Compartmental modeling of reversible intermolecular two-state excited-state processes coupled with rotational diffusion or with added quencher.

Analysis of related time-resolved fluorescence measurements can possibly lead to the determination of the kinetic parameters of excited-state processes. A deterministic identifiability analysis on an error-free fluorescence decay data surface has to be executed to verify whether the parameters of a particular model can be determined and may point to the minimal experimental conditions under which this will become possible. In this work, similarity transformation is chosen as an identifiability analysis approach because it also gives the explicit relationships between the true and alternative model parameters. Results 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 model a, 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 respectively parallel and perpendicular to the electric vector of linearly polarized excitation, are used to define the sum S(t) = I( parallel)(t) + 2 I( perpendicular)(t) and the difference D(t) = I(parallel)(t) - I(perpendicular)(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 model 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.