Vol. 00 no. 00 2012
Detection of differentially expressed segments in tiling
Christian Otto1,2, Kristin Reiche3,1,4, J¨ org Hackerm¨ uller3,1,4∗
1Bioinformatics Group, Department of Computer Science and Interdisciplinary Center for
Bioinformatics, University of Leipzig, 04107 Leipzig, Germany
2LIFE Leipzig Research Center for Civilization Diseases, Universit¨ at Leipzig, 04103 Leipzig,
3Young Investigators Group Bioinformatics and Transcriptomics, Department Proteomics,
Helmholtz Centre for Environmental Research – UFZ, 04318 Leipzig, Germany
4RNomics Group, Fraunhofer Institute for Cell Therapy and Immunology, 04103 Leipzig, Germany
Received on XXXXX; revised on XXXXX; accepted on XXXXX
Associate Editor: XXXXXXX
genome-wide transcriptomics over the last decade.
available approaches to identify expressed or differentially expressed
segments in tiling array data are limited in the recovery of the
underlying gene structures and require several parameters that are
intensity-related or partly dataset-specific.
Results: We have developed TileShuffle, a statistical approach
that identifies transcribed and differentially expressed segments
as significant differences from the background distribution while
considering sequence-specific affinity biases and cross-hybridization.
It avoids dataset-specific parameters in order to provide better
comparability of different tiling array datasets, based on different
technologies or array designs. TileShuffle detects highly and
differentially expressed segments in biological data with significantly
lower false discovery rates under equal sensitivities than commonly
used methods. Also, it is clearly superior in the recovery of exon-
intron structures. It further provides window z-scores as a normalized
and robust measure for visual inspection.
Availability: The R package including documentation and examples
is freely available at http://www.bioinf.uni-leipzig.de/
Supplementary information: Supplementary data are available at
Tiling arrays have been a mainstay of unbiased
During the last decade, tiling arrays have been a mainstay of
unbiased transcriptomics (e.g., Kapranov et al., 2002; Rinn et al.,
2003; Bertone et al., 2004) and continue to contribute to novel
findings. Tiling arrays have recently been applied, e.g., in the
discovery of novel long non-coding RNAs (Guttman et al., 2009),
to the identification of spatio-temporal patterns of gene expression
(Spencer et al., 2011), to the characterization of the transcriptome
∗to whom correspondence should be addressed
in 30 distinct developmental stages as well as in 25 cell lines of
Drosophila melanogaster (Graveley et al., 2011; Cherbas et al.,
2011), and to the identification of a “large complement of novel
loci” with stage-specific expression in Caenorhabditis elegans
(Wang et al., 2011). High-throughput sequencing methods have
recently shown distinct advantages over array-based approaches
(Agarwal et al., 2010; Bradford et al., 2010). However, due to
the availability of large tiling array reference datasets, e.g., from
ENCODE and a clear statistical understanding on how to model
differential expression in microarray data, tiling arrays are an
important experimental approach in transcriptomics, and tilingarray
data analyses is a relevant topic in computational biology.
One of the most widely used methods in tiling array expression
analysis was introduced by Kampa et al. (2004) and is implemented
in the Tiling Array Software (TAS). In brief, the local expression
levels of probes are estimated by calculating the pseudo-
median or Hodge-Lehmann estimator over intensities of probes
within genomic distance of bandwidth. Transcribed segments are
collections of expressed probes, i.e., probes with a smoothed
intensity above a given threshold, with maximal genomic distance
of maxgap and minimal length of minrun. TAS extends the method
of Kampa et al. by estimating the significance of differential
expression using a Wilcoxon signed-rank test. It tests for significant
changes of probe intensities among states applied to local windows
of given width centered around each probe. Hence, p-values for
differential expression are assigned to each probe.
More recently, Johnson et al. introduced an approach that models
the expected probe behavior. It is available in the tool MAT (Johnson
et al., 2006). Originally, it was designed to detect regions enriched
by ChIP-chip but has also been applied to detect transcriptional
activity (Lee et al., 2009; Kadener et al., 2009). In contrast to
TAS, MAT uses a mixture model to normalize probe intensities
by estimating the expected binding affinity on the basis of the
composition and copy number of their nucleotide sequence on
the corresponding genome. To identify (differentially) expressed
probes, the score over all normalized intensities of probes within a
local window, givenby abandwidth parameter, iscompared toanull
distribution. This distribution is composed of all non-overlapping
c ? Oxford University Press 2012.
Otto et al.
window scores that can be calculated on the same array or the
array in a different state during expression or differential expression
analysis, respectively. Hence, it uses a two-step approach with
different background distributions to normalize the probe intensity
and assess its significance within a probe-centered window. In the
detection of (differentially) expressed segments, positive probes
are joined if their genomic distance is below a given maxgap
parameter and segments enclosing more than minprobe probes are
then reported. TileProbe is a variant of MAT, which models
residual probe effects that cannot be explained by the MAT model
by incorporating publicly available datasets (Judy & Ji, 2009).
