Quantifying conformational dynamics using solid-state R₁ρ experiments.

We demonstrate the determination of quantitative rates of molecular reorientation in the solid state with rotating frame (R(1ρ)) relaxation measurements. Reorientation of the carbon chemical shift anisotropy (CSA) tensor was used to probe site-specific conformational exchange in a model system, d(6)-dimethyl sulfone (d(6)-DMS). The CSA as a probe of exchange has the advantage that it can still be utilized when there is no dipolar mechanism (i.e. no protons attached to the site of interest). Other works have presented R(1ρ) measurements as a general indicator of dynamics, but this study extracts quantitative rates of molecular reorientation from the R(1ρ) values. Some challenges of this technique include precise knowledge of sample temperature and determining the R(2)(0) contribution to the observed relaxation rate from interactions other than molecular reorientation, such as residual dipolar couplings or fast timescale dynamics; determination of this term is necessary in order to quantify the exchange rate due to covariance between the 2 terms. Low-temperature experiments measured an R(2)(0) value of 1.8±0.2s(-1) Allowing for an additional relaxation term (R(2)(0)), which was modeled as both temperature-dependent and temperature-independent, rates of molecular reorientation were extracted from field strength-dependent R(1ρ) measurements at four different temperatures and the activation energy was determined from these exchange rates. The activation energies determined were 74.7±4.3kJ/mol and 71.7±2.9kJ/mol for the temperature-independent and temperature-dependent R(2)(0) models respectively, in excellent agreement with literature values. The results of this study suggest important methodological considerations for the application of the method to more complicated systems such as proteins, such as the importance of deuterating samples and the need to make assumptions regarding the R(2)(0) contribution to relaxation.