Kinetic modeling and design of colloidal lock and key assembly

We investigate the kinetics of colloidal lock and key particle assembly by modeling transitions between free, non-specifically and specifically (dumbbells) bound pairs to enable the rapid formation of specific pairs. We expand on a model introduced in a previous publication (Colón-Meléndez et al., 2015) to account for the shape complementarity between the lock and the key particle. Specifically we develop a theory to predict free energy differences between specific and non-specific states based on the interaction potential between arbitrary surfaces and apply this to the interaction of a spherical key particle with the concave dimple surface. Our results show that a lock particle dimple slightly wider than the key particle radius results in optimal binding, but also show escape rates much smaller than those observed in experimental measurements described in the paper cited above. We assess the possible sources of error in experiments and in analysis, including spatial and temporal resolution of the confocal microscopy method used to measure kinetic coefficients, the polydispersity of the lock dimple size, and the sedimentation of the particles in a quasi-two-dimensional layer. We find that the largest sources of variation are in the limited temporal resolution of the experiments, which we account for in our theory, and in the quasi-two-dimensional nature of the experiment that leads to misidentification of non-specific pairs as specific ones. Accounting for these sources of variation results in very good quantitative agreement with experimental data.