Brian E. Coggins

CLEAN is an algorithm for the suppression of artifacts from nonuniform sampling, originally developed in the field of radioastronomy in the 1960s and 1970s. Recognizing similarities between the problem of NMR NUS and astronomical data collection, several NMR groups have applied versions of CLEAN to NMR data. Here, we recount the historical background of CLEAN in astronomy, explain how the algorithm works as applied to NMR, examine the method's theoretical underpinnings, and present examples of its use with NMR experiments. CLEAN shows a number of similarities to methods being used in the compressed sensing community, and recent theoretical results suggest that CLEAN should succeed under the same or similar conditions to those in which convex l 1-norm minimization succeeds.

¹³C-Metabolic Flux Analysis (¹³C-MFA) is rapidly being recognized as the authoritative method for determining fluxes through metabolic networks. Site-specific ¹³C enrichment information obtained using NMR spectroscopy is a valuable input for ¹³C-MFA experiments. Chemical shift overlaps in the 1D or 2D NMR experiments typically used for ¹³C-MFA frequently hinder assignment and quantitation of site-specific ¹³C enrichment. Here we propose the use of a 3D TOCSY-HSQC experiment for ¹³C-MFA. We employ Non-Uniform Sampling (NUS) to reduce the acquisition time of the experiment to a few hours, making it practical for use in ¹³C-MFA experiments. Our data show that the NUS experiment is linear and quantitative. Identification of metabolites in complex mixtures, such as a biomass hydrolysate, is simplified by virtue of the ¹³C chemical shift obtained in the experiment. In addition, the experiment reports ¹³C-labeling information that reveals the position specific labeling of subsets of isotopomers. The information provided by this technique will enable more accurate estimation of metabolic fluxes in large metabolic networks.

In structural studies of large proteins by NMR, global fold determination plays an increasingly important role in providing a first look at a target’s topology and reducing assignment ambiguity in NOESY spectra of fully protonated samples. In this work, we demonstrate the use of ultrasparse sampling, a new data processing algorithm, and a 4-D time-shared NOESY experiment (1) to collect all NOEs in ²H/¹³C/¹⁵N-labeled protein samples with selectively protonated amide and ILV methyl groups at high resolution in only four days, and (2) to calculate global folds from this data using fully automated resonance assignment. The new algorithm, SCRUB, incorporates the CLEAN method for iterative artifact removal but applies an additional level of iteration, permitting real signals to be distinguished from noise and allowing nearly all artifacts generated by real signals to be eliminated. In simulations with 1.2% of the data required by Nyquist sampling, SCRUB achieves a dynamic range over 10000:1 (250× better artifact suppression than CLEAN) and completely quantitative reproduction of signal intensities, volumes, and line shapes. Applied to 4-D time-shared NOESY data, SCRUB processing dramatically reduces aliasing noise from strong diagonal signals, enabling the identification of weak NOE crosspeaks with intensities 100× less than those of diagonal signals. Nearly all of the expected peaks for interproton distances under 5 Å were observed. The practical benefit of this method is demonstrated with structure calculations for 23 kDa and 29 kDa test proteins using the automated assignment protocol of CYANA, in which unassigned 4-D time-shared NOESY peak lists produce accurate and well-converged global fold ensembles, whereas 3-D peak lists either fail to converge or produce significantly less accurate folds. The approach presented here succeeds with an order of magnitude less sampling than required by alternative methods for processing sparse 4-D data.

Recent efforts to reduce the measurement time for multidimensional NMR experiments have fostered the development of a variety of new procedures for sampling and data processing. We recently described concentric ring sampling for 3-D NMR experiments, which is superior to radial sampling as input for processing by a multidimensional discrete Fourier transform. Here, we report the extension of this approach to 4-D spectroscopy as Randomized Concentric Shell Sampling (RCSS), where sampling points for the indirect dimensions are positioned on concentric shells, and where random rotations in the angular space are used to avoid coherent artifacts. With simulations, we show that RCSS produces a very low level of artifacts, even with a very limited number of sampling points. The RCSS sampling patterns can be adapted to fine rectangular grids to permit use of the Fast Fourier Transform in data processing, without an apparent increase in the artifact level. These artifacts can be further reduced to the noise level using the iterative CLEAN algorithm developed in radioastronomy. We demonstrate these methods on the high resolution 4-D HCCH-TOCSY spectrum of protein G’s B1 domain, using only 1.2% of the sampling that would be needed conventionally for this resolution. The use of a multidimensional FFT instead of the slow DFT for initial data processing and for subsequent CLEAN significantly reduces the calculation time, yielding an artifact level that is on par with the level of the true spectral noise.

Projection-reconstruction NMR (PR-NMR) has attracted growing attention as a method for collecting multidimensional NMR data rapidly. The PR-NMR procedure involves measuring lower-dimensional projections of a higher-dimensional spectrum, which are then used for the mathematical reconstruction of the full spectrum. We describe here the program PR-CALC, for the reconstruction of NMR spectra from projection data. This program implements a number of reconstruction algorithms, highly optimized to achieve maximal performance, and manages the reconstruction process automatically, producing either full spectra or subsets, such as regions or slices, as requested. The ability to obtain subsets allows large spectra to be analyzed by reconstructing and examining only those subsets containing peaks, offering considerable savings in processing time and storage space. PR-CALC is straightforward to use, and integrates directly into the conventional pipeline for data processing and analysis. It was written in standard C+ + and should run on any platform. The organization is flexible, and permits easy extension of capabilities, as well as reuse in new software. PR-CALC should facilitate the widespread utilization of PR-NMR in biomedical research.

Projection−reconstruction (PR) NMR enables rapid collection of multidimensional NMR data. NOESY represents a particularly difficult challenge for currently existing reconstruction algorithms, as it requires the quantitative reconstruction of an unknown number of peaks, at full sensitivity. We have demonstrated the successful application of PR−NMR to NOESY by determining the 4D methyl/amide NOESY spectrum of a 29 kDa protein, human carbonic anhydrase II, from 2D projections, using filtered backprojection for reconstruction. Compared with a 3D control spectrum, all expected peaks were faithfully reconstructed, with correct volumes and with no artifacts. Filtered backprojection thus provides a way to obtain high-resolution 4D NOESY data in the time required for conventional 3D data collection.