4PL Dose-Response Curve Fitter
Fit IC50 and EC50 from concentration-response data with a four-parameter logistic model.
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What it does
The 4PL dose-response fitter turns a table of concentration and response measurements into a smooth sigmoidal curve and reports the half-maximal concentration, the Hill slope, and the top and bottom plateaus. It is aimed at assay developers, pharmacologists, and molecular biologists who quantify how a compound, antibody, or stimulus changes a measured signal across a dose range. Paste your data, see the fit and the IC50 or EC50 instantly, and invert the curve to predict the concentration that yields any response you choose, all without leaving the browser.
How it works
The tool fits the four-parameter logistic equation y = bottom + (top - bottom) / (1 + (x / EC50) ^ hill), where x is concentration on a log10 scale. Top is the response at zero dose and bottom is the response at infinite dose, the two asymptotes the curve flattens toward. EC50 (or IC50 for an inhibitor) is the concentration at the midpoint between them, and the Hill slope controls how steep the transition is; a slope of -1 or +1 gives a symmetric sigmoidal curve. The fit is found by nonlinear least squares over the four parameters, and the inverse equation is then used by the solver so you can enter a response and recover its concentration.
Worked example
Take the built-in sample of ten points spanning 0.1 to 3000 nM with response falling from 98.2 to 3.2 percent. Fitting gives the upper response plateau near 102.6 and the lower near 2.5, an IC50 of about 5.45 nM, a Hill slope near -0.80, and R2 of 0.9999, a very tight fit. If you then ask for the concentration at 50 percent response, the solver inverts the curve and returns a value close to the IC50, about 5.5 nM. Doubling the span or removing the extreme points barely moves the estimate, which shows the data comfortably covers both plateaus and the midpoint is well sampled.
When to use it
Use this fitter to summarize a titration as a single potency value, compare compounds by their IC50 or EC50, or convert a target inhibition percentage into the dose you should use. It is also handy for checking whether a curve is well behaved before reporting it. Watch three pitfalls: the fit needs points on both the top and bottom plateaus, so a curve that never reaches a flat region will give an unreliable midpoint; concentrations must be spaced geometrically, not linearly, because the model is logarithmic; and IC50 refers to inhibition while EC50 refers to activation, so label them correctly.
FAQ
- What is a 4PL model and when do I use it?
- The four-parameter logistic (4PL) model describes a sigmoidal dose-response curve with four terms: top and bottom asymptotes, the midpoint concentration EC50 or IC50, and the Hill slope. It is the standard fit for bioassays, ELISA, and inhibitor titrations because most response data plateau at high and low dose. You use it whenever response rises or falls steeply across a concentration range and you need a single potency value.
- What is the difference between IC50 and EC50?
- Both are the midpoint concentration where response is halfway between top and bottom, but the label depends on direction. IC50 is used when the compound inhibits the signal, so response falls as concentration rises, as in this tool's example. EC50 is used when the compound activates or stimulates the signal, so response rises with concentration. They are the same maths, just opposite signs of the Hill slope.
- Why must concentrations be spaced on a log scale?
- The 4PL equation is fitted on log10 concentration, so the curve is symmetric in log space. If you space doses linearly, most points pile up at one end and the midpoint is poorly sampled, giving a noisy or biased EC50. Space them geometrically, for example 0.1, 1, 10, 100 nM, so each decade contributes evenly and the transition region around the IC50 is well covered.
- How many points do I need and what does R2 tell me?
- You need at least four points, but a reliable fit wants eight or more spread across both plateaus and the midpoint. R2 measures how well the curve explains the data; values above 0.95 indicate a good fit, while a low R2 means the model or your data is off, perhaps because concentrations were not log-spaced or a plateau is missing. Use R2 as a first sanity check before trusting the IC50.