We introduce dual-color time-integrated fluorescence cumulant analysis (TIFCA) to analyze fluorescence fluctuation spectroscopy data. Dual-color TIFCA utilizes the bivariate cumulants of the integrated fluorescent intensity from two detection channels to extract the brightness in each channel, the occupation number, and the diffusion time of fluorophores simultaneously. Detecting the fluorescence in two detector channels introduces the possibility of differentiating fluorophores based on their fluorescence spectrum. We derive an analytical expression for the bivariate factorial cumulants of photon counts for arbitrary sampling times. The statistical accuracy of each cumulant is described by its variance, which we calculate by the moments-of-moments technique. A method that takes nonideal detector effects such as dead-time and afterpulsing into account is developed and experimentally verified. We perform dual-color TIFCA analysis on simple dye solutions and a mixture of dyes to characterize the performance and accuracy of our theory. We demonstrate the robustness of dual-color TIFCA by measuring fluorescent proteins over a wide concentration range inside cells. Finally we demonstrate the sensitivity of dual-color TIFCA by resolving EGFP/EYFP binary mixtures in living cells with a single measurement.
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