Bayesian integrated modeling of expression data: A case study on RhoG

Abstract

DNA microarrays provide an efficient method for measuring activity of genes in parallel and even covering all the known transcripts of an organism on a single array. This has to be balanced against that analyzing data emerging from microarrays involves several consecutive steps, and each of them is a potential source of errors. Errors tend to accumulate when moving from the lower level towards the higher level analyses because of the sequential nature. Eliminating such errors does not seem feasible without completely changing the technologies, but one should nevertheless try to meet the goal of being able to realistically assess degree of the uncertainties that are involved when drawing the final conclusions from such analyses.
We present a Bayesian hierarchical model for finding differentially expressed genes between two experimental conditions, proposing an integrated statistical approach where correcting signal saturation, systematic array effects, dye effects, and finding differentially expressed genes, are all modeled jointly. The integration allows all these components, and also the associated errors, to be considered simultaneously. The inference is based on full posterior distribution of gene expression indices and on quantities derived from them rather than on point estimates. The model was applied and tested on two different datasets.
The method presents a way of integrating various steps of microarray analysis into a single joint analysis, and thereby enables extracting information on differential expression in a manner, which properly accounts for various sources of potential error in the process.

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RESEARCH ARTICLE
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Research article
Bayesian integrated modeling of expression data: a
case study on RhoG
Rashi Gupta*
1,2
, Dario Greco
2
, Petri Auvinen
2
and Elja Arjas
1,3
Abstract
Background: DNA microarrays provide an efficient method for measuring activity of genes in parallel and even
covering all the known transcripts of an organism on a single array. This has to be balanced against that analyzing data
emerging from microarrays involves several consecutive steps, and each of them is a potential source of errors. Errors
tend to accumulate when moving from the lower level towards the higher level analyses because of the sequential
nature. Eliminating such errors does not seem feasible without completely changing the technologies, but one should
nevertheless try to meet the goal of being able to realistically assess degree of the uncertainties that are involved when
drawing the final conclusions from such analyses.
Results: We present a Bayesian hierarchical model for finding differentially expressed genes between two
experimental conditions, proposing an integrated statistical approach where correcting signal saturation, systematic
array effects, dye effects, and finding differentially expressed genes, are all modeled jointly. The integration allows all
these components, and also the associated errors, to be considered simultaneously. The inference is based on full
posterior distribution of gene expression indices and on quantities derived from them rather than on point estimates.
The model was applied and tested on two different datasets.
Conclusions: The method presents a way of integrating various steps of microarray analysis into a single joint analysis,
and thereby enables extracting information on differential expression in a manner, which properly accounts for various
sources of potential error in the process.
Background
Microarrays are popular high-throughput biological
assays that measure the expression level of thousands of
genes in the biological samples and generate large, com-
plex datasets. In spite of the advances in technology, it is a
major challenge to produce reliable gene expression data
with a high signal-to-noise ratio, and analyze these large
datasets in an adequate manner. Analyzing microarray
data is usually performed in a step-wise manner, starting
with, (i) normalization of the intensity measurements, to
adjust or account for systematic technical variation, (ii)
correcting dye-bias if dye-bias remains after normaliza-
tion, (iii) identifying differentially expressed genes on the
normalized data, and completing the analysis with (iv)
functional annotation of the differentially expressed
genes. All these steps are regarded as independent, but
they are crucial for any biologically meaningful analysis.
Normalization is an integral part of the analysis, aiming
at retaining the systematic effects resulting from the bio-
logical process of interest while removing the systematic
technical variations occurring due to experimental vari-
ability. Normalization has researched for quite some time
and publications proposing new procedures are available
[1-4]. Some datasets display a consistent bias for a given
probe in either Cy3 or Cy5 direction even after the data
have been normalized using median-centered and lowess
normalization methods. This bias is called dye bias and it
is observed on a variety of platforms and labeling sys-
tems, including PCR-spotted and short oligonucleotide
labeling methods. Many experimentalists and statisti-
cians recommend using a dye-swap design to correct for
this bias. Some publications have shown by considering
experimental data that, if uncorrected, this bias can lead
to the erroneous identification of genes [5-7].
