Statistics of the bleaching number and the bleaching time in single-molecule fluorescence spectroscopy

The kinetics of bleaching in single-molecule fluorescence spectroscopy (SMS) is studied using renewal theory. A five-state model of a dye molecule is considered where bleaching occurs from the excited triplet states. An exact formalism is developed to calculate the distributions of the bleaching number (i.e., the number of photon counts) and bleaching time (i.e., the time before photobleaching). For photostable dyes those distributions are well approximated by exponential distributions determined by the average bleaching number ν and the average bleaching time τ respectively. Exact formulation is developed to calculate ν and τ in terms of the transition rate constants. For photostable dyes the exact ν and τ are well approximated by expressions derived from a steady-state solution to the kinetic rate equations describing the molecule. The theory implies that experimental multiexponential fits to the distributions of the bleaching number and bleaching time are an indication that the SMS system is heterogeneous.