TileProbe has been successfully applied to detect enriched
motifs in ChIP-chip tiling array data, but in contrast to MAT no
application to detect differential expression has been reported. HAT
uses a hypergeometric distribution to assess the probability to
observe a specific number of probes within a window. It is less
sensitive but more specific than MAT and cannot directly be used
to detect differential expression (Taskesen et al., 2010). Lastly,
HMMTiling models probe-specific effects by a normal distribution
defined for each probe individually compared to a control group
(Li et al., 2005), but requires many samples in order to estimate
the variance for a probe correctly which may not be available for
arbitrary types of tiling arrays.
gSAM, is a powerful framework for analyzing differential
response of time series tiling array data (Ghosh et al., 2007). It
generalizes SAM (Tusher et al., 2001) from a gene-centric view
to genomic intervals in an underlying piece-wise model. Under
this model, the time series is subdivided into logical segments
and differential changes are analyzed on each of these segments
separately. gSAM requires replicates which are often not available
for whole genome tiling data. Another method suitable to detect
differential expression on tiling array data is TileMap which
assesses the significance of each probe by averaging over moderated
t-statistics within a pre-defined window size (Ji & Wong, 2005).
Kechris et al. (2010) propose the averaging of p-values instead of
test statistics providing a more flexible framework to evaluate more
complicated experimental designs and to overcome the problem that
the length of a sliding window may not be large enough to assume
normal distribution. However, both methods again require replicates
because probe-wise expression changes are assessed by hypothesis
tests. An HMM-based approach was introduced by Munch et al.
(2006) that adaptively models tiling array data on given annotation
and subsequently predicts expression on the genomic sequence. It
does not require ad-hoc parameters but is limited to expression
analysis and hence cannot predict differential expression.
Huber and colleagues presented a powerful segmentation
approach for tiling array data, which controls for probe-specific
effects by normalizing probe-wise intensities to a reference
experiment with genomic DNA (Huber et al., 2006). Recently,
Karpikov et al. (2011) introduced a wavelet transformation to tiling
array ChIP-chip data in order to discriminate regions of activity
from noisy data.
Our aim is to use tiling array data for identifying novel ncRNAs,
which are differentially expressed in response to critical signaling
pathways or cellular processes. For this purpose, a data analysis
method is required to (i) analyze differential expression in tiling
array data for genome-wide approaches (ii), allow the latter
without using replicate tiling array experiments due to limitations
in the availability of sample material, (iii) identify boundaries
of differentially expressed segments sufficiently precise to allow
transcript annotation, and (iv) avoid the use of data-set specific
parameters which may hamper analyzing differential expression
between arrays of different experiments. In our opinion, none of the
state-of-the-art methods sufficiently fulfills all these requirements.
Here, we present TileShuffle, a novel tiling array analysis
approach that identifies transcribed and differentially expressed
segments in terms of significant differences from the background
distribution by using a permutation test statistic. Significance is
assessed on minimal expected transcriptional units rather than on
a single-probe level. TileShuffle does not require any dataset-
specific parameters, e.g., intensity-related thresholds or parameters
concerning collection of expressed probes. This is particularly
favorable since in common tiling array experiments neither spike-
ins to control the FDR (as in Kampa et al. (2004)) nor sufficiently
large positive and negative sets to optimally adjust these ad-hoc
parameters might be available.
We compare TileShuffle to TAS and MAT in analyzing
differential expression in one human whole genome tiling array
datasets and one spike-in dataset (Sasaki et al., 2007). TAS is
the most widely used tool in tiling array expression analysis
and although MAT was originally designed for ChIP-chip data,
it was successfully applied to detect transcriptional activity. All,
TileShuffle, TAS, and MAT, do not require replicates to
detect differentially expressed transcripts which is in particular
favorable for studies with limited material and costs. At the same
false discovery rate, TileShuffle achieves significantly higher
sensitivities than the other methods. Also, it detects boundaries of
differentially expressed exons with higher precision than TAS and
To determine transcribed segments in tiling array data, we apply
a statistical approach that differentiates expression signals from
the background distribution under consideration of common tiling
array biases. Given the array design of nearly uniformly distributed
probe sequences over the non-repetitive genome, hybridization
affinity and hence signal intensity is highly dependent on the
probe sequence itself, i.e., nucleotide composition and nucleotide
positioning (Royce et al., 2007; Johnson et al., 2006). Analogously,
in absence of specific transcripts, a detected probe signal may
solely originate from non-specific hybridization, e.g., background
noise and cross-hybridization, causing single spikes in the tiling
array data. Here, cross-hybridization refers to the hybridization of
DNA/RNA fragments to probe sequences that are similar or even
Handling common tiling array biases: Even though transcripts are
expected to be detected by several neighboring probes in similar
scale, non-specific hybridization and sequence-specific effects like
nucleotide composition and positioning can largely increase the
detected signal intensity of single probes while having no effect
on the neighboring probes and hence roughen the signal across the
tiling array. For example, probes with high GC content tend to
exhibit increased signal intensities compared to probes with low GC
content. In addition to the GC content, Royce et al. highlighted the
Signal intensity [log2]
0.120.2 0.280.36 0.44 0.520.60.68 0.760.840.92
Frequency within GC content bin
Fig. 1: (a) Boxplot of probe intensities on a tiling array for different GC content in the probe sequence. The relative frequency of probes
with each GC content bin on the tiling array is shown in the overlay graph (red solid line). (b) Boxplot of probe median z-scores for different
GC content in the probe sequences. The probe median z-score is defined as the median over the z-scores of all windows enclosing the probe
where z-scores were estimated by TileShuffle using three GC bins during permutation. Vertical dotted red lines display the boundaries
of different bins while solid red lines indicate the relative frequency of probes with the respective GC content in their bin.
influence of position-specific effects of each nucleotide on the probe
intensities, e.g., higher average intensitiesof probes withGstowards
the probe start or Cs towards the probe end (Royce et al., 2007).
