Dose-response Curves

Dose-response analysis fits a mathematical model to data where a measured response changes as a function of dose or concentration. The goal is typically to estimate the IC50 or EC50 — the dose at which the response is halfway between its minimum and maximum — and to visualize the full sigmoidal relationship.

Data format

Your dataset should have two columns:

• A dose or concentration column — numeric values, typically in molar units, nanomolar, micromolar, or similar. Log₁₀ transformation is handled automatically when the dose range spans multiple orders of magnitude.
• A response column — the measured outcome at each dose. This might be cell viability, percent inhibition, fluorescence intensity, or any other continuous measure.

Each row should represent one measurement. Multiple replicates at the same dose are supported — Licklider will use all replicates in the fit.

Requesting the analysis

Describe the analysis in the Chat:

• "Fit a dose-response curve"
• "Calculate the IC50"
• "Show a 4PL fit"
• "Plot inhibition vs concentration and fit a curve"

Licklider will identify the dose and response columns, apply a log₁₀ transformation to the dose axis when appropriate, and fit the selected model.

Choosing a model

Licklider supports three sigmoidal models:

4PL (four-parameter logistic)

Estimates the bottom asymptote, top asymptote, IC50, and Hill slope independently. Use this when the minimum and maximum response are not known in advance.

3PL (three-parameter logistic)

The bottom asymptote is fixed at zero. Use this when the baseline response is known to be zero — for example, when the response is a percentage inhibition starting from 0%.

Hill model

Both the bottom (0%) and top (100%) are fixed. Use this when the response is expressed as a percentage and the full range is defined.

If no model is specified, Licklider will ask which one to use. For more detail on the models → see Non-linear Regression and IC50/4PL.

Reading the results

The results panel shows:

• IC50 (or EC50) — the estimated dose at which the response is halfway between the bottom and top, reported in the original dose units
• Hill slope — the steepness of the sigmoidal transition. A slope of 1 is typical for simple binding; slopes above 1 suggest cooperativity
• Bottom and top asymptotes — the estimated minimum and maximum response
• R² and RMSE — overall fit quality
• 95% confidence intervals for each parameter
• Convergence status — whether the fitting algorithm reached a stable solution

The figure

The figure shows the individual data points and the fitted curve overlaid. The x-axis uses a log₁₀ scale when the dose spans multiple orders of magnitude. The IC50 value appears in the figure annotation.

When the fit does not converge

Non-convergence usually means one of the following:

• The dose range does not span the full sigmoidal transition — there are no measurements below the lower asymptote or above the upper
• The data is too noisy for the model to find a stable solution
• The model is too complex for the data (try 3PL or Hill instead of 4PL)

If the Hill slope is very large or the IC50 falls far outside the measured dose range, the estimate may be unreliable even if the fit converges. Wide confidence intervals are the signal to interpret the estimate with caution.

Comparing IC50 values between groups

Licklider fits dose-response curves but does not currently support a formal statistical comparison of IC50 values between groups. To compare curves visually, run separate fits for each group and request them in the same figure.

What this page does not cover

• Model details and parameter interpretation → see Non-linear Regression and IC50/4PL