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Theory of the general orientation dependence of ²H NMR spin-lattice relaxation and experiments on model membranes Morrison, Clare

Abstract

Deuterium nuclear magnetic resonance (NMR) spin-lattice relaxation was used to explore molecular motions. A general theory of relaxation rates was developed. Motions fast on the NMR timescale were investigated, model-independently, in the acyl chain and headgroup of phospholipids in the liquid crystalline phase. The general orientation dependence of spin-lattice relaxation of spin-1 nuclei interacting via fluctuating quadrupolar interactions was considered within the Redfield approximation. The NMR spectrum is characterized in terms of the principal axis co-ordinate system (PACS) of the time-averaged electric field gradient tensor. The most general form of the relaxation rates may be written in terms of the polar coordinates(/3, a) of the magnetic field in the PACS. It involves a sum of spherical harmonics up to order four: 1P = E E aoT(,3, a) ,p even Tz P=0 q=,-p where T, represents T1z, TiQ and T2 and the aP9 depend on reduced spectral densities and spherical order parameters which are independent of the orientation of the magnetic field. Tiz and T1Q relaxation times were measured at every carbon position on a perdeuterated palmitoyl acyl chain on 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC). The order parameter S20 (=SCD), was determined, model-independently, to be negative. The rotational diffusion model as formulated by Schindler and Seelig (Biochem.14:2283) is incorrect based on the range of experimentally acceptable S40. The fluctuations of the CD bond were successfully modelled as a uniform distribution. There is a spectrum of correlation times contributing to the reduced spectral densities at 46.2MHz. The addition of 20 mol% cholesterol to POPC primarily affects the trans-gaucheisomerization rate of the first twelve carbon positions on the palmitoyl chain. The rotational diffusion constant is not significantly affected. The temperature dependence of the pure and mixed systems confirm our conclusions. The order parameters S20 of the alpha and beta position of the head group ofdipalmitoyl-sn-glycerol-3-phosphocholine (DPPC) were determined to be negative. Due to the small orientation dependence of Tiz and T1Q, S40 was determined model-independently. The fluctuations of the CD bond were modelled as a uniform distribution. A T1z field-dependent study indicated at least two correlation times, a short and intermediate or long, were necessary. Distributions of correlation times fit equally well indicating a complex array of motions. A method is presented for measuring lateral diffusion of phospholipids along curved surfaces by measuring the transfer of magnetization due to diffusion via spin-lattice relaxation techniques. Experiments were performed on DPPC and a diffusion constant of 4 x 10-12m2s-1 was determined. Polycrystalline hex methylbenzene was investigated as an example of non-axially symmetric motion (17=0.1). A three motion model was evaluated using the general theory and Tlz and T1c2 relaxation spectra.

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