These sequence-specific biases introduce a disparity in the binding
affinity among different probe sequences, subsequently denoted as
We therefore assess the significance of expression on windows of
length l with respect to the background distribution rather than on
single probes. A score Se(w) is assigned to each sliding window
w by applying a scoring function (arithmetic mean trimmed by
maximal and minimal value or median) over the signal intensities
of all probes within the window. Due to the robustness of the
two scoring functions, window scores are less susceptible to signal
intensity variation within a given window originating solely from
outliers. In addition, probes are subdivided into affinity bins with
similar expected sequence-specific affinity and bins are processed
independently from each other. Accordingly, intensities of probes
that belong to different affinity bins must not be interchanged.
Otherwise, the expression analysis might favor windows simply due
to the sequence compositions of their probes, e.g., high GC content.
Assessing significance of expression: In order to estimate the
significance of a window score Se(w), we repeatedly permute all
probe intensities across the array while interchanging only those
that belong to the same sequence-specific affinity bin, recompute
the window scores, and compare them with the original ones. We
use random permutations of probe intensities to remain independent
of any annotation or underlying gene structure.
By counting the number of permuted windows with higher
score, we estimate empirical p-values of windows. Following
a Benjamini-Hochberg multiple testing correction (Benjamini &
Hochberg, 1995), all windows of high significance, i.e., the ones
with corrected p-values (q-values) below a given threshold, are
deemed ‘expressed’. Since permutations necessitate sufficiently
large groups, the binning is only based on the GC content of each
probe sequence as the most dominant bias on hybridization affinity
(see Figure 1a). In accordance with the findings of Johnson et al.
(2006), the copy number of probes, i.e., number of perfect matches
of the probe sequence to the genomic sequence and hence the extent
of potential signal overlay, showed only a minor impact on signal
intensity (see Supplementary Figure S1a). We therefore refrain
from controlling for copy number in favor of larger bins during
permutation. The described algorithm to detect expressed segments
in tiling array data is illustrated in Supplementary Figure S4.
In many cases, tiling array data is available from different cellular
states or other biological conditions and one might be interested in
structural changes in the expression between different conditions.
To avoid that signal intensity variation at the detection limit is
classified as differential expression, we require that differentially
expressed intervals must also be significantly expressed relative
to the background distribution in at least one of the investigated
conditions, and call these intervals highdiff. This is analogous to the
frequently performed unspecific filteringinconventional microarray
Differential expression detection
Assessing significance of differential expression: On the contrary
to one-state expression analyses, signal intensities are normalized
using a quantile-normalization across each tiling array in both
considered conditions (Bolstad et al., 2003). Expression shifts are
then measured in terms of log-fold changes (i.e. differences of
log signals) between probe intensities in both cellular conditions.
In consequence, sequence-specific effects cancel out and affinity
classification as it is done for expression detection is rendered
unnecessary (see Supplementary Figure S1b). Fold changes assume
constant variance among probes, which might not be valid in any
case. However, if replicate data is not available, fold changes are the
only applicable measure for differential signal changes. Otherwise,
Otto et al.
it is possible to use moderated t-statistics in TileShuffle, an
empirical Bayes method to shrink the probe-wise variance towards
a common value. Hence, it is preferable over ordinary t-statistics
(Witten & Tibshirani, 2007).
Due to the two-tailed distribution of fold changes, the estimation
of p-values needs to be adapted. We implemented and compared
two different variants to detect significant changes. In variant A,
window scores Sd(w) of differential expression are calculated
following the same outline as described for the expression analysis
with the exception that two-tailed p-values are estimated in order
to regard both regulation directions, up and down. The multiple
testing correction is then adjusted to account for these additional
comparisons. In variant B, it is assumed that entire windows
represent the smallest unit of expression and are either constant,
or up- or downregulated between two conditions.
behavior of neighboring probes is considered a consequence of
non-specific hybridization. In order to correct for this bias, the
presumed direction of regulation is initially assigned to each
window w on the basis of the sign of its expression score
Se(w). Subsequently, all converse probes, i.e., probes with
negative log-fold change within positive windows or vice versa,
are ignored and neither permuted nor incorporated into the score
calculation for differential expression. Consequently, positive
and negative windows are compared to different background
distributions. To assess the significance of a window score Sd(w) of
differential expression, a one-tailed empirical p-value is estimated
(according to the corresponding background distribution) and
corrected for multiple testing, similar to the one-state analysis.
