KINETICS AND IDENTIFIABILITY OF INTRAMOLECULAR 2-STATE EXCITED-STATE PROCESSES WITH ADDED QUENCHER - GLOBAL COMPARTMENTAL ANALYSIS OF THE FLUORESCENCE DECAY SURFACE

Abstract

The fluorescence decay analysis of intramolecular two-state excited-state processes with added quencher is discussed in terms of compartments. The kinetics specifying the two excited-state species concentrations are derived. The fluorescence decay surface is expressed in terms of the system parameters, namely the rate constants and the spectroscopic parameters b1 and c1. b1 and c1 are respectively the relative absorbance and the normalized spectral emission weighting factor of species 1. The report investigates the prerequisites for obtaining the unique set of system parameters. The results of this identifiability study indicate that the following conditions have to be satisfied in order to make an intramolecular two-state excited-state system with added quencher identifiable. First, the fluorescence decay surface must include at least one set of decay traces measured for a minimum of three different quencher concentrations at the same excitation/emission wavelength setting. One of the quencher concentrations used may be equal to zero. Second, the rate constants of quenching of the two excited species must be different. Third, at least one system parameter, which is not a rate constant of quenching, must be known. Under these conditions, four sets of system parameters are mathematically possible. If the known system parameter is a rate constant, decay traces of a suitable model compound measured at a minimum of two quencher concentrations must be included in the analysis in order to obtain the unique set of values for the rate constants. The unique set of (b1,c1) values can be recovered by including decay curves at a minimum of two quencher concentrations and at an additional excitation wavelength with a different b1, or at another emission wavelength with a different c1. If the known system parameter is a b1 value different from zero and unity, the fluorescence decay surface must include at least nine decay traces measured at four emission wavelengths with different c1 (corresponding to at least three quencher concentrations at the first emission wavelength and at least two quencher concentrations at the other three emission wavelengths), to uniquely determine the set of system parameters. If the known system parameter is a c1 value different from zero and one, at least four excitation wavelengths with different b1 are necessary to obtain the unique set of system parameters. The conclusions of the identifiability study are confirmed by the results from the global compartmental analysis of computer-generated fluorescence decay traces.