Temperature as an extra dimension in multidimensional protein NMR.

Nuclear magnetic resonance spectroscopy (NMR) is a particularly informative method for studying protein structure and dynamics in solution; however, it is also one of the most time-consuming. Modern approaches to biomolecular NMR are based on lengthy multidimensional (ND) experiments whose duration grows exponentially with the number of dimensions. The experimental time may even be several days in the case of 3D and 4D spectra. Moreover, the experiment often has to be repeated in several different conditions, for example in order to measure the temperature-dependent effects in a spectrum (temperature coefficients, TCs). In this paper we propose a new approach that involves joint sampling of indirect evolution times and temperature. This allows us to measure TCs with 3D spectra in even less time than is needed to acquire a single spectrum using the conventional approach. We propose two signal processing methods that are complementary in terms of sensitivity and resolution: a) dividing the data into overlapping subsets followed by compressed sensing reconstruction, and b) treating the complete data set with a variant of the Radon transform. The temperature-swept 3D HNCO spectra of two intrinsically disordered proteins---osteopontin and CD44 cytoplasmic tail---show that our new approach makes it possible to determine TCs and their non-linearities effectively. Non-linearities, which indicate the presence of a compact state, are particularly interesting. We provide the complete package of data acquisition and processing software for this new approach.