The assignment of the significance to a window in case of the
differential expression analysis with both variants is illustrated in
Supplementary Figures S5 and S6. Overall, both variants merely
differ in the window score calculation (independently from the
used scoring function) and multiple testing correction in differential
expression analysis. Due to their difference in treating converse
probe behavior possibly leading to more robustness of variant B,
we implemented and included both of them in our comparative
In addition to the statistical significance, a normalized score can be
reported for each processed window on the tiling array. Since the
score distribution of the permuted windows is a sample from the
background distribution, a z-score of a window w is calculated by
z(w) =x − µ
where x is either the score Se(w) or Sd(w), while µ and σ are
the mean and standard deviation of the permuted window scores,
respectively. To obtain a probe-wise measure, the probe median z-
score z(p) is defined as the median over the z-scores of all windows
enclosing the probe p. In consequence, probe median z-scores may
be used as a normalized measure of probe expression in order to
visually inspect regions of interest.
A custom microarray based on a different manufacturer, labeling
procedure, and probe length has been designed to validate the
tiling array results as an alternative experimental approach. We
used the Agilent eArray procedure1to ensure that probe-specific
biases are minimized and designed probes of 60mer length for both
reading directions of all highdiff regions that have been identified
by TileShuffle and TAS. We, furthermore, verified that the
custom microarray also covers an unbiased sample of the regions
identified by MAT (Supplemental Table S6). In addition, the custom
microarray also includes probes for genomic regions, determined
independently of the tiling array experiment: Probes for all human
mRNAs, for genomic regions predicted to contain a conserved
secondary structure identified by RNAz (Washietl et al., 2005) or
Evofold (Pedersen et al., 2006), and known ncRNAs from public
The custom microarray was run in triplicates and differentially
expressed probes were identified using the statistical software
package R and Bioconductor (Gentleman et al., 2004). Expression
intensities were quantile normalized (Bolstad et al., 2003) and a
linear model was fitted using the Limma R package (Smyth, 2005).
Reliable variance estimations were obtained by empirical Bayes
moderated t-statistics and the false discovery rate was controlled
byBenjamini-Hochbergadjustment (Benjamini&Hochberg, 1995).
A probe on the custom microarray is called significant in case the
adjusted p-value is found to be < 0.05.
In addition to the custom microarray, we tested the performance
of TileShuffle, TAS and MAT on the outcome of a spike-
in dataset comprising 162 full-length cDNA clones at two
concentrations, 0.0055µg and 0.055µg, in the gene-dense regions
of chromosome 22 (Sasaki et al., 2007).
We evaluate the capability of TileShuffle to cope with the most
dominant sequence-specific affinity effects in tiling array data such
as GC content and nucleotide positioning of a probe. Assuming that
most probes show only non-specific hybridization, the correlation
between GC content of probe sequences and their detected signal
intensities (R2= 0.383, Figure 1a) indicates a measurable bias
that needs to be taken into account. Otherwise, intensity-based
analyses may favor windows simply due to their GC-richness. A
signal smoothing as realized by windowing and calculating the
probe median z-score z(p), does not correct for the bias sufficiently
(R2= 0.266, Supplementary Figure S2a).
In theory, the use of affinity-based binning with respect to the GC
content of probe sequences should reduce the general effect whereas
the intensity of outliers and hence potentially expressed probes
remains relatively stable. Supplementary Figure S2b illustrates a
strong reduction of the sequence-specific affinity bias with merely
two GC content bins (R2= 0.037). Higher numbers of bins further
attenuate the correlation between GC content of probe sequences
and their probe median z-score, e.g., R2= 0.019 with three bins
(see Figure 1b). In each case, the distribution of the outliers (black
dots) differsfromtheoriginal dataonlytoaminor extent. According
to these findings, three bins may already suffice to efficiently
attenuate this bias while retaining sufficiently large permutation
RESULTS AND DISCUSSION
Control of tiling array specific biases
A AA A A A AAA
A A AAAAAA
C CC CC
C C CC
GG GG G
G GG G G GG
T T T T T T T T T T
T TT T TT TT
Position in sequence
12 14161820 2224
Normalized change of intensity
T T T T T T T T T T TTT T T T T T T T T T TT
AA A A A A A A A AAAAA A A A A A A A A
C CCCC C C C C CCCC CC C C C C C C C C C
GGGGG G G G G G GG GG GG G GG GG GG GG
Position in sequence
12 1416 1820 22 24
Normalized change of z-score
Fig. 2: Position-specific bias of every nucleotide in each of the 25 positions within the probe calculated on probe signal intensities (a) and
on probe median z-scores (b) by use of the Starr R package (Zacher et al., 2010). The distances of probe intensities and probe median
z-scores are further normalized by dividing them by the standard deviation of the intensity and median z-score distribution, respectively. The
probe median z-score is calculated as the median over the z-scores of all windows enclosing the probe where z-scores were estimated by
TileShuffle using three GC content bins.
