Direct determination of kinetic parameters for diffusion-influenced reactions in solution by analysis of fluorescence decay curves.

Fluorescence decay curves were synthesized using the Smoluchowski-Collins-Kimball (SCK) model for diffusion-influenced bimolecular reactions so as to simulate measurements using the technique of time-correlated single photon counting (TCSPC). The experimental conditions required for successful recovery of the parameters used to generate these decay curves were assessed by direct analysis using the decay function associated with the SCK model, where the term "direct analysis" refers to analysis in which all of the fundamental parameters associated with the SCK model are permitted to vary freely. Analysis of decay curves synthesized using an instrument response function measured using a flash-lamp TCSPC system and having a full-width at halfmaximum (fwhm) of approximately 2.8 ns was unsuccessful for the values of the parameters associated with the SCK model that were used in this work. However, analysis of these synthesized fluorescence decay curves using the long-time approximation to the SCK model was found to be valid. The results of analysis of fluorescence decay curves synthesized using a 37-ps fwhm instrument response function indicate that the long-time approximation becomes a poor description of the kinetics of diffusion on the time scale associated with these decay curves. Furthermore, direct analysis using the function associated with the SCK model of the synthesized fluorescence decay curves convoluted with this response function and containing 5.0× 10(4) or 1.0 × 10(5) counts in the channel of maximum intensity resulted in the recovery of parameter values that are in very good agreement with those used to generate these decay curves. The results obtained using the simple methodology developed in this work demonstrate for the first time that direct analysis of fluorescence decay curves measured using TCSPC according to the decay function derived from the SCK model can yield reliable estimates for values of the relevant parameters under suitable experimental conditions.