* Correspondence: rashi1@live.com
1 Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68,
FIN-00014, Helsinki, Finland
Full list of author information is available at the end of the article

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Identification of differentially expressed genes is usually
the main goal of microarray experiment. Chen et al. [8]
assessed differentially expressed genes by calculating fold
changes between genes under different conditions. Fold-
change method, the simplest and the most intuitive
method for finding genes that are differentially expressed,
has many drawbacks. Later, improved methods based on
t-test, regularized t-test [9,10] were proposed. Model
based approaches have also been published to identify
differentially expressed genes. Most methods listed in the
literature use point estimates of expression and depend
upon replicates available for the estimation of variances.
Step-wise analysis of the microarray data has two major
drawbacks: (i) output from one step acts as direct input to
the next, without attempting to account for the uncer-
tainties associated with the value that was obtained; as a
consequence, (ii) re-analyzing the data by altering the
method used for a single step will often produce conflict-
ing results. For this reason, Bhattacharjee et al. [11] pro-
posed a method that aims at integrating the independent
steps, so that uncertainties from each step could be
accounted systematically. Lewin et al. [12] also proposed
an integration of the normalization and classification step
by using a Hierarchical Bayesian model. These proposed
integrated approaches performed better than their step-
wise approach counterparts. Moreover, the Bayesian for-
mulation enables a much richer output than current step-
wise analyses.
In here, we also propose an integrated statistical model
under the Bayesian framework, where normalization and
differential expression are modeled jointly, and correc-
tion of the saturated signal is also incorporated. Satura-
tion refers to the optical saturation and not chemical
saturation. Such (optical) signal saturation occurs in the
scanning of hybridized arrays when the digitalized signal
from a pixel exceeds the scanner's upper threshold of
detection (216-1 = 65535, for a 16 bit computer storage
system). Saturation causes a downward bias in gene
expression measurements, which then affects high level
analysis, such as class prediction, class comparison or
clustering that utilizes these signals [13].
Usually, data extracted from a single scan and a single
scanner setting is used for all high level analyses. How-
ever, a single setting is unable to capture correctly the
expression of both weakly and highly expressed genes. As
a result, the sensitivity level of the scanner is adjusted to
get reliable measurements from all fluorescent spots
present on the hybridized array. Scanner sensitivity has to
be raised to a certain level to ensure that the signal from
weakly expressed genes exceeds the intrinsic noise level
of the scanner, but this causes saturation for highly
expressed genes. Several methods [14-19] have been pro-
posed for correcting the bias caused by signal saturation.
In here, we extend our previous work (Gupta et al. [19])
on handling signal saturation by using several scans at
varying scanner sensitivities. We propose an integrated
statistical approach where correcting signal saturation,
systematic array effects, gene-specific dye effects, and dif-
ferential expression are modeled simultaneously. We esti-
mate our model in a fully Bayesian way with the
WinBUGS software [20]. The Bayesian framework allows
for joint estimation of a large number of parameters, and
enables us to obtain here the posterior distribution of any
parameter in the model and of any function of such
parameters. We show how to exploit these posterior dis-
tributions to assess differential expression, using multiple
criteria for this purpose. The uncertainties in the parame-
ter estimates are thereby incorporated in a natural man-
ner into a proposed list of candidate genes.
Method
Data
RhoG is a protein belonging to the family of the small
GTPases [21,22]. It is involved in several intracellular sig-
naling pathways regulating cell motility and adhesion to
extracellular matrix. Together with Cdc42 and Rac1,
RhoG is able to elicit formation of both filopodia and
lamellipodia. Neurite formation and regulation of axon
dynamics in neurons are more specific functions in which
RhoG is acting together with other Rho proteins and their
interactors. Within the cells, Rho proteins can be found
in an active form and inactive form. Mutants of RhoG
(RhoG12 and RhoG17) can be used to keep the protein in
a constitutively activated (mutation of the 12th amino
acid) or inactivated (mutation of the 17th amino acid)
form. In this study we investigate effect of mutants
RhoG12 and RhoG17 on the gene expression of HeLa cell
lines.
Dataset-1
The DNA microarrays used for studying the effect of
RhoG17 in HeLa cells were Agilent human 4 × 44 k and
contained about 44000 60-mer oligonucleotide probes.
Three replicate arrays were made initially but only two
were used due to some technical problem in one of the
arrays. Each array was scanned three times using Axon
GenePix 4200AL scanner by varying the photomultiplier
tube (PMT). The design of the experiment along with the
configuration of PMT used to make multiple scans is
given in Table 1. The dataset-1 is available as Additional
file-1.
