Transient Effects and the Identifiability of Excited-State Processes

Abstract

The identifiability of excited-state processes in the presence of transient effects is studied. The Smoluchowski and Collins-Kimball models of diffusion-mediated association are considered. The kinetic parameters of single-species quenching and related kinetic schemes (double-species quenching without excited-state interchange, and irreversible association with separated excited-species spectra) can be uniquely recovered from the same or a smaller number of decay traces than are necessary within classical kinetics where time-invariant rate constants are used. For single-species quenching in low dimensions, 1D and 2D, the system parameters can be uniquely recovered from a single decay trace at one nonzero quencher concentration. In three dimensions, decays traces measured at two concentrations are necessary and sufficient to recover the parameters. For double-species quenching without interchange of the excited states, decay traces at two wavelengths collected in the absence and presence of quencher guarantee local identifiability of the model in each dimension with or without transient effects. Irreversible association with separate excited-species spectra is identifiable in each dimension, given decay traces at two quencher concentrations and two wavelengths.

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

“…[28][29][30][31][32] Furthermore, a series of papers dealt with the identifiability of excited-state processes in the presence of Smoluchowski and Collins-Kimball transient effects. [33][34][35][36][37][38] However, only two reports have been published on the identification of models for fluorescence decays with an underlying distribution of decay rates as observed for an excited probe quenched by molecules or ions that are Poisson-distributed over the micelles. 39,40 In this paper we investigate the deterministic identification of several uncommon models for fluorescence decay with underlying distributions of rate constants which lead to nonexponential fluorescence δ-response functions i(t ).…”

Global Analysis of Kinetic and Stationary Diffusion-Mediated Fluorescence Quenching Data

“…Assuming the SCK model, one can determine the relative diffusion coefficient, i.e., the sum of the diffusion coefficients of the fluorophore and quencher, D = D F* + D Q , the sum of the radii of the fluorophore and quencher, R = R F* + R Q , and the intrinsic quenching rate coefficient k . Deterministic (i.e., assuming errorless data) identifiability analysis of the SCK model shows that one decay trace at a nonzero quencher concentration suffices to determine D , R and k , when the fluorophore fluorescence lifetime τ is known . From a practical point of view, one needs to know whether noisy and sampled fluorescence quenching data allow reliable estimation of the microscopic parameters.…”