Use of Fourier transforms in the analysis of fluorescence data. 1. A general method for finding explicit relationships between photophysical models and fluorescence parameters

In this paper general equations are derived providing explicit relationships in closed form between any physical model and the measurable fluorescence parameters given in the frequency domain. The kinetic equations were solved directly in the frequency domain to obtain the result above. Weber (Weber, G. J. Chem. Phys. 1977, 66, 4081-4091) has pointed out that these relationships can be obtained as a power series of the modulation frequency, but the solutions were not given in closed form. With knowledge of the closed form of the relationships their detailed analysis has been performed pointing out the existence of model parameter invariant properties of the general solutions. By means of these properties one can reduce considerably the number of the possible photophysical models describing a particular fluorescence system. The general relationships found simplify the global analysis of steady-state and phase-modulation fluorescence data by eliminating the need for numerical solution of the kinetic equations of the fluorescence and the transformation of the solution from time to frequency domain. The general ideas outlined in this paper are applied in part 2 and 3 for the case of pyrene-labeled phosphatidylcholine in lipid membrane.