 Software
 Open Access
Analysis of tiling array expression studies with flexible designs in Bioconductor (waveTiling)
 Kristof De Beuf^{1}Email author,
 Peter Pipelers^{1},
 Megan Andriankaja^{2, 3},
 Olivier Thas^{1},
 Dirk Inzé^{2, 3},
 Ciprian Crainiceanu^{4} and
 Lieven Clement^{1, 5}Email author
https://doi.org/10.1186/1471210513234
© De Beuf et al.; licensee BioMed Central Ltd. 2012
 Received: 22 May 2012
 Accepted: 5 September 2012
 Published: 14 September 2012
Abstract
Background
Existing statistical methods for tiling array transcriptome data either focus on transcript discovery in one biological or experimental condition or on the detection of differential expression between two conditions. Increasingly often, however, biologists are interested in timecourse studies, studies with more than two conditions or even multiplefactor studies. As these studies are currently analyzed with the traditional microarray analysis techniques, they do not exploit the genomewide nature of tiling array data to its full potential.
Results
We present an R Bioconductor package, waveTiling, which implements a waveletbased model for analyzing transcriptome data and extends it towards more complex experimental designs. With waveTiling the user is able to discover (1) groupwise expressed regions, (2) differentially expressed regions between any two groups in singlefactor studies and in (3) multifactorial designs. Moreover, for timecourse experiments it is also possible to detect (4) linear time effects and (5) a circadian rhythm of transcripts. By considering the expression values of the individual tiling probes as a function of genomic position, effect regions can be detected regardless of existing annotation. Three case studies with different experimental setups illustrate the use and the flexibility of the modelbased transcriptome analysis.
Conclusions
The waveTiling package provides the user with a convenient tool for the analysis of tiling array trancriptome data for a multitude of experimental setups. Regardless of the study design, the probewise analysis allows for the detection of transcriptional effects in both exonic, intronic and intergenic regions, without prior consultation of existing annotation.
Keywords
 Circadian Rhythm
 Discrete Wavelet Transform
 Design Matrix
 Effect Function
 Tiling Array
Background
In the last few years tiling microarrays have become a wellestablished tool for wholegenome transcriptome analysis. They have shown to be very useful for exploring and unraveling the complex genomewide trancriptional landscape of higher organisms, in which not only protein coding genes, but also noncoding RNAs play an important role [1–4]. The methods that have been developed for transcriptome analysis with tiling arrays either focus on segmentation and transcript discovery within a single biological condition [5–8], or on the detection of differential expression between two distinct conditions [9, 10]. Recently, the focus in tiling array studies has shifted towards more complex experimental designs, such as studies with more than two conditions [11] and studies with several experimental factors [12]. Furthermore, it is recognized that expression is a dynamic rather than a static phenomenon. Hence, more and more timecourse experiments are designed to provide insights into the wholegenome transcript regulation of species during different developmental stages or external periodic changes in the environment [13, 14].
Currently, most tiling array transcriptome analysis pipelines start with summarization of the probelevel data. This can be done by constructing probesets from the groups of probes that map to known annotated genes, (e.g. [11, 15]). Hereby unannotated regions are disregarded. In [12, 13, 16] a sliding windowbased approach is adopted, combined with a thresholding rule for selecting transcriptional units, whereas in [14] segments with piecewise constant intensity levels are constructed first [17]. After the summarization a statistical test or a more heuristic analysis technique is conducted on the summarized expression values of the transcriptional units. In current timecourse and singlefactor studies this is merely done by directly applying traditional microarray analysis methods, such as a pairwise moderated ttest (Limma) [18] conducted in [11] or a permutated ttest (SAM) [19] conducted in [16]. Other studies adopt adhoc approaches to filter the genes or transcriptional units of interest. Transcriptional units in a timecourse experiment, for example, can be filtered based on thresholding the amplitude of the signal [20]. In an alternative approach the correlations between temporal expression patterns are explored and a clustering is performed of genomic regions based on expression profiles in different gene classes showing expression at different timepoints [21]. The tests reported in [13] and [14] on the other hand are less ad hoc, but very specific for the periodic timecourse design apparent in these studies [22–24]. The aforementioned methods either lack flexibility by only focusing on one specific experimental design, or they first summarize probes to probesets based on existing annotation, hence not exploiting the genomewide nature of the data to the full extent.
Here, we present waveTiling, a R Bioconductor package for transcriptome analysis of tiling arrays with flexible designs. The package is based on and provides an extension to a recently introduced waveletbased functional model for transcriptome analysis [25]. While the methodology in [25] was initially developed to conduct the simultaneous tasks of transcript discovery and detection of differential expression, their framework can be easily extended by adapting the model design matrix. After modeling the specific effect function of interest, probewise inference can be conducted for detecting affected regions. The probewise analysis allows for the detection of transcriptional units in both exonic, intronic and intergenic regions, without prior consultation of existing annotation. Currently, waveTiling provides a standard analysis flow for transcriptome analysis on singlefactor experiments with two or more biological conditions, the detection of linear and quadratic effects and circadian rhythms in timecourse experiments, and the analysis of twofactor experiments, while more experienced users can also specify customized designs. Furthermore, it generates alonggenome plots and contains functions to easily extract the detected genes and unannotated regions. The Implementation section gives an overview of the main functionalities of the waveTiling package and describes the model for the different designs, as well as the associated inference procedures. In Results and Discussion we illustrate the use of the package and the model on three different case studies with very distinct experimental designs.
Implementation
The waveTiling package is an addon package to the Bioconductor project [26] written in the programming language and statistical environment R [27]. It provides all the tools necessary to conduct a full analysis of tiling microarray experiments for flexible designs based on the recently introduced waveletbased functional model for trancriptome analysis [25]. The package uses the standard Bioconductor S4class data structures making it fully compatible with existing packages. The data is imported with the aid of the oligopackage [28] and the resulting object inherits from TilingFeatureSet, which is specifically designed for representing tiling array data and in turn extends ExpressionSet. Existing instance methods from oligo and other Bioconductor packages supporting this structure are therefore applicable as well. Before starting the analysis the probes can be remapped to the existing annotation. Moreover, probes that contain duplicated sequences for perfect match and mismatch probes or for probes on different strands can be filtered because they are deemed unreliable due to crosshybridization effects. The main transcriptome analysis consists of two consecutive steps: (1) fitting the waveletbased functional model to the data, and (2) modelbased inference to identify transcriptionally affected regions. The fitted model is stored in a WfmFitclass object. Depending on the design of the study a WfmFitFactor (factorial design), WfmFitTime (timecourse design), WfmFitCircadian (circadian rhythm design) or WfmFitCustom (custom design) subclass is used. Part of the code for fitting the model is implemented in C to speed up computation. In the second step, different inference procedures can be conducted depending on the research question. The inference procedure that can be conducted depends on the WfmFitsubclass. The results are stored as a WfmInf class object. There are 3 main subclasses: WfmInfCompare which contains the results of a pairwise comparison between two groups or time points; WfmInfMeans with the results of transcript discovery for each individual group or time point; and WfmInfEffects which contains results with linear or quadratic time effects for timecourse designs and circadian rhythm effects for circadian designs. All transcriptionally affected regions can be extracted from the WfmInf class objects and are stored as IRangesclass objects [29]. The model fitting and inference steps are described in more detail in the Statistical Methods part.
The results can be visually explored by means of a general plot function. The implementation is based on the GenomeGraphs package [30]. For any genomic region the fitted expression values and transcriptionally affected regions can be plotted along the genomic coordinate. Furthermore, two functions are available for further postprocessing of the results. Provided a suitable annotation file is given, the transcriptionally affected regions are mapped against the existing annotation. The first function outputs the genes that are transcriptionally affected, while the second function provides a list of the detected unannotated regions. The output of both functions is a list of GRangesclass objects [31].
