Identifiability via the Method of Similarity Transformation of Models for Reversible Intermolecular Two-State Excited-State Processes with Species-Dependent Rotational Diffusion or with Added Quencher

Deterministic identifiability analyses via similarity transformation are presented for two kinetic models of a reversible intermolecular two-state excited-state process in isotropic environments: (a) with coupled species-dependent rotational diffusion described by Brownian reorientation, and (b) with added quencher. For (a), both spherically and cylindrically symmetric rotors, with no change in the principal axes of rotation in the latter, are considered. The fluorescence δ -response functions I||(t) and I⊥(t), for fluorescence polarized respectively parallel and perpendicular to the electric vector of linearly polarized excitation, are used to define the sum S(t) = I||(t) + 2 I⊥(t) and the difference D(t) = I||(t) − I⊥(t) function. The identifiability analysis is carried out using the S(t) and D(t) functions. The analysis involving S(t) shows that two physically acceptable possible solutions for the overall rate constants of the excited-state process exist. Inclusion of information from polarized fluorescence measurements on the rotational kinetic behavior contained in D(t) results in the unique set of rate constants and rotational diffusion coefficients when the rotational diffusion coefficients are different. For (b), it is shown that addition of quencher plays formally the same role as rotational diffusion as far as the identification is concerned. When the quenching rate constants are different, the rate constants of a reversible intermolecular two-state excited-state process with added quencher can be uniquely determined. The explicit relationships between the true and alternative model parameters are obtained.