Molecular dynamics in lipid bilayers. Anisotropic diffusion in an odd restoring potential.

Recent 2H nuclear magnetic resonance spin relaxation studies have questioned the influence of restoring potential parity on the description of lipid or molecular reorientational dynamics. In biomembranes the polar head groups of lipid and sterol constituents are expected to associate with the aqueous interface; therefore, realistic descriptions of molecular reorientation in bilayer systems should use an odd restoring potential. The multiexponential correlation functions and related spectral density functions for small-step anisotropic diffusion in a pseudo-restoring potential of the form U(beta) = -lambda cos beta are evaluated as a function of molecular ordering <P2(cos beta)>. From analysis of these results the single exponential approximation used in previous investigations is found to overestimate the decay rate at lower order, but is reliable for <P2(cos beta)> > 0.6. The exception to this trend is the decay constant for the G11 (omega; t) correlation function, which is not accurately portrayed by the first-order approximations. A second-order single exponential approximation is presented, and is shown to be equivalent to the weighted sum of the multidecay constants. In general, the potential parity is found to have only minor effects on the spin relaxation rates obtained to describe molecular reorientation in lipid bilayers.