Effective potentials and electrostatic interactions in self-assembled molecular bilayers II: The case of biological membranes

In order to study the electrostatic properties of a single biological membrane (not an stack of bilayers), we propose a very simple and effective external potential that simulates the interaction of the bilayer with the surrounding water and that takes into account the microscopic pair distribution functions of water. The electrostatic interactions are calculated using Ewald sums but, for the macroscopic electrostatic field, we use an approximation recently tested in simulations of Newton black films that essentially consists in a coarsed fit (perpendicular to the bilayer plane) of the molecular charge distributions with Gaussian distributions. The method of effective macroscopic and external potentials is extremely simple to implement in numerical simulations, and the spatial and temporal charge inhomogeneities are then roughly taken into account. As examples of their use, several molecular dynamics simulations of simple models of a single biological membrane, of neutral or charged polar amphiphilics, with or without water (using the TIP5P intermolecular potential for water) are included. The numerical simulations are performed using a simplified amphiphilic model which allows the inclusion of a large number of molecules in these simulations, but nevertheless taking into account molecular charge distributions, flexible amphiphilic molecules, and a reliable model of water. All these parameters are essential in a nanoscopic scale study of intermolecular and long range electrostatic interactions. This amphiphilic model was previously used by us to simulate a Newton black film, and, in this paper, we extend our investigation to bilayers of the biological membrane type.