Kinetics and Identifiability of an Intermolecular Two-State Excited-State Process in the Presence of a Fluorescent Impurity

Abstract

This paper presents a study analyzing the conditions for the recovery of the rate constants and the spectral parameters from the fluorescence decay surface due to three-state excited-state processes. The studied system models a situation when, in addition to a fluorescence indicator which undergoes an excited-state reaction with a co-reactant, a fluorescent impurity is present. It is demonstrated theoretically that, if the fluorescence decay surface contains traces measured in the absence of co-reactant and additionally at two nonzero coreactant concentrations, all five rate constants can always be recovered. In some cases the measurement in the absence of co-reactant is not necessary. If the fluorescence decay surface is collected at three different emission wavelengths and two co-reactant concentrations, the ratios of the absorbances of the free and bound form of the fluorescent indicator can be determined. If two different emission wavelengths are used in combination with three excitation wavelengths (or three co-reactant concentrations), the ratios of the emission weighting factors of the free and bound form of the fluorescent indicator can be obtained. Under both previous conditions no spectral information about the fluorescent impurity can be acquired. The ground-state dissociation constant can be determined from the fluorescence decay traces excited at an isosbestic point.

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.…”

“…Evaluation of eqn (19) at t = 0 and the identifiability condition of eqn (31) leads to i ˜(0) = i(0). Since the exponential function e x and the complementary error function, erfc(y) = 1 − erf(y) (with x and y defined by eqn (43.1) and (43.2), respectively), can never reproduce each other, we have the following straightforward identifiability equations: x ˜= x and y ˜= y (eqn (43.3) and (43.4)).…”

“…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).…”

“…All the tested photophysical models for time-resolved fluorescence with underlying distributions of rate constants leading to non-exponential functions i(t ) given by eqn (12) (Kohlrausch function), (13) (modified Kohlrausch function), (15) and (17) (Becquerel function), (18) (Förster type energy transfer),(19) (Gaussian distribution of rate constants),(22) (exponential distribution of rate constants), (25) (uniform distribution of rate constants), (27) (function with extreme subexponential behavior), (29) (Mittag-Leffler function) and (30) (Heaviside's function) are uniquely identifiable. This means that for each model with associated i(t ) there is a single set of true parameters Σ that describe i(t ).…”

Transient Effects and the Identifiability of Excited-State Processes

“…Although identifiability analyses have been extensively used in biomedicine, pharmacology, ecology, and engineering, 1,2 their use in photophysics is of recent vintage. [3][4][5][6][7][8][9][10][11][12][13][14] We have reported on the deterministic identifiability of inter-and intramolecular two-state and three-state excited-state processes in the presence and absence of added quencher. 3,[5][6][7][8][9][10][11][12][13] For the linear, timeinvariant models that we considered, the parameters to be identified are rate constants and spectral parameters related to absorption (the excited-state species concentrations at time zero) and emission (the emission weighting factors).…”