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Genome Biology 2005, 6:P5
Deposited research article
A non-parametric approach for identifying differentially expressed
genes in factorial microarray experiments
Qihua Tan*, Jesper Dahlgaard*, Werner Vach
†
, Basem M Abdallah
‡
,
Moustapha Kassem
‡
and Torben A Kruse*
Addresses: *Department of Clinical Biochemistry and Genetics, Odense University Hospital, Denmark. †Department of Statistics, University
of Southern Denmark, Denmark. ‡Department of Endocrinology, Odense University Hospital, Denmark.
Correspondence: Qihua Tan. E-mail:
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Posted: 10 March 2005
Genome Biology 2005, 6:P5
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1


A non-parametric approach for identifying differentially expressed genes in
factorial microarray experiments

Qihua Tan
*
, Jesper Dahlgaard
*
, Werner Vach
†
, Basem M. Abdallah
‡
, Moustapha Kassem
‡
, Torben
A. Kruse
*

*
Department of Clinical Biochemistry and Genetics, Odense University Hospital, Denmark
†
Department of Statistics, University of Southern Denmark, Denmark
‡
Department of Endocrinology, Odense University Hospital, Denmark



Address for correspondence:
Dr. Qihua Tan
Department of Clinical Biochemistry and Genetics (KKA)
Odense University Hospital
Sdr. Boulevard 29
DK-5000 Odense C
Denmark
Tel. +45 65412822 Fax: +45 65411911 e-mail:




2



Abstract

We introduce a non-parametric approach using bootstrap-assisted correspondence analysis to
identify and validate genes that are differentially expressed in factorial microarray experiments.

Model comparison showed that although both parametric and non-parametric methods capture the
different profiles in the data, our method is less inclined to false positive results due to dimension
reduction in data analysis.














3
Background
As a high-throughput technique, microarray capable of simultaneously measuring mRNA levels for
thousands of genes is becoming an increasingly important tool for researchers in biomedical
science. At the same time, interpreting the large amount of data produced in microarray experiments
imposes a major challenge to bioinformaticians [1]. Among the major issues in data analysis is the
clustering of genes that are co-regulated in a biological process (for example cell cycle, treatment
response, disease development) in high dimensional microarray experiments. Many clustering
algorithms have been proposed to cluster genes using unsupervised [2-4] and supervised or
knowledge-based [5,6] approaches.
In unsupervised gene clustering, the classes are unknown a priori and need to be discovered from
the observed data. This is especially true for microarray studies using complex experiment designs
due to the intricate relationships both between and within the multiple genetic and experiment

factors including interactions which can’t be predefined. Factorial experiment design (FED),
characterized by simultaneous measurement of the effects of multiple experiment factors (the main
effects) and the effects of interactions between the factors, is an economic yet efficient complex
design popular in use in biomedical studies [7]. The nice features of FED have also made it well
accepted in microarray experiments [8-11]. At the same time, statistical methods that take into
account the experiment complexity are demanding for dealing with data produced in factorial
microarray experiments. Kerr et al. [12] and Pavlidis [13] applied the analysis of variance model
(ANOVA) to factorial microarray data using the parametric linear regression approach by assuming
(1) normality in the log intensity of gene expressions and (2) linear relationship between log
intensity and the effects of main experiment factors and their interactions. In their approaches,
multiple replicates are required to insure model identifiability and then statistical procedures applied
to correct the significance for multiple testing.
4
The singular value decomposition (SVD) [14] and SVD-based multivariate statistical methods, for
example, principal components analysis [4,15] and correspondence analysis (CA) [16,17] have been
applied in analyzing multidimensional microarray time-series data. Although such exploratory
methods can be used for dimension reduction and for pattern discovery through data visualization,
validity of the clusters or the selected genes has rarely been examined [18]. By bootstrapping the
gene contributions on the reduced dimensions, we combine the resampling method with CA to
identify the various gene expression profiles and to validate the significance of the differentially
expressed genes in replicated factorial microarray experiments. We show in this paper, together
with comparison with ANOVA, how an application of our methods to a microarray study on stem
cells has helped us to find genes that are differentially regulated by the experiment factors and by
their interactions. Additional applications of the methods in biomedical studies are suggested at the
end of the discussion.

Methods
Correspondence analysis
As a multivariate data analyzing method, CA has been widely applied to process high-dimensional
data in, for example, sociology, environmental science, and marketing research. Recently, the

method has been applied to analyze microarray time-series data in cell cycle [16] and in diabetes
research [17] to look for genes displaying distinct time-course expression profiles. In microarray
experiments using a factorial design, we are actually facing a more sophisticated situation where we
are interested not only in the effects of the multiple factors but also in the effects of interactions
between them. Because FED represents a different complexity in high-dimensional microarray
experiments, we apply the SVD-based CA to identify genes that are differentially regulated due to
the experiment factors or as a result of their interactions. The idea is that main effects of the
5
multiple factors together with their interactions which dominate the variance in the data can be
captured by the reduced dimensions in the newly transformed data space.
Suppose in a factorial microarray experiment, there are two experiment factors A and B with p
levels in A and q levels in B. Then there will be pxq hybridizations each representing an interactive
variable [19] or combination of experiment factors in the design. If, after gene filtering, we have a
total of n genes, the data can be summarized by a large nx(pxq) matrix with n stands for the number
of rows (genes) and pxq for the number of columns (hybridizations or interactive variables). To
carry out CA, we divide each entry in the matrix by the total of the matrix so that the sum of all the
entries in the resulted matrix equals 1. We denote the new matrix by
P and its elements by
ijk
p ( i
stands for the genes from 1 to
n, j for the levels of factor A from 1 to p and likewise, k for the
levels of factor
B from 1 to q). In matrix P, the sum of row i,
∑∑
=
jk
ijki
pp
.

