Quantum mechanical behaviour of deuterated methyl groups

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 (2)H 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.

Comparative dynamics of leucine methyl groups in FMOC-leucine and in a protein hydrophobic core probed by solid-state deuteron nuclear magnetic resonance over 7-324 K temperature range

Quantitative dynamics of methyl groups in 9-fluorenylmethyloxycarbonyl-leucine (FMOC-leu) have been analyzed and compared with earlier studies of methyl dynamics in chicken villin headpiece subdomain protein (HP36) labeled at L69, a key hydrophobic core position. A combination of deuteron solid-state nuclear magnetic resonance experiments over the temperature range of 7-324 K and computational modeling indicated that while the two compounds show the same modes of motions, there are marked differences in the best-fit parameters of these motions. One of the main results is that the crossover observed in the dynamics of the methyl groups in the HP36 sample at 170 K is absent in FMOC-leu. A second crossover at around 95-88 K is present in both samples. The differences in the behavior of the two compounds suggest that some of the features of methyl dynamics reflect the complexity of the protein hydrophobic core and are not determined solely by local interactions.

Theory of damped quantum rotation in NMR spectra. I. Fundamental aspects

The damped quantum rotation (DQR) theory, formulated originally for methyl-like atomic groupings, is now extended to hindered (N>3)-fold molecular rotors, such as the cyclopentadienyl, benzene, and cycloheptatrienyl rings in solid phase environments. It heightens the significance of the Pauli principle in shaping up the stochastic dynamics of such objects, reflected in NMR line shapes. The corresponding NMR line-shape equation is derived; its stochastic part is shown for the first time to have the double commutator form for any values of the quantum-mechanical (coherence-damping) rate constants entering it. Constraints on the relative magnitudes of such constants are determined under which the DQR line-shape equation is converted into the phenomenological Alexander-Binsch equation describing classical jumps of the rotor. When all the quantum rate constants happen to be equal, the phenomenological model of equal jump rates between any two of the N (equivalent) orientations of the rotor is reproduced. On the other hand, the seemingly most plausible (for N>3) nearest-neighbor hopping model does not have any peculiar grounds in the DQR approach. For the special instances of stochastic molecular motions addressed in this work, the extended DQR formalism affords a quantification of the "degree of classicality" represented by a complete set of the relevant quantum rate constants. In view of our earlier experimental findings for the methyl rotors, the very occurrence of the nonclassical DQR effects seems unquestionable even for the objects of the size of benzene. The question of under what circumstances such effects can be big enough to be detected experimentally will be addressed in Part II of this work.

Tacticity effects on the barriers to rotation of the ester methyl group in poly (methyl methacrylate): A deuteron magnetic resonance study

In isotactic poly(methyl methacrylate) (PMMA), we investigate the dynamics of the ester methyl groups by means of deuteron magnetic resonance (DMR) in a deuterated sample. We find that the motion of the CD(3)-group affects the deuteron spin-lattice relaxation as well as the DMR line shape in a characteristic way. Quadrupolar order spin lattice relaxation measurements between T=291 K and T=70 K reveal a broad temperature dependent probability distribution of autocorrelation times tau(c) for the 2pi/3 reorientation. This broad distribution corresponds to a temperature independent Gaussian distribution of activation energies rho(E(a)) with variance sigma(E(a) )=13.8+/-0.5 meV (1.33 kJ/mol). The line shape transition between T=70 K and T=23 K is explained with the freezing in of the methyl group reorientation. By comparing our results in an 88% isotactic sample with results obtained from a 50% syndiotactic, 30% atactic, and 20% isotactic sample of a previous investigation, we demonstrate the higher local order of the 88% isotactic sample, which corresponds to a ratio of 1.6 in the relative width sigma(E(a) )/E(a) of the E(a) distribution. We show that different stereospecific forms of PMMA can be easily distinguished by the characteristics of their line shape transition between T=70 K and T=23 K.

Iterative lineshape analysis of quadrupolar echo spectra of a damped CD(3) quantum rotor: preliminary evidence of a novel mechanism of stochastic spin exchange

It is demonstrated that the wealth of information about damped quantum rotation of CD(3) groups, contained in quadrupolar echo spectra, can be fully explored in a broad temperature range using a method of iterative analysis of the spectral lineshapes. The recently reported lineshape equation which, apart from the quantum tunneling and the dissipative Alexander--Binsch terms, contains an additional dissipative term having no classical analog is shown to be capable of describing even subtle details of the spectra of a crystal of acetylsalicylic acid--CD(3) oriented specifically in the magnetic field. Preliminary evidence of the occurrence of this novel dissipative mechanism in the system studied is reported. The results obtained seem to suggest that there is no "classical limit" in the dissipative behavior of this system.