Measurement of Coupling Constants using S3E/S3CT spectra.

This tool measures coupling constants from a set of S3E or S3CT 2D spectra. The method is described in A. Meissner, J. Duus, O. W. Sørensen: J. Magn. Reson. (in press) J. Biomol. NMR (in press).

The principle is, that after having recorded and processed your spectrum, you end up with two spectra. The first spectrum contains the left halves of the subpeaks in a cross peak, and the other spectrum contains the right halves.

Figure 1: Example of a cross peak from two S3CT spectra. The cyan contours show the contours from the left spectrum, and the magenta contours from the right spectrum. The crosses mark the center of the peaks in the two spectra. The data are provided by Morten Dahl Sørensen.

Locate the cross peaks in the two spectra, and start the S3E Coupling Constant Measuring Tool.

Figure 2: Insert the cross peaks in the two fields at the top. Press Calculate and the coupling constant is measured and listed in the window!

The calculation is carried out as follows:

Slices are analysed on at a time, starting from the center of the peak. When the center value of the slice reaches w1 range percent of the center value of the center slice, the analysis is stopped. An area is selected from the slice of the left and right spectrum: The interval spans the points whose intensity is above w2 range percent of the center value. The points are splined using a cubic spline function to increase the digital resolution.

Three ways of determining the coupling constant are possible, by setting the appropriate value of the Max. type parameter:

Convolution function:

This function is described in the article above. In short, the splined right slice is moved to the left point-by-point, and the sum of the products with the points in the left slice is calculated. The shift at which this sum has a maximum is taken as the coupling constant for this slice. An average weighted by the intensity of the slice is calculated as the overall coupling constant.

Difference between local Maxima:

The position of the maxima in the splined slices are determined. The coupling constant is calculated as the offset between the maxima in the two slices. The overall coupling constant is calculated as a weighted average, as above.

Convolution+Fit:

This is the default method. First, an initial guess for the coupling constant is made using the convolution function, as above. The program makes a least squared fit of the right slice to match the left slice. Three parameters are fitted: The coupling constant (the shift in -x direction), the scaling of the slice, and a baseline shift. The coupling constant determined by fitting is averaged as above.

An input file for the XMGR program is produced as specified in the XMGR output filename parameter. By default, this is stored in the $PRONTO_WORK directory, unless a full path is included. When this file is loaded into the XMGR program, a series of plots is made. Two graphs are displayed for each slice analysed. The left graph contains four curves: The slice from the left spectrum, the right spectrum, the right spectrum fitted to match the left spectrum, and the residual function (i.e. the fitted spectrum subtracted from the left spectrum). The right graph contains a plot of the convolution function.

Figure 3: This is plotted using the XMGR program. The X axis is measured in Hz. The black curve is data from the left slice of the center slice in the cross peak listed in Figure 1. The data have been splined to a resolution of 0.05 Hz. The red curve is data from the right spectrum. The green curve is the right curve moved and scaled to match the left curve, and the blue curve is the residual function.

Carlsberg Laboratory, Department of Chemistry, Gamle Carlsberg Vej 10, DK-2500 Valby, Denmark mk@crc.dk