, is the mass of row i
and the sum of the column representing the interactive variable
A
j
B
k
,
∑
=
i
ijkjk
np
.
, is the mass of
that column. With the row and column masses, we derive a new matrix
C with elements
''
/)(
ijkijkijkijk
pppc −= where
jkiijk
ppp

'
= is the expected value for each element in matrix P. By
submitting matrix
C to SVD, we get
'VUC Λ=
where U is the eigenvectors of
'CC

, V is the
eigenvectors of
CC'
, Λ is a diagonal matrix containing the ranked eigenvalues of C,
l
λ
(l=1, 2,
….
pxq). Since the total inertia
∑
l
l
2
λ
equals the sum of
2
ijk
c in C, the major variance in the original
data is captured by the dimensions corresponding to the top elements in
Λ.
One big advantage of CA is that, with the SVD results, we can simultaneous project genes and
interactive variables into a new space with the projection of gene
i on axis l calculated as
.
/
iillil
pug
λ
= where
il

u is the i-th row and the l-th column in U, and similarly the projection of
6
A
j
B
k
along axis l is
jkjklljkl
pvh
.
/
λ
= where
jkl
v is the element in the l-th column in V that
corresponds to A
j
B
k
. In practice, a biplot [20] is used to display the projections. The biplot is very
useful for visualizing and inspecting the relationships between and within the genes and the
interactive variables. In the biplot, genes projected to a cluster of interactive variables associated
with one experiment factor are up-regulated due to that factor. Especially, genes projected to a
single or standing-alone interactive variable A
j
B
k
are highly expressed as a result of interaction
between the experiment factors A and B. As the inertia along the l-th axis can be decomposed into
components for each gene, i.e.

∑
=
i
ilil
gp
2
.
2
λ
, we can calculate the proportion of the inertia of the l-
th axis explained by the i-th gene as,
22
.
/
liliil
gpac
λ
= which is the absolute contribution of the i-th
gene to the
l-th axis. The sum of
il
ac for a group of selected genes stands for the proportion of the
total variance explained by these particular genes. If all the
n genes are randomly distributed along
the axis, the null contribution (random mean) by each gene would be expected as
n/1
. The random
mean contribution will be used for calculating the bootstrap p-values in the next section.
Non-parametric bootstrapping
Since the top dimensions of CA can represent effects of both the experiment factors and their

interactions, our aim is to identify the genes that make significant contributes to the dimensions.
Although, for each dimension, the gene contribution can be ranked, directly picking up the top rank
genes ignores variability in each of the estimated contributions and is thus unreliable. The bootstrap
technique was applied by Kerr and Churchill [21] to assess pattern reliability based on the estimated
error distribution in their ANOVA models applied in replicated microarray time-course
experiments. Ghosh [18] introduced the resampling method to SVD analysis of time-course data to
bootstrap the variability of the modes that characterize the time-course patterns in microarray data.
Here we combine the non-parametric bootstrapping with the correspondence analysis of factorial
7
microarray data to evaluate the significance of genes in their contributions to the leading
dimensions that feature the effects of main factors as well as the effects arising from their
interactions. When there are
w replicates available, we randomly pick up with replacement w arrays
for each interactive variable to form a bootstrap sample of gene expression values which is of the
same size as the real sample. The bootstrap distributions of the contributions on each dimension by
each gene are obtained by repeating the bootstrapping for
B times. Based on the distributions, we
obtain the bootstrap p-value for comparing the estimated contributions with the random mean as
∑
=
≤≡
B
t
ot
BacacIp
1
/)( where I(·) is the indicator function, ac
t
is the absolute contribution
estimated for each gene in bootstrap sample t and ac

o
is the mean random contribution. Note that
since we are restrictively resampling the replicate arrays for each interactive variable, the functional
dependency among the genes are preserved in the bootstrap samples.
Clustering of significant genes
The selected significant genes can be clustered according to their observed expression profiles using
gene clustering methods [22]. The different expression patterns in the clusters can be examined to
look for genes that are differentially regulated in response to experiment factors (the main effects)
or due to their interactions. Because some genes can significantly contribute to more than one top
dimensions, the clustering is performed for all the genes that make significantly high contributions
to at least one dimension in CA. The clustering of significant genes can help to establish
biologically meaningful associations between the genes and the experiments.

Results
Application to a data in stem cell study
We use data from a microarray experiment (using Affymetrix HG-U133A 2.0 chips each containing
22,000 genes) on stem cells conducted in our lab as an example. In the experiment, two lines of
8
human mesenchymal stem cells (hMSC), telomerase-immortalized hMSC (hMSC-TERT) and
hMSC-TERT stably transduced with the full length human delta-like 1 (Dlk1)/Pref-cDNA (hMSC-
dlk1), were treated with vitamin D to examine the effects of Dlk1, vitamin D and their interaction
on hMSC growth and differentiation and to look for genes that are differentially expressed in the
process. The experiment was done using a 2x2 factorial design. Twelve hybridizations in total were
conducted with each of the four interactive variables in triplicates: hMSC-TERT untreated by
vitamin D or tert-control (designated as tC), hMSC-TERT treated with vitamin D (tD), hMSC-dlk1
untreated with vitamin D or dlk-control (dC), hMSC-dlk1 treated with vitamin D (dD). We first
normalized our raw data (at probe level) using the quantile normalization method as described by
Bolstad et al. [23]. Then we summarized the intensities for the probes in each probe-set using the
robust multi-array average approach [24] to use as the expression value for each gene. Both data
normalization and gene expression value calculation were done by the affy package in Bioconductor

