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EC50 and IC50 curve fitting without writing code

How to fit a dose-response curve, which model to choose, and the mistakes that produce a confident but wrong EC50.

The number is easy to produce and easy to get wrong. The model matters more than most people assume.

Choose the model before you look at the fit

Four-parameter logistic (4PL) is the default for dose-response work. It fits bottom, top, EC50 and Hill slope. Use it unless you have a reason not to.

Three-parameter logistic (3PL) fixes the Hill slope at 1. Use it when your data cannot constrain the slope, typically few concentrations or a noisy plateau. A 4PL fitted to thin data will return a slope of 6 and an EC50 you should not trust.

Michaelis-Menten is enzyme kinetics, not dose-response. Different question.

Biphasic is for when one sigmoid genuinely does not describe the data, such as a compound acting on two receptor populations. Do not reach for it because the 4PL residuals look untidy.

Where the number goes wrong

No plateau. If your highest concentrations have not reached a top, the curve is extrapolating. Extend the range rather than reporting it.

Fitting on a linear x-axis. Log-transform concentrations before fitting.

No confidence interval. A wide interval is information, not an embarrassment.

Comparing across plates without normalising. Plate-to-plate variation will exceed the difference you are looking for.

In Plotara

Eleven curve-fitting models including 4PL, 3PL Hill, Michaelis-Menten, one- and two-phase decay, Gompertz and biphasic dose-response, with confidence intervals on fitted parameters and exportable Python.

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