Logarithmic Binding and Stretched-Exponential Kinetics in Peripheral Protein Interactions with Lipid Membrane Surfaces

Motivated by the astonishingly broad spectrum of binding constants reported for interactions between peripheral proteins and membranes, we investigate possible reasons by analyzing a theoretical model of protein binding that involves seven identical contacts with the membrane surface. We demonstrate that, depending on the experimental design, the multiplicity of weak binding interactions can cause significant stretching of the binding curves. In the case of lipid surface titration by the excess of free protein in the bulk, this may result in "logarithmic binding", wherein the amount of bound protein is roughly proportional to a logarithm of its bulk concentration within many orders of magnitude. The origin of this logarithmic dependence is a gradual decrease in the average number of available contacts, accompanied by a corresponding redistribution of active contacts in the bound protein population, as the surface density of protein increases. We also show that the unbinding kinetics are described by stretched exponentials.