Conformational chain statistics in a model lipid bilayer: Comparison between mean field and Monte Carlo calculations

A comparison between a mean field theory of chain packing in membranes and micelles and Monte Carlo simulations is presented for model lipid bilayers. In both approaches the "lipids" are modeled as freely jointed (but self-avoiding) chains of spherical segments. The first segment of the chain represents the head group, anchored to the bilayer interface by a harmonic binding potential. The simulations are performed for symmetric bilayers composed of 200 chains, with periodic boundary conditions. Both pure and mixed bilayers (composed of long and short chains) are analyzed. In the simulation nonbonded segments interact via Lennard-Jones potentials, ensuring nearly uniform segment density in the bilayer core, as assumed in the mean field theory. The lateral pressure profiles governing the probability distribution of chain conformations in the mean field theory are related and compared to the tangential pressure profiles calculated from the simulations using Kirkwood-Buff s molecular theory. The two pressure profiles show very good agreement. We also calculate two conformational chain properties: end-segment distributions and orientational bond order parameters. The end-segment distributions calculated by the two approaches show excellent agreement. The order parameters compare somewhat less satisfactorily, yet we found that the order parameters derived from the simulations depend rather sensitively on the details of the interaction potential. In general, the results of the simulations support the use of the mean field theory as a (simple) tool for studying conformational chain statistics in confined environments and related thermodynamic properties, such as membrane curvature elasticity.