New Statistical Algorithms for the Analysis of Mass - FU Berlin, FB MI ...

Figure 3.4.8: A zoom
into a common raw spectrum
with some clearly
identifyable large peaks
inbetween many small
peaks usually regarded
as noise. We left out
the scale since we want
to draw the attention to
these two scales (noise vs.
signal).
36 CHAPTER 3. MATHEMATICAL MODELING AND ALGORITHMS
3.4 Highly Sensitive Peak Detection
3.4.1 Introduction
In this (second) stage of the pipeline the detection of signals (peaks) in mass
spectra is performed. Since only some peaks detected in this step have a
biological meaning (that is, represent peptides) subsequent peak evaluation
processes are crucial. These evaluations determine whether a given peak is
just noise or actually represents a peptide. In later stages of the pipeline these
peptide peaks are used to find differences between two groups of spectra (e.g.
“diseased” vs. “healthy”).
Recall that a spectrum consists of (x, y) value pairs that reflect the number
of measured particles (y value) of a particular mass (x value). We define a
peak as
Definition 3.4.1. Peak: A set of successive x values (xi . . . xj)
with corresponding y-values greater than zero where yi−1 = 0 and
yj+1 = 0.
In other words, all connected areas of a spectrum where the MALDI-TOF
machine’s detector did measure a signal are regarded as potential peaks.
The according step to peak detection in the Lego example is
the detection of the bricks borders (see section 2.2). The same idea
holds with the peak detection: a mass spectrum contains many peaks
where we want to find start- and end-point (therefore the borders) of.
In other words, the raw signal is scanned for regions that intersect
the x-axis twice (begin and end) and start with positive slope. We
call these regions candidate peak since we do not know yet whether
or not they are real peptide peaks. Just as in the Lego example, we
face the problem that if we cannot detect the borders reliably the
algorithm might take two or more peaks for being one. This might
be - for example - because
� the shape is often not clearly recognizable (noisy)
� peaks are convoluted (do overlay)
� noisy parts might look - just by chance - like a peak
� peaks might be very small, that is, below the noise level
The basic approach to detect these errors is to compare the candidate
peaks with a previously learned model. In other words, if we
know how a peak shape should look like, we can check if a candidate
peak is valid, or we missed a border, or just detected noise.
The key assumption we use in our algorithm is that most peaks consist of
Gaussian-like shapes (sub-peaks). To understand why this is a good model,
let us recall the functioning of a mass spectrometer and some chemical basics.
If we were in a perfect world, each molecule in a sample would have a welldefined
mass and represented as a very thin peak at exactly this mass. So
why do we see a Gaussian-like peak ? The first - simple - reason is the
inaccuracy of the measurement process, since (imprecise) time-of-flight data is
converted into (molecule) mass and small errors can occur. This leads to small
shifts in x direction and broadens the peak. Secondly, due to the existence of