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

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 S_CD 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 T₁^-1 = Aτ_f + BS_CD² ω₀^-1/2 as observed for simpler nematic and smectic liquid crystals. The first (A) term is suggested to correspond primarily 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 τ_f∼10^-11 s obtained by extrapolating T₁^-1 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.