Reading Tiling Arrays

Tiling Arrays are a cheap and fast way to have low-resolution nucleosome coverage maps. They have been widely used in literature [@Yuan2005, @Lee2007, @Mavrich2008], but complex statistical methods were needed for their processing [@Liu2007].

This kind of microarrays cover a part of the genome with certain spacing between probes which causes a drop in the resolution and originates some problems. The nucleosome calling from Tiling Array data required hard work on bioinformatics side and use of heavy and artificious statistical machinery such as Hidden Markov Models [@Yuan2005, @Lee2007] or higher order Bayesian Networks [@Kuan2009].

presents a new method based on a simple but effective peak calling method which achieves a great performance at low computing cost that will be presented in subsequent sections.

In order to standardize the data coming both from Tiling Arrays and NGS, the array fluorescence intensities (usually the ratio of the hybridization of nucleosomal and control sample) are converted to 1bp resolution by inferring the missed values from the neighboring probes. This is done by the function processTilingArray:

processTilingArray(data, exprName, chrPattern, inferLen=50)

An example of a processed dataset is provided in this package. See the help page of tilingArray_preproc for details on how it has been created. This object is a numeric vector covering the 8000 first positions of chromosome 1 in yeast (Saccharomices cerevisiae genome SacCer1).

library(nucleR)
library(ggplot2)
library(IRanges)
library(GenomicRanges)
data(nucleosome_tiling)
head(nucleosome_tiling, n=25)
#>  [1] 1.273222 1.281978 1.290734 1.299490 1.308246 1.352696 1.397145 1.441595
#>  [9] 1.486044 1.501795 1.517547 1.533298 1.549049 1.547577 1.546105 1.544633
#> [17] 1.543161 1.539886 1.536612 1.533337 1.530063 1.488922 1.447782 1.406642
#> [25] 1.365502

This values represent the normalized fluorescence intensity from hybridized sample of nucleosomal DNA versus naked DNA obtained from . The values can be either direct observations (if a probe was starting at that position) or a inferred value from neighboring probes. This data can be passed directly to the filtering functions, as described later in the section @ref(peaks).

Importing BAM files

Additionally, the function importBAM, allows to directly import into the mapped reads of a NGS experiment contained in a BAM file. The user has to specify whether the file contains paired-end or single-end read fragments.

sample.file <- system.file("extdata", "cellCycleM_chrII_5000-25000.bam",
    package="nucleR")
reads <- readBAM(sample.file, type="paired")
head(reads)
#> GRanges object with 6 ranges and 0 metadata columns:
#>       seqnames    ranges strand
#>          <Rle> <IRanges>  <Rle>
#>   [1]    chrII 5790-5912      *
#>   [2]    chrII 5791-5920      *
#>   [3]    chrII 5809-5914      *
#>   [4]    chrII 5811-5983      *
#>   [5]    chrII 5815-5934      *
#>   [6]    chrII 5822-6096      *
#>   -------
#>   seqinfo: 17 sequences from an unspecified genome; no seqlengths

Next Generation Sequencing

NGS has become one of the most popular technique to map nucleosome in the genome in the last years [@Kaplan2009, @Schones2008, @Xi2010]. The drop of the costs of a genome wide sequencing together with the high resolution coverage maps obtained, made it the election of many scientists.

The package allows reading of the data coming from many sources (Bowtie, MAQ, Illumina pipeline…) and has become one of the most popular packages in / for NGS data manipulation.

A new package, called , has been recently created to perform preprocessing and quality assesment on NGS experiments. supports most of the output generated by the functions on that package and recommends its use for quality control and correction of common biases that affect NGS.

handles ShortRead and RangedData data formats. The dataset nucleosome_htseq includes some NGS reads obtained from a nucleosome positioning experiment also from yeast genome, following a protocol similar to the one described in [@Lee2007].

