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

Nikolai Gouliaev·John F. Nagle
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Abstract

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 sigma. A new 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 non-harmonic interactions. Finite size scaling is demonstrated and used to obtain accurate values for P and sigma in the limit of a large continuous membrane. The results are compared with perturbation theory approximations, and numerical differences are found in the non-harmonic 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.

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Nikolai Gouliaev, John F. Nagle. 1998-05-02. Simulations of a single membrane between two walls using a Monte Carlo method. https://doi.org/10.1103/physreve.58.881

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