One of the conventionally accepted requirements for parallel factor analysis (PARAFAC) to handle the fluorescence excitation emission matrices (EEMs) is the independence of each component's absorption and emission spectra in simple mixtures of fluorophores. EEMs of samples in which Förster resonance energy transfer (FRET) occurs between fluorophores seem to fail to meet this requirement. A rigorous theoretical treatment of the steady-state kinetics in the present work indicates that the fluorescence in the presence of FRET, excited by relatively weak excitation light intensity, can be reasonably separated into additive contributions from three parts: donors, acceptors and FRET. This prediction is for the first time verified experimentally in sodium dodecyl sulfate micellar solutions containing biphenyl as the energy donor and 2,5-diphenyloxazole as the energy acceptor. The experimental EEMs were well fitted to three components as predicted. A well accepted diagnostic test called core consistency (CC), specifically designed for modeling simple mixtures of fluorophores with PARAFAC, was found to be negative for the 3-component model in the present study. The simultaneous occurrence of good model fit and significantly negative CC when modeling fluorophore mixtures by conventional PARAFAC would be indicative of the presence of physical/chemical processes (e.g., FRET) that deviate from the conventional working requirements for PARAFAC. The extent of FRET has been independently measured or calculated by three methods: 1) decrease in steady state fluorescence of donor; 2) lifetime measurements with population analysis; and 3) Poisson statistics based on PARAFAC-determined distribution constants. The results of the three methods are consistent. The normalized scores of the three components found by PARAFAC also agree to within a few percent with relative concentrations in aqueous and micelle phases determined from distribution constants for the solutions prepared with nine different combinations of total donor and acceptor concentrations. Our theoretical treatment also for the first time spells out in detail the relationship between the PARAFAC scores and concentrations of components, in terms of photophysical constants of the components and spectral shape factors.
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