SEP 2017

The left to right model has the property that, as the time increases,
the state transition increases, that is, the states moves from left to
right. This process is conveniently able to model data whose prop-
erties change over time.
The forward algorithm calculates the forward probabilities of
a sequence of observation. This is the probability of getting a
series of observation given that the HMM parameters (A, B, π) are
known. This computation is usually expensive computationally.
The time invariance of the probabilities can however be used to
reduce the complexity of this algorithm by calculating the prob-
abilities recursively. These probabilities are calculated by comput-
ing the partial probabilities for each state from times t = 1 to t = T.
The sum of all the final probabilities for each states is the prob-
ability of observing the sequence given the HMM and this was
used in this research to compute the likelihood of a sequence given
the HMM. The algorithm is in 3 stages and illustrated as follows:
Initialization stage
This initializes the forward probability, which is the joint probabil-
ity of starting at state and initially observing O1.
( )
()
1 1
i
i i
b O i Nα π= ≤ ≤
Induction stage
( ) ( )
( )
1
1
1 , 1 1
N
i i ij j t
i
t t b O t Tα α α
+
=
 
 
+ = ≤ ≤ −
 
 
∑
This is the joint probability of observation and state 3 at time
t + 1 via state at time t (i.e. the joint probability of observing o at
state 3 at time t+1 and form state and time t). This is performed at
all states and is iterated for all times from t = 1 to T-1.
Termination stage
This computes all the forward variables, which is the P(o|M).
( ) ( )
1
|
N
i
i
P o M Tα
=
=
∑
Where:
αij = transition from state i to j
bi(o) = probability of emitting a symbol in a particular state
t = time
M = model
αi = forward variable of state i
π = probability of starting at a particular state
The backward algorithm like the forward algorithm calculates
backward probabilities instead. The backward probability is the
probability of starting in a state at a time t and generating the rest
of the observation sequence Ot + 1,…, OT. The backward probabil-
ity can be calculated by using a variant of the forward algorithm.
Therefore, instead of starting at time t = 1, the algorithm starts at
time t = T and moves backwards from OT to Ot + 1. In this work,
the backward algorithm was used alongside the forward algorithm
to re-estimate the HMM parameters. This algorithm also involves
three steps and is illustrated below.
Initialization
This is the initial probability of being in a state Si at time T and gen-
erating nothing. The value of this computation is usually 1.
( )
1, 1
iT i Nβ= ≤ ≤
Induction
This step calculates the probabilities of partial sequence observa-
tion from t+1 to end given state at time t and the model λ.
1 1
1
( ) ( ) ( ) 1, 2, ,1.
N
i ij j t t
j
t b O j t T T …β α β
+ +
=
= = − −
∑
Termination
It calculates all the backward variables which is the P(Ot+1, …,
OT|Q1 = Si).
1
, ,
1 1
( | ) ( )
t
T i i
tT
P O O Q S t
…
β
=
+
= = ∑
Where:
αij = transition from state i to j
bj(o) = probability of emitting a symbol in a particular
βt(j) = backward variable of state i in time t
The Baum-Welch algorithm, sometimes called the forward-
backward algorithm makes use of the results derived from this algo-
rithm to make inference. The Baum-Welch algorithm is a special
form of the Expectation Maximization algorithm used for finding
the maximum likelihood estimate of the parameters of the HMM. It
was used in this work to train the various sized HMM parameters.
The E part of the algorithm calculates the expectation count for
both the state and observation. The expectation of state count is
denoted by γt(i). It is the probability of being in state at time t giving
observation sequence and the model.
1
( ) ( )
( | )
( ) ( | ) ( ) ( )
N
i
i
t
t
i j
j
t b t
P q i
iP o t b t
α
λ
λα
=
=
γ = =
∑
(3)
The expectation of transition count is denoted by εij(t). it is the prob-
ability of being in state Si at time t and state Sj at time t + 1 given
an observation sequence and the model.
1
1
1
1 1
( ) ( 1) ( )
( ) ( , | , ) ( ) ( 1) ( )
N N
i ij j j t
t
ij t
i ij j j t
i i
t b t b o
t P q i q j o
t b t b o
α α
ε λ
α α
+
+
+
= =
+
= = = = +
∑ ∑
(4)
Based on the expectation probabilities, we can now estimate the
parameters that will maximize the new model. This is the M step
of the algorithm.
