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

3.4. HIGHLY SENSITIVE PEAK DETECTION 37
isotopes 4 , the more complex a molecule is the more different varieties, with
respect to mass, exist. For example, oxygen occurs in nature as three different
(stable) isotopes: 16 O (99.765%; 8 protons, 8 neutrons), followed by the rare
isotope 18 O (0.1995%; 8 protons, 10 neutrons) and the even rarer isotope 17 O
(0.0355%; 8 protons, 9 neutrons ). Obviously, the more complex the molecule,
the more combinations of isotopes (and hence masses) are possible. Since
some combinations are more likely than others, the isotopes are independent
of each other, and there is usually a high number of a particular molecule we
see a Gaussian-like shape (Central limit theorem). Depending on the type of
machine used this shape can be resolved in its isotopic components (see Figure
3.4.9).
The knowledge of the isotope distributions enables us to exactly
calculate the shape and position a molecules peak will (should) have.
So if we find a peak-like shape at a certain position we can determine
the similarity to the calculated shape and accept this shape or perform
further analysis.
3.4.2 Common Approaches
Almost all peak detection algorithms rely on the shape comparison technique
described above. They usually differ in how they detect candidate
peaks. What they have in common is the usage of threshold driven detection
techniques. That is, each candidate peak must be higher than
a predetermined signal-to-noise threshold depending on the calculated
noise level (see e.g. (McDonough and Whale, 1995)).
Drawbacks of common Approaches
As shown exemplarily in Fig. 3.4.10, by assuming a noise level of 50 5 and using
a signal-to-noise ratio of 3 6 about 85% of the 1332 potential (candidate) peaks
in this particular spectrum would be discarded and their assigned information
lost. Although most of these peaks essentially are noise, some might carry
important information. This means, that these artificially introduced barriers
would prevent detection of small signals in a very early pre-processing stage.
The subsequent sections describe our new approaches to overcome this
signal-to-noise barrier, that means increasing sensitivity without decreasing
specificity.
3.4.3 Our Approach
To avoid loss of potentially important information by not considering (small)
peaks in the preprocessing we take the most simple solution and regard everything
as a candidate peak that has a start point Pi,s ∈ S and an end point
Pi,e ∈ S, S = s2 . . . sn being the set of n points defining a spectrum. Then
the tuple (Pi,s, Pi,e) defines the ith candidate peak ranging from Ss . . . Se. The
requirements for these points to meet are:
4 Atoms with the same number of electrons and protons, but different numbers of neutrons,
are called isotopes. Different isotopes belong to the same element because they have the same
number of electrons, which means that they all behave almost the same in chemical reactions.
It was discovered during the Second World War that isotopes of the same element can be
separated by physical and chemical methods.
5 different noise-estimators compute values ranging from 50 to 150
6 a commonly used value to get reliable results
Figure 3.4.9: Sample
Spectrum. The inset
shows a comparison of (a)
experimental and (b) calculated
isotope distribution
patterns for the peak
at m/z 811.