Cross-correlated relaxation of dipolar coupling and chemical-shift anisotropy in magic-angle spinning R1ρ NMR measurements: Application to protein backbone dynamics measurements

Transverse relaxation rate measurements in magic-angle spinning solid-state nuclear magnetic resonance provide information about molecular motions occurring on nanosecond-to-millisecond (ns–ms) time scales. The measurement of heteronuclear (13C, 15N) relaxation rate constants in the presence of a spin-lock radiofrequency field (R1ρ relaxation) provides access to such motions, and an increasing number of studies involving R1ρ relaxation in proteins have been reported. However, two factors that influence the observed relaxation rate constants have so far been neglected, namely, (1) the role of CSA/dipolar cross-correlated relaxation (CCR) and (2) the impact of fast proton spin flips (i.e., proton spin diffusion and relaxation). We show that CSA/D CCR in R1ρ experiments is measurable and that the CCR rate constant depends on ns–ms motions; it can thus provide insight into dynamics. We find that proton spin diffusion attenuates this CCR due to its decoupling effect on the doublet components. For measurements of dynamics, the use of R1ρ rate constants has practical advantages over the use of CCR rates, and this article reveals factors that have so far been disregarded and which are important for accurate measurements and interpretation.