() for R (). Finally, genes are filtered by
dropping those whose expressions failed to vary across the hybridizations or arrays (standard
deviation/mean>0.03) which resulted in 2227 genes for subsequent analyses.
The biplots from the correspondence analysis of our stem cell data is shown in Figure 1 where
projections of both the genes and the four combinatory variables (between cell lines and vitamin D
treatments, the suffix number indicates replicate) along the first dimension or axis are plotted
against that along the second (Figure 1a) and the third (Figure 1b) axes. In Figure 1 the first axis,
which accounts for 64.7% of the total variance, separates the two cell lines in the data. It is
interesting to see that both tC and tD are projected to the left panel and closely coordinated on the
first axis while both dC and dD are projected to the right although with some distance between
them. It is easy to find that the second axis (accounting for 21% of the total variance) mainly
represents the effect of vitamin D treatment in the hMSC-dlk1 cell line (Figure 1a). Unlike Figure
9
1a, inspection on Figure 1b does not reveal any biological significance. This is understandable
because the third axis explains only 4.8% of the total variance. Since the variance in the data is
overwhelmingly dominated by the first and the second axes, Figure 1 reveals that significance in the
experiment is represented firstly by genes differentially expressed in the two cell lines, and
secondly by genes regulated in response to vitamin D treatment in the hMSC-dlk1 cell line. In
addition, note that our gene filtering procedure has left a hole in the cloud of genes in the center of
Figure 1a.
We use the described bootstrap procedure to obtain the empirical distributions of gene contribution
on the different axes and calculate their bootstrap p-values for significance inferences. By
resampling for 1000 times, we find highly significant genes (p<0.001) that contribute to the first
(274 genes) and the second (203 genes) axes. These genes explain 50.5% and 41.7% of the total
variance along each of the two axes. For a significance level of p<0.01, we have 294 genes
contributing to the first axis and 260 genes to the second axis which account for about half (51.9%
and 47%) of the total variance carried by the first two axes. The procedure detected only 4 genes
contributing to the third axis with p<0.05 but no gene with p<0.01. Figure 2 is the boxplot showing
the bootstrap distribution of gene contribution on the first (Figure 2a) and the second (Figure 2b)
axes by the selected highly significant genes (p<0.001). The distributions of the bootstrap

contribution are all well above the random contribution (1/2227=0.00045) indicated by the dashed
horizontal line. Because the genes are ranked according to their observed contributions in CA,
Figure 2 also shows that it is important to take into account the variations in gene contribution in
evaluating their significances because high rank genes tend to exhibit big variations. Figure 3a
displays expression profiles for genes highly significantly (p<0.001, 439 genes) contribute to the
first two axes. It is easy to see that genes in blocks 1 and 2 are mainly up or down-regulated in the
hMSC-TERT cell line which represents a cell line effect. Genes in blocks 3-5 are genes showing
10
interaction effects between the cell lines and vitamin D treatment with genes highly expressed in the
hMSC-dlk1 cell line but without vitamin D treatment (block 3), and down expressed when
administrated with vitamin D (block 4). Contrary to block 4, block 5 represents another interaction
pattern for genes highly expressed in the hMSC-dlk1 cell line with vitamin D treatment. Finally, at
the bottom of Figure 3a (block 6), we have a small cluster of genes exhibiting the main effects of
vitamin D which are up-regulated in both cell lines. It is necessary to point out that, although genes
in the upper part of block 1 are up-regulated in the hMSC-TERT cell line, their activities are
suppressed in the hMSC-dlk1 cell line conditionally on the vitamin D treatment effect which may as
well be seen as interactions. Such a situation tells us that, in practice, there may not always be a
black and white distinction between the main and the interaction effects as predefined by the linear
parametric model in ANOVA.
Comparison with ANOVA
We also analyzed the same data set using the existing parametric approach, i.e. ANOVA model,
with aim at comparing the performances of the two methods. In the analysis, we fit the expression
level of a gene (E) as a linear function of the cell line effect (C), the treatment effect (D) and their
interaction (C⋅D) (Pavlidis, 2003), i.e. we fit
ε
µ
+⋅+++= DCDCE
where µ is the mean expression level of the gene, ε is the random error. Because for each of the
2227 genes, the model independently tests the main effects and their interactions, we introduce the
false discovery rate (FDR) [25] to establish the p value threshold and to help to correct for multiple

