Effect of bin time on the photon counting histogram for one-photon excitation

We have demonstrated that our photon counting histogram (PCH) model with the correction for one-photon excitation is valid at multiple bin times. The fitted apparent brightness and concentration follow the three-dimensional diffusion model. More importantly, the semi-empirical parameter, F, introduced in the PCH model for one-photon excitation to correct for the non-Gaussian shape of the observation volume, shows small variations with different bin times. These variations are consistent with the physical interpretation of F, and they do not affect the resolving power of the PCH model for one-photon excitation. Based on these findings, we extend the time-independent PCH analysis to time-dependent photon counting multiple histograms (PCMH). This model considers the effect of bin time on the PCH parameters in a way that is similar to fluorescence intensity multiple distribution analysis (FIMDA). From the same set of data, PCMH extracts time-dependent parameters (diffusion time and triplet-state relaxation time) as well as time-independent parameters (true specific brightness and true average number of molecules). Given a three- to fourfold experimental difference in molecular brightness, we find that PCMH can resolve each species in a two-species sample and extract their respective diffusion times even when fluorescence correlation spectroscopy cannot.