The ECF Formula
When your dose-response curve runs from 0 to 100%, the ECF (the concentration that produces F% of the maximum response) can be computed from the EC50 and the Hill slope (h) using this formula:
For example, to compute the EC90 with an EC50 of 10 nM and a Hill slope of 1.0:
With a steeper Hill slope (h = 2), the EC90 would be much closer to the EC50 because the curve is steeper.
Built-In Prism Equations
Prism provides two built-in methods to fit for any ECF directly, without manual calculation:
Dose Response - Special - ECF
A sigmoidal dose-response equation that directly returns an ECF value as one of the fitted parameters. You specify the F value (e.g., 90 for EC90) and Prism fits that concentration directly.
ICanything
Available under Dose Response - Special. Lets you specify any inhibition fraction (e.g., IC90 for 90% inhibition) and returns the corresponding concentration as a fitted parameter.
Incomplete Curves
The ECF formula above applies only when the curve runs from a baseline of 0 to a maximum of 100%. If your curve does not reach a clear plateau, you need to be more careful:
- If the top plateau is not clear from the data, Prism cannot reliably determine the EC90 (or any high ECF) because it depends heavily on the fitted top.
- Prism can still fit the EC50 from the inflection point, but the EC90 estimate will have very wide confidence intervals when the top is not well-defined.
- Consider constraining the top to 100% if you know from the biology that the maximum response is 100%.
Why EC100 Cannot Be Determined
The sigmoidal dose-response equation is asymptotic. It approaches 100% response as the dose approaches infinity, but it never actually reaches 100%. Plugging F = 100 into the ECF formula gives a division by zero (100 - 100 = 0). Therefore, EC100 is mathematically undefined for a standard sigmoidal curve and cannot be determined from curve fitting.
Quick Reference: Common ECF Values (Hill slope = 1)
| ECF | Ratio to EC50 |
|---|---|
| EC10 | EC50 × 0.111 |
| EC20 | EC50 × 0.25 |
| EC50 | EC50 × 1.0 |
| EC80 | EC50 × 4.0 |
| EC90 | EC50 × 9.0 |
| EC99 | EC50 × 99.0 |
Ratios change substantially with Hill slopes other than 1. Steeper slopes bring ECF values closer to EC50.