Kinetics and identifiability of intramolecular 2-state excited-state processes - Global compartmental analysis of the fluorescence decay surface

Abstract

This report discusses the fluorescence decay analysis of intramolecular two-state excited-state processes in terms of compartments. The kinetic equations specifying the fluorescence decay and the time course of the two excited-state species concentrations are derived in terms of the rate constants k(ij), 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 structural identifiability study demonstrates that at least three parameters of the intramolecular two-state excited-state process must be known in order to recover the relevant information. These three parameters can be (a) two rate constants and one spectroscopic parameter [(1) 2 k(ij) and 1 b1, (2) 2 k(ij) and 1 c1]; (by) one rate constant and two spectroscopic parameters [(3) 1 k(ij), 1 b1, and 1 c1, (4) 1 k(ij) and 2 b1, (5) 1 k(ij) and 2 c1]; and (c) three spectroscopic parameters [(6) 2 b1 and 1 c1, (7) 1 b1 and 2 c1, (8) 3 b1, (9) 3 c1]. The conditions (3), (6), and (7) require that the known (b1,c1) values do not belong to a decay trace where the preexponentials alpha-1,alpha-2 have the same absolute values but opposite signs (alpha-1/alpha-2 = -1) corresponding to (b1,c1) = (1,0) or (0,1). Conditions (6) to (9) indicate that spectroscopic information alone can suffice for the system to be identifiable. Finally, the unknown parameters are estimated from computer-generated fluorescence decay traces. The results confirm the conclusions of the identifiability study.