Amplitudes and time scales of picosecond-to-microsecond motion in proteins studied by solid-state NMR: a critical evaluation of experimental approaches and application to crystalline ubiquitin

Solid-state NMR provides insight into protein motion over time scales ranging from picoseconds to seconds. While in solution state the methodology to measure protein dynamics is well established, there is currently no such consensus protocol for measuring dynamics in solids. In this article, we perform a detailed investigation of measurement protocols for fast motions, i.e. motions ranging from picoseconds to a few microseconds, which is the range covered by dipolar coupling and relaxation experiments. We perform a detailed theoretical investigation how dipolar couplings and relaxation data can provide information about amplitudes and time scales of local motion. We show that the measurement of dipolar couplings is crucial for obtaining accurate motional parameters, while systematic errors are found when only relaxation data are used. Based on this realization, we investigate how the REDOR experiment can provide such data in a very accurate manner. We identify that with accurate rf calibration, and explicit consideration of rf field inhomogeneities, one can obtain highly accurate absolute order parameters. We then perform joint model-free analyses of 6 relaxation data sets and dipolar couplings, based on previously existing, as well as new data sets on microcrystalline ubiquitin. We show that nanosecond motion can be detected primarily in loop regions, and compare solid-state data to solution-state relaxation and RDC analyses. The protocols investigated here will serve as a useful basis towards the establishment of a routine protocol for the characterization of ps-μs motions in proteins by solid-state NMR.