Page 5 of 12
F1000Research 2017, 6:1706 Last updated: 19 SEP 2017

The new initial probability distribution can be calculated as
follows.
(1)
i
γπ =
′
(5)
The re-estimated transition probability distribution is also
calculated as follows:
1
1
1
1
( )
( )
T
T
ij
t
ij
i
t
t
t
ε
α
γ
−
−
=
=
=
′
∑
∑
(6)
Finally, the new observation matrix is calculated using the formula
below
1
1
1
1
( )1( )
( )
T
T
i
t
i
t
j
i
t
t o k
b
t
γ
γ
−
−
=
=
=
=
′
∑
∑
The pseudo code of the training algorithm is represented below:
i. Begin with some randomly initialized or preselected
model, π
ii. Run O through the current model to estimate the
expectations of each model parameter using the forward
backward algorithm.
iii. Change the model to maximize the values of each path
using the new π′, α′ij and b′i(t).
iv. Repeat until change in log likelihood is less than a
threshold value or when the maximum number of
iterations is reached.
For global optimal results, this algorithm is usually iterated depend-
ing on the size of the dataset.
Results and discussion
Likelihood estimation
After implementing the HMM algorithms, the discretized data was
parsed into the program. The dataset was trained using HMMs with
cluster size from cluster 2 to 10. The likelihood of each HMM was
calculated using likelihood ratio test and three clusters were identi-
fied. The likelihood ratio test of the dataset from cluster 2 to 10
is shown in Table 1 below. A positive LRT show that increasing
the number of parameters is still worthwhile while a negative LRT
shows that increasing the parameter would not give a better model.
From the calculations below, the optimal number of clusters in the
dataset based on the likelihood ratio test is 3. The log likelihoods
of each cluster is also illustrated in Figure 2 below. It shows
that the log likelihood increases with more parameters added ini-
tially but from cluster 3, there was no significant increase in log
likelihood showing that the optimal number of clusters has been
attained.
Clustering results
The dataset was trained using the Baum-Welch algorithm and the
probability that an observation sequence belongs to a cluster was
calculated using the forward algorithm. Genes with discretized
value of zeros were also removed. After the likelihood ratio test
was calculated and the optimal number of clusters found, each
data was then separated into clusters using the forward algorithm.
The first cluster consists of 502 genes, the second cluster had
481 genes and the third cluster had 668 genes. These results are
represented in the Figure 3.
Table 1. Table showing LRT calculations. The LRT becomes
negative after three (3) clusters giving the optimal number as 3.
K Log Likelihood LR (Likelihood
Ratio)
LRT(Likelihood
Ratio Test)
2 -143.34
3 -102.28 41.06 7.02E+01
4 -95.62 6.66 1.42E+00
5 -89.17 6.45 1.00E+00
6 -86.89 2.28 -7.34E+00
7 -84.8 2.09 -7.72E+00
8 -8.44E+01 0.38 -1.11E+01
9 -8.27E+01 1.71 -8.48E+00
10 -8.10E+01 1.75 -8.40E+00
Figure 2. Log likelihoods for different numbers of clusters. The log likelihood values increase with the number of clusters sizes. After 3
clusters, there is not a significant increase in the log likelihood.
Page 6 of 12
F1000Research 2017, 6:1706 Last updated: 19 SEP 2017

Functional-induced/determined clustering of plasmodium
falciparum protein by the algorithm
Erythrocyte membrane protein1(pfEMP1) –Clusters 1 and 2
The clustering algorithm efficiently clustered the differentially
expressed genes into 3 clusters based on their functions. It is
noteworthy that the most abundant genes are the erythrocyte
membrane protein 1 (PfEMP1). The proteins are grouped in clus-
ter 1 and cluster 2. PfEMP1 is an ubiquitously expressed pro-
tein during the intraerythrocytic stage of the parasite growth that
determined the pathogenicity of P. Falciparum25. The virulence of
P. falciparum infections is associated with the type of P. falci-
parum PfEMP1 expressed on the surface of infected erythro-
cytes to anchor these to the vascular lining. PfEMP1 represents
an immunogenic and diverse group of protein family that
mediate adhesion through specific binding to host receptors25.
