Compartmental analysis in photophysics: Kinetics and identifiability of models for quenching of fluorescent probes in micelles

The parameters describing the kinetics of excited-state processes can possibly be recovered by analysis of the fluorescence decay surface measured as a function of the experimental variables. The identifiability analysis of a photophysical model assuming errorless time-resolved fluorescence data can verify whether the model parameters can be determined. In this work, we have used the methods of similarity transformation and Taylor series to investigate the identifiability of two models utilized to describe the time-resolved fluorescence quenching of stationary probes in micelles. The first model assumes that exchange of the quencher between micelles is much slower than the fluorescence decay of the unquenched probe (the ‘immobile’ quencher model). The second model assumes that quenchers exchange between the aqueous and micellar phases (the ‘mobile’ quencher model). For the ‘immobile’ quencher model, the rate constants for deactivation (k0) and quenching (kq) of the excited probe are uniquely identified together with the average number of quencher molecules per micelle. For the ‘mobile’ quencher model, the rate constants k0 and kq are uniquely identified, as are the rate constants for entry (k+) and exit (k−) of one quencher molecule into and from a micelle, and the micellar aggregation number. The concomitant rate equations describing the time-resolved fluorescence are solved using z-transforms.