Contents

1 Version Info

R version: R version 4.2.0 RC (2022-04-21 r82226)
Bioconductor version: 3.16
Package version: 1.63.0

2 Overview of MassSpecWavelet

MassSpecWavelet R package is aimed to process Mass Spectrometry (MS) data mainly based on Wavelet Transforms. The current version supports the peak detection based on Continuous Wavelet Transform (CWT). The algorithms have been evaluated with low resolution mass spectra (SELDI and MALDI data), we believe some of the algorithms can also be applied to other kind of spectra.

If you use MassSpecWavelet, please consider citing our work:

Du P, Kibbe WA, Lin SM (2006). “Improved peak detection in mass spectrum by incorporating continuous wavelet transform-based pattern matching.” Bioinformatics, 22, 2059-2065.

3 Peak detection by using CWT-based pattern matching

Motivation: A major problem for current peak detection algorithms is that noise in Mass Spectrometry (MS) spectrum gives rise to a high rate of false positives. The false positive rate is especially problematic in detecting peaks with low amplitudes. Usually, various baseline correction algorithms and smoothing methods are applied before attempting peak detection. This approach is very sensitive to the amount of smoothing and aggressiveness of the baseline correction, which contribute to making peak detection results inconsistent between runs, instrumentation and analysis methods.

Results: Most peak detection algorithms simply identify peaks based on amplitude, ignoring the additional information present in the shape of the peaks in a spectrum. In our experience, ‘true’ peaks have characteristic shapes, and providing a shape-matching function that provides a ‘goodness of fit’ coefficient should provide a more robust peak identification method. Based on these observations, a Continuous Wavelet Transform (CWT)-based peak detection algorithm has been devised that identifies peaks with different scales and amplitudes. By transforming the spectrum into wavelet space, the pattern-matching problem is simplified and additionally provides a powerful technique for identifying and separating signal from spike noise and colored noise. This transformation, with the additional information provided by the 2-D CWT coefficients can greatly enhance the effective Signal-to-Noise Ratio (SNR). Furthermore, with this technique no baseline removal or peak smoothing preprocessing steps are required before peak detection, and this improves the robustness of peak detection under a variety of conditions. The algorithm was evaluated with real MS spectra with known polypeptide positions. Comparisons with two other popular algorithms were performed. The results show the CWT-based algorithm can identify both strong and weak peaks while keeping false positive rate low.

3.1 Continuous wavelet transform with Mexican Hat wavelet

Load the example data

data(exampleMS)

Continuous wavelet transform with Mexican Hat wavelet. The 2-D CWT coefficients image of MS spectrum in [5000, 11000] is shown in Figure 1

scales <- seq(1, 64, 2)
 wCoefs <- cwt(exampleMS, scales = scales, wavelet = "mexh")
## Plot the 2-D CWT coefficients as image (It may take a while!)
xTickInterval <- 1000
plotRange <- c(5000, 11000)
image(
  plotRange[1]:plotRange[2],
  scales,
  wCoefs[plotRange[1]:plotRange[2],],
  col=terrain.colors(256),
  axes=FALSE,
  xlab='m/z index',
  ylab='CWT coefficient scale',
  main='CWT coefficients'
)
axis(1, at=seq(plotRange[1], plotRange[2], by=xTickInterval))
axis(2, at=c(1, seq(10, 64, by=10)))
box()
2-D CWT coefficient image

Figure 1: 2-D CWT coefficient image

3.2 Peak identification process

Identify the ridges by linking the local maxima. The identified local maxima is shown in Figure 2

## Attach the raw spectrum as the first column
wCoefs <- cbind(as.vector(exampleMS), wCoefs)
colnames(wCoefs) <- c(0, scales)
localMax <- getLocalMaximumCWT(wCoefs)
plotLocalMax(localMax, wCoefs, range=plotRange)
Identified local maxima of CWT coefficients at each scale

Figure 2: Identified local maxima of CWT coefficients at each scale

Identify the ridge lines by connecting local maxima of CWT coefficient at adjacent scales

ridgeList <- getRidge(localMax)
plotRidgeList(ridgeList,  wCoefs, range=plotRange)
Identified ridge lines based on 2-D CWT coefficients

Figure 3: Identified ridge lines based on 2-D CWT coefficients

Identify the identified ridges lines and SNR using identifyMajorPeaks(). The returns of identifyMajorPeaks() include the peakIndex, peakSNR, etc. All these elements carry peak names, which are the same as the corresponding peak ridges. See function getRidge() for details.

SNR.Th <- 3
nearbyPeak <- TRUE
majorPeakInfo <- identifyMajorPeaks(
  exampleMS,
  ridgeList,
  wCoefs,
  SNR.Th = SNR.Th,
  nearbyPeak=nearbyPeak
)
## Plot the identified peaks
peakIndex <- majorPeakInfo$peakIndex

Plot the spectra with identified peaks marked with red circles.

plotPeak(
  exampleMS,
  peakIndex,
  range=plotRange,
  main=paste('Identified peaks with SNR >', SNR.Th)
) 
Identified peaks

Figure 4: Identified peaks

All of the above steps are encapsulated as a main function of peak detection main:

data(exampleMS)
SNR.Th <- 3
nearbyPeak <- TRUE
peakInfo <- peakDetectionCWT(exampleMS, SNR.Th=SNR.Th, nearbyPeak=nearbyPeak)
majorPeakInfo = peakInfo$majorPeakInfo
peakIndex <- majorPeakInfo$peakIndex
plotRange <- c(5000, length(exampleMS))
plotPeak(
  exampleMS,
  peakIndex,
  range=plotRange,
  log='x',
  main=paste('Identified peaks with SNR >', SNR.Th)
)