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Fluorescence cumulants analysis with non-ideal observation profiles

One of the challenges of fluorescence fluctuation fpectroscopy (FFS) is an adequate approximation of a brightness profile. The key feature of fluorescence intensity distribution analysis (FIDA) is a polynomial approximation of a brightness profile. A broad range of brightness profile shapes can be well described by this approximation. A different approach consisting of the introduction of additional fitting parameters, defined as a relative difference between integrals of the actual brightness profile and its Gaussian approximation, is used in photon counting histogram (PCH) analysis. It is sufficient to introduce only one additional fitting parameter (first-order correction) to get an adequate fit to the experimental data in many practical applications. In the current study, we apply these approaches to the theory of time integrated fluorescence cumulants analysis. We demonstrate that developed corrections improve results of FFS analysis applied to simulated and experimental data. The use of different brightness profile approximations and normalizations in PCH and FIDA leads to different estimates of brightness and the number of molecules, even though they represent the same physical quantities. Based on the developed theory, we derive equations that relate brightness and the number of molecules in PCH and FIDA.