Analysis
Standard curve
Fit a standard curve with a linear or four-parameter model and read unknown concentrations off it, for ELISA, Bradford, BCA and qPCR.
Standards
Unknown samples
ELISA data usually fit better with the four-parameter model on a log axis, because both ends of the curve saturate. Samples marked with an asterisk have signals outside the standard range, so their concentrations are extrapolated.
Formula
y = D + (A − D) ÷ (1 + (x ÷ C)^B)
- A
- the upper asymptote, the signal at infinite concentration
- D
- the lower asymptote, the signal at zero
- C
- the concentration halfway between the asymptotes — the EC50
- B
- the slope of the curve at that midpoint
Worked example
Why a straight line misreads ELISA data
- standards from 0.1 to 30 ng/ml
- signal saturating between 0.12 and 2.05
- At low concentrations the curve is nearly straight and a linear fit works.
- At high concentrations the signal reaches its ceiling and the slope goes to zero.
- A straight line cannot see that saturation and underestimates high-signal samples.
- The four-parameter model captures both ends and gives an R² near one.
Answer four-parameter on a log axis for sigmoidal data, linear within the straight range
Common mistakes
- Extrapolating beyond the standards. A sample reading above the top standard should be diluted and re-run, not read off an extended curve. The tool marks such samples with an asterisk.
- Trusting R² on its own. A sigmoid fitted with a straight line can still give an R² above 0.95 while being badly wrong at both ends; look at the residuals, not just the coefficient.
- Forgetting to subtract the blank. Without it the lower asymptote sits somewhere other than zero and every low concentration comes out too high.
- Forcing the curve through the origin. Background signal in an ELISA is never zero, and forcing it introduces a systematic error.
Frequently asked
Which model should I choose?
If the plotted data form an S with flat ends, the four-parameter model. If you only covered the straight middle section, the linear model is simpler and more stable.
What does the C parameter mean?
The concentration at which the signal sits exactly halfway between the asymptotes. In a competitive assay it is the IC50; in a direct assay it is a measure of the assay\u2019s sensitivity.
How many standards do I need?
At least three for a linear fit, preferably five. The four-parameter model estimates four parameters and needs at least six points; below that the fit is unstable.