Origins of concentration dependence of waiting times for single-molecule fluorescence binding

Binary fluorescence time series obtained from single-molecule imaging experiments can be used to infer protein binding kinetics, in particular, association and dissociation rate constants from waiting time statistics of fluorescence intensity changes. In many cases, rate constants inferred from fluorescence time series exhibit nonintuitive dependence on ligand concentration. Here, we examine several possible mechanistic and technical origins that may induce ligand dependence of rate constants. Using aggregated Markov models, we show under the condition of detailed balance that non-fluorescent bindings and missed events due to transient interactions, instead of conformation fluctuations, may underly the dependence of waiting times and thus apparent rate constants on ligand concentrations. In general, waiting times are rational functions of ligand concentration. The shape of concentration dependence is qualitatively affected by the number of binding sites in the single molecule and is quantitatively tuned by model parameters. We also show that ligand dependence can be caused by non-equilibrium conditions which result in violations of detailed balance and require an energy source. As to a different but significant mechanism, we examine the effect of ambient buffers that can substantially reduce the effective concentration of ligands that interact with the single molecules. To demonstrate the effects by these mechanisms, we applied our results to analyze the concentration dependence in a single-molecule experiment EGFR binding to fluorophore-labeled adaptor protein Grb2 by Morimatsu et al. [Proc. Natl. Acad. Sci. U.S.A. 104, 18013 (2007)].