Identifiability of Irreversible Intermolecular Two-State Excited-State Processes

Abstract

This report analyzes which kinetic and spectral parameters can be recovered by global compartmental analysis for intermolecular two-state excited-state processes when k 21 [M] (Scheme 1) is negligible. The time-resolved fluorescence of such a photophysical system will decay as a biexponential function with invariant decay times. The ratio of the amplitudes associated with the decay times will depend on [M]. Although the association rate constant k 21 is known to be zero, this knowledge is not helpful in determining unique values for the remaining parameters. It is shown that the available information which can be derived from timeresolved fluorescence data only is strongly limited. When k 12 is not negligible, the values of k 01 , (k 02 + k 12 ), and the relation connecting k 12 and the ground-state dissociation constant can be obtained from two decay traces collected for two different concentrations of M. For such a system it is impossible to determine the ground-state dissociation constant from time-resolved fluorescence measurements exclusively. The identifiability analysis shows that additional decay curves measured at different concentrations of M and excitation or emission wavelengths do not provide independent information useful for the unique determination of the remaining parameters. If the ground-state dissociation constant can be obtained from fluorimetric titration, the photophysical system becomes identifiable. In the limiting case when k 12 ) 0, the relation between k 12 and the ground-state dissociation constant vanishes. The addition of quencher to intermolecular two-state excited-state processes when k 21 [M] is negligible does not provide additional information useful for the unique determination of the kinetic and spectral parameters.

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.…”

Photophysics and kinetics of naphthopyran derivatives, part 2: Analysis of diarylnaphthopyran kinetics. Degeneracy of the kinetic solution

“…These two challenges are respectively known in the literature as the distinguishability and identifiability problems 43–54. They raise the fundamental questions of the uniqueness of the specific attributes of a kinetic problem and whether there may be ambiguity in the reaction model even with a good fit between the experimental data and the chosen model.…”

Identifiability of models for time-resolved fluorescence with underlying distributions of rate constants

“…Examples of numerical identifiability studies can be found in ref. 14,[16][17][18][19][20]51, 70-72.…”

“…Since the first identifiability study of an intermolecular twostate excited-state process, 12 identification studies of a broad range of models of intermolecular and intramolecular twostate and three-state excited-state processes have been reported [13][14][15][16][17][18][19][20][21][22][23][24] (see ref. 25 and 26 for supplementary literature data).…”