Multiway Decomposition of NMR Spectra with Coupled Evolution Periods

Abstract

Coupling evolution periods in NMR experiments on proteins has recently attracted much attention for its substantial savings in measurement time. Using the concept of multiway decomposition, which already proved useful in many types of NMR applications, the novel tool PRODECOMP decomposes sets of spectra with coupled evolution periods and attempts to provide all information that would be found in a corresponding full-dimensional spectrum. It offers the following advantages: (1) all experimental spectra are used simultaneously, avoiding sensitivity loss associated with individual examination of the spectra, (2) folding (aliasing) caused by the linear combinations of individual shifts in the projected spectra is automatically resolved, allowing for better resolution due to smaller spectral widths, (3) various types of schemes for the coupling of evolution periods are possible, (4) reconstructions of various high-dimensional spectra, including the corresponding full-dimensional spectrum, are straightforward, (5) overlap in both the projected and the directly detected dimensions is efficiently resolved. The capabilities of PRODECOMP are illustrated for a 14 kD protein, for which 12 projections of a five-dimensional spectrum with the nuclei N, HN, CO, Calpha, and Halpha are analyzed.

Sampling of the NMR time domain along concentric rings

“…This distribution has the property that the number of points on each ring grows as a linear function of the ring number, which becomes clear when Eq. [16] is rewritten as:…”

“…With the recent push to discover faster methods for measuring multidimensional NMR spectra, significant attention has been focused on alternatives to the conventional Cartesian sampling of the time domain, such as the "radial" approaches, which measure points along radial spokes [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], or the methods that measure a randomly-selected subset of the points from a Cartesian grid, often weighted according to the signal envelope [18][19][20][21][22]. These efforts have been motivated by the discovery that it is possible, in many cases, to use one of the new patterns coupled to a suitable processing method to obtain very high resolution spectral information, with very limited sampling of the time domain.…”

“…These efforts have been motivated by the discovery that it is possible, in many cases, to use one of the new patterns coupled to a suitable processing method to obtain very high resolution spectral information, with very limited sampling of the time domain. Until very recently, most groups exploring these techniques have employed alternative methods for processing the data to produce spectral information, rather than the conventional multidimensional Fourier transform (FT), such as reconstruction from projections [8][9][10]13,16,17,23], analysis of projected peak positions [1][2][3][4][5][6][7]14,15,24,25], maximum entropy reconstruction [18][19][20]22,26] or multidimensional decomposition [21,27].…”

Novel Sampling Approaches in Higher Dimensional NMR

“…In GFT, the following chemical shift combinations for a N-dimensional signal (O 1 O 3 ), or the variation of the proportionality factor between the different shifts; the latter is usually referred to as allowing any projection angle ("45 " would correspond to the same number of time increments in all projected dimensions). The restriction to projection angles of " 45 " often simplifies the direct interpretation of the projections, where peak picking or reconstructions are deferred to a later stage; an example is multi-way decomposition with PRODECOMP [14]. Reconstruction of the full-dimensional spectrum, for example with the various back-projection schemes implemented in Projection-Reconstruction (Chap.…”

Multi‐way decomposition of projected spectra obtained in protein NMR

“…The projected spectra become (after Fourier transform t → ω, t M → ω M ; denotes convolutions): Multi-way decomposition takes a set of projections P (ω, ω M ) as input, delivering the shapes F k i as output ( Fig.1) [2][3]. PRODECOMP is an implementation of multi-way decomposition relying on the FNNLS algorithm [4].…”