The paired-end reads coming from Illumina Genome Analyzer II sequencer were mapped using Bowtie and imported into using . Paired ends where merged and sorted according the start position. Those in the first 8000bp of chromosome 1 where saved for this example. Further details are in the reference [@Deniz2011]:

data(nucleosome_htseq)
class(nucleosome_htseq)
#> [1] "GRanges"
#> attr(,"package")
#> [1] "GenomicRanges"
nucleosome_htseq
#> GRanges object with 18001 ranges and 0 metadata columns:
#>           seqnames    ranges strand
#>              <Rle> <IRanges>  <Rle>
#>       [1]     chr1     1-284      +
#>       [2]     chr1     5-205      +
#>       [3]     chr1     5-205      +
#>       [4]     chr1     5-209      +
#>       [5]     chr1     5-283      +
#>       ...      ...       ...    ...
#>   [17997]     chr1 7994-8151      +
#>   [17998]     chr1 7994-8151      +
#>   [17999]     chr1 7994-8151      +
#>   [18000]     chr1 7994-8152      +
#>   [18001]     chr1 7994-8152      +
#>   -------
#>   seqinfo: 1 sequence from an unspecified genome; no seqlengths

Now we will transform the reads to a normalized format. Moreover, as the data is paired-ended and we are only interested in mononucleosomes (which are typically 147bp), we will discard the reads with a length greater than 200bp, allowing margin for some underdigestion but discarding extra long reads. Note that the behaviour of fragmentLen is different for single-ended data, see the manual page of this function for detailed information.

As our final objective is identifying the nucleosome positions, and does it from the dyad, we will increase the sharpness of the dyads by removing some bases from the ends of each read. In the next example, we will create two new objects, one with the original paired-end reads and another one with the reads trimmed to the middle 40bp around the dyad (using the trim argument).

# Process the paired end reads, but discard those with length > 200
reads_pair <- processReads(nucleosome_htseq, type="paired", fragmentLen=200)

# Process the reads, but now trim each read to 40bp around the dyad
reads_trim <- processReads(nucleosome_htseq, type="paired", fragmentLen=200,
    trim=40)

The next step is obtain the coverage (the count of how many reads are in each position). The standard package function coverage will work well here, but it is a common practice to normalize the coverage values according to the total number of short reads obtained in the NGS experiment. The common used unit is reads per milon (r.p.m.) which is the coverage value divided by the total number of reads and multiplied per one milion. A quick and efficient way to do this with is the coverage.rpm function. ¹

# Calculate the coverage, directly in reads per million (r.p.m)
cover_pair <- coverage.rpm(reads_pair)
cover_trim <- coverage.rpm(reads_trim)

In Figure @ref(fig:figcover) we can observe the effect of trim attribute plotting both coverages. Note that the coverages are normalized in the range 0–1:

MNase bias correction

Variation in the sharpness of the peaks using attribute.

The Microccocal Nuclease is a widely used enzyme that has been proved to have a biase for certain dinucleotide steps [@Deniz2011]. In this package we offer a quick way to inspect the effect of such artifact by correcting the profiles of nucleosomal DNA reads with a mock sample of naked DNA digested with MNase.

The use of this function requires a paired-end control sample and a paired end or extended single-read nucleosomal DNA sample. A toy example generated using synthetic data can be found in Figure @ref(fig:figmnase).

# Toy example
map <- syntheticNucMap(as.ratio=TRUE, wp.num=50, fuz.num=25)
exp <- coverage(map$syn.reads)
ctr <- coverage(map$ctr.reads)
corrected <- controlCorrection(exp, ctr)

Toy example of MNase biase correction. Random nucleosomal and control reads have been generated using function and corrected using .

Noise removal

NGS and specially Tiling Array data show a very noisy profile which complicates the process of the nucleosome detection from peaks in the signal. A common approach used in the literature is smooth the signal with a sliding window average and then use a Hidden Markov Model to calculate the probabilities of having one or another state.

Original intensities from tiling array experiment. Smoothing using a sliding window of variable length (0, 20, 50 and 100 bp) is presented.

As can be seen in Figure @ref(fig:fignoise), data needs some smoothing to be interpretable, but a simple sliding window average is not sufficient. Short windows allow too much noise but larger ones change the position and the shape of the peaks.

proposes a method of filtering based on the Fourier Analysis of the signal and the selection of its principal components.

Any signal can be described as a function of individual periodic waves with different frequencies and the combination of them creates more complex signals. The noise in a signal can be described as a small, non periodic fluctuations, and can be easily identified and removed [@Smith1999].

uses this theory to transform the input data into the Fourier space using the Fast Fourier Transform (FFT). A FFT has a real and a imaginary component. The representation of the real component it’s called the power spectrum of the signals and shows which are the frequencies that have more weight (power) in the signal. The low frequency components (so, very periodic) usually have a huge influence in the composite signal, but its rellevance drops as the frequency increases.