testing. Our analysis detected highly significant genes (p<0.001) that are differentially expressed
between the two cell lines (601 genes), between the vitamin D treated and untreated groups (56
genes) and as a result of interaction effects (220 genes). The expression profiles of these genes are
shown in Figure 3b for cell line effect, Figure 3c for interaction effect, and Figure 3d for the vitamin
11
D treatment effect. Although for the same significance level, we obtain much higher number of
genes in the ANOVA model, the main patterns revealed by the parametric model are captured by
our non-parametric approach with Figure 3b corresponds to blocks 1 and 2 in Figure 3a, Figure 3c
to blocks 3-5 and top of block 1 in Figure 3a, Figure 3d to blocks 6 and 5 in Figure 3a. The
correspondence in the results produced by both methods indicate that our non-parametric approach
can be used as an alternative to the parametric ANOVA model to identify differentially expressed
genes in factorial microarray experiments.
To further compare with our non-parametric approach, we calculated the total contributions of the
highly significant genes in ANOVA on the top two axes in CA. The 601 genes in Figure 3b explain
36.39% of the total variance in the first axis and 16.05% of that in the second axis. The 220 genes in
Figure 3c contribute to 17.02% of the variance in the first axis, 25.12% of that in the second axis
and the 56 genes in Figure 3d account for only 1.91% of the total variance in the first axis and
3.58% of that in the second axis. These results reflect that, the interaction effect in ANOVA is
represented by both the first and mainly the second axes but the cell line effect by the first axis
which is in consistency with our non-parametric approach. Note that although both methods
detected a relatively small number of genes showing a vitamin D treatment effect independent of
the cell lines, such a main effect was not revealed by the biplots in Figure 1 where both genes and
the samples are projected onto the most important dimensions. This is sensible given their very
small contributions to the major axes. To further link the ANOVA results with that from our non-
parametric approach, we examine the variations in the contribution of the highly significant genes
in ANOVA on the different dimensions of CA. In Figure 4, we show the boxplots of bootstrap
contributions (ranked according to their observed contributions in CA) on the first two axes by the
highly significant genes in the ANOVA model that show cell line effect (Figure 4a and b,
p<0.000001, 60 genes), interaction effect (Figure 4c and d, p<0.0001, 62 genes), and effect of
12

vitamin D treatment (Figure 4e and e, p<0.001, 56 genes). Figure 4 reconfirms that very highly
significant genes displaying cell line effect in ANOVA mainly significantly contribute to the first
axis in CA. Meanwhile, genes estimated as showing highly significant interaction effect in ANOVA
can significantly contribute to both the first and the second axes. Moreover, genes as detected to
display the effect of vitamin D treatment mainly contribute to the second axis in CA.
It is necessary to point out that even though some of the selected genes in ANOVA make significant
contributions to the top dimensions in CA, there are also others that show only random
contributions. One obvious example is the genes detected to show significant vitamin D treatment
effect in Figure 4e and f. We think that the situation reflects the problem of false positive results in
ANOVA even after adjusting for multiple testing.

Discussion
We have presented a non-parametric approach for analyzing high-dimensional microarray data
produced in replicated factorial experiments. Application of the method to our stem cell data has
helped us to find genes that display contrasting expression profiles in the two cell lines. Our method
also detected genes turned on/off due to vitamin D treatment in the hMSC-dlk1 cell line. The results
are important in deepening our understanding in the genetic control of stem cell differentiations. As
a widely used exploratory method for visualizing multi-dimensional data, CA displays the
associations of gene expression with the effects of experiment factors as well as with the interaction
effects between the factors. In the linear regression based ANOVA model, unsupervised analysis of
FED data requires that parameters be assigned to each of the factors as well as to each of the
interaction terms which can easily run into model identifiability problem and false positive results
due to increased multiple testing. By data visualization using the biplot, CA reveals the main effects
and interactions that dominate the major variations in the data and thus results in increased
13
efficiency in data analysis through dimension reduction. Although our example data is in a 2x2
factorial design, generalization of our method to more factors is just straightforward.
In the ANOVA model, parameters are assigned to stand for either the main effects or the
interactions. However, such a black-and-white assertion may not always hold in biological reality.
In Figure 3a, although genes in the upper part of bock 1 display a cell line effect (high expression in

the hMSC-TERT cell line), they are also up or down-regulated in the hMSC-dlk1 cell line but
conditional on vitamin D treatment, a situation which may reflect an interaction effect. On the
contrary, the interaction effects (up and down regulation) between hMSC-dlk1 cell line and vitamin
D treatment are clearly represented by genes in blocks 3 and 4 in Figure 3a. The example illustrates
the necessity of model-free approach in modeling biological data.
Kerr and Churchill [21] emphasized the importance of replicates in microarray experiments. In their
linear regression based ANOVA model [12], sufficient replications are needed to ensure model
identifiability and accuracy of the parameter estimates as well as to examine their model
assumptions (normality, linearity, etc). In our non-parametric approach, replicates are solely used
for assessing the distribution of gene contributions on the major dimensions that dominate the
variance in the observed data. This operating characteristic should naturally enable our method to
deal with data in high order FEDs in an efficient manner. Most importantly, in our bootstrap
resampling procedure, the inherent functional dependency among the genes is kept intact. This is
different from the ANOVA model which ignores the correlation in gene activities by testing the
genes independently.
Another nice feature in our non-parametric approach is that CA can also help to standardize the
variance in the data. Because the individual elements in matrix C which is submitted to SVD can be
viewed as the standardized residuals, the algorithm helps to compensate for the larger variance in
genes with stronger signals and the smaller variance in genes with weaker signals. This feature thus
14
serves as an additional way to alleviate the intensity-dependent variance problem in microarray data
[26].
Although in this paper we focus on applying our method to analyze microarray data from complex
factorial experiments, we are planning to introduce the same approach to other types of clinical
investigations, for example, tumor classifications. In that case, the bootstrap-assisted CA could help
us to cluster the genes while associating them with the clustered tumor subclasses and moreover to
validate the differences between the tumor classes. Such practice is important because the global
gene expression profiles characterized by the significant marker genes can provide useful
information for tumor diagnosis, treatment strategies and outcome predictions.

Conclusion
Factorial experiments have the advantage of giving greater precision for estimating overall factor
effects, of enabling interactions between different factors to be explored [27]. These nice features
promote the use of FED in miroarray studies [11]. We have shown how our non-parametric
procedures can be applied to identify the clusters of genes that exhibit differential expression
profiles induced by the main factors or by interactions between the factors, and meanwhile to
validate their significances. We hope our model-free procedures introduced in this paper can serve
as an alternative to the existing ANOVA model in analyzing microarray gene expression data in
factorial design.





