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 incor porated in a vesicle membrane) on the colloid surface to crosslinking agent s (multifunctional receptors such as avidin or streptavidin) in solution. A distinct transition occurs between limited and complete aggregation as a f unction of the ligand-to-receptor ratio. The "limited" aggregates formed ar e spherical in nature with a fractal dimension of 2.9. The size of the aggr egates depends on the overall concentration of surface accessible biotin-li gands, which can be controlled either by the biotin-lipid fraction in the b ilayer at fixed vesicle concentration, or by increasing the vesicle concent ration at fixed biotin-lipid fraction. The spherical shapes and concentrati on dependence are the result of the free diffusion of the ligands on the ve sicle surfaces; A simple model of the process based on Smolukowski aggregat ion kinetics coupled with a Langmuir-type surface reaction is consistent wi th 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.