Statistical Methods
We start by presenting an overview of the basic model introduced by [25]. Subsequently, we show how we accomodate for several sampling schemes in timecourse experiments or other experiments with more flexible designs.
Basic waveletbased model for transcriptome analysis
with i=1,.. N, _{ Y i }(t) the measured log_{2}transformed expression values for the probe with position t (t=1,.. T) on array i (i=1,.. N). T is the number of probes that are more or less equally spaced along the genomic position of the chromosome, and N=_{N1} + _{N2} is the number of tiling arrays in the experiment, with _{N1} the number for biological condition 1, say _{C1}, and _{N2} the number for biological condition 2, say _{C2}. Further, _{X1,i} is a dummy variable which is 1 for _{C1}and −1 for _{C2}, and _{ E i }(t) is a zero mean error term. It is assumed that _{ E i }(1),.._{ E i }(T) are jointly MVN(0_{ Σ ε }). Here, MVN(μ Σ) denotes the density function of a multivariate normal distribution with mean μ and variancecovariance matrix Σ.
with ${N}_{\mathbf{1}}={N}_{\mathbf{2}}=\frac{N}{\mathbf{2}}$.
where ${\beta}_{m}^{\ast}(j,k)$ is the element of ^{B∗} corresponding to scale j and location k and m=1,2. In (4) N(μ^{σ2}) denotes the density function of a normal distribution with mean μand variance ^{σ2}. The smoothing parameters _{ τ m }(j k) and the error variances ${\sigma}_{\epsilon}^{\mathbf{2}}(j,k)$ are estimated by marginal maximum likelihood using a GaussSeidel algorithm. The estimated ${\widehat{\tau}}_{m}(j,k)$ induce a regularization of the wavelet coefficients of the effect functions. When backtransforming the modified coefficients to the original data space, this leads to a denoised expression signal whereby the main features are retained. The method has proven to be very fast which is essential when analyzing large datasets. For more details, see [25].
Waveletbased models for transcriptome analysis in more flexible designs
To extend the modeling framework reviewed in the previous section and to make it suitable for the analysis of tiling array data with more flexible designs, the design matrix X needs to be adapted in an appropriate way. Firstly, the adaptation must enable the model to answer the specific research questions provoked by the experimental design. Secondly, it must allow us to use the same fast algorithms introduced in [25]. This second argument comes down to the preservation of the orthogonality of X. In the first part of this section we focus on general timecourse designs and singlefactor designs for more than 2 groups. The second part aims at specific timecourse designs for assessing circadian rhythms in the transcriptome. The section concludes with looking specifically at nonorthogonal designs, typically encountered in multifactor studies.
General timecourse designs
In tiling array timecourse experiments one is often interested in the detection of differentially expressed regions between any two different time points. An additional concern might be to detect significant effects of transcriptional activity in time, e.g. linearly increasing or decreasing transcriptional expression of certain regions. These two possible research aims can be dealt with by considering a functional relationship of the designed time points described by orthogonal polynomials. This approach has also been used in quantitative trait associated expression studies based on traditional microarrays [32]. In that paper the functional relationship with phenotype is considered instead of with time.
Just like for the polynomials, the design matrix Xbased on Helmert contrasts still needs to be normalized if the same smoothing for all factor effects is desired.
Designs for circadian rhythms
To estimate a common smoothing parameter for inducing the same amount of smoothing for all effect functions, X can again be normalized as described previously.
Nonorthogonal designs
Design matrices for two or multiplefactor designs are typically nonorthogonal. Using these in the waveletbased model would imply that the fast algorithms presented in [25] would have to be adapted. This would lead to undesirably increased computation time during parameter estimation. A solution to this problem is to apply the GramSchmidt process to orthogonalize Xand subsequently estimate the model parameters based on the orthogonalized design matrix. The GramSchmidt orthogonalization comes down to a QRdecomposition [34] of X into an uppertriangular matrix _{ X tri } and an orthogonal matrix _{ X orth }, which is now used to fit the model. Afterwards, the estimated parameters have to be transformed back to obtain the parameter values for the original X. This is possible by premultiplying them with ${\left({\mathit{X}}_{\mathrm{orth}}^{T}\mathit{X}\right)}^{\mathbf{1}}$. Similar to singlefactor and timecourse designs, the coding of the initial design matrix X still determines how the parameters can be interpreted, and may thus be constructed according to the specific research interest.
Statistical inference: detection of transcriptional effect regions
Based on the size of A(t) circadian effect regions can be detected. In the case of nonorthogonal designs in multiplefactor studies, there are several possibilities for the choice of $F\left\{\mathit{\beta}\left(t\right)\right\}$, depending on the aim of the analysis. The idea remains the same, however.
Results and discussion
The use and flexibility of the waveTiling package is illustrated in three case studies for transcriptome analysis with different experimental setups.
Case study 1: Timecourse experiment
The first data set consists of a tiling array expression study for identifying the molecular events associated with early leaf development of the plant species Arabisopsis thaliana[11]. Unraveling the underlying mechanisms of on one hand the transition from cell division to cell expansion and on the other hand the transition from nonphotosynthetic to photosynthetic leaves, was the focus of this study. Trancriptome analysis for six developmental time points (day 8 to day 13) was conducted with AGRONOMICS1 tiling arrays [36], with three biological replicates per time point. Primarily, the researchers were focusing on the detection of differentially expressed regions between any two pairs of developmental time points. This specific study design, however, also allows for the detection of expression regions that change linearly over time. The functions and code used for this case study are described in more detail in the package vignette (see Additional file 1).
Pairwise comparison
We evaluate the regions detected by the waveletbased analysis against the genes produced by the wellestablished and often used RMA method [37]. This is done by comparing the results of a gene set enrichment analysis based on both methods. By mapping the genomic regions found by the waveletbased method to the Arabidopsis thaliana TAIR9 annotation [38], a list of genes is created for this method. Only genes that showed an overlap of at least 15% with the detected regions were retained. The enrichment analysis as performed with Plaza [39] revealed a strong overlap in the processes detected by both methods. A total of 483 enrichments were identified using both genesets of which 360 common enrichments were shared. The RMA gene list had 75 specific enrichments, while the waveletbased gene list had 48.
 1.
Region was not in or near an exon or promoter from an annotated gene.
 2.
Longer regions containing more differentially expressed probes were preferentially selected.
 3.
Regions showing homogeneous probe directionality (all probes going in the same direction) across the entire region of differential expression were preferentially selected.
Using these criteria 12 regions were selected and qRTPCR analysis was performed (see Additional file 2: Table S1). Of the 12 regions, 11 could be confirmed to contain differentially expressed transcripts during the timecourse analysis. Only 1 region had no detectable transcriptional products. Log fold changes were calculated for confirming the expression and differential expression, as well as the directionality of the differential expression. From this analysis 9 of the 11 regions showed the same log fold change directionality as previously identified from the tiling arrays, and 2 regions showed opposite log fold change directionality. However, these 2 regions had the lowest log fold changes in the waveletbased analysis. More details about the methods of enrichment and qRTPCR analysis can be found in Additional file 2.
Linear and quadratic time effects
Case study 2: Circadian rhythms
The second case study concerns an expression analysis to examine circadian rhythms in Arabisopsis thaliana[13]. It is known that photosynthetic organisms anticipate changes in the daily environment with an internal oscillator, called the circadian clock. The aim of the study was to explore the genomewide extent of the rhythmic expression patterns governed by this oscillator. In this experiment, 12 samples were collected from Arabidopsis thaliana seedlings that were placed under a 12 h light / 12 h dark cycles regime. Every 4 hours 2 samples were taken and hybridized to the Affymetrix AtTile 1.0F and 1.0R tiling arrays. More information about the experiment can be found in [13].
Circadian effect for 9 genes put forward in the Hazen study
Gene ID  Name  Overlap  Max. Eff.  Top 20 