To illustrate the influence of position-specific effects of each
nucleotide on the probe intensities,
Starr (Zacher et al., 2010) on probe intensities (see Figure 2a)
and on probe median z-scores z(p) after applying TileShuffle
with three GC content bins (see Figure 2b). Using Starr, we
can assess the position-specific bias of every nucleotide in each
of the 25 positions within the probe sequence for given probe
scores (e.g, probe intensities or probe median z-scores). More
precisely, for anypositionandnucleotide, itcalculatesthedifference
between the mean score of probes, where the nucleotide is at this
particular position within the probe sequence, and the overall mean
probe score. To obtain comparable scales, the changes of probe
intensities and probe median z-scores are normalized by dividing
them by the standard deviation of their distributions. Overall,
even though position-specific biases are not explicitly considered
in our framework, the combination of affinity-based permutations
and overlapping windows is capable of greatly reducing position-
specific biases in the tiling array data (Figure 2b). Correction
of this bias is not only a consequence of windowing, but also
depends on affinity-based permutations: Performing the analysis
on probe median z-scores after applying TileShuffle with only
one GC bin and hence without affinity-based permutations does not
sufficiently remove the bias (Supplementary Figure S3).
we use the R package
We evaluate the potential of TileShuffle to detect differentially
expressed regions in comparison to MAT and TAS, which are the
two most widely used algorithms for analyzing expression tiling
array data and are both applicable to non-replicated data which is
frequently the case for expensive whole genome tiling experiments.
The three algorithms are evaluated in two different scenarios. In the
first, we apply the different algorithms to a tiling array dataset of
human foreskin fibroblasts (HFF) which are synchronized by serum
Comparison with MAT and TAS
starvation in G0 or in G1 phase of thecell cycle. Thistranscriptome-
wide variation study is based on the Affymetrix Human Tiling
1.0 array set2. It consists of 14 arrays where probes are tiled
at approx. 35 bp intervals across the whole human genome with
gaps of approx. 10 base pairs. The tiling array data is compared
to a custom array experiment with considerably lower FDR as a
reference. This allows to assess the performance of the algorithms
applied to real biological data and to perform statistics on a large
number of differentially expressed elements. In the second scenario,
we apply all three algorithms to a spike-in dataset of 162 full-
length cDNA clones, which are hybridized at two, ten-fold different
concentrations toan Affymetrixchr21/22 array (Sasaki et al., 2007).
In this scenario, positives and negatives are more clearly defined
than above, but the number of differentially expressed intervals
is comparably low and the extent of differential expression and
complexity of the sample is more artificial.
For MAT and TAS, the expression and differential expression
analysis is carried out independently from each other: Highdiff
regions are obtained by intersecting intervals identified as
differentially expressed with those intervals deemed as ‘expressed’
in at least one of the compared biological states. TileShuffle,
in contrast, takes regions found to be significantly expressed in at
least one of the compared states (one-state analysis) as input for the
two-state analysis, and assesses differential expression solely on the
expressed segments and directly reports highdiff regions.
For one-state analyses, i.e., determination of expressed regions,
parameters for TAS have been set following Kampa et al. (2004).
Parameters for MAT as given in Johnson et al. (2006) are geared
towards ChIP-chip analysis and not suitable for expression analysis.
Upon inspection of positive control transcripts, we identified
2Array data and experimental details can be accessed at GEO (see
Supplementary Table S1).
Otto et al.
0 0.1 0.20.30.4
TileShuffle (variant A)
TileShuffle (variant B)
0 0.2 0.40.6 0.8
TileShuffle (variant A)
TileShuffle (variant B)
Fig. 3: ROC curve after evaluating the outcome of TAS, MAT, and TileShuffle applied to the G0/G1 transition of the cell cycle tiling
arraydataset (a) and tothe spike-in tilingarray dataset comparing hybridizations of 0.0055µg and 0.055µg cDNA (b) over a range of different
p/q-value cutoffs in the differential analysis. In the cell cycle dataset, the positive set is obtained by conducting and evaluating verification
experiments using a custom-designed microarray in triplicate. In the spike-in dataset, the positive set is comprised of regions covered by the
162 full-length cDNA clones which were spiked in. Note that the whiskers express the variation in the outcome of TileShuffle after
five repetitions, i.e., smallest and highest value on the x-axis (or y-axis) for each differential significance threshold, with the median result
shown on the solid line. The inlay in the right panel magnifies the area with an x-coordinate close to zero (same units on axes). Due to the
intersection of high and differential intervals in highdiff at fixed parameters for high, some intervals are never identified and thus the curves
do not reach (1,1). Sensitivity versus FDR curves are given in Supplementary Figures S7.
optimal parameters for MAT as the same or analogous values as used
for TAS. In summary, we set bandwidth = 35, i.e. on average the
probe intensities are smoothed by calculating the Hodges-Lehman
estimator over three probes, and the maximal gap between positive
probes to be included in a positive interval maxgap = 40. The
minimal length or minimal probe count of segments to be reported
were set to minrun = 90 and minprobe = 3, for TAS and
MAT, respectively. Perfect match (PM) and mismatch (MM) probe
intensities were utilized in TAS using an intensity threshold of 150.
For expression analyses with MAT, which uses only PM
intensities, a p-value threshold is set to 0.05 which yielded the best
results in terms of sensitivity and FDR in the analysis of the cell
cycle tiling array dataset. P-value cutoffs were tested in the range of
10−10to 0.05. TileShuffle was applied using only PM probes,
the arithmetic mean trimmed by maximal and minimal value as
scoring function, 10000 permutations, and a q-value threshold of
0.05. TileShuffle was applied using window sizes, 20, 200,
and 400 and different numbers of GC bins ranging from 1 to 9, to
assess the effect of these two parameters. The intermediate window
size of 200 was chosen in order to include an adequate number of
probes in the calculation of the window scores Se and Sd, and to
ensure that the majority of known exons is spanned by one single
window. The median exon length of known protein-coding genes is
118bp, while 90% of the exons are shorter than 228bp according to
GENCODE version 3c (Harrow et al., 2006).