The Var genes encode the PfEMP1 family, and each parasite
genome contains ~60 diverse Var genes. The differential
expression of the proteins in this family has been reported
to determine morbidity from P. falciparum infection26. This
differential expression during infection and among patients could
have accounted for its clustering into 2 different clusters by
the algorithm.
Apart from clustering cell adhesion proteins into a sub-cluster,
the algorithm also clustered the proteins involved in actin bind-
ing, transmembrane transportation and ATP binding. While the
genes involved in ATP binding a largely conserved with their func-
tions yet to be experimentally determined, the transport proteins
are bet3 transport protein and aquaporin. Aquaporin is a
membrane spanning transport proteins that is essential in the main-
tenance of fluid homeostasis and transport of water molecules
and it has been identified as good therapeutic target27. Bet3
transport protein on the other hand is involved in the transport of
proteins by the fusion of endoplasmic reticulum to Golgi transport
vesicles with their acceptor compartment28.
The second cluster also has sub-cluster of PfEMP1 with other sub-
clusters for GTP and ATP binding /ATP-dependent helicase activity
as well as structural components of ribosome and ubiquitin pro-
tein ligase activity. Apart from PfEMP1, other sub-clusters are
involved in protein turnover-protein synthesis and degradation29.
These include the RNA helicases that prepare the RNA for trans-
lation and initiate translation, the ribosomal and GTP binding
proteins that are integral part of the ribosome assembly involved
in translation and the ubiquitin-conjugating enzymes are carry
out the ubiquitination reaction that targets a protein for degradation
via the proteasome30–32.
The genes coding for proteins involved in catabolic activi-
ties such as breakdown of proteins and hydrolysis of lipids are
clustered in cluster 3. This cluster also included sub-clusters for
genes involved in motor activity and DNA structural elements.
The DNA structural elements include histone proteins and tran-
scriptional initiator elements which are involved in epigenetic
control of gene expression33. The ability of P. falciparum to grow
and multiply both in the warm-blooded humans and cold-blooded
insects is known to be under tight epigenetic regulation and it
has been suggested as a good therapeutic target25.
Functional annotation
The Functional Enrichment analysis tool was used to determine
functionally enriched genes in each cluster. Each cluster was loaded
separately based on their unique gene identifier. Genes are matched
against the UniProt background database or by using a custom
database that allows users load their own predefined Gene
Ontology Term (GOTerm). We used the custom database and
loaded annotations downloaded from PlasmoDB for our functional
enrichment. The result of the 3 clusters is summarized in Table 2.
FunRich was only able to identify 164 of the 502 genes in
cluster 1. Cluster 1 has five functional annotations, 7.3% of the
genes are functionally annotated with cell adhesion molecule,
Figure 3. clustering results showing all the genes in each cluster. The x-axis shows the likelihood of each genes in each of the cluster
and the y-axis shows the total number of genes in each cluster.
Page 7 of 12
F1000Research 2017, 6:1706 Last updated: 19 SEP 2017

Table 2. Functional annotation of each clusters. Cluster 1 has four GO annotations, cluster 2
has five and cluster 3 has seven functional annotations.
