Abstract:
Multidimensional nuclear magnetic resonance (NMR) spectroscopy has become
one of the most important techniques available for studying the structure and function of
biological macromolecules at atomic resolution. The conventional approach to
multidimensional NMR involves the sampling of the time domain on a Cartesian grid
followed by a multidimensional Fourier transform (FT). While this approach yields high
quality spectra, as the number of dimensions is increased the time needed for sampling on
a Cartesian grid increases exponentially, making it impractical to record 4-D spectra at
high resolution and impossible to record 5-D spectra at all.
This thesis describes new approaches to data collection and processing that make
it possible to obtain spectra at higher resolution and/or with a higher dimensionality than
was previously feasible with the conventional method. The central focus of this work has
been the sampling of the time domain along radial spokes, which was recently introduced
into the NMR community. If each radial spoke is processed by an FT with respect to
radius, a set of projections of the higher-dimensional spectrum are obtained. Full spectra
at high resolution can be generated from these projections via tomographic
reconstruction. We generalized the lower-value reconstruction algorithm from the
literature, and later integrated it with the backprojection algorithm in a hybrid
reconstruction method. These methods permit the reconstruction of accurate 4-D and 5-
D spectra at very high resolution, from only a small number of projections, as we
demonstrated in the reconstruction of 4-D and 5-D sequential assignment spectra on
small and large proteins. For nuclear Overhauser spectroscopy (NOESY), used to
measure interproton distances in proteins, one requires quantitative reconstructions. We
have successfully obtained these using filtered backprojection, which we found was
equivalent to processing the radially sampled data by a polar FT. All of these methods
represent significant gains in data collection efficiency over conventional approaches.
The polar FT interpretation suggested that the problem could be analyzed using
FT theory, to design even more efficient methods. We have developed a new approach to
sampling, using concentric rings of sampling points, which represents a further
improvement in efficiency and sensitivity over radial sampling.