AT1G22770  GIGANTEA  0.529  2.28  yes 
AT1G68050  FLAVINBINDING KELCH DFB PROTEIN1  0.867  2.90  yes 
AT2G25930  EARLY FLOWERING3  0.562  1.46  yes 
AT2G46790  PSEUDO RESPONSE REGULATOR9  0.473  1.38  yes 
AT2G46830  CIRCADIAN CLOCK ASSOCIATED1  0.867  3.89  yes 
AT3G22380  TIME FOR COFFEE  0.040  0.06  no 
AT3G46640  LUX ARRHYTHMO  0.717  1.69  yes 
AT5G57360  ZEITLUPE  0.350  0.41  no 
AT5G61380  TIMING OF CAB2 EXPRESSION1  0.797  1.74  yes 
Case study 3: Nonorthogonal twofactor design
Twofactor model genewise effects
${\widehat{\beta}}_{\mathbf{0},\mathrm{gene}}$  ${\widehat{\beta}}_{\mathbf{1},\mathrm{gene}}$  ${\widehat{\beta}}_{\mathbf{2},\mathrm{gene}}$  ${\widehat{\beta}}_{\mathbf{3},\mathrm{gene}}$  ${\widehat{\beta}}_{\mathbf{4},\mathrm{gene}}$  ${\widehat{\beta}}_{\mathbf{5},\mathrm{gene}}$  

