Biomedical Engineering Reference
In-Depth Information
mass-frequency spectrum may represent a protein. If the peak distribution
of the spectra in a small neighborhood is about symmetric, then f(x) will
have a bell shaped graph in the neighborhood with a peak at x.
Since f(x) projects a stack of mass spectra, which can be viewed as
a 3D image, into a 2D mass-frequency graph, we call the peak frequency
function f(x) the projecting spectrum. Following the notation in [5], we
dene maximum bin width function to determine the window width as
w(x) = a + bx, where a and b are parameters and x is the current
mass value. The window width can be a function other than the linear
format. To generate a projecting spectrum in real application as the mass
window moving along the whole mass range, we need to discretize the mass
range by dening a so-called shifting unit s(x), which is usually a function
of x. In practice, the parameters a and b, along with the shifting unit
function are determined by empirical experiences. They can be dened using
more sophisticated statistical estimating models. In the shifting process,
we use the middle mass value x of the window to represent the window
location. Associating with each window, the peak frequency is calculated
as the number of peaks in the window across all spectra. Thus, each window
has a pair of mass value and peak frequency. In this way, we obtain a discrete
data set, the projecting spectrum of the given spectra.
Figure 2 shows an example of a segment of projecting spectrum with
mass range from about 5,000 Da to 6,000 Da. The entire spectrum has about
19,087 mass-frequency pairs generated using our empirical parameters with
mass ranging from 2,000 Da to 25,000 Da. From the projecting spectrum,
we can see the peak locations clearly. Afterwards, a binning procedure can
be carried out.
In a mass-frequency spectrum, peaks can be quite close to each other.
To prevent two bins from being too close, we add a restriction that if the
distance of the two peaks is less than certain shifting units, they will be
combined as a one-bin. The peak location of the projecting spectrum is
considered as the middle point of each bin. Following this, the bin range is
then extended to certain shifting units from the binning center. The binning
width should be controlled by an upper bound, which is usually called the
maximum window width function, w(x). If overlapping occurs between two
bins, the dip point between the two peaks is the splitting point of two bins.
In the projecting spectrum, there are many small peaks representing a
small percentage of peaks that appeared in the spectra at those points. In
most cases, those small peaks of projecting spectrum represent the \noisy"
peaks in the spectra. Therefore, we need to set up a percentage cut-o level
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