Theory of spin-lattice relaxation in lipid bilayers and biological membranes. Dipolar relaxation

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Abstract
In this work we have calculated spin-lattice (T1) relaxation time expressions for the homo- and heteronuclear dipolar relaxation of lipid bilayers, in addition to the heteronuclear Overhauser enhancement (NOE), using correlation functions derived previously. The results can be applied to the analysis of the 1H and 13C T1 times of lipid bilayers and the 13C–1H NOE. Three different models for the segmental fluctuations of the membraneous lipid molecules have been considered: (i) a simple diffusion-type model for the local segmental motions; (ii) a noncollective model in which relatively slow bilayer fluctuations are described by a single correlation time; and (iii) a collective model for the slow motions characterized by a continuous distribution of correlation times. For the diffusion model, the dependence on the bilayer orientation, order parameters 〈 P2〉 and 〈 P4〉, and the diffusion tensor anisotropy have been included in a general manner. Depending on the degree of segmental ordering and the anisotropy of the diffusion tensor, the maximum 13C–1H NOE can be either greater or less than the value of 2.988 obtained in the absence of an ordering potential. The various relaxation models were fit to 13C T1 data recently obtained for vesicles of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) at seven different magnetic field strengths, i.e., resonance frequencies, in the liquid crystalline state. A simple diffusion-type model (i) based on analogies to paraffinic liquids provides a very poor fit to the above 13C T1 data as a function of temperature and frequency, even for extreme values of the ordering and diffusion tensor anisotropy, and thus can be rejected at the present time. The 13C results can be fit satisfactorily over the range 15.0–126 MHz by models which include contributions from relatively slow bilayer fluctuations. A noncollective model (ii) with three or four adjustable parameters or a collective model (iii) with two parameters both describe the data to within experimental error. At present, the 13C T1 results suggest that the relaxation of the bilayer hydrocarbon region, in the liquid crystalline state, can best be accounted for by a collective model with a relaxation expression of the type T−11≂Aτ(2)f+BS2CH ω−1/2I, as concluded from a similar analysis of the 2H T1 data for DPPC multilamellar dispersions. In the above expression, τ(2)f is the correlation time for the local motions, SCH(=SCD) is the observed bond segmental order parameter, ωI is the resonance frequency, and A and B are constants which depend on the nucleus considered. Thus, the observed relaxation rate includes contributions from fast or local-type motions, in addition to cooperative fluctuations of a more long-range character. For the collective model, extrapolation of the 13C T−11 values obtained for the DPPC vesicles to infinite frequency yields estimates of τ(2)f which agree with those calculated from the frequency-independent T−11 rates of n-hexadecane at the same absolute temperature, suggesting that the segmental microviscosities of the two systems are similar, in agreement with 2H NMR studies.