Resolving heterogeneity on the single molecular level with the photon- counting histogram

The diffusion of fluorescent particles through a small, illuminated observation volume gives rise to intensity fluctuations caused by particle number fluctuations in the open observation volume and the inhomogeneous excitation-beam profile. The intensity distribution of these fluorescence fluctuations is experimentally captured by the photon-counting histogram (PCH). We recently introduced the theory of the PCH for diffusing particles (Chen et al., Biophys. J., 77:553-567), where we showed that we can uniquely describe the distribution of photon counts with only two parameters for each species: the molecular brightness of the particle and the average number of particles within the observation volume. The PCH is sensitive to the molecular brightness and thus offers the possibility to separate a mixture of fluorescent species into its constituents, based on a difference in their molecular brightness alone. This analysis is complementary to the autocorrelation function, traditionally used in fluorescence fluctuation spectroscopy, which separates a mixture of species by a difference in their diffusion coefficient. The PCH of each individual species is convoluted successively to yield the PCH of the mixture. Successful resolution of the histogram into its components is largely a matter of the signal statistics. Here, we discuss the case of two species in detail and show that a concentration for each species exists, where the signal statistics is optimal. We also discuss the influence of the absolute molecular brightness and the brightness contrast between two species on the resolvability of two species. A binary dye mixture serves as a model system to demonstrate that the molecular brightness and the concentration of each species can be resolved experimentally from a single or from several histograms. We extend our study to biomolecules, where we label proteins with a fluorescent dye and show that a brightness ratio of two can be resolved. The ability to resolve a brightness ratio of two is very important for biological applications.