AT1G69530  4.76  8.70  3.98  −0.82  −4.34  −7.09 
AT1G61520  4.27  0.13  0.72  0.13  5.11  −0.44 
Conclusions
In this paper, we have described the R package waveTiling for modelbased analysis of tiling array expression studies with flexible designs. It implements the recently proposed waveletbased model for transcriptome analysis [25] and extends its applicability towards more complex experimental setups. Unlike most currently applied methods, transcriptional activity is modeled at probelevel instead of gene or exonlevel. This probewise analysis allows for the detection of transcriptional units in both exonic, intronic and intergenic regions, without prior consultation of existing annotation. By appropriate adaptations of the basic model design matrix it becomes possible to easily analyze the transcriptome for singlefactor experiments with more than two biological conditions, to detect linear and quadratic time effects or a circadian rhythm effect in timecourse experiments, and to even conduct two or multiplefactor studies. The package’s use and flexibility are illustrated with three case studies on the reference plant Arabidopsis thaliana. These cases show the potential of the package and method to cope with a multitude of study designs and associated specific research questions and still provide reliable results. The waveTiling package will be freely available as part of the Bioconductor project.
Availability and requirements

Project name: waveTiling

Project home page: http://rforge.rproject.org/projects/wavetiling/

Operating system(s): Platform independent

Programming language: R

Other requirements: R >= 2.14

License: GNU GPL

Any restrictions to use by nonacademics: None
Declarations
Acknowledgements
Part of this research was supported by IAP research network grant no. P6/03 of the Belgian government (Belgian Science Policy) and Ghent University (Multidisciplinary Research Partnership “Bioinformatics: from nucleotides to networks”).
Authors’ Affiliations
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