Resolution Enhancement in Protein NMR Spectra by Deconvolution with Compressed Sensing Reconstruction

Multidimensional NMR spectroscopy is one of the basic tools for determining the structure of biomolecules. Unfortunately, the resolution of the spectra is often limited by inter-nuclear couplings. This limitation cannot be overcome by common ways of increasing resolution, i.e. non-uniform sampling (NUS) followed by compressed sensing (CS) reconstruction. In this paper, we show how to enrich CS processing with virtual decoupling leading to an increase in resolution, sensitivity, and overall quality of NUS reconstruction. A mathematical description of the decoupling by deconvolution approach explains the effects of noise, modulation of the sampling schedule, and reveals relation with the underlying assumption of the CS. The gain in resolution and sensitivity is demonstrated for the basic experiment used for protein backbone assignment 3D HNCA applied to two large protein systems: intrinsically disordered 441-residue Tau and a 509-residue globular bacteriophytochrome fragment.