Receptor-ligand rebinding kinetics in confinement

Rebinding kinetics of molecular ligands plays a critical role in biomachinery, from regulatory networks to protein transcription, and is also a key factor for designing drugs and high-precision biosensors. In this study, we investigate initial release and rebinding of ligands to their binding sites grafted on a planar surface, a situation commonly observed in single molecule experiments and which occurs during exocytosis in vivo. Via scaling arguments and molecular dynamic simulations, we analyze the dependence of non-equilibrium rebinding kinetics on two intrinsic length scales: average separation distance between the binding sites and dimensions of diffusion volume (e.g., height of the experimental reservoir in which diffusion takes place or average distance between receptor-bearing surfaces). We obtain time-dependent scaling laws for on rates and for the cumulative number of rebinding events (the time integral of on rates) for various regimes. Our analyses reveal that, for diffusion-limited cases, the on rate decreases via multiple power law regimes prior to the terminal steady-state regime, in which the on rate becomes constant. At intermediate times, at which particle density has not yet become uniform throughout the reservoir, the number of rebindings exhibits a distinct plateau regime due to the three dimensional escape process of ligands from their binding sites. The duration of this regime depends on the average separation distance between binding sites. Following the three-dimensional diffusive escape process, a one-dimensional diffusive regime describes on rates. In the reaction-limited scenario, ligands with higher affinity to their binding sites (e.g., longer residence times) delay the power laws. Our results can be useful for extracting hidden time scales in experiments where kinetic rates for ligand-receptor interactions are measured in microchannels, as well as for cell signaling via diffusing molecules.