Adhesion of colloids on a cell surface in competition for mobile receptors

In this letter, we study theoretically the adhesion of colloidal particles (such as virus, liposomes, nanovectors...) on the surface of a cell. The Brownian colloidal particles bear specific ligands at their surface and might bind to one or several freely diffusing receptors present in the membrane. We are interested in the statics and dynamics of this ensemble of particles adsorbed on the cell as a function of the concentration in the bulk. Proposing a very simple thermodynamical approach, we show the existence of two regimes. At low concentration, the amount of adherent colloids varies linearly with the volume fraction, with a fixed number of links per object, whereas at higher concentration, the number of links per object decreases with the number of fixed colloids, revealing their competition to access to the receptors. Consequently, the time spent by each colloid at the surface depends on the volume concentration and this might be relevant for biological processes such as endocytosis.