15




Acknowledgements
This work was financed by the Danish Biotechnology Instrument Center (DABIC) under the
biotechnological research program of the Danish Research Agency, and supported by the Clinical
Institute at OUH and by the Danish Center for Stem Cell Research.

16
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19



Figure captions:

Figure 1. Biplots showing the projections by both genes and the interactive variables (samples) on
the first axis against that on the second (1a) and the third (1b) axes. The first axis is mainly
dominated by the variance in gene expression in the two cell lines while the second axis by the
interaction effect between vitamin D treatment and the hMSC-dlk1 cell line. However, the pattern
in the third axis is not meaningful.

Figure 2. Boxplots showing the bootstrap distributions of gene contribution on the first (2a) and the
second (2b) axes for genes whose bootstrap p-value<0.001.

Figure 3. Expression profiles for genes that significantly contribute to the first tow axes (3a)
(p<0.001) in CA and for significant genes (p<0.001) detected as displaying the cell line effect (3b),
the interaction effect (3c), and effect of vitamin D treatment (3d) in the ANOVA model.

Figure 4. Boxplots showing the bootstrap distributions of gene contribution on the first two axes for
significant genes that display cell line effect (4a and b, p<0.000001), interaction effect (4c and d,
p<0.0001), and vitamin D treatment effect (4e,f, p<0.001) in the ANOVA model.


−0.15 −0.05 0.00 0.05 0.10 0.15 0.20
−0.15 −0.05 0.00 0.05 0.10 0.15 0.20
a
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2nd axis
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221039_s_at
221050_s_at
221058_s_at
221059_s_at
221085_at
221127_s_at
221207_s_at
221244_s_at
221258_s_at
221267_s_at
221269_s_at
221276_s_at
221430_s_at
221436_s_at
221477_s_at
221485_at
221500_s_at
221506_s_at
221509_at
221511_x_at
221520_s_at
221521_s_at

221530_s_at
221539_at
221543_s_at
221556_at
221563_at
221565_s_at
221571_at
221577_x_at
221582_at
221591_s_at
221601_s_at
221628_s_at
221677_s_at
221683_s_at
221692_s_at
221703_at
221704_s_at
221729_at
221748_s_at
221750_at
221760_at
221778_at
221785_at
221787_at
221815_at
221823_at
221841_s_at
221864_at
221865_at
221871_s_at

221872_at
221881_s_at
221897_at
221905_at
221915_s_at
221917_s_at
221918_at
221920_s_at
221931_s_at
221943_x_at
221960_s_at
221974_at
221976_s_at
221995_s_at
221997_s_at
222001_x_at
222020_s_at
222027_at
222036_s_at
222037_at
222038_s_at
222039_at
222051_s_at
222067_x_at
222077_s_at
222108_at
222118_at
222150_s_at
222156_x_at
222162_s_at

222173_s_at
222201_s_at
222288_at
222294_s_at
222383_s_at
32088_at
32836_at
34478_at
35201_at
35626_at
35820_at
36711_at
37462_i_at
37996_s_at
38037_at
38158_at
38241_at
39402_at
40148_at
40489_at
40850_at
44783_s_at
45297_at
45633_at
45714_at
48808_at
52837_at
55872_at
63825_at
87100_at

91816_f_at
AFFX−BioB−3_at
AFFX−BioB−5_at
AFFX−BioB−M_at
AFFX−BioC−3_at
AFFX−BioC−5_at
AFFX−BioDn−5_at
AFFX−HUMRGE/M10098_3_at
AFFX−HUMRGE/M10098_5_at
AFFX−HUMRGE/M10098_M_at
AFFX−M27830_5_at
AFFX−r2−Ec−bioB−3_at
AFFX−r2−Ec−bioB−5_at
AFFX−r2−Ec−bioB−M_at
AFFX−r2−Ec−bioC−3_at
AFFX−r2−Ec−bioC−5_at
−0.04 −0.02 0.00 0.02 0.04 0.06
−0.04 −0.02 0.00 0.02 0.04 0.06
dC1
dC2
dC3
dD1
dD2
dD3
tC1
tC2
tC3
tD1
tD2
tD3

−0.10 0.00 0.05 0.10 0.15 0.20
−0.10 0.00 0.05 0.10 0.15 0.20
b
1st Axis
3rd axis
1053_at
160020_at
177_at
200001_at
200075_s_at
200601_at
200602_at
200606_at
200617_at
200622_x_at
200623_s_at
200628_s_at
200629_at
200632_s_at
200636_s_at
200644_at
200646_s_at
200648_s_at
200649_at
200653_s_at
200658_s_at
200678_x_at
200679_x_at
200680_x_at
200690_at

200691_s_at
200692_s_at
200696_s_at
200727_s_at
200730_s_at
200742_s_at
200743_s_at
200752_s_at
200758_s_at
200759_x_at
200760_s_at
200772_x_at
200783_s_at
200784_s_at
200785_s_at
200800_s_at
200808_s_at
200824_at
200827_at
200831_s_at
200832_s_at
200841_s_at
200842_s_at
200853_at
200862_at
200866_s_at
200872_at
200878_at
200899_s_at
200908_s_at

200922_at
200924_s_at
200935_at
200959_at
200962_at
200965_s_at
200974_at
201014_s_at
201020_at
201026_at
201034_at
201040_at
201041_s_at
201042_at
201050_at
201058_s_at
201082_s_at
201090_x_at
201091_s_at
201106_at
201107_s_at
201108_s_at
201109_s_at
201110_s_at
201112_s_at
201115_at
201123_s_at
201129_at
201141_at
201167_x_at

