Cumulant analysis in two-color fluorescence fluctuation spectroscopy

Abstract

Fluorescence Fluctuation Spectroscopy (FFS) studies the fluctuating fluorescent signal from a small illumination volume and extracts the concentration and dynamical information of fluorophores. Detecting the fluorescence in two detector channels introduces the possibility of differentiating the fluorophores based on color. We introduce bivariate cumulant analysis for Two-Color Fluorescence Fluctuation Spectroscopy and derive an analytical expression for the bivariate factorial cumulants of photon counts at arbitrary sampling times. Fits of the data to the analytical model determine the brightness of each channel, occupation number and diffusion time of each fluorescent species. The statistical accuracy of each cumulant is described by its variance, which we calculate by the moments-of-moments technique. The theory is experimentally verified using model dye system. We also performed first experiments in living cells, and develop a model that takes nonideal detector effects into account. This technique is useful for optimizing the spectroscopic separation of heterogeneous biological samples by FFS. INRODUCTIONFluorescence fluctuation spectroscopy (FFS) derives information about physical processes by detecting the spontaneous variation of the fluorescence signal within an observation volume of < 1 fl created by modern two-photon and confocal microscopy 1-2 . Statistical analysis techniques such as fluorescence correlation spectroscopy (FCS) 3 and photon counting histogram (PCH) 4-5 are used to extract kinetic and dynamic information from the stochastic fluorescence signal. FCS employs the correlation function to capture the temporal information of the physical process, while PCH use the amplitude distribution of the fluctuations to characterize the concentration and brightness of the fluorescent species. Moment analysis is another technique to study the fluctuating fluorescence signals. It has been developed in the late 80s and early 90s with the aim to resolve heterogeneous biomolecular samples by FFS experiments 6-9 . Subsequent developments of moment analysis are fluorescence cumulant analysis (FCA) 10 and time-integrated fluorescence cumulant analysis (TIFCA) 11 . Cumulants are special moments with mathematical properties particular suited for independent random variables. FCA uses simple analytical expressions that relate the factorial cumulants of the photon counts to the molecular brightness and occupation number in the observation volume. TIFCA generalizes cumulant analysis to arbitrary sampling times, and thus allows extracting dynamic information as well as concentration and brightness information about fluorescent species. The exact theoretical treatment of TIFCA also allows the optimization of the signal-to-noise ratio in the analysis of FFS experiments.Conventional FFS collects all the light with a single detector. In two-channel FFS, the fluorescent signal is split by a dichroic mirror into two different detectors based on the color of the fluorophore. Two-channel FFS makes it possible to resolve fluor...