Identifiability of the Model of the Intermolecular Excited-State Proton Exchange Reaction in the Presence of pH Buffer

Abstract

In this report, we describe the fluorescence kinetics and the deterministic identifiability of the intermolecular excited-state proton dissociation reaction and how the addition of pH buffer affects both. In the absence of buffer, the time-resolved fluorescence decays as a biexponential function with decay times that are invariant with pH. The information that the proton association rate in the excited state is negligible in combination with fluorescence decay traces measured at different pH, excitation, or emission wavelengths does not provide enough useful information for the unique determination of the rate constants and the spectral parameters related to absorption and emission. Hence, the model of intermolecular excited-state proton dissociation in the absence of pH buffer is not identifiable. When a pH buffer is added to this photophysical system, the proton exchange becomes reversible and the decay times now are a function of pH and buffer concentration. The deterministic identifiability analysis shows that for the unique determination of all rate constants one should collect a minimum of three fluorescence decays characterized by at least two different pH and at least two different nonzero buffer concentrations. In addition to these three traces, minimally one biexponential fluorescence trace corresponding to the pH probe in the absence of buffer has to be recorded. The requirement that at least two of these traces should be collected at the same pH, excitation, and emission wavelengths leads to unique identifiability.