Theory of spin-lattice relaxation in lipid bilayers and biological membranes. 2H and 14N quadrupolar relaxation

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Abstract
Based on a previous, more approximate treatment [M. F. Brown, J. Magn. Reson. 35, 203 (1979)], expressions are derived for the quadrupolar spin‐lattice (T1) relaxation rates of 2H and 14N in lipid bilayers. Results are presented for the most general, anisotropic rotational diffusion model describing the segmental or molecular reorientation in lipid bilayers, and the analysis is extended to include relatively slow fluctuations of the local director with respect to the macroscopic bilayer normal. Numerically computed values of T1 for the diffusion model suggest that, even for extremes of ordering and motional anisotropy, such a model cannot by itself quantitatively account for the observed 2H T1 values of multilamellar dispersions of 1,2‐dipalmitoyl‐sn‐glycero‐3‐phosphocholine (DPPC), in the liquid crystalline state, as a function of temperature and frequency. The contribution from relatively low frequency motions is modeled in terms either (i) a simple noncollective model in which the slow motions are described in terms of a single effective correlation time, or (ii) a collective model in which the relatively slow reorientation is described by a distribution of correlation times, corresponding to collective fluctuations of the instantaneous director. The experimentally observed dependence of the 2H T1 relaxation rates on the acyl chain segmental order parameter SCD and the resonance frequency ω0 are most consistent with a collective model for slow molecular reorientations in lipid bilayers. The 2H T1 data for the saturated DPPC bilayer, in the liquid crystalline state, can be quantitatively described by a relaxation law of the form T−11 = Aτf+BS2CD ω−1/20 as observed for simpler nematic and smectic liquid crystals. The first (A) term is suggested to correspond to trans–gauche isomerizations of the lipid acyl chains, while the (B) term describes collective bilayer modes which predominantly influence the frequency dependence of the relaxation. In contrast to earlier conclusions [M. F. Brown et al., J. Chem. Phys. 70, 5045 (1979)], the dominant contribution to the 2H T1 relaxation rates of the saturated DPPC bilayer may arise from collective order fluctuations rather than fast local motions. The value of τf∼10−11 s obtained by extrapolating T−11 to infinite frequency or zero ordering is consistent with the correlation times calculated from 2H or 13C T1 data for n‐alkanes of equivalent chain lengths, suggesting that the microviscosity of the bilayer hydrocarbon region is not appreciably different from that of paraffinic liquids.