Identifiability analysis of models for reversible intermolecular two-state excited-state processes coupled with species-dependent rotational diffusion monitored by time-resolved fluorescence depolarization

Abstract

A deterministic identifiability analysis of the kinetic model for a reversible intermolecular two-state excited-state process with species-dependent rotational diffusion described by Brownian reorientation is presented. The cases of both spherically and cylindrically symmetric rotors, with no change in the principal axes of rotation on interconversion in the latter case, are specifically considered. The identifiability analysis is carried out in terms of compartmental modeling based on the S(t) identical with I( parallel)(t)+2I( perpendicular)(t) and D(t) identical with I( parallel)(t)-I( perpendicular)(t) functions, where I( parallel)(t) and I( perpendicular)(t) are the delta-response functions for fluorescence, polarized, respectively, parallel and perpendicular to the electric vector of linearly polarized excitation. It is shown that, from polarized time-resolved fluorescence data collected at two concentrations of coreactant and three appropriately chosen emission wavelengths, (a) a unique set of rate constants for the overall excited-state process is always obtained by making use of polarized measurements and (b) the rotational diffusion constants and geometrical factors associated with the different anisotropy decay components can be uniquely determined and assigned to each species. The geometrical factors are determined by the absorption and emission transitions in the two rotating species. For spherical rotors, these factors depend directly on the relative orientations of the transition moments, while for cylindrically symmetric rotors they depend on the orientations with respect to each other and to the symmetry axis.

Fluorescence anisotropy measurements in solution: Methods and reference materials (IUPAC Technical Report)

“…To make an identifiability analysis feasible, one assumes that all the rate constants are independent of the instantaneous orientation of the species and that there is no change in the principal axes of rotation on interconversion between the species. It is shown that, from polarized time-resolved decay data surfaces collected at two concentrations of the coreactant and three appropriately chosen emission wavelengths, (a) a unique set of rate constants for the overall excited-state process is always obtained and (b) the rotational diffusion constants and geometrical factors associated with the different anisotropy decay components can be uniquely determined and assigned to each species [44].…”

“…In a photophysical context, a compartment is a subsystem composed of a distinct type of species that acts kinetically in a unique way. Also, the motion of a Brownian rotor can be modeled in terms of a compartmental model [44,69].…”

Compartmental modeling and identifiability analysis in photophysics: Review

“…Next, models for reversible intermolecular two‐state excited‐state processes in the absence 9, 10 and presence 11 of quencher as monitored by the total (or “magic angle”‐selected) fluorescence are discussed. Finally, the model of a reversible intermolecular two‐state excited‐state process coupled with species‐dependent rotational diffusion described by Brownian reorientation is considered 12, 13.…”

Levitation effect: Size-dependent maximum in rotational diffusion in confined systems

“…For example, the importance of rotational motion of water is demonstrated in reverse micelles by means of quasielastic neutron scattering as well as molecular dynamics simulations. 3 The rotational diffusion of symmetric top molecules in a dc electric field is investigated. 2 Time-resolved fluorescence depolarization measurements of rotational diffusion of spherically and cylindrically symmetrical rotors are studied and the relevance of these studies to real systems in which reaction occurs leading to transformation of species A to species B is discussed.…”