Lipid bilayer dynamics from simultaneous analysis of orientation and frequency dependence of deuterium spin-lattice and quadrupolar order relaxation

Simultaneous analysis of the deuterium ${(}^2\mathrm{H})$ NMR spin relaxation rates of lipid bilayers as a function of both frequency and sample orientation may be decisive in evaluating different models for the dynamics of membranes. Angular dependent ${}^2\mathrm{H}$ spin-lattice ${(R}_{1Z})$ and quadrupolar order ${(R}_{1Q})$ ${}^2\mathrm{H}$ relaxation rates have been measured at 46.1 and 76.8 MHz for macroscopically oriented bilayers of 1,2-diperdeuteriomyristoyl-$\mathrm{sn}$-glycero-3-phosphocholine (DMPC-$d_{54}),$ with perdeuterated acyl chains, in the liquid-crystalline ${(L}_{\alpha })$ state. The data have been simultaneously fitted to various dynamical models, together with frequency dependent ${}^2\mathrm{H}$ $R_{1Z}$ data for vesicles of specifically ${}^2\mathrm{H}$-labeled DMPC. The same mechanism for the nuclear spin relaxation in lipids has been assumed for both oriented bilayers and vesicles, except for the presence of orientational averaging and a possible contribution from vesicle tumbling in the latter case. A noncollective model describing individual molecular reorientations in the presence of a potential of mean torque is able to adequately account for the orientation dependence; however, the quality of the fits to the frequency dispersion is less satisfactory. By contrast, a three-dimensional director fluctuation model accounts for the frequency dispersion for DMPC vesicles, but does not fit the orientation dependence of the $R_{1Z}$ and $R_{1Q}$ relaxation data. Higher-order director fluctuations have also been included, which do not significantly improve the quality of the fits to the collective model. Therefore, a composite membrane model is proposed including both noncollective molecular motions and director fluctuations. The model adequately describes both the frequency and orientation dependent data along the entire acyl chain simultaneously, which suggests that both dynamical processes can be detected by analyzing the ${}^2\mathrm{H}$ NMR relaxation rates in the MHz range. Quantitative information about the bilayer dynamics including lipid reorientation rates, degree of molecular ordering, relative contributions from collective and noncollective motions, and director-frame spectral densities of motion has been obtained. The results suggest the bilayer dynamics in the MHz regime reflect molecular reorientations that are superimposed onto nematiclike deformations of the membrane interior in the liquid crystalline state.