ELISA Data Analysis With Four-Parameter Curve Fit

ELISA Data Analysis With Four-Parameter Curve Fit
Author Affiliation: 
PBL Assay Science


Enzyme-linked immunosorbent assays (ELISA) are specific and highly sensitive procedures for identifying and quantifying analytes such as proteins in samples. This assay is based on the binding of a target molecule (analyte/antigen) to antibodies which recognize the compound. The presence of an antigen-antibody complex is detected using a secondary enzyme-conjugated antibody. Detection is obtained by addition of a substrate which yields a measurable product. Enzyme-linked immunosorbent assays are routinely used in many areas of biological research. The determination of the analyte concentration relies upon construction of a calibration curve. The standard curve is prepared by performing a dilution series of a known concentration of the analyte across a range of concentrations near the expected unknown concentration. The calibration curves are then used to calculate the concentration of an unknown sample.

For most analyses, a plot of response versus concentration will create a linear relationship, at least within a certain range of concentrations, and can be analyzed with linear regression. However, for those calibration plots which are sigmoid (a curve having an “S” shape), performing a linear fit can lead to errors in estimating sample concentration These inaccuracies are most significant at the extremes of the standard curve, most often in the low end but sometimes in the high end as well. In this study we compare the results of using linear fit and 4-parameter analysis on ELISA data and report our findings.



Standard curves were prepared using kits from two different ELISA products, VeriKine Mouse Interferon-Beta (Cat. No. 42400) and VeriKine Human Interferon-Alpha (Cat. No. 41100). The assays were performed following protocols for each product. After completion of each assay, plates were read at OD 450nm using Vmax Kinetic Plate Reader (Molecular Devices Corp., CA, USA). Triplicate measurements were performed for each data set. Data was analyzed using SoftMax Pro software (Molecular Devices Corp., CA, USA).



The Mean of the ODs @ 450 nm, %CV of the ODs @ 450 nm, and the Standard Deviation between the ODs @ 450 nm for each data point of the standard curve was calculated. the concentration was plotted on the X-axis. the Mean OD@ 450 nm was plotted on the Y-axis


Standard curves were prepared using Mouse IFN-β ELISA kit and Human IFN-α ELISA kit. For each data set, two standard curves were created. One standard curve was plotted using a 4-parameter fit algorithm and the second one generated using linear fit analysis. Mean OD@450 nm for all data points vs. the actual concentration in pg/ml corresponding to that data point were plotted.

Figures 1A (L) and 1B (R): Standard curves for mouse IFN-β ELISA with 4-parameter fit (1A) and linear fit (1B).


Figures 2A (L) and 2B (R): Shows the same data set plotted with four-parameter curve fit.


Comparing the backfitted interferon concentration values, four -parameter fit versus linear analysis, reveals disparities between the two methods. The largest discrepancies are noted at the lower concentrations. This trend is observed for both the Mouse IFN Beta and Human Alpha products (data not shown). Overall, the estimated interferon concentration values more closely match the actual concentration when applying a four-parameter fit (Table 1). Significant differences are seen for Mouse IFN beta at 15.625 pg/ml (~278%).


Table 1: The backfitted concentrations calculated with 4-parameter fit and linear fit for points on the standard curve for mouse IFN-β ELISA

    4-Parameter fit Linear fit
Actual Concentration (pg/ml) Mean OD @ 450 nm Backfit Concentration (pg/ml) % Difference: Backfit and Actual Concentration Backfit Concentration (pg/ml) % Difference: Backfit and Actual Concentration
15.625 0.167 14.75 2.48 -27.05 278.84
31.25 0.268 35.86 14.75 6.59 78.91
62.5 0.374 58.72 6.05 41.90 32.96
125 0.645 120.42 3.66 132.16 5.73
250 1.186 258.74 3.50 312.26 24.90
500 1.943 494.51 1.10 564.52 12.90
1000 3.112 1001.53 0.15 954.01 4.60

 Different methodologies are applied to mathematically fit data generated from ELISA experiments. To force an assay to fit the best straight line when the response is nonlinear will certainly introduce inaccuracy into your results. Thus, we recommend using four-parameter fit algorithm for plotting standard curves prepared using ELISA kits manufactured by PBL.

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