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Manual |
This manual part describes the Gaussian analysis and decomposition operations using non symmetrical (skewed, distorted) Gaussians. The dataset we will use as an example is the same HPLC-SAXS analysis of Aldolase that is used to demonstrate the linear baseline operations (see here):
The type of distorted Gaussian to be utilized is chosen in the Options panel accessed by pressing the Options button:
We will start with the Exponentially modified Gaussian (EMG) function. After selecting it and returning to the HPLC-SAXS main panel, a EMG button will replace the default Gaussians button. Pressing it will bring up the EMG settings:
Since an SVD analysis (see here) on this dataset (not shown) indicated that four components were at least needed to describe it, four EMG Gaussians are initally positioned:
Note that four fields are now present in the third commands row. The first three are the center, width and amplitude of each Gaussian, as in normal Gaussian operation, while the fourth is the EMG Gaussian distorsion (set to 0 at the beginning). All other commands are identical as for normal Gaussian operations. Once the intial set of EMG Gaussians is positioned, pressing Fit will bring up again the Gaussian Fit module:
Note that in respect to the normal Gaussians operation, there is an additional distorsion field with its checkboxes (Fix distortion 1, % variation, and From initial value), and a Common distorsion 1 checkbox. The latter is selected by default, because it is assumed that similar species will have similar distorsions on eluting from the column. This makes the Gaussian fitting more robust. If necessary, once an initial round of fitting is performed, this constraint can be released, to verify if any further improvements are possible while still keeping resonable peak shapes for all Gaussians.
As with normal Gaussain operation, it is advisable to do a first fit while keeping the Fix Gaussian centers checkbox selected:
Followed by a round with the centers restrained by the % variation 5 from initial value:
Bringing in the SD and releasing all constraints but the Common distorsion produces a slightly improved fit:
Releasing also the Common distorsion will produce a further small improvement in the fit, but at the cost of a highly unlikely situation with EMG Gaussian #1 extending for a long range:
We can perform the same analysis using the Half-Gaussian modified Gaussian function:
As can be seen from the fit χ2 (next to the Fit button), this function performs worse for this dataset. A function combining the EMG and GMG Gaussians (EMG+GMG) can be also tested. The correstonding Fit module will present extra fields:
see here for a complete description description of the Fit module. The results of the EMG+GMG fitting are shown below:
As can be seen, there is a small improvement versus using the EMG Gaussians alone. We will then proceed with this set, first by doing Global Gaussians on a subset:
And then proceeding with Global fit:
Here, by looking at the Residuals, the fit appears to be not optimal, but the apparently large residuals especially around the main peak are due to the very low SD associated with the data, amplifying the discrepancies. After propagating the EMG+GMG Gaussians to all chromatogram with Global Gaussians, we can check the results on a single chromatogram:
where the goodness of the reconstructed curve (yellow) superimposed to the original data (cyan) can be appreciated notwithstanding the not optimal residuals plot.
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Last modified on May 15, 2014.