201168_x_at
201169_s_at
201170_s_at
201171_at
201195_s_at
201200_at
201202_at
201222_s_at
201226_at
201227_s_at
201236_s_at
201242_s_at
201243_s_at
201248_s_at
201261_x_at
201262_s_at
201275_at
201286_at
201287_s_at
201288_at
201289_at
201291_s_at
201292_at
201295_s_at
201301_s_at
201302_at
201309_x_at
201310_s_at
201313_at
201340_s_at

201348_at
201357_s_at
201360_at
201361_at
201367_s_at
201369_s_at
201378_s_at
201381_x_at
201392_s_at
201393_s_at
201397_at
201409_s_at
201416_at
201417_at
201445_at
201462_at
201466_s_at
201467_s_at
201468_s_at
201469_s_at
201473_at
201476_s_at
201477_s_at
201482_at
201502_s_at
201508_at
201516_at
201518_at
201528_at
201529_s_at

201531_at
201533_at
201548_s_at
201549_x_at
201555_at
201556_s_at
201559_s_at
201565_s_at
201573_s_at
201574_at
201578_at
201579_at
201596_x_at
201601_x_at
201602_s_at
201611_s_at
201625_s_at
201626_at
201627_s_at
201631_s_at
201645_at
201654_s_at
201655_s_at
201663_s_at
201664_at
201666_at
201668_x_at
201675_at
201697_s_at
201714_at

201724_s_at
201733_at
201734_at
201739_at
201744_s_at
201752_s_at
201753_s_at
201755_at
201761_at
201764_at
201769_at
201770_at
201774_s_at
201787_at
201790_s_at
201791_s_at
201795_at
201796_s_at
201801_s_at
201808_s_at
201818_at
201825_s_at
201826_s_at
201829_at
201841_s_at
201842_s_at 201843_s_at
201846_s_at
201852_x_at
201853_s_at
201855_s_at

201858_s_at
201860_s_at
201867_s_at
201874_at
201875_s_at
201890_at
201893_x_at
201896_s_at
201897_s_at
201911_s_at
201927_s_at
201928_at
201930_at
201939_at
201951_at
201952_at
201963_at
201970_s_at
201981_at
201982_s_at
201996_s_at
201998_at
202001_s_at
202006_at
202012_s_at
202013_s_at
202016_at
202028_s_at
202034_x_at
202035_s_at

202036_s_at
202037_s_at
202057_at
202066_at
202067_s_at
202068_s_at
202073_at
202074_s_at
202076_at
202085_at
202091_at
202095_s_at
202107_s_at
202122_s_at
202129_s_at
202130_at
202131_s_at
202139_at
202145_at
202146_at
202147_s_at
202154_x_at
202177_at
202181_at
202202_s_at
202206_at
202207_at
202208_s_at
202209_at
202211_at

202213_s_at
202214_s_at
202218_s_at
202219_at
202234_s_at
202237_at
202238_s_at
202240_at
202241_at
202245_at
202247_s_at
202275_at
202283_at
202284_s_at
202309_at
202310_s_at
202311_s_at
202330_s_at
202338_at
202345_s_at
202351_at
202388_at
202393_s_at
202397_at
202411_at
202412_s_at
202413_s_at
202431_s_at
202438_x_at
202450_s_at

202458_at
202464_s_at
202468_s_at
202478_at
202479_s_at
202481_at
202487_s_at
202503_s_at
202516_s_at
202532_s_at
202533_s_at
202534_x_at
202539_s_at
202540_s_at
202551_s_at
202552_s_at
202557_at
202562_s_at
202572_s_at
202580_x_at
202581_at
202589_at
202598_at
202627_s_at
202628_s_at
202633_at
202643_s_at
202644_s_at
202648_at
202655_at

202660_at
202663_at
202664_at
202667_s_at
202668_at
202669_s_at
202672_s_at
202674_s_at
202675_at
202685_s_at
202705_at
202708_s_at
202709_at
202715_at
202721_s_at
202722_s_at
202726_at
202727_s_at
202732_at
202733_at
202743_at
202760_s_at
202761_s_at
202769_at
202770_s_at
202771_at
202808_at
202814_s_at
202827_s_at
202828_s_at

202833_s_at
202840_at
202842_s_at
202843_at
202847_at
202855_s_at
202856_s_at
202859_x_at
202870_s_at
202888_s_at
202896_s_at
202897_at
202901_x_at
202902_s_at
202911_at
202920_at
202934_at
202942_at
202948_at
202952_s_at
202954_at
202957_at
202969_at
202971_s_at
202983_at
202990_at
202994_s_at
202995_s_at
202997_s_at
202998_s_at

203022_at
203023_at
203028_s_at
203029_s_at
203030_s_at
203032_s_at
203038_at
203041_s_at
203042_at
203046_s_at
203062_s_at
203066_at
203083_at
203085_s_at
203088_at
203108_at
203123_s_at
203124_s_at
203131_at
203137_at
203138_at
203145_at
203164_at
203165_s_at
203167_at
203180_at
203184_at
203189_s_at
203200_s_at
203209_at

203210_s_at
203213_at
203214_x_at
203222_s_at
203231_s_at
203232_s_at
203239_s_at
203252_at
203254_s_at
203255_at
203270_at
203276_at
203297_s_at
203298_s_at
203315_at
203344_s_at
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203355_s_at
203358_s_at
203362_s_at
203370_s_at
203373_at
203386_at
203387_s_at
203388_at
203395_s_at
203407_at
203409_at
203416_at
203418_at