Dataset-2
The DNA microarrays used for studying the effect of
RhoG12 in HeLa cells were produced by the Turku Cen-
ter for Biotechnology, University of Turku, Finland and
contained 16,000 human cDNAs spotted in duplicate.

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Three arrays comparing wild type HeLa cells with
RhoG12 mutant were prepared. One of the replicate
arrays had the labeling orientation of the sample reversed.
Each array was scanned three times using ScanArray
5000 scanner by varying the laser power. Table 2 shows
design of the experiment along with configuration of
photomultiplier tube (PMT) and laser power (LP) used to
make multiple scans. The dataset-2 is available as Addi-
tional file-2.
For details about RNA extraction, probes labeling, and
microarray hybridization for the two datasets, see Addi-
tional file-3.
Bayesian hierarchical model
The model aims at finding differentially expressed genes
under cmax conditions (here cmax = 2, experimental and
control, but cmax can be more than two, for example,
when comparing multiple conditions over time), each
replicated on rmax arrays (here rmax = 2 (for dataset-1) and
3(for dataset-2)), and each array scanned s times (here
smax = 3) under different scanner settings. We assume
that, under condition c, each gene i has an underlying sig-
nal, which cannot be measured directly. We call this sig-
nal the true latent intensity of the gene under condition c
and denote it by Tic, c = 1, 2; i = 1, 2, ..., N, where N is the
number of spots used in the experiment. The entire
model is defined on the logarithmic scale, base e.
Signal correction is done separately for each replicate
by combining three scans made by varying the scanner
settings for that replicate. Let Qicr represent latent inten-
sity of gene i under condition c on replicate r. The scan-
ner settings used in the first scan for each replicate are
chosen to correspond to the situation, where only a single
scan would be made; therefore these first scans form a
natural basis for calibrating the latent intensities Qicr.
They are also expected to capture, without a downward
bias caused by saturation, spots that do not have abun-
dant levels of RNA. The second and the third scans were
made by choosing the scanner settings so that their mea-
sured signals would be weaker. Latent intensities corre-
sponding to the second and third scans are now assumed
to be linked to Qicr by simple functional relationships,
Table 2: Design details along with the combinations of PMT and LP used to obtain multiple scans for three replicate arrays
of dataset-2.
Dye Array 1 Array 2 Array 3
Control Control RhoG12
Cy3 PMT Gain 80 85 80
Scan-1 (LP) 90 100 90
Scan-2 (LP)809080
Scan-3 (LP)708070
RhoG12 RhoG12 Control
Cy5 PMT Gain 90 98 90
Scan-1 (LP) 100 100 100
Scan-2 (LP)909090
Scan-3 (LP)808080
Table 1: Design details along with the configuration of PMT used to obtain multiple scans for two replicate arrays of
dataset-1.
Dye Array 1 Array 2
RhoG17 RhoG17
Cy3 Scan-1 (PMT) 460 460
Scan-2 (PMT) 410 410
Scan-3 (PMT) 360 360
Control Control
Cy5 Scan-1 (PMT) 680 680
Scan-2 (PMT) 630 630
Scan-3 (PMT) 580 580

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respectively by fcr2(Qicr) and fcr3(Qicr) (discussed briefly
later).
Let Yicrs denote the observed intensity for spot i under
condition c and scan s of replicate r. As discussed in
Gupta et al. [19], the relation between the observed and
the latent intensity is non-linear. If there were no mea-
surement errors, we could write the observed intensity
Yicrs in the form Yicrs = fcrs(Qicr). However, extraction of
intensities of genes from scanned microarrays always
involves some measurement errors. Here we assume that
the errors are modulated by the latent signal level in a
log-additive fashion. More exactly, we assume that for the
observed intensities, which are below a certain threshold
so that saturation has no effect, the relationship between
observed and latent intensities can be expressed as:
where, εicrs is the error associated with spot i under con-
dition c and scan s of replicate r. We further assume that
the estimated latent intensity Qicr of gene i under condi-
tion c on replicate r can be modeled with additive gene,
array and dye effects:
where, Tic is the true latent intensity of a gene i under
condition c, Air is the array effect, and βi is the gene-spe-
cific dye effect. Since for cDNA experiments both the
control and the experimental samples are hybridized on
the same array, the array effect (Air) is not dependent on
the condition c. The gene-specific dye-bias correction (βi)
is only applied when the values are taken from Cy5 inten-
sity data, as enforced by the indicator function I(Cy5)cr.
