Accounting for the temperature dependence of 13C spin–lattice relaxation of methyl groups in the glycyl–alanyl-leucine model system under MAS with spin diffusion

Abstract

The difficulties in quantitatively modeling the temperature dependence of spin–lattice relaxation in a model isotope-enriched peptide are explored as a prelude to obtaining dynamics parameters for motions in proteins from such measurements. The degree to which this can be handled by adding spin diffusion to a bath in standard rate matrix relaxation theory is studied using a small tri-peptide model system, glycyl–alanyl-leucine (GAL). We observe in this molecule that the relaxation of backbone carbons CO and Cα is not dominated by local fluctuations of the 13C–1H dipolar couplings, but rather by 13C–13C spin diffusion to nearby methyl relaxation sinks. A treatment of the methyl relaxation itself, which ignores 13C–13C spin diffusion effects back to the otherwise slowly relaxing bath, provides poor agreement between theory and experimental data obtained for the temperature dependence of the methyl relaxation rates. Closed form approximate spectral densities and relaxation rates for a methyl group during magic angle spinning are obtained to compute the needed transition rates. These average computed rates, in conjunction with an extended form of the Solomon equations, are found to adequately model the temperature dependence of the methyl relaxation rates when spin diffusion is included. The barrier to rotation for the alanine methyl in GAL is determined to be 3.5 kcal mol−1.Electronic supplementary materialThe online version of this article (10.1007/s10858-019-00261-5) contains supplementary material, which is available to authorized users.

Solid-state NMR spectroscopy

“…Here, care has to be taken to avoid spin diffusion, which can average relaxation rates between neighbouring sites, especially when fast-relaxing methyl groups are present 92,93 .…”

Deuteration for High-Resolution Detection of Protons in Protein Magic Angle Spinning (MAS) Solid-State NMR

“…For the fit of the data for α-SH3, a combination of 15 N- R 1 relaxation rates measured at different fields, , 1 H– 15 N dipole, 15 N-CSA cross-correlated relaxation rates η, ,, as well as CPPI derived dipolar order parameters were employed. Spin diffusion can potentially affect the quantification of R 1 relaxation rates. ,, If magnetization flows to remote nuclei, e.g., to methyl groups which have a short relaxation time, the relaxation rate will appear systematically larger. Cross-correlated relaxation rates η yield frequency independent spectral density functions, similar to transversal R 2 rates in solution.…”

Magic angle spinning effects on longitudinal NMR relaxation: 15N in L-histidine

“…1,2 Longitudinal relaxation is an incoherent process that returns the longitudinal component of nuclear magnetization to its thermal equilibrium through internal dynamics of the molecule. 3 It has previously been pointed out that spin diffusion may influence the measured relaxation rate constants, 4,5 as the apparent longitudinal relaxation rate constant R * 1 determines the combination of both coherent and incoherent contributions to the change of nuclear magnetization. 3,6 The incoherent, or stochastic, contribution to signal decay contains information on the time-dependent fluctuation of bond vectors and samples the spectral density function.…”