(484c) Theory of Kinetics of Lock-Key Particle Pair Formation

A first-passage-time theory is developed for the binding kinetics of pairs of colloidal particles, one of which (the Lock particle) has an axisymmetric patch where strong irreversible “specific” binding occurs with the other particle (the Key particle), which has isotropic attractive interactions. When the key particle contacts the lock particle away from this strong-binding patch, “non-specifically-bound particle pairs can form, but these pairs are weakly, and reversibly, bound. Starting from lock-key pairs that are non-specifically bound, predictions are made for the rates of formation of both specific lock-key binding, and of breakage of non-specifically-boudn particle pairs to form free, non-interacting, spheres.  In these first-passage-time calculations, hydrodynamic interactions appear as combinations of normal modes of motion which combine rotation, sliding-translation and rotation-translation correlations. These are combined into an effective diffusion coefficient controlling the rate of variation in the angle between the line separating particle centers and the director describing the orientation of the attractive patch of the key particle. The first-passage-time predictions of the binding kinetics for ideal Lock-Key colloids are compared with Stokesian Dynamics simulations to validate the model. First-passage-time predictions are used to study the effect of the interaction potential on kinetics of non-specific to specific binding and of non-specific binding to free particles, and results are compared with experiments from the Solomon group. Knowledge of binding kinetics is important for novel hierarchical self-assembly applications where intermediate assemblies are required to build desired structures, and as models for predicting protein association and dissociation kinetics.