However, the symmetric model in which the correction is
applied to Cy3 channel only would perform identically
with the difference that the bias terms would be negated.
A similar gene-specific dye bias correction was used in
Kelley et al. [7].
The functions fcr2 and fcr3 in equation (1) are unknown
and need to be estimated from the data. We assume these
functions to be increasing and continuous. For their esti-
mation, we decided to break the whole range of gene
expression data (loge(200), loge(65535)) into small inter-
vals yet ensuring enough data points in each of these
intervals. We call these intervals as I1, I2, ... Ik, and assume
a simple linear form for fcr2 and fcr3 in each interval. In
other words, we set
where, L(Ik) is the length of the kth interval. The array
effects (Air) are estimated over the set of intervals I1, I2, ...
Ik, subject to the constraints r Ajr = 0, j = 1, 2, ...., k to
ensure identifiability. Estimation of array effects over a set
of intervals is similar to the intensity based estimation of
array effects previously reported in Yang et al. [1] and
Dudoit et al. [4].
To complete the specification of the model, we
assumed Uniform prior distribution over the interval [0,
15] on logarithmic scale for Tic. The array effects Ajr were
assigned Normal priors with mean 0 and precision 0.1
(inverse of variance). The parameters bjcr and djcr were
assigned Uniform priors over the interval [0, 5]. Gene
specific dye effects βi were also assigned Normal priors
with mean 0 and precision 0.1. The errors εicrs are
assumed to be independent and identically distributed
Normal random variables with mean 0 and interval
dependent variances η2jcrs, where s = 1, 2, 3; j = 1, 2, ...., k.
The interval dependent precision parameters (ηjcr12, ηjcr22,
and ηjcr32; j = 1, 2, ..., k) were assigned gamma priors with
parameters (0.001, 0.001).
Finally, as per Gupta et al. [19], to account for the effect
of saturation, we treated signal measurements exceeding
the threshold of loge(45000) as 'missing data'. We com-
pensated for the resulting loss of information by applying
model-based data augmentation and using the measure-
ments taken from the second and/or the third scan which
had been obtained by varying scanner settings.
Implementation
The model was formulated in BUGS language and
parameter estimation was performed using WinBUGS
[20].
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Rules for selecting genes
Using the Bayesian model as specified above and with the
available data, we can estimate, for each gene i, i = 1,.....,
N, the joint posterior distribution of (Ti1, Ti2), i.e., of the
true underlying expression levels for the two conditions
involved. Based on this, we can further determine the
posterior distribution of Di = Ti1 -Ti2, i = 1,....., N, which
represent the differential expression between conditions
1 and 2 in gene i. There are several ways in which the pos-
terior distribution of Di can be exploited with the aim of
identifying differential expression. Here we propose a
method where we first select suitable threshold values
Dthres+ and Dthres- for such differences and then consider a
ranking based on the posterior probabilities:
Genes are selected as being potentially up-regulated if
pi+ > pcut and down-regulated if pi- > pcut, where again the
cut-off point pcut needs to be chosen in advance. These
posterior probabilities (pi+ and pi-) are easily estimated by
counting the proportion of MCMC samples in which the
chosen criteria are satisfied. The choice of the controlling
threshold values pcut, Dthres+ and Dthres- depends on the
biological question being studied, and can be problematic
to choose. However, in practice, the values are chosen
only after a preliminary analysis of the data.
The above-mentioned criterion is quite similar to the
criterion used in Lewin et al. [12], for selecting interest-
ing genes. Other criteria for ranking genes include the use
of standardized differences, zi = mean(Di)/sd(Di), and
determining the highest percentile for which the credibil-
ity interval for Di does not cover zero [23]. It is important
to note that identification of differentially expressed
genes is here based directly on determining the gene-wise
posterior probabilities that the latent 'true' difference in
expression in the two conditions exceeds a certain thresh-
old. Thus our method does not use the general frame-
work of statistical hypothesis testing, involving, for
example, p-values, or corrections of significance levels to
account for multiple testing. Unlike Lewin et al. [12], we
also have here not made an attempt to calibrate the cho-
sen thresholds on the basis of frequentist criteria such as
False Discovery/Non-Discovery Rate.