We can look at the power spectrum of the example dataset with the following command:

fft_ta <- filterFFT(nucleosome_tiling, pcKeepComp=0.01, showPowerSpec=TRUE)

Power spectrum of the example Tiling Array data, percentile 1 marked with a dashed line.

In the Figure @ref(fig:figfft) only the half of the components are plotted, as the spectrum is repeated symmetrically respect to its middle point. The first component (not shown in the plot), has period 1, and, in practice, is a count of the lenght of the signal, so it has a large value.

High frequency signals are usually echoes (repeating waves) of lower frequencies, i.e. a peak at 10 will be the sum of the pure frequence 10 plus the echo of the frequency 5 in its 2nd repetition. Echoes can be ignored without losing relevant information.

The approach follows is supposing that with just a small percentage of the components of the signal, the input signal can be recreated with a high precision, but without a significant amount of noise. We check empirically that with 1% or 2% of the components (this means account 1 or 2 components for each 100 positions of the genomic data) it’s enough to recreate the signal with a very high correlation (>0.99). Tiling Array could require more smoothing (about 1% should be fine) and NGS has less noise and more components can be selected for fitting better the data (about 2%), See Figure @ref(fig:figfft) for the selected components in the example.

In order to easy the choice of the pcKeepComp parameter, includes a function for automatic detection of a fitted value that provides a correlation between the original and the filtered profiles close to the one specified. See the manual page of pcKeepCompDetect for detailed information.

In short, the cleaning process consists on converting the coverage/intensity values to the Fourier space, and knock-out (set to 0) the components greater than the given percentile in order to remove the noise from the profile. Then the inverse Fast Fourier Transform is applyied to recreate the filtered signal. In Figure @ref(fig:figfft2) the filtered signal is overlapped to the raw signal.

The cleaning of the input has almost no effect on the position and shape of the peaks, mantaining a high correlation with the original signal but allowing achieve a great performance with a simple peak detection algorithm:

Filtering in Tiling Array (up, blue) (1% comp.) and NGS (down red) (2% comp.).

tiling_raw <- nucleosome_tiling
tiling_fft <- filterFFT(tiling_raw, pcKeepComp=0.01)
htseq_raw <- as.vector(cover_trim[[1]])
htseq_fft <- filterFFT(htseq_raw, pcKeepComp=0.02)

cor(tiling_raw, tiling_fft, use="complete.obs")
#> [1] 0.7153782
cor(htseq_raw, htseq_fft, use="complete.obs")
#> [1] 0.9937643

Peak detection and Nucleosome Calling

After noise removal, the calling for nucleosomes is easy to perform. In nucleosome positioning, in contrast with other similar experiments like ChIP, the problem for the peaks detection algorithms is deal with the presence of an irregular signal which causes lots of local maxima (i.e., peaks due to noise inside a real peak). Here, we avoid this problem applying the FFT filter, allowing the detection of peaks in a simple but efficient way just looking for changes in the trend of the profile. This is implemented in the peakDetection function and results can be represented with the function plotPeaks:

peaks <- peakDetection(htseq_fft, threshold="25%", score=FALSE)
peaks
#>  [1]  218  368  452  518  623  715  776  836  983 1213 1331 1437 1549 1603 1672
#> [16] 1785 1945 2005 2053 2241 2330 2546 2605 2702 2764 2899 3124 3285 3354 3518
#> [31] 3710 3869 4009 4137 4233 4305 4383 4524 4596 4832 4912 4981 5171 5241 5291
#> [46] 5366 5458 5529 5598 5688 5752 5906 5978 6065 6123 6238 6312 6410 6472 6669
#> [61] 6834 6892 7002 7048 7100 7152 7314 7405 7457 7545 7615 7684 7775 7932 8042

plotPeaks(peaks, htseq_fft, threshold="25%", ylab="coverage")

Output of function. Peaks are spotted in red and detection threshold marked with an horitzontal line.

All the peaks above a threshold value are identified. Threshold can be set to 0 for detecting all the peaks, but this is not recommended as usually small fluctuations can apear in bottom part of the profile. This package also provides an automatic scoring of the peaks, which accounts for the two main features we are interested in: the height and the sharpness of the peak.