CLUSTERS GO-ANNOTATION GENE ID NUMBER OF GENES
Cluster 1 Cell adhesion molecule, receptor activity PFD0005w
PFD1015c
PFE0005w
PFD0635c
PFD1005c
PFF0845c
PF07_0048
PF07_0049
PF07_0050
MAL7P1.55
MAL7P1.56
PF08_0142
12
Acting binding PFE0880c
PFE1420w
2
Transporter activity PFD0895c
PF08_0097
2
ATP binding PFB0115w
PFD0365c
PFD0735c
PFF0390w
PF07_0074
PF08_0101
6
Cluster 2 Structural constituent of the ribosome PFB0455w
PFB0830w
PFB0885w
PFC0200w
PFC0290w
PFC0295c
PFC0300c
PFC1020c
PFD0770c
PFD1055w
PFE0185c
PFE0300c
PFE0350c
PFE0845c
PFE0975c
PFF0700c
PFF0885w
PF07_0043
PF07_0079
PF07_0080
PF08_0039
PF08_0075
22
Cell adhesion molecule receptor activity PFA0005w
PFD0020c
PFD0615c
PFD0625c
PFD0995c
PFF0010w
PFF1580c
MAL7P1.50
PF07_0051
PF08_0103
PF08_0107
PF08_0140
12
Page 8 of 12
F1000Research 2017, 6:1706 Last updated: 19 SEP 2017

CLUSTERS GO-ANNOTATION GENE ID NUMBER OF GENES
ATP binding and ATP dependent in a
helicase activity
PFB0860c
PFD0245c
PFD1060w
PFE1390w
PF08_0042
5
Ubiquitin protein ligase activity PFC0255c
PFE1350c
MAL8P1.23
3
GTP binding PFC0565w
PFE1215c
PFE1435c
PFF0625w
4
Cluster 3 Cysteine-type peptide activity PFB0330c
PFB0335c
PFB0340c
PFB0345c
PFB0350c
PFB0360c
PFD0230c
7
Endopeptidase activity PFA0400c
PFC0745c
PFE0915c
PFF0420c
PF07_0112
MAL8P1.14
2
6
Hydrolase activity PFC0065c
PFE0910w
PFD0185c
PF07_0040
4
ATP binding, action binding and monitor
activity
PFE0175c
PFF0675c
2
DNA binding PFD0325w
PFE0305w
PF07_0035
3
Unfolded protein binding PFF0860c
PFF0865w
2
DNA binding, protein heterodimerization
activity
PFE0595w
PF07_0103
2
receptor activity, 1.2% are annotated with acting binding, 1.2%
with transporter activity and 3.7% with ATP binding as shown
in Figure 4. The remaining genes has no GO functions. We can
deduce that since these genes are in the same cluster, they are likely
to have functions as the genes with GO annotation.
In cluster 2, FunRich was able to identify 308 genes. In cluster 2,
7.1% of the genes are functionally annotated with the structural con-
stituent of the ribosome, 3.9% with cell adhesion molecule receptor
activity, 1.6% with ATP binding and ATP-dependent in a helicase
activity, 1.0% with ubiquitin protein ligase activity and 1.3% with
GTP binding which gives a total of five functional annotations
as shown in Figure 5. The rest of the genes in cluster 2 are also
predicted to have similar functions as with the genes with known
GO annotation.
In cluster 3, FunRich was able to identify 249 of the 668 genes
in the cluster set. This cluster has the largest GO annotation as it
is enriched with seven functions. 2.8% of the genes are enriched
with cysteine-type peptide activity, 2.4% with endopeptidase activ-
ity, 1.6% with hydrolase activity, 0.8% with ATP binding, action
binding and monitor activity, 1.2% with DNA binding, 0.8%
with unfolded protein binding and 0.8% with DNA binding, pro-
tein heterodimerization activity as shown in Figure 6. We can
Page 9 of 12
F1000Research 2017, 6:1706 Last updated: 19 SEP 2017

Figure 4. Functional annotation of cluster 1. The x-axis shows the percentage genes in the cluster with specific functional annotation while
the y-axis shows the function of these genes.
Figure 5. Functional annotation of cluster 2. The x-axis shows the percentage genes in the cluster with specific functional annotation while
the y-axis shows the function of these genes.
Page 10 of 12
F1000Research 2017, 6:1706 Last updated: 19 SEP 2017

Figure 6. Functional annotation of cluster 3. The x-axis shows the percentage genes in the cluster with specific functional annotation while
the y-axis shows the function of these genes.
also deduce that in cluster 3, the genes with unknown functions
are also predicted to have the same functions as with the known
ones.
Conclusion
Clustering has been found to be a very useful technique in analyz-
ing gene expression data. It has the ability to display large datasets
in a more interpretable format. Several approaches have been devel-
oped to cluster gene expression data. The HMM has a better advan-
tage over them because of its strong mathematical background and
its ability to model gene expression data successfully. The HMM
algorithms were implemented to perform cluster analysis on the
P. falciparum gene expression dataset. 2000 genes were used and
3 clusters were identified. Sixteen major functional enrichment
were identified for the clusters.
Data availability
The data sets used in this study are freely available in www.ncbi.
nlm.nih.gov/pubmed/20141604
Competing interests
There is no competing interests declared.
Grant information
The author(s) declared that no grants were involved in supporting
this work.
Acknowledgements
We are grateful to Covenant University for providing the platform
to carrying out this research.
