Simulations of a single membrane between two walls using a Monte Carlo method

Quantitative theory of interbilayer interactions is essential to interpret x-ray scattering data and to elucidate these interactions for biologically relevant systems. For this purpose Monte Carlo simulations have been performed to obtain pressure $P$ and positional fluctuations σ. An alternative method, called Fourier Monte Carlo (FMC), that is based on a Fourier representation of the displacement field, is developed and its superiority over the standard method is demonstrated. The FMC method is applied to simulating a single membrane between two hard walls, which models a stack of lipid bilayer membranes with nonharmonic interactions. Finite-size scaling is demonstrated and used to obtain accurate values for $P$ and σ in the limit of a large continuous membrane. The results are compared with perturbation theory approximations, and numerical differences are found in the nonharmonic case. Therefore the FMC method, rather than the approximations, should be used for establishing the connection between model potentials and observable quantities, as well as for pure modeling purposes.