Compartmental modeling and identifiability analysis in photophysics: Review

Abstract

The main objective of this review is to show how the concepts of compartmental modeling can be introduced and applied in photophysics. The term "compartment" in a photophysical context is defined as a subsystem composed of a distinct type of species that acts kinetically in a unique way. Compartments can be divided into groundstate and excited-state compartments, depending on the state of the composing species. In photophysics, a compartmental system is perturbed by a light pulse (photo-excitation), and its dynamics is followed via fluorescence within the time range from picoseconds to several hundred nanoseconds. In this review, we present the fluorescence delta-response functions for compartmental systems consisting of one excited-state compartment, two reversibly interconnected excited-state compartments, and their corresponding ground-state compartments. In deterministic identifiability, one investigates whether the parameters of a specific model can be uniquely defined, assuming perfect time-resolved fluorescence data. The identifiability is presented for the model with one excited-state compartment and three models of reversible intermolecular two-state excited-state processes in isotropic environments: (i) without external quencher, (ii) with added quencher, and (iii) with coupled species-dependent rotational diffusion described by Brownian reorientation. The parameters that have to be identified are time-invariant rate constants and parameters related to excitation and emission. The conditions under which the relevant parameters can be identified are discussed. For all models, the explicit relationships between the true and alternative model parameters are shown.