Origin of Abrupt Rise in Deuteron NMR Longitudinal Relaxation Times of Protein Methyl Groups below 90 K

In order to examine the origin of the abrupt change in the temperature dependence of ²H NMR longitudinal relaxation times observed previously for methyl groups of L69 in the hydrophobic core of villin headpiece protein at around 90 K (Vugmeyster et al. J. Am. Chem. Soc. 2010, 132, 4038−4039), we extended the measurements to several other methyl groups in the hydrophobic core. We show that, for all methyl groups, relaxation times experience a dramatic jump several orders of magnitude around this temperature. Theoretical modeling supports the conclusion that the origin of the apparent transition in the relaxation times is due to the existence of the distribution of conformers distinguished by their activation energy for methyl three-site hops. It is also crucial to take into account the differential contribution of individual conformers into overall signal intensity. When a particular conformer approaches the regime at which its three-site hop rate constant is on the order of the quadrupolar coupling interaction constant, the intensity of the signal due to this conformer experiences a sharp drop, thus changing the balance of the contributions of different conformers into the overall signal. As a result, the observed apparent transition in the relaxation rates can be explained without the assumption of an underlying transition in the rate constants. This work in combination with earlier results also shows that the model based on the distribution of conformers explains the relaxation behavior in the entire temperature range between 300 and 70 K.