The height of a peak is a direct measure of the reads coverage in the peak position, but represented as a probability inside a Normal distribution.

The sharpness is a measure of how fuzzy is a nucleosome. If a peak is very narrow and the surrounding regions are depleted, this is an indicator of a good positioned nucleosome, while wide peaks or peaks very close to each other are probably fuzzy nucleosomes (despite the coverage can be very high in this region).

Scores can be calculated with the peakScoring function or directly with the argument score=TRUE in peakDetection.

peaks <- peakDetection(htseq_fft, threshold="25%", score=TRUE)
head(peaks)
#>   peak     score
#> 1  218 0.9749612
#> 2  368 0.6824909
#> 3  452 0.2675856
#> 4  518 0.3829457
#> 5  623 0.4858367
#> 6  715 0.8408881

plotPeaks(peaks, htseq_fft, threshold="25%")

function with .

The scores in Figure @ref(fig:figpeak2) only account for the punctual height of the peak. As said previously, this measure can be improved by accounting the fuzzyness of a nucleosome call (the sharpness of the peak). This requires a way to account for longer range peaks, which can be obtained with the width argument. In this way one can convert the identified nucleosome dyads to whole nucleosome length ranges and account for its degree of fuzzyness:

peaks <- peakDetection(htseq_fft, threshold="25%", score=TRUE, width=140)
peaks
#> GRanges object with 74 ranges and 3 metadata columns:
#>        seqnames    ranges strand |     score   score_w   score_h
#>           <Rle> <IRanges>  <Rle> | <numeric> <numeric> <numeric>
#>    [1]        *   148-287      * |  0.821330  0.667698  0.974961
#>    [2]        *   298-437      * |  0.638517  0.594543  0.682491
#>    [3]        *   382-521      * |  0.315751  0.363916  0.267586
#>    [4]        *   448-587      * |  0.518273  0.653601  0.382946
#>    [5]        *   553-692      * |  0.518244  0.550651  0.485837
#>    ...      ...       ...    ... .       ...       ...       ...
#>   [70]        * 7475-7614      * |  0.864565  0.755884  0.973245
#>   [71]        * 7545-7684      * |  0.212056  0.176273  0.247838
#>   [72]        * 7614-7753      * |  0.787492  0.654098  0.920887
#>   [73]        * 7705-7844      * |  0.471688  0.455279  0.488097
#>   [74]        * 7862-8001      * |  0.913530  0.827060  1.000000
#>   -------
#>   seqinfo: 1 sequence from an unspecified genome; no seqlengths

plotPeaks(peaks, htseq_fft, threshold="25%")

output with and .

Note than in Figure @ref(fig:figpeak3) overlapped peaks in a width and tall region are penalized, meanwhile the peaks with surrounding depleted regions have a higher relative score. This is the approach recommended for working with nucleosome calls.

Nucleosome calls filtering, merging or classification can be performed with standard Biocpkg{IRanges} functions, shuch as reduce, findOverlaps or disjoint.

The next example shows a simple way to merge those nucleosomes which are overlap accounting them as a fuzzy regions:

nuc_calls <- peaks[peaks$score > 0.1, ]
red_calls <- reduce(nuc_calls)
red_class <- GRanges(red_calls, isFuzzy=width(red_calls) > 140)
red_class
#> GRanges object with 20 ranges and 1 metadata column:
#>        seqnames    ranges strand |   isFuzzy
#>           <Rle> <IRanges>  <Rle> | <logical>
#>    [1]        *   148-287      * |     FALSE
#>    [2]        *   298-905      * |      TRUE
#>    [3]        *  913-1052      * |     FALSE
#>    [4]        * 1143-1854      * |      TRUE
#>    [5]        * 1875-2122      * |      TRUE
#>    ...      ...       ...    ... .       ...
#>   [16]        * 5836-6541      * |      TRUE
#>   [17]        * 6599-6738      * |     FALSE
#>   [18]        * 6764-7221      * |      TRUE
#>   [19]        * 7244-7844      * |      TRUE
#>   [20]        * 7862-8001      * |     FALSE
#>   -------
#>   seqinfo: 1 sequence from an unspecified genome; no seqlengths

Simple example of ranges manipulation to plot fuzzy nucleosomes.