Analysis of differential expression was performed with the same
parameters, except bandwidth = 150 for TAS and MAT and 100000
permutations for TileShuffle, both aiming at accommodating
the more rugged nature of the expression difference signal (log-fold
For the whole genome scenario, highdiff intervals were generated
with all three tools over a range of q-value and p-value cutoffs,
respectively. The custom microarray was run in triplicates for each
of the biological conditions of the tiling array experiment and was
used as a reference to estimate sensitivity, specificity, and false
discovery rate (FDR), defined as follows:
specificity = 1 −FP
FP + TP
The number of true positives (TP) corresponds to the number
of nucleotides which are highdiff in the tiling array analysis and
overlap with a probe that was found significantly differentially
expressed in the corresponding custom microarray experiment.
The number of false positives (FP) is defined as the number of
those nucleotides in highdiff intervals that overlap a probe that is
not significantly differentially expressed in the custom microarray
experiment. The number of positive nucleotides (P) is defined as the
sum of all nucleotides of probes that are significantly differentially
expressed in the custom microarray experiment (FDR < 0.05),
while the number of negative nucleotides (N) corresponds to
the sum of all nucleotides of probes that are not significantly
differentially expressed in the custom microarray experiment
(FDR ≥ 0.05).
The results for each algorithm are illustrated as receiver operating
characteristic (ROC) curve and as a function of sensitivity versus
FDR (see Figure 3a and Supplementary Figure S7a). Overall,
TileShufflein both tested variants A and B clearly outperforms
the two other algorithms. For example, at a maximal FDR of 20%,
both variants of TileShuffle yield a sensitivity of around 23%,
which is an approximately 4-fold and 11-fold increase compared
to TAS and MAT, respectively. Both TileShuffle variants
differ only to a minor extent from each other but variant B is
generally more restrictive and hence recommended as the default
choice. Evaluating the three algorithms based on counts of intervals
rather than on nucleotides yields concordant results with the latter
(Supplementary Figure S8).
In this test scenario, we also investigated the influence of the
number of GC bins and different window sizes on the ROC curve.
The worst performance is observed for one GC bin. This shows
that probes with low GC content tend to exhibit lower signal
intensities than probes with high GC content and hence are less
likely to be found in the right tail of the signal intensity distribution
(Supplementary Figure S16). A number of three GC bins results
in higher sensitivity at similar FDR, while increasing the number
of GC bins further yields only minor improvements at high FDR
values. Following Occam’s razor, we hence select the simpler
model, and recommend to use three GC bins as the default for the
one-state analysis. A window size of 400 bp leads to the best ROC
curve, but exhibits to fail in exon boundary detection described in
section 3.3 (Supplementary Figures S17-S20). A window size of
20 bp delivers only very few highdiff regions, resulting in very low
sensitivities. Thus, a window size of 200 bp seems to be the optimal
trade-off between good sensitivity and good recovery of exon-intron
structures at low FDR values.
In similar manner, we estimated the sensitivity, specificity, and
FDR in case of the spike-in dataset. Therein, the positive set
comprises all genomic regions covered by the 162 full-length cDNA
clones, i.e. 877 exonic regions, whichwerespiked inattwo different
concentrations. The set of negative regions comprises all unique
protein coding exons annotated in GENCODE version 3c that do
not overlap with any positive region. The GENCODE annotation
was converted from human genome version hg18 to hg17 using the
UCSC liftover tool. The number of true positives (TP) corresponds
to the number of nucleotides in positive regions which are highdiff
in the tiling array analysis. The number of false positives (FP) is
defined as the number of nucleotides in negative regions which are
in highdiff in the tiling array analysis. Accordingly, the number
of positive nucleotides (P) is defined as the sum of all nucleotides
in positive regions, while the number of negative nucleotides (N)
corresponds to the sum of all nucleotides in negative regions. The
resulting ROC curves are depicted in Figure 3b and Supplementary
Figure S7b. In summary, all three methods recover the differentially
expressed exons as all reach high sensitivity values at high
specificity or low FDR values. However, TileShuffle reaches
maximal sensitivity at comparable FDR values. Even though a
spike-in experiment allows precisely define TP and FP rates, it is
artificial and different from real expression perturbation studies as
much less noise is observed (see Supplementary Figure S22 for an
Due to the resampling step in TileShuffle, results may vary
between runs with different random number generator seeds. We
therefore plot the median of five different runs where the number
of permutations was set to 10000 for the one-state and 100000 for
the two-state analysis, and illustrate minimal and maximal values
as whiskers in x and y direction. Only negligible variation in
sensitivity and FDR is found for the most restrictive significance
thresholds. Thisisanexpected consequence of increasing variability
in sampling when the tails of the background distribution are
estimated. Hence, the numbers of required permutations of 10000
and 100000 for the one-state and two-state analysis, respectively,
mark a sufficient trade-off between running time and variation in
sensitivity and false discovery rate. Due to the high degree of
variation observed for fold changes, the tails of the background
distributions for two-state analysis must be well estimated with
an increased number of permutations. We adapted the code for
the two-state analysis to ensure that a sufficiently large number
of permutations can be computed within a feasible time scale. On
a single 2.66GHz 64-Bit Intel Xeon CPU, a one-state analysis of
a single array under the given parameters took around 12 hours
while a single two-state analysis took approximately 9h and 14h
with variant A and B, respectively. Since an array comprises
sufficient information to sample from the background distribution
and hence eliminate array-wide effects, the arrays can be analyzed
independently from each other.