203422_at
203432_at
203455_s_at
203456_at
203460_s_at
203467_at
203474_at
203477_at
203498_at
203504_s_at
203505_at
203507_at
203518_at
203542_s_at
203543_s_at
203554_x_at
203557_s_at
203560_at
203564_at
203574_at
203575_at
203592_s_at
203603_s_at
203625_x_at
203626_s_at
203629_s_at
203636_at
203637_s_at
203642_s_at
203660_s_at

203675_at
203680_at
203683_s_at
203686_at
203693_s_at
203696_s_at
203708_at
203710_at
203725_at
203739_at
203743_s_at
203751_x_at
203755_at
203758_at
203764_at
203788_s_at
203789_s_at
203803_at
203805_s_at
203819_s_at
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203821_at
203827_at
203828_s_at
203832_at
203837_at
203851_at
203856_at
203868_s_at
203870_at

203879_at
203880_at
203883_s_at
203884_s_at
203889_at
203890_s_at
203895_at
203904_x_at
203908_at
203910_at
203912_s_at
203925_at
203927_at
203945_at
203946_s_at
203960_s_at
203967_at
203968_s_at
203973_s_at
203975_s_at
203976_s_at
203983_at
204005_s_at
204010_s_at
204014_at
204015_s_at
204017_at
204023_at
204026_s_at
204032_at

204033_at
204035_at
204040_at
204058_at
204059_s_at
204062_s_at
204063_s_at
204069_at
204075_s_at
204081_at
204088_at
204092_s_at
204094_s_at
204115_at
204126_s_at
204127_at
204128_s_at
204140_at
204141_at
204146_at
204151_x_at
204158_s_at
204159_at
204162_at
204163_at
204165_at
204170_s_at
204174_at
204188_s_at
204194_at

204203_at
204221_x_at
204222_s_at
204224_s_at
204236_at
204240_s_at
204252_at
204270_at
204271_s_at
204273_at
204275_at
204285_s_at
204286_s_at
204288_s_at
204293_at
204298_s_at
204306_s_at
204318_s_at
204326_x_at
204337_at
204338_s_at
204339_s_at
204341_at
204345_at
204347_at
204359_at
204363_at
204371_s_at
204385_at
204396_s_at

204400_at
204403_x_at
204407_at
204417_at
204419_x_at
204421_s_at
204422_s_at
204435_at
204439_at
204441_s_at
204444_at
204452_s_at
204457_s_at
204462_s_at
204463_s_at
204464_s_at
204468_s_at
204470_at
204472_at
204480_s_at
204491_at
204493_at
204501_at
204504_s_at
204507_s_at
204510_at
204512_at
204523_at
204529_s_at
204531_s_at

204558_at
204559_s_at
204595_s_at
204596_s_at
204597_x_at
204602_at
204603_at
204608_at
204610_s_at
204614_at
204615_x_at
204616_at
204619_s_at
204627_s_at
204638_at
204639_at
204641_at
204646_at
204653_at
204654_s_at
204658_at
204669_s_at
204693_at
204709_s_at
204719_at
204720_s_at
204726_at
204727_at
204728_s_at
204742_s_at

204748_at
204749_at
204752_x_at
204766_s_at
204767_s_at
204768_s_at
204774_at
204775_at
204780_s_at
204781_s_at
204789_at
204790_at
204817_at
204818_at
204822_at
204825_at
204830_x_at
204831_at
204835_at
204848_x_at
204863_s_at
204864_s_at
204868_at
204886_at
204887_s_at
204897_at
204900_x_at
204905_s_at
204906_at
204932_at

204933_s_at
204948_s_at
204962_s_at
204971_at
204972_at
204975_at
204979_s_at
205003_at
205005_s_at
205006_s_at
205016_at
205024_s_at
205032_at
205034_at
205046_at
205047_s_at
205048_s_at
205051_s_at
205053_at
205059_s_at
205061_s_at
205063_at
205066_s_at
205067_at
205068_s_at
205076_s_at
205080_at
205081_at
205084_at
205085_at

205088_at
205100_at
205111_s_at
205112_at
205117_at
205122_at
205128_x_at
205130_at
205133_s_at
205139_s_at
205167_s_at
205176_s_at
205190_at
205194_at
205199_at
205205_at
205207_at
205235_s_at
205236_x_at
205239_at
205240_at
205251_at
205254_x_at
205259_at
205260_s_at
205264_at
205266_at
205279_s_at
205280_at
205296_at

205302_at
205321_at
205330_at
205339_at
205341_at
205342_s_at
205343_at
205345_at
205353_s_at
205357_s_at
205361_s_at
205379_at
205381_at
205393_s_at
205394_at
205395_s_at
205407_at
205410_s_at
205422_s_at
205425_at
205426_s_at
205443_at
205449_at
205453_at
205463_s_at
205476_at
205519_at
205523_at
205529_s_at
205541_s_at

205547_s_at
205573_s_at
205576_at
205579_at
205580_s_at
205602_x_at
205608_s_at
205609_at
205627_at
205628_at
205644_s_at
205645_at
205659_at
205673_s_at
205681_at
205730_s_at
205733_at
205738_s_at
205767_at
205799_s_at
205805_s_at
205809_s_at
205825_at
205828_at
205832_at
205844_at
205856_at
205862_at
205880_at
205882_x_at

