Molecular motions in lipid bilayers. I. Statistical mechanical model of acyl chain motion

A statistical mechanical model of bilayer membranes is developed, based on the two-dimensional Ising ferromagnet formalism. Definite average geometries are proposed for the acyl chains in the gel and liquid crystalline states, allowing separation of the chain order parameter contributions arising from intramolecular and bulk motions. The model contains no freely disposable parameters, but the thermodynamic predictions are sensitive to the assumed energy difference (Eg) between gauche and trans states in the acyl chain. Best overall agreement (±∼10%) with experimental transition data for C12–C22 lipids requires Eg = 2.57 kJ/mol. Semiquantitative prediction of the effects of cis or trans chain unsaturation on the transition thermodynamics is obtained. Bulk motional order parameters inferred from the model geometry are consistent with reported data for rigid spin probes, and also with the results of a simple liquid crystal treatment of the bilayer. The model provides a rationalization for the apparent failure of lecithins with chains lengths less than 12 carbons to form stable bilayers.