Accounting for the temperature dependence of 13C spin\u2013lattice relaxation of methyl groups in the glycyl\u2013alanyl-leucine model system under MAS with spin diffusion

Van C Phan,Elizabeth A Fry,Kurt W Zilm

doi:10.1007/s10858-019-00261-5

Van C Phan, Elizabeth A Fry + Show 1 more

Open Access

https://doi.org/10.1007/s10858-019-00261-5

Copy DOI

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.

Highlights

It is increasingly recognized that molecular dynamics are as relevant as molecular structure in determining the function of biologically important macromolecules (Kempf and Loria 2003)
Before the advent of high resolution 2D and 3D magic angle spinning (MAS) NMR methods for solid proteins, Solid state NMR (ssNMR) studies of relaxation in biochemically relevant systems required the use of site specific labels, for example the use of deuterium relaxation experiments to determine the barrier to rotation in methyl groups (Batchelder et al 1983)
We investigate what is needed to extract dynamical parameters from 13C relaxation measurements of methyl groups under MAS made over a wide range of temperatures

Summary

Introduction

It is increasingly recognized that molecular dynamics are as relevant as molecular structure in determining the function of biologically important macromolecules (Kempf and Loria 2003). Experimental results with a natural abundance sample finds the relaxation rate of the bath centers in the absence of 13C–13C spin-diffusion very slow, justifying setting all but the cross relaxation component of the R′BB term to zero.

Results

Conclusion