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

Abstract

The deterministic identifiability analysis of photophysical models for the kinetics of excited-state processes, assuming errorless time-resolved fluorescence data, can verify whether the model parameters can be determined unambiguously. In this work, we have investigated the identifiability of several uncommon models for time-resolved fluorescence with underlying distributions of rate constants which lead to non-exponential decays. The mathematical functions used here for the description of non-exponential fluorescence decays are the stretched exponential or Kohlrausch function, the Becquerel function, the Förster type energy transfer function, decay functions associated with exponential, Gaussian and uniform distributions of rate constants, a decay function with extreme sub-exponential behavior, the Mittag-Leffler function and Heaviside's function. It is shown that all the models are uniquely identifiable, which means that for each specific model there exists a single parameter set that describes its associated fluorescence δ-response function.