UltraScan Version

Manual


SOMO HPLC-SAXS Module: Gaussians with distorsion(s) operations

Last updated: July 2015

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):

SOMO HPLC-SAXS Skewed Gaussians 1

The type of distorted Gaussian to be utilized is chosen in the Options panel accessed by pressing the Options button:

SOMO HPLC-SAXS HPLC-SAXS Options: EMG

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:

SOMO HPLC-SAXS Skewed Gaussians 2

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:

SOMO HPLC-SAXS Skewed Gaussians 3

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:

SOMO HPLC-SAXS Skewed Gaussians Fit EMG

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:

SOMO HPLC-SAXS Skewed Gaussians 4

Followed by a round with the centers restrained by the % variation 5 from initial value:

SOMO HPLC-SAXS Skewed Gaussians 5

Bringing in the SD and releasing all constraints but the Common distorsion produces a slightly improved fit:

SOMO HPLC-SAXS Skewed Gaussians 6

However, the cost paid to achieve this apparently quite satisfactory fit is that the contribution of peak #1 appears to be exaggerated.

We can perform the same analysis using the Half-Gaussian modified Gaussian function:

SOMO HPLC-SAXS Skewed Gaussians GMG

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 corresponding Fit module will present extra fields:

SOMO HPLC-SAXS Gaussian Fit with distorsions panel

see here for a complete description description of the Fit module. In addition, we will also restrict the fitting region, to help improve the fitting. The results of this EMG+GMG fitting are shown below:

SOMO HPLC-SAXS Skewed Gaussians 9

As can be seen, there is an improvement, mainly due to the exclusion of the small bump before the first peak. We will then proceed with this set, first by doing Global Gaussians on a subset, and then proceeding with Global fit:

SOMO HPLC-SAXS Skewed Gaussians global fit

Here, by looking at the Residuals, the fit appears to be somewhat improved, and the apparently larger 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:

SOMO HPLC-SAXS Skewed Gaussians final gaussian

where the goodness of the reconstructed curve (yellow) superimposed to the original data (cyan) can be appreciated, with the residuals evenly distributed.


www contact: Emre Brookes

This document is part of the UltraScan Software Documentation distribution.
Copyright © notice.

The latest version of this document can always be found at:

http://somo.uthscsa.edu

Last modified on July 2, 2015.