Sampling of the NMR time domain along concentric rings

Abstract

We present a novel approach to sampling the NMR time domain, whereby the sampling points are aligned on concentric rings, which we term concentric ring sampling (CRS). Radial sampling constitutes a special case of CRS where each ring has the same number of points and the same relative orientation. We derive theoretically that the most efficient CRS approach is to place progressively more points on rings of larger radius, with the number of points growing linearly with the radius, a method that we call linearly increasing CRS (LCRS). For cases of significant undersampling to reduce measurement time, a randomized LCRS (RLCRS) is also described. A theoretical treatment of these approaches is provided, including an assessment of artifacts and sensitivity. The analytical treatment of sensitivity also addresses the sensitivity of radially sampled data processed by Fourier transform. Optimized CRS approaches are found to produce artifact-free spectra of the same resolution as Cartesian sampling, for the same measurement time. Additionally, optimized approaches consistently yield fewer and smaller artifacts than radial sampling, and have a sensitivity equal to Cartesian and better than radial sampling. We demonstrate the method using numerical simulations, as well as a 3-D HNCO experiment on protein G B1 domain.

Narrow peaks and high dimensionalities: Exploiting the advantages of random sampling

“…Sparse data sets may be of different kind, requiring various methods of processing in order to obtain spectra. Some of these methods are: Back-Projection Reconstruction [3][4][5], Reduced Dimensionality [6][7][8] and Multi-Way Decomposition [9] employing radial sampling, Polar Fourier Transform with radial [10][11][12] or concentric ring sampling [13], Maximum Entropy Methods [14,15], Hyperdimensional Spectroscopy [16] and Multidimensional Decomposition [17] for sampling using points placed randomly (often on Cartesian grid). Measurements of multidimensional spectra in a single scan where also presented, employing spatial encoding [18] or correlating data of lower dimensionality [19].…”

Optimized sampling patterns for multidimensional T2 experiments

“…This is assuming a simple reconstruction, but we also seek to reduce the artifacts, because they can obscure neighbouring peaks. See [7] for an example of an optimized undersampling pattern.…”

“…For the first problem, the assignment problem, there has been considerable recent interest in reduced dimensionality methods, which sample the signal in the time domain differently [4][5][6][7][8][9][10]29]. Depending on the complexity of the spectrum, this may lead to dramatically shorter acquisition times.…”

4D Non-uniformly sampled HCBCACON and 1 J(NCα)-selective HCBCANCO experiments for the sequential assignment and chemical shift analysis of intrinsically disordered proteins

“…Those include reduced dimensionality experiments (Szyperski et al 1993) rooted in the concept of the ''accordion'' spectroscopy Ernst 1981, 1982), methods based on projections of multi-dimensional spectra (Ding and Gronenborn 2002;Kim and Szyperski 2003;Kupče and Freeman 2003;Hiller et al 2005), and experiments exploiting true random sampling in the indirect dimensions Schmieder et al 1994;Orekhov et al 2001;Stern et al 2002;Malmodin et al 2005;Marion 2006;Kazimierczuk et al 2006;Coggins and Zhou 2007). Compared to the standard processing protocols of multi-dimensional NMR data based on the Fast Fourier Transform, special processing procedures are needed to calculate the spectra from the incomplete, sparsely sampled data sets Zhou 2007, 2008;Kupče and Freeman 2008;Kazimierczuk et al 2010;Orekhov and Jaravine 2011).…”