Results and Discussion
Application to dataset-1
The model under "Bayesian hierarchical model" without
parameter (βi) was applied to dataset-1 to illustrate the
criterion presented under "Rules for selecting genes".
Since both replicate arrays from dataset-1 have the same
dye-orientation, the dye-bias in the data cannot be
assessed.
Computational details and parameter estimation
For dataset-1, foreground median values for each condi-
tion without background correction were used for the
analysis. As a result, we had no negative values. This par-
ticular dataset had 43,376 genes (on single array) × 2 (rep-
licates used) × 3 (scans used) × 2 (dyes/conditions) =
520,512 data points to be used for the analysis. The cur-
rent model runs in OpenBUGS version 2.01 on Intel Pen-
tium processor 2.80 GHz with 1 GB RAM and takes
approximately 4 seconds per iteration using two chains in
parallel. Convergence was monitored visually (i.e. by the
mixing of two chains) and two chains of 10,000 iterations
each were generated to check the convergence of the
parameter estimates under consideration. Thereafter a
sample of size 10,000 was generated to make inference.
Owing to the intensity based structure and for compu-
tational convenience, the entire range of gene expression
was divided into four intervals: I1 = (loge(200),
loge(2000)), I2 = (loge(2000), loge(5000)), I3 = (loge(5000),
loge(11000)), I4 = (loge(11000), -). This division was based
on the measurement reading from scan-1. The posterior
median estimates of the parameters (bjcr, djcr) over the
two conditions and for a single replicate are summarized
in Table 3. The estimates are not the same over the four
intervals in any of the two replicates, thus providing evi-
pDD
pDD
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P data
|
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(4)
Table 3: Posterior median estimates of the parameters (b, d) for two conditions over replicate-1 of dataset-1.
Intensity-range Posterior median estimate of b, d (median ± sd) for the two condition over replicate-1
Lower limit Upper limit Condition 1 Condition 2
bdbd
loge(200) loge(2000) 0.9158 ± 0.0001 0.8370 ± 0.0001 0.9009 ± 0.0001 0.7952 ± 0.0001
loge(2001) loge(5000) 0.9084 ± 0.0003 0.8275 ± 0.0003 0.9230 ± 0.0003 0.8325 ± 0.0003
loge(5001) loge(11000) 0.9116 ± 0.0005 0.8354 ± 0.0005 0.9344 ± 0.0005 0.8554 ± 0.0005
loge(11001) - 0.9206 ± 0.0006 0.8554 ± 0.0006 0.9436 ± 0.0006 0.8798 ± 0.0006

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dence of the intensity dependent structure of our data.
The array effects (Ajr) were also estimated over the same
intervals, subject to the constraints r Ajr = 0 to ensure
identifiability. The array effects (in terms of posterior
median and sd) over the two replicates are shown in
Table 4 .
The breakpoints were selected using visual inspection,
but it would also be possible to treat them as model
parameters and then estimate them jointly with bjcr, djcr
and Ajr. This was not done here because of the additional
computational burden that would have resulted in ana-
lyzing the huge dataset.
Discussion of decision rules
As discussed before, the posterior distribution of the
parameter Di = Ti1-T2 represents the differential expres-
sion between conditions 1 and 2 in a gene. The uncer-
tainty in its estimation is reflected in the shape of its
distribution. A highly consistent response leads to a
tighter posterior distribution, and a less consistent pat-
tern will result in a flatter (sometimes multi-modal) pos-
terior distribution. Genes that are not differentially
expressed have their posterior distribution centered
around zero. This can be seen in Figure 1 (upper panel,
left) for a non-differentially expressed gene. Similar pos-
terior distributions are shown for an up-regulated gene
(upper panel, center) and a down-regulated gene (upper
panel, right). The corresponding posterior distributions
of the latent variables (Tic) under the two conditions lead-
ing to the estimation of the posterior distribution of the
difference (Di) are also shown in Figure 1 (lower panel).
Table 4: Posterior median estimates of the array effect over the four intervals and over two replicates of dataset-1.
