Mathematical analysis of sensors based on affinity interactions between competitive receptor-protein pairs

Affinity sensors with detection principle of competitive displacement of a responsive protein from an immobilised receptor by an analyte were subject to mathematical analysis. The model considered two competing binding reactions between the analyte and the responsive protein for the immobilised receptor in the solid phase. A cubic algebraic equation generated from the analysis was solved to get theoretical calibration curves for the sensor relating the signal generated, which is the bulk concentration of the responsive protein detected in solution, to the analyte concentration. The simulated results indicated several important system variables to consider when optimising the sensor's performance. They are the concentration of the responsive protein initially loaded, the density of the immobilised receptor, and the relative binding strength of both the analyte and the responsive protein toward the receptor. To test this model, experiments were carried out with a hypothetical sensor system, using bovine chymosin as the responsive protein, pepstatin-agarose as the immobilised receptor, and pepsin as the analyte. The model in general can describe the behavior of this type of affinity sensor reasonably well. From kinetic study of chymosin displacement in the model system, the effect of binding strength between responsive protein and receptor on the response of the sensor was also discussed.