Relaxation spectrum of a concentration quench of Brownian particles.

Single-molecule or SPR (Surface Plasmon Resonance) experiments rely on the relaxation of concentration quenches of initially surface-bound molecules into confined reservoirs to determine molecular kinetic rates. Similarly, biological processes such exocytosis, in which small molecules are emitted into the intracellular cleft for cellular communication, can be considered to be a relaxation process of an effective concentration quench. We study a model system closely related to the above cases in which weakly interacting Brownian particles are released from their binding sites into a confined volume by using molecular dynamics simulations and scaling arguments. Our results suggest that the rebinding rate of released particles exhibits various power laws until the confined volume is entirely filled by the particles. Furthermore, the cumulative rebinding rate, which is the time integration of the rebinding rate, exhibits a novel plateau behavior. This plateau is a result of the decreasing number of collisions between sparsely-placed binding sites and dissociated ligands. Our results can have important consequences for molecular signaling as well as for the interpretation of kinetic measurements of ligand-receptor interactions.