Identifiability of models for intramolecular two-state excited-state processes with added quencher and coupled species-dependent rotational diffusion

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 and may lead to the minimal experimental conditions under which this is possible. In this work, we used the method of similarity transformation to investigate the identifiability of three kinetic models utilized to describe the time-resolved fluorescence of reversible intramolecular two-state excited-state processes in isotropic environments: (1) model without added quencher, (2) model with added quencher, (3) model with added quencher coupled with species-dependent rotational diffusion described by Brownian reorientation. Without a priori information, model 1 is not identifiable. For model 2, two sets of quenching rate constants and combinations of excited-state deactivation/exchange rate constants are possible, but they cannot be allocated to a specific excited-state species. For both sets, upper and lower limits on the excited-state deactivation/exchange rate constants can be obtained. For model 3, both spherically and cylindrically symmetric rotors, with no change in the principal axes of rotation in the latter, are considered. The fluorescence delta-response functions I(parallel)(t) and I(perpendicular)(t), for fluorescence polarized parallel and perpendicular, respectively, to the electric vector of linearly polarized excitation, are used to define the sum S(t) identically equal to I(parallel)(t) + 2 I(perpendicular)(t) and the difference D(t) identically equal to I(parallel)(t) - I(perpendicular)(t). The identifiability analysis is performed using the S(t) and D(t) functions. Also for model 3, two sets of kinetic parameters (i.e., quenching rate constants, combinations of deactivation/exchange rate constants, and rotational diffusion coefficients) exist, but these parameters cannot be assigned unequivocally to a specific species. For the three models, an infinite number of alternative spectroscopic parameters associated with excitation and emission are found.