NUS for COSY experiments

Non Uniform Sampling (NUS) reduces the time taken to acquire multi-dimensional NMR spectra by predicting a fraction of the normal data instead of measuring it. The most commonly used algorithm for reconstructing the missing data requires the collected data to be properly phased in the indirect dimension. For this reason I have not recommended using NUS with HMBC and gCOSY experiments. However, last month's post showed that unphaseable HMBC experiments cope with NUS just as well as the phaseable LR-HSQMBC. In this post I compare the unphaseable gCOSY experiment with the phaseable CLIP-COSY to see how they are impacted by NUS

The sample for the experiments was the same halogenated steroid in chloroform-d that was used previously. This compound only shows signals between 0.0 and 5.0 ppm, so reduced sweep widths were used. The standard Bruker pulse sequences, cosygpqf and clipcosy, were used. Four spectra were collected for each experiment, the first without NUS, then 50% NUS, 25% and 12.5%. The number of points in the indirect dimension was 256 for the fully sampled experiment. The 100% spectra were recorded in about 60 minutes, while the 12.5% took 8 minutes. All spectra were processed with TopSpin 4.0.8 using the Bruker implementation of the Iterative Soft Thresholding (IST) algorithm.

The figure below shows the eight spectra. For ease of comparison the gCOSY spectra had to be plotted with a contour threshold a factor of 4 lower than the CLIP-COSY spectra. The intervals between the contours are the same in all spectra. Click on the figure for a larger version.

For both experiments the quality decreases as the sampling is reduced; peaks disappear, artifacts become numerous, and t₁ noise increases. The majority of peaks are present in both experiments but there are some peaks that are present only in the gCOSY spectra and some only in the CLIP-COSY.

For a more detailed examination of the quality of the spectra, columns were extracted from all experiments at 1.294 ppm. The gCOSY columns are shown below. Only the region between 3.0 and 0.0 ppm is shown as there were no signals downfield of 3.0 ppm. The peak with the shoulder near 1.3 ppm is the diagonal peak, while the peak at 1.97 ppm is an expected three bond correlation. Other expected correlations are a geminal coupling at 1.44 ppm, and vicinal couplings at 0.75, and 1.10 ppm, but these show only weak signals. As the amount of sampling is reduced the 1.97 ppm signal decreases dramatically, some of the weak correlations disappear completely, and artifacts appear. The 50% NUS column, though, is little different from the 100% column, indicating that the gCOSY experiment could be run with 50% NUS without a significant loss of quality.

Columns extracted from the CLIP-COSY spectra appear in the figure below. These were extracted at the same frequency as the gCOSY columns above and should show the same signals. The most intense peaks correspond to the expected signals; the diagonal (1.29 ppm), a geminal correlation (1.44 ppm), and three vicinal correlations (1.97, 1.10, and 0.75 ppm). The medium intensity signals (1.76 and 0.98 ppm) appear to be five-bond correlations. Like the gCOSY columns, the CLIP-COSY columns show a significant loss of quality as the sampling is reduced below 50%; peak intensities are reduced, some correlations disappear entirely, and artifacts begin to appear.

The columns from the two sets of spectra show that both experiments cope with reduced sampling similarly; 50% sampling shows little decrease in quality, but at 25% and 12.5% there is significant signal loss. Like the previous comparison of the HMBC and LR-HSQMBC experiments, I am surprised that the unphaseable experiment (gCOSY) copes with NUS as well as the phaseable experiment (CLIP-COSY). Perhaps the Bruker reconstruction algorithm has been modified to cope with unphaseable data. With these COSY experiments, though, 50% sampling seems to be the limit. This may be because the homonuclear COSY experiments contain more signals in each column than the heteronuclear HMBC and LR-HSQMBC. Successful NUS reconstruction requires sparse data. In the Facility's standard parameter sets the NUS sampling will be set to 50% for homonuclear experiments and 25% for heteronuclear.

Acknowledgments
Once again, Prof. Ted Molinski is acknowledged for preparing and providing the sample used to record the data presented here.