Resolving fluorescent species by their brightness and diffusion using correlated photon-counting histograms

Fluorescence fluctuation spectroscopy (FFS) refers to techniques that analyze fluctuations in the fluorescence emitted by fluorophores diffusing in a small volume andcan be used to distinguish between populations of molecules that exhibit differences inbrightness or diffusion. For example, fluorescence correlation spectroscopy (FCS)resolves species through their diffusion by analyzing correlations in the fluorescenceover time; photon counting histograms (PCH) and related methods based on momentanalysis resolve species through their brightness by analyzing fluctuations in thephoton counts. Here we introduce correlated photon counting histograms (cPCH),which uses both types of information to simultaneously resolve fluorescent species bytheir brightness and diffusion. We define the cPCH distribution by the probability to detect both a particular number of photons at the current time and another number at a later time. FCS and moment analysis are special cases of the moments of the cPCH distribution, and PCH is obtained by summing over the photon counts in eitherchannel. cPCH is inherently a dual channel technique, and the expressions we developapply to the dual colour case. Using simulations, we demonstrate that two speciesdiffering in both their diffusion and brightness can be better resolved with cPCH thanwith either FCS or PCH. Further, we show that cPCH can be extended both to longerdwell times to improve the signal-to-noise and to the analysis of images. By betterexploiting the information available in fluorescence fluctuation spectroscopy, cPCHwill be an enabling methodology for quantitative biology.