One of the advantages of tiling arrays over conventional expression
arrays is information on the intron–exon–structure of transcripts,
as probes are tiled in an unbiased way across the genome. We
manually inspected a small set of genes that are known to be
cell cycle regulated (Bar-Joseph et al., 2008). In several cases,
we observed that TileShuffle is capable of detecting a higher
fraction of exons of a transcript as highdiff and identifies the intron-
exon boundaries more accurately than TAS or MAT. Supplementary
Figure S21 displays examples of known cell cycle regulated genes
where the three algorithms perform remarkably different.
To substantiate this finding and to exclude that the above
mentioned observation is merely a consequence of the increased
sensitivity of TileShuffle, we studied the accuracy in detecting
intron-exon boundaries on a global scale.
All unique exons of all protein-coding transcripts annotated
in GENCODE version 3c (Harrow et al., 2006) were extracted,
resulting in 293000 annotations. Highdiff intervals of the G0/G1
transition of the cell cycle dataset were computed with all three
methods. To increase comparability, significance thresholds were
adjusted to yield comparable FDR values, i.e. 18% FDR in case
of TAS (q=0.05), 17% in case of MAT (p=1e-6), and 19% and
18% in case of TileShuffle variant A (q=0.05) and variant
B (q=0.1), respectively. For each method, the overall reported
nucleotides identified as highdiff in the G0/G1 transition of the cell
cycle dataset including the absolute and relative base pair coverage
with GENCODE version 3c annotations is given in Supplemental
Table S5. The absolute number of reported nucleotides and their
length greatly differs among the methods (see Supplementary
Detection of transcript structures
Otto et al.
Table S3). An analogous analysis for high intervals is shown in
Supplementary Tables S4 and S2.
expressed intervals or highdiff intervals) with all annotated exons
no matter of the annotated reading strand direction for exons, since
strand information cannot be inferred from the Affymetrix Human
Tiling 1.0 array set. For each overlapping pair of tiling array interval
and annotated exon, the genomic distances between the inferred
and annotated 5′- and 3′-ends, respectively, are summarized in an
empirical cumulative distribution function (ecdf). We do not only
include the pair with minimal distance but consider all overlaps
of several tiling array intervals with one exon, as well as all
overlaps of several exons with one tiling array interval in the ecdf.
This penalizes the distance distribution in cases where one exon is
represented by many small tiling array intervals. It also penalizes
intronic tiling array intervals that partly overlap with an exon. Due
to the higher sensitivity of TileShuffle, the number of regions
included inthisanalysisissignificantlyhigher compared totheother
methods. We therefore normalize the ecdf to the total number of
overlaps of the respective method.
TileShuffle clearly outperforms the other two methods in
detecting exon-intron boundaries in highdiff data (Figure 4). The
results are more balanced for expression analysis, where TAS finds
a higher proportion of exons boundaries with an offset below the
window size of TileShuffle, while overall, TileShuffle
identifies a higher proportion of boundaries (Supplementary Figure
S9). Of all window sizes tested for TileShuffle, 200 bp
performs best. A window of 400 bp further extends exons and a
window size of 20 bp, i.e. comprising just one probe, shortens exons
remarkably. Different GC bins for the one-state analysis do not have
a considerable impact on exon boundary detection (Supplementary
Supplementary Figures S10 and S11 further illustrate the
orientation in the offset to annotated exons. Both, for expression
and differential expression analysis, TileShufflehas a tendency
to extend the reported region beyond the exon boundaries with the
largest extension observed for long window sizes as i.e. 400 bp.
Again, if the window includes just one probe (window size set to
20 bp), TileShuffle tends to shorten exons (Supplementary
Figure S17-S20). TAS and MAT tend to find exons shorter than
annotated, caused by a comparable offset at 5’- and 3’-boundaries
in the case of expression analysis (Supplementary Figure S10).
Boundaries of differentially expressed exons are hardly detected
correctly by TAS and MAT, but again with a tendency to shortening
(Supplementary Figure S11). This bias in the offset to the correct
exon boundary is not unexpected: Considering windows of length
200, TileShuffle will always extend expressed exons smaller
than the window size, which constitutes a significant proportion of
exons in the human genome. TAS and MAT extend regions probe-
wise and thus can detect exons more precisely if the signal across
the exon is smooth. On the other hand, exon signals, strongly
affected by sequence-specific affinitiesor cross-hybridization across
the exon, may prevent correct extension and lead to fragmentation
into several intervals or shortening. This may explain, why overall,
TileShuffle identifies a greater proportion of boundaries.
