Shapes of finite two-dimensional lipid domains

Distinct lipid domains with different two-dimensional density can be visualized in monomolecular films at the air-water interface by using fluorescence microscopy, when the monolayers are doped with a low concentration of fluorescent lipid probe. The shapes of these domains are determined to a large extent by a competition between line tension and long-range electrostatic dipolar repulsions. The line tension favors compact, often circular shapes, whereas the long-range electrostatic dipolar repulsions favor other shapes, such as thin stripes. A line integral technique is described for calculating the dipolar energies of these two-dimensional domains. Calculations are given for various domain shapes and shape transitions. It is shown that as domains grow in area they tend to thin in one dimension because of long-range dipolar forces. It is also shown how these long-range dipolar forces contribute to the formation of chiral domain shapes.