Compressed sensing reconstruction of undersampled 3D NOESY spectra: application to large membrane proteins

Central to structural studies of biomolecules are multidimensional experiments. These are lengthy to record due to the requirement to sample the full Nyquist grid. Time savings can be achieved through undersampling the indirectly-detected dimensions combined with non-Fourier Transform (FT) processing, provided the experimental signal-to-noise ratio is sufficient. Alternatively, resolution and signal-to-noise can be improved within a given experiment time. However, non-FT based reconstruction of undersampled spectra that encompass a wide signal dynamic range is strongly impeded by the non-linear behaviour of many methods, which further compromises the detection of weak peaks. Here we show, through an application to a larger α-helical membrane protein under crowded spectral conditions, the potential use of compressed sensing (CS) l (1)-norm minimization to reconstruct undersampled 3D NOESY spectra. Substantial signal overlap and low sensitivity make this a demanding application, which strongly benefits from the improvements in signal-to-noise and resolution per unit time achieved through the undersampling approach. The quality of the reconstructions is assessed under varying conditions. We show that the CS approach is robust to noise and, despite significant spectral overlap, is able to reconstruct high quality spectra from data sets recorded in far less than half the amount of time required for regular sampling.