Fig. 2

Relative precision of absolute concentration of analyte assuming \(5.0\times 10^{-10}\) M antibody concentration while the surrogate \(K_d\) of antibodies are varied. X-axis is the concentration of couplexes, while Y-axis represents the true \(K_d\) value. The color coded values are the logarithm of the ratio of the calculated and real \(a_0\). The upper graphs show the low side while the bottom graph represent the high side of the curve, \(\log _{10}(2)=0.3\), which indicates the two-fold difference, was taken as an precision threshold. Based on this analysis, it is evident that the choice of a surrogate \(K_d\) is flexible, provided it exceeds the saturation concentration of the given antibody. When using a surrogate \(K_d\) of 10 pM or lower (also a safe default is 50 pM), the low-side exhibits remarkable precision, particularly when the true \(K_d\) falls below 200 pM. It’s noteworthy that the peak region, situated at the right edge of the graph and neighbored by a mathematically inapplicable white area, maintains precision akin to the entire curve on the low side or only nuancely influenced by the couplex concentration on the high side. Therefore, using the the model of \(p = (b_{01}, b_{02}, \xi )\) even the peak region attains high precision using a proper surrogate \(K_d\), however to avoid \(K_d\) above the threshold it is recommended conducting IT experiments to ensure high precision.