Molecular dynamics simulation of pattern formation of two-dimensional model membranes

Structural changes in a two-dimensional model membrane are studied with the aid of the molecular dynamics (MD) technique. The model parameters of the membrane forming molecules are that of a simplified phospholipid head group: each molecule consists of three spheres which represent choline, phosphate and the ester group. The head group molecule is treated as a rigid body. Their translational motion is constrained to two dimensions. The interaction of the molecules is modelled by Lennard-Jones and Coulomb interactions. Time dependent configurations of a system with 120 molecules (with periodic boundary conditions) are analyzed by visual inspection of trajectory plots and by the study of radial distribution functions and local order parameters. The ensemble of model particles is studied as a function of the interaction parameters and the temperature. For high temperatures the system shows liquid type behaviour. For moderate and low temperatures the formation of patterns is observed. There are definitely two trends of ordering. For strong dipole-dipole interaction (relative to the dispersion attraction) of the model particles the individual molecules form ordered chains with decreasing temperature. However, this trend is not monotonous. For T = 400 K the local order parameter has a maximum as a function of temperature which is interpreted as an interference between dipole-dipole ordering and an ordering principle which is related to the molecular shape. A different order phenomenon occurs when the dispersive attraction of the molecular force centers is increased while the dipole-dipole interaction is kept constant. For relatively larger dispersion attraction the dipoles are orientally trapped by this ordering principle leading to the breakdown of dipole order. Although the present model approach cannot be overinterpreted with respect to real biomembranes, it may be very useful for the systematic studies on the interaction of bulky molecules with membranes and the study of the influence of external parameters (like pressure) on structure building.