Non Uniform Sampling in Routine 2D Correlation Experiments

Introduction

Two-dimensional NMR experiments are incredibly useful for structure elucidation of complex molecules, especially when their one-dimensional spectra feature overlapping peaks. However, some experiments require significant amounts of time in order to yield data with adequate resolution or signal to noise for unambiguous interpretation. Any means of reducing the total acquisition time is useful. Non Uniform Sampling (NUS) is a method that can be used to speed up data collection and can be employed using our Delta™ software on JEOL Spectrometers.


Sampling of Indirect Dimensions

In typical 2D correlation experiments the indirect dimension is sampled as a series of 1D measurements where a delay (sometimes called the evolution time) is incremented so that the effects of a desired interaction, such as J-coupling between protons in a COSY or the proton and carbon chemical shifts in an HSQC, can be observed. The example below (Figure 1) is from an HSQC data set sampled with 128 points. The size of the steps is the inverse of the spectral width. In this case, a time step of 0.05 ms corresponds to a sweep width of 20,000 Hz, or approximately 200 ppm at 100 MHz (the frequency of 13C on a 400 MHz system). Similarly, the resolution is determined by the total time elapsed. In this particular case, 6.4 ms of total acquisition time (i.e., the longest time interval) corresponds to a resolution of 157 Hz in the indirect dimension.

As an alternative, with Non Uniform Sampling (NUS), we can collect a smaller sample of the 1D spectra in the indirect dimension in order to speed up the experiment. In this example, we collect only a portion of the points (in Figure 2 below, 25%) and fill in the missing 1D increments with zeroes.

HSQC data set before and after applying NUS

Because the total acquisition time in the 2nd dimension as well as the time steps between the samples are kept the same, the spectral width and resolution are identical to the uniformly sampled data.


Iterative Soft Thresholding

Iterative soft thresholding is a reconstruction technique for reconstructing the “missing” data points and then yields a conventional FID (Figure 3). See the "more information" section below for more information on the details of reconstruction.

A reconstructed time-domain Y slice of an HSQC collected with 25% sampling.

Overlay of the time-domain Y slice of conventionally sampled data (blue), and Result of the Fourier Transform of the data.


Comparisons

The following spectra of lasalocid (acetone-d6) were all obtained on an ECZ400S equipped with a ROYAL probe. Directly below in figure 5 is a a typical 1H spectrum of lasalocid

1H spectrum of lasalocid at 400 MHz.

Spectrum A in Figure 6 is a traditional, uniformly sampled C2HSQC with 128 Y points, a 200 ppm sweep width, 8 scans, and multiplicity editing. The total runtime of the experiment that produced the spectrum was approximately one hour. Note the congestion of the aliphatic region even in the 2D spectra. Spectrum B was acquired with a 25% sampling rate and all other parameters kept constant. Thus, the total acquisition time was cut down to 15 minutes. Spectra C and D maintained the 25% sampling, but increased the scans (C, to 32) or the Y points (512), in order to keep the total experiment time at one hour like spectrum A. Expansions of the aliphatic regions for these four spectra can be found in Figure 6. Note the increase in Y resolution (128 to 512 Y points) that is necessary to distinguish the overlapped peaks at 0.8 ppm as well as 1.3 ppm.

C2HSQC spectra of lasalocid at 400 MHz

C2HSQC spectra of lasalocid at 400 MHz

Figure 6. (Top) C2HSQC spectra of lasalocid at 400 MHz (Bottom) Expansion of the aliphatic region. Note the peaks that are resolved with 512 Y points (Spectrum D)

Below are expansions of the aliphatic regions from the above four spectra.

Expansion of the aliphatic region

Expansion of the aliphatic region

Non Uniform Sampling can be employed in other types of 2D experiments as well, like 1H-13C and 1H-15N HMBCs. The 1H-15N HMBCs (or HSQCs) in particular are good candidates for NUS due to their relatively simple 2D spectra in small molecules and low signal to noise, allowing for quick “scout” type experiments to find 15N resonances when only their approximate chemical shifts are known (Figure 7). This is particularly useful when the sample concentration is low or the sample is not 15N enriched, making direct detection of 15N impossible.

H-N gHMBCAD of brucine (50 mg, chloroform-d)

The ability to acquire multiplicity edited HSQCs (like the CRISIS-HSQCAD) with significantly reduced experiment time can be very valuable. For example, the spectrum of 50 mg of brucine (Figure 8) was acquired with 25% sampling, leading to a total experiment time of just under 5 minutes. In addition to giving 1H-13C connectivities, it also yields carbon multiplicity (methyls and methines phased opposite of methylenes, represented by blue and red peaks, respectively), rendering the acquisition of a slower, less sensitive 13C-detected DEPT unnecessary.

CRISIS-HSQCAD of brucine (50 mg, chloroform-d)


A Note of Caution

One should use caution regarding the sampling percentage chosen. For example, a system with multiple frequencies per Y slice (like an HMBC, or very congested HSQCs) can produce spectral artifacts during the reconstruction process when sampling rates are too low. In practice, this means ~25% for HSQCs and ~50% for HMBCs. While also possible, NUS is not currently recommended for homonuclear 2Ds like COSYs where there may be large number of correlations per Y slice, and NOESYs where the diagonal may be significantly more intense than the correlation peaks. As the field of NUS is one of ongoing research, the reader is encouraged to check the literature for new strategies in experimental design as well as data processing.

Conclusion

Employing Non Uniform Sampling allows for additional flexibility in total experiment time. One can increase scans to build up signal to noise or collect higher resolution data without sacrificing the other. As an alternative, one can obtain quicker “scout” 2Ds trading the potential for artifacts for quicker results. This can be useful to obtain a rough spectrum to see if running a much longer experiment is justified.

NUS is included in Delta. To download a free copy, please visit nmrsupport.jeol.com.


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