Abstract
NMR relaxometry plays crucial role in studies of protein dynamics. The measurement of longitudinal and transverse relaxation rates of ^{15}N is the main source of information on backbone motions. However, even the most basic approach exploiting a series of ^{15}N HSQC spectra can require several hours of measurement time. Standard non-uniform sampling (NUS), i.e. random under-sampling of indirect time domain, typically cannot reduce this by more than 2–4times due to relatively low “compressibility” of these spectra. In this paper we propose an extension of NUS to relaxation delays. The two-dimensional space of t_1/t_{relax} is sampled in a way similar to NUS of t_1/t_2 domain in 3D spectra. The signal is also processed in a way similar to that known from 3D NUS spectra i.e. using one of the most popular compressed sensing algorithms, iterative soft thresholding. The 2D Fourier transform matrix is replaced with mixed inverse Laplace-Fourier transform matrix. The peak positions in resulting 3D spectrum are characterized by two frequency coordinates and relaxation rate and thus no additional fitting of exponential curves is required. The method is tested on three globular proteins, providing satisfactory results in a time corresponding to acquisition of two conventional ^{15}N HSQC spectra.
Highlights
Dynamics of protein molecules is typically studied by heteronuclear NMR relaxation measurements (Key et al 1989)
To obtain the relaxation rates (R) from the datasets processed with ITAMeD, the peak-picking was performed by a MATLAB script that imported the frequency coordinates from the peak list manually prepared from the 1H–15N projection and used Gaussian fit in the “relaxation” dimension
To check the dependence of reconstruction quality on the sampling level, non-uniform sampling (NUS) spectra were reconstructed from various numbers of NUS points from t1/trelax space (128–256)
Summary
Dynamics of protein molecules is typically studied by heteronuclear NMR relaxation measurements (Key et al 1989). To co-processing using multidimensional decomposition (coMDD), the method treats a series of 2D datasets as one 3D object, but (as all CS algorithms) exploits the fact, that such an object has a sparse representation in certain domain It has two advantages over 3D coMDD processing discussed recently in Linnet and Teilum (2016). It allows joint NUS of both domains, which means, that extensive sampling of a relaxation decay is possible, even for low sampling levels. It provides relaxation rates at the output since “relaxation dimension” is processed with inverse Laplace transform [as proposed before for full sampling (Koskela et al 2004)]. We show that fast and accurate results can be obtained in the case of protein relaxation experiments
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