## Abstract

In this work we have calculated spin-lattice (T_{1}) 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 ^{1}H and ^{13}C T_{1} times of lipid bilayers and the ^{13}C-^{1}H 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 〈P_{2}〉 and 〈P_{4}〉, 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 ^{13}C-^{1}H 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 ^{13}C T_{1} 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 paraflinic liquids provides a very poor fit to the above ^{13}C T_{1} 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 ^{13}C 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 ^{13}C T_{1} 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_{1} ^{-1}≅Aτ_{f}^{(2)}+B_{CH} ^{2}ω_{1} as concluded from a similar analysis of the ^{2}H T_{1} data for DPPC multilamellar dispersions. In the above expression, τ_{f}^{(2)} is the correlation time for the local motions, S_{CH}(=S_{CD}) is the observed bond segmental order parameter, ω_{1} 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 ^{13}C T_{1}^{-1} values obtained for the DPPC vesicles to infinite frequency yields estimates of τ_{f}^{(2)} which agree with those calculated from the frequency-independent T_{1}^{-1} rates of n-hexadecane at the same absolute temperature, suggesting that the segmental microviscosities of the two systems are similar, in agreement with ^{2}H NMR studies.

Original language | English (US) |
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Pages (from-to) | 2808-2831 |

Number of pages | 24 |

Journal | The Journal of Chemical Physics |

Volume | 80 |

Issue number | 6 |

State | Published - Dec 1 1983 |

Externally published | Yes |

## ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry