Testing the identifiability of a model for reversible intermolecular two-state excited-state processes

Abstract

The modeling of excited-state processes in photophysics can conveniently be done within the framework of compartmental analysis. In compartmental analysis substantial attention has been devoted to the study of deterministic identifiability, which verifies whether it is possible to determine the parameters of the compartmental model from error-free data. In this paper the similarity transformation approach is applied to the identifiability problem of the photophysical model for reversible intermolecular two-state excited-state processes. This method provides straightforward relations between the true and alternative sets of the system parameters. This allows one to explore directly the parameter space for identifiability. Since absolute values for the spectral parameters associated with excitation and emission are not available from time-resolved fluorescence experiments, the original similarity transformation approach to the identifiability problem was reformulated in terms of normalized spectral parameters, which are experimentally accessible. It is shown that six decay traces—measured at two coreactant concentrations and three emission wavelengths—are required for the model to be locally identifiable. Two sets of rate constants and associated spectral parameters may be found under these conditions. Enclosure in the analysis of the monoexponential decay at very low coreactant concentration results in global identifiability. The non-negativity requirement of the spectral parameters also can lead to the unique solution. If the fluorescence decays are independent of the emission wavelength, additional information about the photophysical system is necessary for identifiability.

Identifiability of Models for Fluorescence Quenching in Aqueous Micellar Systems

“…[3] Since the first identification of an intermolecular two-state excited-state process, [3] identifiability studies of a broad range of compartmental models of intermolecular and intramolecular two-and three-state excited-state processes have been reported (see ref. [4] for literature data). For the linear, time-invariant models, the parameters to be identified are time-invariant rate constants and spectral parameters related to excitation and emission.…”

Global Compartmental Analysis of the Excited-State Reaction between Fluorescein and (±)-N-Acetyl Aspartic Acid

“…However, its use in photophysics is of recent date. [13][14][15][16][20][21][22][23][24][25] In a photophysical framework a compartment is a subsystem composed of a distinct type of species that acts kinetically in a unique way. The concentration of the constituting species can change when the compartments exchange material through intermolecular (or intramolecular) processes.…”

Controllability and Observability of the Photophysical System of Intermolecular Two-State Excited-State Processes

“…A number of alternative approaches to identifiability analysis are available and have been employed for the analysis of the identification of common photophysical models. We have extensively used Markov parameters and elementary functions of the rate constants for this purpose (see literature references in [9] and [10]). …”

“…we have studied the identifiability of the controllable and observable, intermolecular, two-state excited-state system via the similarity transformation approach. The identifiability analysis for the non-controllable system is formally equivalent to that described in Ref [10], but one has to exploit the required independence of t i of the …”

“…Since the first identification analysis of an intermolecular two-state excited-state process, 8 identifiability studies of a broad range of photophysical models of intermolecular as well as intramolecular two-state and three-state excited-state processes have been reported (see Refs [9] and [10] for literature data). Recently, we have described identifiability analyses of models for rotational diffusion monitored by timeresolved fluorescence depolarization 11,12,13,14,15 and of models for fluorescence quenching in aqueous micellar systems.…”