Self-Limiting Aggregation by Controlled Ligand−Receptor Stoichiometry

Colloidal aggregation can be made self-limiting by controlling the ratio of reactive groups (ligands such as biotin coupled to phospholipids and incorporated in a vesicle membrane) on the colloid surface to cross-linking agents (multifunctional receptors such as avidin or streptavidin) in solution. A distinct transition occurs between limited and complete aggregation as a function of the ligand-to-receptor ratio. The “limited” aggregates formed are spherical in nature with a fractal dimension of 2.9. The size of the aggregates depends on the overall concentration of surface accessible biotin-ligands, which can be controlled either by the biotin-lipid fraction in the bilayer at fixed vesicle concentration, or by increasing the vesicle concentration at fixed biotin-lipid fraction. The spherical shapes and concentration dependence are the result of the free diffusion of the ligands on the vesicle surfaces. A simple model of the process based on Smolukowski aggregation kinetics coupled with a Langmuir-type surface reaction is consistent with experiment. This process might be generalized to any system of colloids with surface reactive groups that can be coupled by a soluble cross-linking agent.