Modeling of immunosensors under nonequilibrium conditions. I. Mathematic modeling of performance characteristics

Immunosensors for the detection of small analytes that use analyte-enzyme conjugates as signal generators require special attention if operated under nonequilibrium conditions. If the size of the analyte and the analyte-enzyme conjugate differ substantially, the two antigens do not diffuse at the same rate. This can cause time-dependent shifts in the sensitivity of competitive immunoassays. Therefore, immunosensors operating at short incubation times require precise timing that meets closely the specifications for which the sensors were calibrated. As an example, we have analyzed kinetic binding curves for the quantitative determination of progesterone with an immobilized monoclonal antibody and a conjugate between horseradish peroxidase and progesterone as signal generator. Mathematical paradigms have been developed to simulate the diffusion, antigen-antibody complex formation, and competitive binding processes in this analytical system. Dose-response curves obtained under nonequilibrium conditions can vary substantially from those obtained at equilibrium of antigen-antibody interaction. The degree of this variation depends on the performance characteristics of the major components of the immunosensor. The developed mathematical solutions reflect experimental results and can be used to model optimal conditions for immunosensors operating under nonequilibrium conditions. In this paper (Part I), we report on the mathematical modeling of the interaction between analyte, analyte-enzyme conjugate, and an immobilized antibody. In Part II (W. Schramm and S.-H. Paek (1991) Anal. Biochem. 196), we present experimental results and compare them with the theoretical models.