Generalized Reconstruction of n-D NMR Spectra from Multiple Projections: Application to the 5-D HACACONH Spectrum of Protein G B1 Domain

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Abstract
Reconstructing multidimensional NMR spectra from 2-D projections significantly reduces the time needed for data collection over conventional methodology. Here, we provide a generalization of the projection-reconstruction process to spectra of arbitrary dimensionality, using a concept of coordinate rotation to produce explicit expressions for reconstruction. These expressions allow one to reconstruct subsets of the higher dimensionality space without producing the full spectrum, permitting convenient analysis of the data. We demonstrate the effectiveness of these procedures in the reconstruction of the 5-D HACACONH spectrum of protein G B1 domain from 12 2-D projections collected in five experiments. We further demonstrate that the base spectra of GFT-NMR are equivalent to projections of the 5-D spectrum at fixed angles.

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