Angular dependence of deuterium spin-lattice relaxation rates of macroscopically oriented dilauroylphosphatidylcholine in the liquid-crystalline state
Authors: Trouard Theodore P. , Alam Todd M. , Brown Michael F. 
Published: July 2002

Deuterium (2H) NMR relaxation plays a major role in the study of lipid reorientational dynamics, with the angular dependence of the relaxation rates providing a novel and critical test of proposed motional models. Spin-lattice relaxation rates (R1Z) were measured for macroscopically oriented bilayers of 1,2-diperdeuteriolauroyl-sn-glycero-3-phosphocholine (DLPC-d46) in the liquid-crystalline (Lα) phase. The results for different positions along the chain (index i) were dependent on the angle θ between the macroscopic bilayer normal and the static external magnetic field, and allowed the anisotropy of R(i)1Z to be determined for nine resolved quadrupolar resonances. Angular-dependent relaxation data were evaluated using simple models of anisotropic rotational diffusion within an odd or even potential of mean torque as a framework for describing (i) segmental reorientations of the chains, or alternatively (ii) noncollective molecular motions within the bilayer. Moreover, (iii) a simple quasi-hydrodynamic formulation involving collective fluctuations of a local director axis was considered (continuum model).
For segmental motions the static electric field gradient (EFG) tensor due to the electronic structure of the C–2H bond is averaged by local reorientations of the acyl chains, e.g., due to trans–gauche rotational isomerizations and/or torsional oscillations. The second and third formulations assume the static EFG tensor is preaveraged by local motions, yielding a residual EFG tensor which is further modulated by order fluctuations due to relatively slow motions of larger amplitude; separation of time scales is implicit. The latter treatments differ in that the molecular model allows for variation in both the principal values and principal axes of the residual EFG tensor, and includes the possibility of a nonzero effective asymmetry parameter ηeff. By contrast, the collective model considers an axially symmetric residual EFG tensor (ηeff=0), in which the relatively slow motions are described in terms of continuum fluctuations of a local director axis within the small-angle approximation. Each of the three models can account for the observed angular anisotropy of the R(i)1Z relaxation rates along the chains to a greater or lesser degree of success, depending on the number of adjustable parameters.
The collective formulation has the fewest parameters and may be an oversimplification for description of the relaxation anisotropy. In addition, for each bilayer orientation, profiles of the relaxation rates R(i)1Z and order parameters ‖SCD(i)‖ as a function of acyl position exhibited a square-law functional dependence within experimental error. This observation points to an influence on the relaxation arising from relatively slow fluctuations in the order gradient set up along the chains by faster internal motions, viz. order fluctuations due to noncollective molecular motions or collective excitations of the bilayer. Finally, the rather small contribution from local internal motions suggests that the microviscosity of the bilayer interior corresponds to essentially liquid hydrocarbon. These new results illustrate the utility of R(i)1Z angular anisotropies of phospholipids having perdeuterated acyl chains in experimental and theoretical investigations of molecular dynamics in liquid-crystalline bilayers. The implications of the findings in relation to previous biophysical studies of membranes are discussed.