Intensity range Posterior median estimate of array effect (median ± sd) over
replicates
Lower Limit Upper Limit Replicate 1 Replicate 2
loge(200) loge(2000) 0.0018 ± 0.0006 -0.0094 ± 0.0006
loge(2001) loge(5000) -0.3107 ± 0.0039 0.3143 ± 0.0039
loge(5001) loge(11000) -0.3288 ± 0.0061 0.3302 ± 0.0061
loge(11001) - -0.2883 ± 0.0049 0.2910 ± 0.0049
Figure 1 Plot of posterior distribution of Di = Ti1-Ti2 for three genes. In the upper panel, posterior distributions of the difference Di = Ti1-Ti2 are
shown for three genes of dataset-1: a non-differentially expressed gene (left), an up-regulated gene (center), and a down-regulated gene (right). In
the lower panel, the corresponding posterior distributions are shown for the latent variable Ti1 corresponding to the experimental condition (solid
line), and for Ti2 corresponding to the control (dotted line).

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Figure 2 shows point estimates (posterior means) of
log-fold change Di versus overall expression (Ti1 + Ti2)/2.
We declared here genes as up-regulated if pi+ > pcut and
down-regulated if pi- > pcut, with pcut = 0.99 and Dthres+ =
Dthres- = 0.3 (on log scale). 270 genes came up as differen-
tially expressed using these threshold values, 212 with pi+
> 0.99 and 58 with pi- > 0.99. The gene RhoG, which was
expected to be up-regulated in this experiment, is also
marked in Figure 1. It was identified with pi+ = 0.91 and
with a fold change of + 1.99 (on the natural scale). The
up-regulation of both transgene and endogenous RhoG
was validated (see Additional file 1, qPCR results) and
suggests that there might be mechanisms by which RhoG
regulates its own expression.
Among the 270 genes, we searched for RhoG- related
genes in Pubmed literature database using the software
Bibliosphere http://www.genomatix.de/products/Biblio-
Sphere/. Among the list of candidate genes, nine genes
were identified as being co-cited with RhoG. A pictorial
representation of the relation of these nine genes is
shown in Figure 3. The black edges depict co-citation of
the two genes and green edges indicate possible regula-
tory roles of JUN and NFKB1. Table 5 presents the esti-
mated fold change of these 9 genes along with brief
comments, their estimated posterior probabilities and
Pubmed Id (PMID).
Gene ontology categories enriched among the
differentially expressed genes
Our aim was to identify the GO terms that were enriched
among the 270 genes identified as differentially expressed
using DAVID annotation tool [24]. Several categories
were over represented with Fisher's exact test p-value
0.05 but we present in Table 6 a few selected categories
that contain novel genes that might be functionally
related to RhoG based on published data. The list of GO
terms associated with the differentially expressed genes is
available as Additional file 4.
Regulation of actin cytoskeleton dynamics is one of the
central effects of RhoG on cells. RhoF (or Rif) was one of
the genes that showed up in this category [25]. RhoF is
involved in the filopodia formation through mDia2.
Among the small GTPases, RhoA is a key regulator of
actin cytoskeleton. Presently, little is known about the
possible functional relationships of RhoA and RhoG.
However, we identified several interesting candidate
genes that could participate in the possible cross-talk
between these Rho proteins: ROCK2 is a classical RhoA-
Figure 2 Plot of point estimates (posterior means) of log-fold change Di against the overall expression (Ti1 + Ti2)/2 for dataset-1. Genes with
pi+ ≥ 0.99 are plotted with diamonds and those with pi- ≥ 0.99 are plotted with triangles. The gene RhoG with pi+ = 0.91 is plotted with a red circle.

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linked regulator of actin [26] and two RhoA GEFs
(ARHGEF10L [27] and ARHGEF3 [28]) exhibit ways in
which RhoG could regulate the activity of RhoA by
inducing the expression of their regulators.
We also identified Cdc42 regulators (Chiamerin, see
Additional file 1, qPCR results) indicating that there are
unknown cross-talk between RhoG and other RhoGT-
Pases in regulating actin cytoskeleton homeostasis.
Moreover, ARPC3, a part of the Arp2/3 complex, was
identified [29,30]. This complex is one of the actin nucle-
ation apparatuses responsible for many actin-related
functions like endosytosis, lamellipodia formation and
filopodia formation. Our list of candidate genes helps us
understand how regulatory genes like RhoG are perform-
ing their multitasking in cell dynamics.
