A simple theory of peptide interactions on a membrane surface: excluded volume and entropic order

A simple theory of the interactions of peptides bound onto a lipid membrane is developed, modeling the peptides as rods on a surface. At low peptide surface-concentration, excluded volume dominates the peptide-peptide interactions and the orientation of the peptides is random, resulting in an isotropic configuration. However, at high peptide density on the membrane, the peptides become orientationally ordered, resulting in an anisotropic configuration. This effect is entirely entropic in origin, and simply reflects the fact that peptides can be exchanged more easily on the surface if they are equally aligned, resulting in a larger number of possible configurations. In three dimensions, this phenomenon corresponds to the well-known isotropic-nematic phase transition. In two dimensions, the problem is not as well understood. The theoretical treatment presented here yields a simple, manageable expression which can be compared with experimental data. Two-dimensional ordering results in an increase in the apparent binding constant of peptides to membranes at high concentration of peptides relative to what is expected from the effect of excluded volume alone. The possible implications of side-by-side alignment for several biological processes, such as peptide translocation across membranes and plaque formation in Alzheimer's disease, are discussed.