Binding kinetics of lock and key colloids.

Using confocal microscopy and first passage time analysis, we measure and predict the rates of formation and breakage of polymer-depletion-induced bonds between lock-and-key colloidal particles and find that an indirect route to bond formation is accessed at a rate comparable to that of the direct formation of these bonds. In the indirect route, the pocket of the lock particle is accessed by nonspecific bonding of the key particle with the lock surface, followed by surface diffusion leading to specific binding in the pocket of the lock. The surprisingly high rate of indirect binding is facilitated by its high entropy relative to that of the pocket. Rate constants for forward and reverse transitions among free, nonspecific, and specific bonds are reported, compared to theoretical values, and used to determine the free energy difference between the nonspecific and specific binding states.