Step-wise analysis using existing approaches
For a comparison, dataset-1 was also analyzed in a step-
wise manner using the existing popular softwares/proce-
dures. The data from the multiple scans of each replicate
and from the two dyes were first combined using the
multiscan package in R. The multiscan package imple-
ments the method of Khondoker et al. [17], for estimating
gene expressions from multiple laser scans of hybridized
microarrays. The method proposed in Khondoker et al.
Figure 3 A pictorial representation of the relation of nine genes
co-cited with RhoG. The blue boxes (nodes) represent the genes. The
"black" edges indicate co-citation of two genes in the PubMed data-
base; the "green" edges indicate a possible regulatory role of JUN and
NFKB1 on the expression of RhoG.
Table 5: Brief description and comments on some genes (of datset-1) found to be differentially expressed and associated
with RhoG from literature.
Gene Comment Fold change(natural
scale)
Pubmed Id (PMID) Posterior
probabilities
ARHGEF3 ARHGEF3 form complex with G proteins and stimulate Rho-
dependent signals.
2.2 12221096 p+ = 1
ICAM1 ICAM1 binds to integrins of type CD11a/CD18, or CD11b/CD18
and stimulates intercellular signaling.
1.6 17875742 p+ = 0.9913
IL6 IL6 is an immunoregulatory cytokine that activates a cell
surface signaling assembly composed of IL6, IL6RA, and the
shared signaling receptor gp130.
4.2 15578470 p+ = 1
JUN This gene encodes a protein which interacts directly with
specific target DNA sequences to regulate gene expression.
1.8 12739001, 1620121,
9671479, 10744696
p+ = 0.9935
NFKB1 NFKB is a transcription regulator that is activated by various
intra-and extra-cellular stimuli. Activated NFKB translocates
into the nucleus and stimulates the expression of genes
involved in a wide variety of biological functions.
1.9 12670394, 11803464,
12376551
p+ = 0.9942
NISCH NISCH is involved in the regulation of cell migration and cell
invasion.
1.9 12890925 p+ = 0.9965
PCNA PCNA is found in the nucleus and is a cofactor of DNA
polymerase delta. The encoded protein helps increase the
processivity of leading strand synthesis during DNA
replication.
0.76 12167123 p- = 1
PTGS2 Prostaglandin-endoperoxide synthase is the key enzyme in
prostaglandin biosynthesis, and acts both as a dioxygenase
and as a peroxidase.
2.3 10974444 p+ = 1
RHOF RHOF functions cooperatively with CDC42 and Rac to
generate filopodia increasing the diversity of actin-based
morphology.
3.7 15894457 p+ = 0.9994

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[17] has already been compared with a similar method
from Gupta et al. [19] which was utilized in this paper for
estimating gene signals from multiple scans. Gupta et al.
[19] also showed that the estimated gene signal from mul-
tiple scans gave better results when utilized for high level
analysis than the gene signal data from a single scan.
The combined signals from the multiple scans of the
three replicates and for the two dyes were normalized
using Quantile normalization method in R [31]. Limma
was used to fit a model and to identify differentially
expressed genes. We used DAVID [24] for the functional
annotation of the selected genes. This step-wise analysis
identified three broad functionalities "cell differentiation",
"cell cycle" and "developmental process" (also listed in
Table 6, results from integrated approach) but failed to
identify other specific functionalities associated with the
experiment.
Assessing dye bias
Dataset-2 was used to assess the dye-biasness (βi) as it has
three replicates of which one has dye orientation
reversed. Since the true positives are not known for this
dataset, we assessed the dye bias aspect using a house-
keeping gene that was replicated 56 times on the array.
This is the "Human glyceraldehyde-3-phosphate dehy-
drogenase (GAPDH, housekeeping gene)", which is
assumed to be expressed at a relatively constant level
across many different conditions. As a result, the differ-
ence Di = Ti1 -Ti2, i = 1,.....,56, between the two conditions
for GAPDH should be near zero. Figure 4 displays histo-
grams plotted using the point estimates (median of the
posterior distribution) of Di = Ti1 -Ti2, i = 1,.....,56,
obtained from the model. This histogram is centered
around zero (as expected) and the non-zero point esti-
mates (median of the posterior distribution) of βi, i = 1,
2,..., 56, for the replicated gene GAPDH indicating the
presence of dye-bias (see Figure 5).