Page 11 of 12
F1000Research 2017, 6:1706 Last updated: 19 SEP 2017

References
1. Huang QW, Wu LY, Qu JB, et al.: Analyzing time-course gene expression
data using profile-state hidden Markov model. In: Systems Biology (ISB), IEEE
International Conference. 2011; 351–355.
Publisher Full Text
2. Spellman PT, Sherlock G, Zhang MQ, et al.: Comprehensive identification of cell
cycle–regulated genes of the yeast Saccharomyces cerevisiae by microarray
hybridization. Mol Biol Cell. 1998; 9(12): 3273–3297.
PubMed Abstract
|
Publisher Full Text
|
Free Full Text
3. Slonim DK: From patterns to pathways: gene expression data analysis comes
of age. Nat Genet. 2002; 32 Suppl: 502–508.
PubMed Abstract
|
Publisher Full Text
4. Eisen MB, Spellman PT, Brown PO, et al.: Cluster analysis and display of
genome-wide expression patterns. Proc Natl Acad Sci U S A. 1998; 95(25):
14863–14868.
PubMed Abstract
|
Publisher Full Text
|
Free Full Text
5. Segal E, Shapira M, Regev A, et al.: Module networks: identifying regulatory
modules and their condition-specific regulators from gene expression data.
Nat Genet. 2003; 34(2): 166–176.
PubMed Abstract
|
Publisher Full Text
6. Howell GR, Macalinao DG, Sousa GL, et al.: Molecular clustering identifies
complement and endothelin induction as early events in a mouse model of
glaucoma. J Clin Invest. 2011; 121(4): 1429–44.
PubMed Abstract
|
Publisher Full Text
|
Free Full Text
7. Hughes TR, Marton MJ, Jones AR, et al.: Functional discovery via a
compendium of expression profiles. Cell. 2000; 102(1): 109–126.
PubMed Abstract
|
Publisher Full Text
8. Hopcroft LE, McBride MW, Harris KJ, et al.: Predictive response-relevant
clustering of expression data provides insights into disease processes.
Nucleic Acids Res. 2010; 38(20): 6831–6840.
PubMed Abstract
|
Publisher Full Text
|
Free Full Text
9. Schliep A, Schönhuth A, Steinhoff C: Using hidden Markov models to analyze
gene expression time course data. Bioinformatics. 2003; 19 Suppl 1: i255–i263.
PubMed Abstract
|
Publisher Full Text
10. Tavazoie S, Hughes JD, Campbell MJ, et al.: Systematic determination of genetic
network architecture. Nat Genet. 1999; 22(3): 281–285.
PubMed Abstract
|
Publisher Full Text
11. Tamayo P, Slonim D, Mesirov J, et al.: Interpreting patterns of gene expression
with self-organizing maps: methods and application to hematopoietic
differentiation. Proc Natl Acad Sci U S A. 1999; 96(6): 2907–2912.
PubMed Abstract
|
Publisher Full Text
|
Free Full Text
12. Friedman N: Inferring cellular networks using probabilistic graphical models.
Science. 2004; 303(5659): 799–805.
PubMed Abstract
|
Publisher Full Text
13. Brown MP, Grundy WN, Lin D, et al.: Knowledge-based analysis of microarray gene
expression data by using support vector machines. Proc Natl Acad Sci U S A.
2000; 97(1): 262–267.
PubMed Abstract
|
Publisher Full Text
|
Free Full Text
14. De Fonzo V, Aluffi-Pentini F, Parisi V: Hidden Markov Models in Bioinformatics.
Curr Bioinform. 2007; 2(1): 49–61.
Publisher Full Text
15. Ji X, Li-Ling J, Sun Z: Mining gene expression data using a novel approach
based on hidden Markov models. FEBS Lett. 2003; 542(1–3): 125–131.
PubMed Abstract
|
Publisher Full Text
16. Geng H, Deng X, Ali HH: Applications of Hidden Markov Models in Microarray
Gene Expression Data. Huimin Department of Computer Science, University of
Nebraska at Omaha, Omaha, NE 68182 USA.
Publisher Full Text
17. Lees KT: Identifying Gene Clusters and Regulatory Themes using Time Course
Expression Data, Hidden Markov Models and Transcription Factor Information.
Bioinformatics. 2006.