205890_s_at
205893_at
205909_at
205919_at
205920_at
205924_at
205925_s_at
205935_at
205939_at
205961_s_at
205967_at
205984_at
205990_s_at
205991_s_at
205997_at
206011_at
206026_s_at
206027_at
206042_x_at
206066_s_at
206084_at
206085_s_at
206100_at
206101_at
206102_at
206280_at
206300_s_at
206307_s_at
206316_s_at
206336_at

206364_at
206381_at
206382_s_at
206385_s_at
206396_at
206421_s_at
206429_at
206474_at
206498_at
206504_at
206508_at
206515_at
206522_at
206529_x_at
206532_at
206543_at
206566_at
206569_at
206571_s_at
206632_s_at
206665_s_at
206693_at
206734_at
206746_at
206765_at
206766_at
206767_at
206785_s_at
206795_at
206866_at

206907_at
206924_at
206931_at
206932_at
206943_at
206950_at
206956_at
206969_at
207012_at
207017_at
207018_s_at
207030_s_at
207034_s_at
207038_at
207043_s_at
207071_s_at
207091_at
207131_x_at
207149_at
207165_at
207177_at
207191_s_at
207196_s_at
207198_s_at
207303_at
207332_s_at
207335_x_at
207345_at
207387_s_at
207392_x_at

207419_s_at
207425_s_at
207447_s_at
207463_x_at
207510_at
207528_s_at
207535_s_at
207536_s_at
207558_s_at
207564_x_at
207590_s_at
207595_s_at
207688_s_at
207700_s_at
207722_s_at
207723_s_at
207739_s_at
207761_s_at
207765_s_at
207777_s_at
207788_s_at
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219410_at
219416_at
219430_at
219432_at
219434_at
219437_s_at
219483_s_at
219487_at
219493_at
219494_at

219502_at
219505_at
219512_at
219520_s_at
219528_s_at
219540_at
219555_s_at
219557_s_at
219558_at
219561_at
219571_s_at
219588_s_at
219599_at
219600_s_at
219603_s_at
219610_at
219622_at
219628_at
219634_at
219648_at
219650_at
219655_at
219682_s_at
219691_at
219703_at
219723_x_at
219729_at
219754_at
219759_at
219763_at

219773_at
219787_s_at
219802_at
219806_s_at
219819_s_at
219850_s_at
219874_at
219882_at
219892_at
219908_at
219918_s_at
219922_s_at
219927_at
219935_at
219959_at
219975_x_at
219978_s_at
219990_at
219994_at
220014_at
220038_at
220057_at
220060_s_at
220079_s_at
220081_x_at
220085_at
220147_s_at
220169_at
220174_at
220227_at

220232_at
220239_at
220266_s_at
220295_x_at
220327_at
220330_s_at
220334_at
220342_x_at
220387_s_at
220392_at
220407_s_at
220470_at
220486_x_at
220494_s_at
220495_s_at
220557_s_at
220608_s_at
220651_s_at
220655_at
220682_s_at
220748_s_at
220817_at
220840_s_at
220892_s_at
220975_s_at
220987_s_at
220992_s_at
220999_s_at
221012_s_at
221019_s_at

221029_s_at
221038_at
221039_s_at
221050_s_at
221058_s_at
221059_s_at
221085_at
221127_s_at
221207_s_at
221244_s_at
221258_s_at
221267_s_at
221269_s_at
221276_s_at
221430_s_at
221436_s_at
221477_s_at
221485_at
221500_s_at
221506_s_at
221509_at
221511_x_at
221520_s_at
221521_s_at
221530_s_at
221539_at
221543_s_at
221556_at
221563_at
221565_s_at

221571_at
221577_x_at
221582_at
221591_s_at
221601_s_at
221628_s_at
221677_s_at
221683_s_at
221692_s_at
221703_at
221704_s_at
221729_at
221748_s_at
221750_at
221760_at
221778_at
221785_at
221787_at
221815_at
221823_at
221841_s_at
221864_at
221865_at
221871_s_at
221872_at
221881_s_at
221897_at
221905_at
221915_s_at
221917_s_at

221918_at
221920_s_at
221931_s_at
221943_x_at
221960_s_at
221974_at
221976_s_at
221995_s_at
221997_s_at
222001_x_at
222020_s_at
222027_at
222036_s_at
222037_at
222038_s_at
222039_at
222051_s_at
222067_x_at
222077_s_at
222108_at
222118_at
222150_s_at
222156_x_at
222162_s_at
222173_s_at
222201_s_at
222288_at
222294_s_at
222383_s_at
32088_at

32836_at
34478_at
35201_at
35626_at
35820_at
36711_at
37462_i_at
37996_s_at
38037_at
38158_at
38241_at
39402_at
40148_at
40489_at
40850_at
44783_s_at
45297_at
45633_at
45714_at
48808_at
52837_at
55872_at
63825_at
87100_at
91816_f_at
AFFX−BioB−3_at
AFFX−BioB−5_at
AFFX−BioB−M_at
AFFX−BioC−3_at
AFFX−BioC−5_at

AFFX−BioDn−5_at
AFFX−HUMRGE/M10098_3_at
AFFX−HUMRGE/M10098_5_at
AFFX−HUMRGE/M10098_M_at
AFFX−M27830_5_at
AFFX−r2−Ec−bioB−3_at
AFFX−r2−Ec−bioB−5_at
AFFX−r2−Ec−bioB−M_at
AFFX−r2−Ec−bioC−3_at
AFFX−r2−Ec−bioC−5_at
−0.04 −0.02 0.00 0.02 0.04 0.06
−0.04 −0.02 0.00 0.02 0.04 0.06
dC1
dC2
dC3
dD1
dD2
dD3
tC1
tC2
tC3
tD1
tD2
tD3