Use of Non-Uniform Sampling (NUS) in 2D NMR

Non-Uniform Sampling (NUS) has found increasing use in small molecule 2D NMR in recent years. The NUS method, when done with moderate (~ 50%) sparse sampling along an indirect dimension, cuts down data collection time in half with little to no loss in data quality. Alternatively, NUS can be used to dramtically enhance the resolution of crowded 2D peaks with little time penalty. This instruction provides the simple steps you may take to set up a 2D experiment with NUS under Bruker Topspin or IconNMR. For further reading about the history and applications of NUS in NMR, refer to the Background section and the literature references below.

Steps to Set up NUS

NUS has been integrated into both Bruker's Topspin software and the data processing software Mnova. All 2D data collection under Topspin is set to use uniform sampling by default. To turn the same 2D setup to use NUS, follow the few steps below. Due to the consistent artifacts observed in our test data with very low sampling amount (i.e. 25%), stay with 50% sparse sampling. If the default amount is lower, set it to 50%.

Select NUS

Adjust sparse sampling amount (%) along indirect (F1) dimension. NUSPOINTS changes accordingly.

1. In IconNMR, select/set up the 2D experiment as usual. Then, highlight the 2D experiment. In the top menu items, click Parameters→Edit All Parameters.
2. Go to ACQUPARS panel. Under FnTYPE, select non-uniform sampling.
3. In the left panel list, click NUS and check the amount of sparse sampling NusAMOUNT. Leave all other NUS related parameters alone. In most cases, the default is 50%. In HSQC, the default may be 25%. Change it to 50%. This effectively halves the data collection time of the uniform sampling (leading to NusPOINTS of 128 instead of 256 as shown under QF in the left figure in this example). If you click the clock icon in the top menu, the experiment time drops by half.
4. To go back to the acquisition panel to adjust other parameters, click the Experiment panel in the top left corner. Here, optionally, you may use the time saving to add more scans. Or, you may change the simple parameters through IconNMR.
5. After the adjustment, click Return to IconNMR and submit the experiment under IconNMR.

Data Processing

NUS data are automatically recognized in Mnova and Topspin although data processing takes longer. No user adjustment is needed except in NOESY.

• In Mnova, in addition to all normal data processing steps: Apodization, Phasing (for phase-senstitive data, i.e. HSQC, NOESY), and Baseline Correction, there is separate NUS Settings under Processing→More .... The default mode Static should be left alone except in NOESY.
All other parameters should be left alone.
• In NOESY, the default Static gives severe artifacts in some cases. Select Dynamic under Processing→More ...→NUS Settings. The following illustrates the artifacts with the Static setting and the dramatic improvement with Dynamic. The severity and appearance of the artifacts also depend on the data. Mestrelab tech support has been contacted to address the source of this problem.

  NOESY: artifacts seen with the default Static NUS Setting.	Normal spectrum with Dynamic under NUS Settings.
  Note the NOEs from this large rigid polymer has the same sign as the diagonal peaks. For small molecules with much faster tumbling rates, the NOEs are in opposite sign with the diagonal peaks. Data courtesy of Parker Morris from the Bates group

Example Data

1H-13C HSQC: artifacts with less sampling	Small peaks are weakened with less sampling.
1H-13C HMBC: mostly artifacts free	Small peaks are weakened with less sampling.
1H-1H TOCSY: significant artifacts observed with 25% sampling	Expanded region of TOCSY

Background

Traditional NMR data collection is done with discrete, uniform sampling (US), that is, equal time increment and digitization, in both the direct and indirect dimensions. For example, with a spectral width of 10,000 Hz ( ~ 20 ppm for 1H at 500 MHz) in the direct dimension and an acquisition time of 2 sec, the data is recorded every 1/10,000 sec or every 0.1 msec, for a total of 2/0.0001 or 20,000 complex points.

In a 2D phase-sensitive, 1H-13C HSQC experiment, if the indirect 13C dimension is set with 170 ppm width (or ~ 21,250 Hz on Bruker 500) and 256 points (Real + Imaginary, or 128 complex points), then an increment of 1/21,250 sec or 0.047 msec is used for 128 complex points along the 13C dimension; the longest 13C evolution recorded is 128*0.047 msec or ~ 6 msec. For this 2D experiment, a total of 256 (Real + Imaginary) unique 1H FIDs are recorded, each encoded at an evenly spaced 13C increment. With 8 scans, a recycle delay of 1.5 sec and an acquisition time of 0.2 sec, the 2D takes 8*(1.5+0.2)*256 ~ 3,482 sec or 58 min. Fourier Transform (FT) of these time-domain data relies on the discrete and uniform sampling.

The NUS technique records the data with a non-uniform schedule along the roughly exponential, temporal decay curve. This isn't useful for the direct dimension, but the sparse data collection with optimized spacing along the indirect dimension in 2D NMR has been shown to save time with little to no loss in data quality. In the 2D HSQC above, with NUS and 50% sparse sampling (or 128 points), the data collection time is cut in half to 29 mins.

The primary limitations of NUS are the sample concentration and spin relaxation times. Cautions must be used when aggressively cutting down data sampling amount; artifacts and missing peaks may occur in such extreme cases (see examples below). For the best data quality, if possible, always use more material (higher concentration) with US or NUS at 50%. You may also use more scans with the NUS time saving. Keep in mind that the primary goal of NUS is time saving. Its quality approaches that of US (with longer data collection time) but doesn't surpass it.

References

Original Work

• Exponential Sampling, an Alternative Method for Sampling in Two-Dimensional NMR Experiments. J. C. J. BARNA, E. D. LAUE, M. R. MAYGER, J. SKILLING, AND S. J. P. WORFZALL, J. Magn. Reson. 73 (1987), 69-77.
• Conventional and Exponential Sampling for 2D NMR Experiments with Application to a 2D NMR Spectrum of a Protein J.C.J. Barna, E.D. Laue, J. Magn. Reson., 75 (1987), 384-389.

Recent Work

• NUS data processing in Mnova
• Resolution-enhanced 2D NMR of complex mixtures by non-uniform sampling
• Non-Uniform Sampling for All: More NMR Spectral Quality, Less Measurement Time. Frank Delaglio, Gregory S. Walker, Kathleen A. Farley, Raman Sharma, Jeffrey C. Hoch, Luke W. Arbogast, Robert G. Brinson, and John P. Marino. Am Pharm Rev. 2017 20(4), 339681.
• Systematic Evaluation of Non-Uniform Sampling Parameters in the Targeted Analysis of Urine Metabolites by 1H,1H 2D NMR Spectroscopy. Schlippenbach, T.v., Oefner, P.J. & Gronwald, W. Sci Rep 8, 4249 (2018). https://doi.org/10.1038/s41598-018-22541-0
• Non-Uniform Sampling in NMR Spectroscopy and the Preservation of Spectral Knowledge in the Time and Frequency Domains. Manpreet Kaur, Callie M. Lewis, Aaron Chronister, Gabriel S. Phun, and Leonard J. Mueller. The Journal of Physical Chemistry A 2020 124 (26), 5474-5486 DOI: 10.1021/acs.jpca.0c02930
• Poisson-Gap Sampling and Forward Maximum Entropy Reconstruction for Enhancing the Resolution and Sensitivity of Protein NMR Data. Sven G. Hyberts, Koh Takeuchi, and Gerhard Wagner, Journal of the American Chemical Society 2010 132 (7), 2145-2147. DOI: 10.1021/ja908004w

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Posted on December 7, 2022 By H. Zhou