A three-parameter langmuir-type model for fitting standard curves of sandwich enzyme immunoassays with special attention to the α-fetoprotein assay

Abstract

In a simplified approach to the reaction kinetics of enzyme-linked immunoassays, a Langmuir-type equation y = [ux/(b + x)] + c was derived. This model proved to be superior to logit-log and semilog models in the curve-fitting of standard curves. An assay for a-fetoprotein developed in our laboratory with a sensitivity of 2 g/liter and a between-day coefficient of variation of about 15% was used for comparison of the different models. The proposed model has the advantage that it is based on the law of mass action and that blank determinations can be included in the calculation of the curves without giving a disproportionate bias. o 1987 Academic Press, Inc.

I-STOD: a new standardization method for analysing indirect-ELISA results of a schistosomiasis field study

“…The OD-C (optical density and concentration) linear model and the log-log model also lack a theoretical foundation (Plikaytis et al 2000). The 3-parameter Langmuir-type model is based on a sandwich-ELISA used to detect the antigen concentration in serum (Kortlandt et al 1987), but no further application has been reported. The 4-parameter logistic-log model, which was first largely applied in radioimmunoassays to quantify antigen concentration (Finney, 1976) and then replaced by ELISA, is currently the most popular assay for protein, and sometimes for antibody quantification when a corresponding standard reference is available.…”

“…To evaluate the fitness of the I-STOD model to experimental data of SR, we compared it with 5 other methods, including the 3-parameter Langmuir-type model (Kortlandt et al 1987), the OD-C linear model (Vestergaard et al 2002), the semi-log model (Karpinski et al 1987), the log-log model (Plikaytis et al 1991; Okuma et al 2005), and the 4-parameter logistic-log model (Plikaytis et al 1991). In the following equations, OD is the optical density value, C stands for the antibody concentration, and b 0 , b 1 , b 2 , and b 3 are parameters to be determined by the SRs on the sample plates.I-STOD model.…”

“…By using an appropriate serum (even if the antibody concentration is unknown) as the reference on each multi-well plate to construct the I-STOD calibration curve, results on different plates can be standardized and compared. To evaluate the fitness of the I-STOD model to experimental data, we compared it with 5 other methods available for ELISA standardization to define protein concentration: (1) 3-parameter Langmuir-type (3pL) (Kortlandt et al 1987), (2) OD-C (concentration) (Vestergaard et al 2002), (3) semi-log (Karpinski et al 1987), (4) log-log (Plikaytis et al 1991; Okuma et al 2005), and (5) 4-parameter logistic-log (4pLL) (Plikaytis et al 1991), by the adjusted R 2 values of the calibration curves. Then, the CVs (coefficient of variation) of results between plates were assessed before and after implementation of the I-STOD standardization method.…”

Comparisons of standard curve-fitting methods to quantitate Neisseria meningitidis group A polysaccharide antibody levels by enzyme-linked immunosorbent assay

“…Several mathematical models have been developed to describe standard or calibration curves for use in quantitative radioimmunoassays (24,25) and ELISAs (6,14,15,19). The method used to form the calibration curve dictates the working range of the assay and the overall accuracy of calculating concentrations of antibody in patients (24)(25)(26).…”

“…There is no consensus on which curve-fitting method to use routinely for these immunoassays. However, some methods describe the data with greater precision than others (6,14,15). In many reports, the method used for determination of antibody levels is not given, so judgments on its accuracy cannot be made.…”