Mathematical modeling of immunochromatographic test systems in a competitive format: Analytical and numerical approaches

Abstract

The wide application of immunochromatographic assays in modern diagnostic practice makes their theoretical description relevant, which makes it possible to predict the influence of various factors on assay characteristics. We propose a new analytical model of the immunochromatographic assay in a competitive format for non-equilibrium conditions, a distinctive feature of which is the approximation of an irreversible reaction that allows us to obtain a symbolic solution of differential equations describing the system. We show that due to the rapid nature of the immunochromatographic assay, this approximation is satisfied with a high accuracy within the actual range of kinetic dissociation constants characteristic of immune interactions. The criterion for the applicability of such a model is that the kinetic dissociation constant of the immune complex is less than 10−3 s-1. Using the developed model, the requirements for immunoreagents were established, which are limiting factors of the assay. The influence of reagent concentrations, association–dissociation constants, and durations of assay stages on the concentration of the detectable complex in the analytical zone of a test strip were estimated. The obtained results from analytical modeling were confirmed with numerical simulation using the COPASI software package and experimental studies.