Reference Source
18. Zeng Y, Garcia-Frias J: A novel HMM-based clustering algorithm for the
analysis of gene expression time-course data. Comput Stat Data Anal. 2006;
50(9): 247–2494.
Publisher Full Text
19. Durbin RM, Eddy SR, Krogh A, et al.: Biological Sequence Analysis:
Probabilistic Models of Proteins and Nucleic Acids (1st ed.). Cambridge:
Cambridge University Press, 1998.
Publisher Full Text
20. Beal M, Krishnamurthy P: Gene expression time course clustering with
countably infinite hidden markov model. arXiv preprint arViv: 1206.6824.
Reference Source
21. Iyer VR, Eisen MB, Ross DT, et al.: The transcriptional program in the response
of human fibroblasts to serum. Science. 1999; 283(5398): 83–87.
PubMed Abstract
|
Publisher Full Text
22. Cho RJ, Campbell MJ, Winzeler EA, et al.: A genome-wide transcriptional
analysis of the mitotic cell cycle. Mol Cell. 1998; 2(1): 65–73.
PubMed Abstract
|
Publisher Full Text
23. Otto TD, Wilinski D, Assefa S, et al.: New insights into the blood-stage
transcriptome of Plasmodium falciparum using RNA-Seq. Mol Microbiol. 2010;
76(1): 12–24.
PubMed Abstract
|
Publisher Full Text
|
Free Full Text
24. Knab B, Schliep A, Steckemetz B, et al.: Model-Based Clustering With Hidden
Markov Models and its Application to Financial Time-Series Data. Between
Data Science and Applied Data Analysis. Springer. 561–569.
Publisher Full Text
25. Ay F, Bunnik EM, Varoquaux N, et al.: Multiple dimensions of epigenetic gene
regulation in the malaria parasite Plasmodium falciparum: gene regulation via
histone modifications, nucleosome positioning and nuclear architecture in P.
falciparum. Bioessays. 2015; 37(2): 182–194.
PubMed Abstract
|
Publisher Full Text
|
Free Full Text
26. Besteiro S, Williams RA, Coombs GH, et al.: Protein turnover and differentiation
in Leishmania. Int J Parasitol. 2007; 37(10): 1063–1075.
PubMed Abstract
|
Publisher Full Text
|
Free Full Text
27. Hansen M, Beitz E, Schultz JE: An Aquaporin Gene in Plasmodium Falciparum:
Molecular cloning and functional expression. Molecular Biology and Physiology
of Water and Solute Transport. Springer. 2000; 389–392.
Publisher Full Text
28. Jankowsky A, Guenther UP, Jankowsky E: The RNA helicase database. Nucleic
Acids Res. 2011; 39(Database issue): D338–41.
PubMed Abstract
|
Publisher Full Text
|
Free Full Text
29. Lavstsen T, Turner L, Saguti F, et al.: Plasmodium falciparum erythrocyte
membrane protein 1 domain cassettes 8 and 13 are associated with severe
malaria in children. Proc Natl Acad Sci U S A. 2012; 109(26): E1791–E1800.
PubMed Abstract
|
Publisher Full Text
|
Free Full Text
30. Meena LS, Rajni: Cloning and characterization of engA, a GTP-binding protein
from Mycobacterium tuberculosis H37Rv. Biologicals. 2011; 39(2): 94–99.
PubMed Abstract
|
Publisher Full Text
31. Nandi D, Tahiliani P, Kumar A, et al.: The ubiquitin-proteasome system. J Biosci.
2006; 31(1): 137–155.
PubMed Abstract
32. Rossi G, Kolstad K, Stone S, et al.: BET3 encodes a novel hydrophilic protein
that acts in conjunction with yeast SNAREs. Mol Biol Cell. 1995; 6(12):
1769–1780.
PubMed Abstract
|
Publisher Full Text
|
Free Full Text
33. Rottmann M, Lavstsen T, Mugasa JP, et al.: Differential expression of var gene
groups is associated with morbidity caused by Plasmodium falciparum
infection in Tanzanian children. Infect Immun. 2006; 74(7): 3904–39.
PubMed Abstract
|
Publisher Full Text
|
Free Full Text
Page 12 of 12
F1000Research 2017, 6:1706 Last updated: 19 SEP 2017