Probe-wise extension largely fails in detecting highdiff exons. The
expression difference signal is rugged and can reverse signs within
one exon. TileShuffle, which combines a robust windowing
approach and scoring function with “window-wise” extension, is
clearly advantageous over the other methods that rely on probe-wise
We finally investigated whether the observed differences in
detecting boundaries of highdiff exons are biased by the selected
significance thresholds. Over a range of q-value thresholds,
TileShuffle displays only minor variation in the ecdf of
distances to exon boundaries and nearly constant results for
distances below the window size (see Supplementary Figures S12
and S13). In contrast, the ecdf of TAS and MAT vary strongly
between the different thresholds (see Supplementary Figures S14
and S15) and for significance threshold below 0.5, TAS and MAT
obtain significantly lower accuracies than TileShuffle at any
Most published tiling array studies have focused on discovery
of novel expressed transcripts rather than unbiased detection of
differential expression and the choice of software for the latter task
is limited. Variants of the maxgap/minrun algorithm (Kampa et al.,
2004; Royce et al., 2005) like TAS require dataset-specific cutoff
parameters and MAT has been developed for ChIP-chip data analysis
and requires adapted parameters to be applicable to expression
tiling array data. Both hampers the applicability of these methods
in different scenarios without manually inspecting a small set of
expected positive regions.
We have presented TileShuffle, a method specifically
designed for expression and differential expression analysis of
tiling array data. It implements a statistical approach to detect
expression or differential expression in terms of differences
from the background distribution that avoids any intensity-related
parameters. TileShuffle reduces the most dominant tiling array
biasesusing anaffinity-dependent permutation inconjunction witha
windowing approach. A related resampling approach has been used
by Guttman et al. (2009), which does however not consider probe
affinities and is not applied to detection of differential expression.
We compared TileShuffle, TAS, and MAT in two different
test scenarios. In the cell cycle dataset, where a custom array was
used for validiation, TileShuffle achieved significantly lower
false discovery rates under equal sensitivities. This test scenario has
the advantages of building on a biologically meaningful experiment
with the associated noise in expression signals and transcriptome
complexity and of calculating sensitivity and specificity on a large
number of intervals. However, the custom array data has an FDR
itself, which is better controlled and significantly lower than for the
tiling array, but still providing a surrogate for a true reference.
In the second scenario, the algorithms are compared using a
spike-in dataset (Sasaki et al., 2007). The differences between
the three algorithms are smaller than in the previous scenario.
TileShuffle, however, is the only one obtaining sensitivities
above 50%. The spike-in experiment has the advantage of a clear
definitionof positve and negative intervalsfor calculating sensitivity
and specificty. However – though large for a spike-in experiment –
162differentiallyexpressed elements isasmall number compared to
the cell cycle experiment, the noise is low, the basal expression level
is already high and a ten-fold differential expression a strong effect
in biological experiments. The scenario is thus rather artificial.
0 100 200300400 500
Absolute value of distance to 5’-end of exon
Cumulative fraction of overlaps
TileShuffle (variant A)
TileShuffle (variant B)
0 100 200 300400 500
Absolute value of distance to 3’-end of exon
Cumulative fraction of overlaps
TileShuffle (variant A)
TileShuffle (variant B)
Fig. 4: Empirical cumulative distribution function of the absolute distances between 5′- (a) and 3′-end (b), respectively, of exon and reported
interval for all overlapping pairs of unique GENCODE annotated exons and reported intervals. Overlapping here means any overlap in
genomic coordinates ignoring strand. Only every 10th data point is drawn as a symbol. For each method, the set of highdiff intervals in the
G0/G1 transition of the cell cycle tiling array dataset is used as input dataset. The significance thresholds of the three methods for differential
analysis were adjusted to obtain similar FDRs as estimated before using the custom microarray, i.e., 18% FDR in case of TAS (q=0.05),
17% in case of MAT (p=1e-6), and 19% and 18% in case of TileShuffle with variant A (q=0.05) and variant B (q=0.1), respectively. The
absolute number of overlaps is 15835 and 13479 with TileShuffle and variant A and B, respectively, 4337 with TAS, and 2381 with
Apart from the ROCs, TileShuffle clearly outmatches TAS
and MAT in the recovery of transcript structures by identifying the
intron-exon structure more accurately. However, TileShuffle
fails to detect very short exons because of the windowing approach.
Additionally, TileShufflecanincorporate replicateexperiments
and supports input data as custom-formatted files and hence is not
dependent on any technology or tiling array design and can also
be applied to ChIP-chip data by selecting a larger window size.
The required computation time of TileShuffle is considerably
higher than for TAS and MAT. However, it is negligible compared to
efforts for the genome-wide tiling array experiment and thus does
not constitute a bottleneck in the analysis work flow.
This publication was supported in part by the Initiative and
Networking Fund of the Helmholtz Association (VH-NG-738),
by LIFELeipzig Research Center for Civilization Diseases,
Universit¨ at Leipzig. LIFE is funded by means of the European
Union, by the European Regional Development Fund (ERDF) and
by means of the Free State of Saxony within the framework of the
excellence initiative. The funders had no role in study design, data
collection and analysis, decision to publish, or preparation of the
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