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

The modeling of excited-state processes in photophysics can conveniently be done within the framework of compartmental analysis. In compartmental anal ysis substantial attention has been devoted to the study of deterministic i dentifiability, which verifies whether it is possible to determine the para meters of the compartmental model from error-free data. In this paper the s imilarity 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 th e true and alternative sets of the system parameters. This allows one to ex plore directly the parameter space for identifiability. Since absolute valu es for the spectral parameters associated with excitation and emission are not available from time-resolved fluorescence experiments, the original sim ilarity transformation approach to the identifiability problem was reformul ated in terms of normalized spectral parameters, which are experimentally a ccessible. It is shown that six decay traces-measured at two coreactant con centrations and three emission wavelengths-are required for the model to be locally identifiable. Two sets of rate constants and associated spectral p arameters 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 para meters also can lead to the unique solution. If the fluorescence decays are independent of the emission wavelength, additional information about the p hotophysical system is necessary for identifiability. (C) 2000 American Ins titute of Physics. [S0021-9606(00)00218-X].