Elementary theory of Brownian motion of trapped domains in lipid monolayers

An elementary theoretical model is described for the Brownian motion of circular lipid domains electrostatically trapped within larger circular lipid domains in monolayers at the air-water interface. Earlier work is briefly reviewed, in which it is shown that the r.m.s. amplitude of the trapped Brownian motion follows a simple Maxwell-Boltzmann distribution, and can be used to determine the absolute value of the difference of dipole densities in the two co-existing phases [mu]. A comparison of this dipole density difference with that obtained from surface potential measurements provides a critical test of the theoretical model. It is also shown that the kinetics of Brownian motion can be analyzed to provide information on monolayer fluid mechanics and to provide a further test of the model. It is pointed out that the ease with which domain movements can be observed in the fluorescence microscope, coupled with the fact that the energies involved are only of the order of magnitude of kT, suggests that lipid monolayers can be used to detect weak specific intermolecular bonds between ligands incorporated in the lipid monolayer, and receptors fixed in the aqueous subphase.