Lipid vertical motion and related steric effects in bilayer membranes

We present a theoretical model of a lipid bilayer in its gel state which explicity couples the vertical displacements of the lipid chains to their conformational state. In this model the chains are free to move longitudinally under a potential due to the neighbouring chains. The potential is due to a restoring force with a force constant k and thus acts to keep them in the local plane as defined by their nearest neighbours. It is demonstrated that the force constant k is directly related to the internal bilayer pressure, , and that if a value =33 dynes/cm is assumed then k=17.3 dynes/cm. Steric effects are explicity included by allowing chains to twist into free volume created by the vertical displacement of neighbouring chains. The Hamiltonian is expressed in terms of the projection operators, P _ij , describing the displacement of chain i relative to a neighbour j, and G _ij describing the direction of a twist in chain i. The model is solved both analytically and via Monte Carlo simulations for a one-dimensional system. The possibility of phase-transitions in two-dimensions and the relevance to the bilayer pre-transition is discussed.This work was first presented in poster form at the Canadian Biochemical Society Conference held in Banff, Alberta, Canada, April 29–May 4, 1984Work supported in part by the Natural Sciences and Engineering Research Council of Canada, Le Fonds Formation des Chercheurs et Action a la Recherche du Quebec, and the Advisory Research Council of Queen's University