Availability and requirements
Project name: Bayesian Integrated analysis
Availability: Model code (Additional file 5), sample data
(Additional file 6), initial conditions (Additional file 7)
Operating system(s): Platform independent
Programming language: WinBUGS
License: Code is freely available for usage and modifica-
tions; however, appropriate reference of this article is
essential.
Conclusions
Our focus has been on modeling differential gene expres-
sion between two experimental conditions, by proposing
an integrated statistical solution where signal correction,
Table 6: Some selected GO categories, along with the numbers of varying and analyzed genes from dataset-1.
Gene ontology categories Number of genes estimated as varying Number of genes analyzed
GTPase activity 6 212
Endosome transport 3 41
developmental process 46 3262
cell proliferation 15 796
cell cycle 16 894
vesicle-mediated transport 13 509
endocytosis 8 197
cell differentiation 32 1835
Cellular component organization and biogenesis 48 2723
Organelle organization and biogenesis 22 1195
Establishment and/or maintainence of chromatin architecture 9 315
Figure 4 Histograms of point estimates (median of posterior dis-
tribution) of Di for GAPDH. These point estimates are of the 56 repli-
cates (on the same array) for a house keeping genes (GAPDH) of
dataset-2.
0
2
4
6
8
10
12
14
16
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Fold change (log scale)
Frequency

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systematic array and dye effects, and differential expres-
sion, were all modeled jointly. All processing steps were
integrated into a common statistically coherent frame-
work, allowing all components and their associated errors
to be considered simultaneously. The inference was based
on the full posterior distribution of gene expression indi-
ces and of their derived quantities, such as difference (Di),
rather than on point estimates. In this respect, our
approach differs in a fundamental way from most alterna-
tive methods which have been proposed in the literature
and are build on the idea of statistical significance testing.
The key advantages of the proposed integrated analysis
are: (i) robustness of final results towards small variations
in outcomes of intermediate steps of the analysis, and (ii)
straightforward interpretability of results, when stated in
terms of the posterior distributions of differences
between the true expression levels obtained under differ-
ent experimental conditions.
The Bayesian hierarchical models considered here are a
step towards a complete integrated approach to the anal-
ysis of gene expression data. In future, the model pre-
sented here can be extended to include other common
steps in the analysis, such as background correction,
quality inspection, functional annotation, and clustering.
Simultaneous consideration of such additional steps can
be expected to lead to further improvements in the esti-
mates and thus to more reliable inferences.
The current model was successfully implemented using
WinBUGS software. WinBUGS provides a user-friendly
and easily modifiable implementation of Bayesian hierar-
chical models. This ease of handling and modifying com-
plicated models is balanced by the running time when
dealing with large genomic application data. All future
extensions (say, incorporating background correction)
need to be implemented in C or C++ for a realistic run-
ning time of the models. However, comparison of multi-
ple conditions using the integrated model in BUGS
(described in here) can be easily speeded up by running
the same model with different conditions on different
machines.
The results we have obtained from the RhoG experi-
ments are very interesting and provide us several interest-
ing candidate genes for further studies. Many of the genes
identified suggest novel links with the cellular machinery.
Additional material
Authors' contributions
RG was responsible for model construction, implementation, functional analy-
sis and paper writing. DG helped in the functional analysis and comparison
study. PA provided the data and validated the results. EA provided valuable
insights in the model construction and helped in paper writing. All authors
have read and approved the final manuscript.
Acknowledgements
The authors thank Andrew Thomas for his help and comments during imple-
mentation and Panu Somervuo for helping us with the preliminary analysis. We
also thank Eeva-Marja Turkki for running the qPCR analysis. This study was sup-
ported by the Maj and Tor Nessling Foundation.
Author Details
1Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68,
FIN-00014, Helsinki, Finland, 2Institute of Biotechnology, University of Helsinki,
P.O. Box 56, FIN-00014, Helsinki, Finland and 3National Institute for Health and
Welfare (THL), Mannerheimintie 166, 00300 Helsinki, Finland
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This article is available from: http://www.biomedcentral.com/1471-2105/11/295© 2010 Gupta 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.BMC Bioinformatics 2010, 11:295
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Cite this article as: Gupta et al., Bayesian integrated modeling of expression
data: a case study on RhoG BMC Bioinformatics 2010, 11:295