ELISA Curve Fitter

Four-Parameter vs Five-Parameter Logistic Models

The 4PL (four-parameter logistic) model describes a symmetric sigmoidal curve: y = D + (A−D) / [1 + (x/C)^B]. The four parameters are the minimum asymptote (A), Hill slope (B), inflection point or EC50 (C), and maximum asymptote (D). This is sufficient for most well-behaved sandwich ELISAs.

The 5PL model adds an asymmetry parameter (E): y = D + (A−D) / [1 + (x/C)^B]^E. When E ≠ 1, the curve approaches its upper and lower plateaus at different rates — a pattern common in competitive ELISAs and multiplex assays. In practice, 5PL fitting can substantially reduce residual error for asymmetric dose-response curves, particularly at the extremes of the standard range.

Why Weighting Matters

In an unweighted fit, all data points contribute equally to the sum of squared residuals. But ELISA data is heteroscedastic — the variance of OD readings increases with signal magnitude. Without weighting, high-concentration standards dominate the fit, sacrificing accuracy at the low end where sensitivity matters most.

1/Y weighting (inverse response weighting) gives each point influence proportional to 1/OD, restoring balance. 1/$\text{Y}^{2}$ provides even stronger correction, which is preferred when low-concentration precision is critical (e.g., biomarker detection near the limit of quantification).

Standard Curve Quality Control

A good standard curve is the foundation of accurate ELISA quantification. Key QC metrics include:

Back-calculated recovery: For each standard, the fitted curve is used to back-calculate its concentration from the measured OD. Recovery should be 80-120%. Points outside this range indicate a poor fit or a bad standard preparation.

%CV of replicates: The coefficient of variation between replicate ODs at each standard level should be < 20%. High CV suggests pipetting error, incomplete mixing, or plate inconsistency.