Non-uniform sampling in quantitative assessment of heterogeneous solid-state NMR line shapes

Non-uniform sampling has been successfully used for solution and solid-state NMR of homogeneous samples. In the solid state, protein samples are often dominated by inhomogeneous contributions to the homogeneous line widths. In spite of different technical strategies for peak reconstruction by different methods, we validate that NUS can generally be used also for such situations where spectra are made up of complex peak shapes rather than Lorentian lines. Using the RMSD between subsampled and reconstructed data and those spectra obtained with uniform sampling for a sample comprising a wide conformational distribution, we quantitatively evaluate the identity of inhomogeneous peak patterns. The evaluation comprises Iterative Soft Thresholding (hmsIST implementation) as a method explicitly not assuming Lorentian lineshapes, as well as Sparse Multidimensional Iterative Lineshape Enhanced (SMILE) algorithm and Signal Separation Algorithm (SSA) reconstruction, which do work on the basis of Lorentian lineshape models, with different sampling densities. Even though individual peculiarities are apparent, all methods turn out principally viable to reconstruct the heterogeneously broadened peak shapes.