Sparse Sampling NMR The high probability of degenerate frequencies in NMR spectra of complex biopolymers such as proteins presented a great barrier to detailed analysis. The combination of multidimensional NMR spectroscopy and high magnetic field strengths has overcome the resulting resonance assignment problem for proteins less than 50 kDa. Furthermore, recent advances in NMR instrumentation have largely removed sensitivity as a limiting parameter for protein samples in the millimolar concentration range. As a consequence, the orthogonal linear sampling requirements of conventional multidimensional NMR spectroscopy have required longer acquisition times than potentially needed with respect to signaltonoise. A number of approaches have been introduced to escape the linear sequential sampling requirements of the standard fast Fourier transform that is usually employed to deal with processing of the time domain NMR signal. Sparse sampling offers tremendous potential for overcoming the time limitations imposed by traditional Cartesian sampling of indirectly detected dimensions of multidimensional NMR data. Importantly, in many instances sensitivity rather than time remains of foremost importance when collecting data on protein samples. We are exploring how to optimize the collection of radial sampled multidimensional NMR data to achieve maximal signaltonoise in a variety of contexts. 

Recently the two dimensional Fourier transformation (2DFT) has been reintroduced to transform arbitrarily sampled time domain signals. In principle the 2DFT allows the use of nonlinear time domain sampling. In this respect, the socalled radial sampling protocol, where two incremented time dimensions (t1 and t2) are sampled such that t1 = t cos a and t1 = t cos a, is especially appealing because of the absence the aliasing artifacts of random sampling that occur upon Fourier transformation. However, transformation of radially sampled time domain data results in a fundamental artifact manifested as a ridge of intensity extending through the peak positions perpendicular to +/ the radial sampling angle. A number of algorithms have been introduced to remove these ridges but behave poorly for nonabsorptive line shapes. We have introduced a Cartesian sampled data is represented as a twodimensional signal with 4 quadrature components per increment and radial sampled data is represented as a one dimensional signal also with four quadrature components per increment. Significant advantage is obtained if the subsequent processing involves a true multidimensional Fourier transform as opposed to the sequential application of one dimensional fast Fourier transforms as is used by the GFT approach. The use of a true multidimensional FT allows for rigorous phasing of the resulting spectrum, for example. A method to optimize signaltonoise has been developed that exploits our rigorous definition of the minimal set of radial sampling angles required to resolve all peaks of interest in combination with a fundamental statistical property of radial sampled data. The approach appears general and can achieve a substantial sensitivity advantage over Cartesian sampling for the same total data acquisition time. Termed Sensitivity Enhanced nDimensional or SEnD NMR, the method involves three basic steps. First, data collection is optimized using routines to determine a minimal set of radial sampling angles required to resolve frequencies in the radially sampled chemical shift evolution dimensions. Second, appropriate combinations of experimental parameters (transients and increments) are defined by simple statistical considerations in order to optimize signaltonoise in single angle frequency domain spectra. Finally, the data is processed with a direct multidimensional Fourier transform and a statistical artifact and noise removal step is employed. This general strategy has a number of potential applications. Two prominent ones are its use in sensitivitylimited reverse micelle preparations of proteins where the effective protein concentration is often limited to 100 to 150 mM. Another is an adaptation for acquisition of hydrogen exchange data of large proteins. All of this has required the development of a comprehensive NMR data processing package based on the true multidimensional Fourier transform and radial sampling strategies. This package, called Al, will soon be made generally available to the academic community for noncommerical applications. Current Project Personnel
OnGoing & Future Projects
Useful papers: Gledhill & Wand (2010) JMR 
