Compartmental modeling in photophysics: Identifiability of models for intramolecular three-state excited-state processes

In this paper, we investigate if the rate constants and spectral parameters that describe models for intramolecular three-state excited-state events can be uniquely determined from ideal time-resolved fluorescence data. For the general model, in which there are reversible transformations between the three excited species, values of nine rate constants and four spectral parameters related to excitation and emission must be defined. Without prior knowledge of rate constants and spectral parameters there is an infinite number of these model parameters that fit the time-resolved fluorescence data and hence the model is not identifiable. Even simplified models leading to single exponential decay kinetics of some excited species concentrations are unidentifiable if such prior knowledge is not available. It is shown for each simplified model what kinetic information can be extracted from perfect time-resolved fluorescence data when the individual excited species concentrations can be monitored. Guidelines to the experimentalist are given for using a priori knowledge to make a distinction among the different models.