  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. (PNAS,104:18013,2007).
