Dose–Response

Shape a response curve and explore what your concentration range and noisy readings can reveal.

Shape, range and uncertainty

Set a known response curve, then sample it. Explore how a limited concentration range or noisy readings can hide the curve you prescribed.

Swipe the graph horizontally to see the full concentration range.

Known curve (dashed outside sampling)Synthetic readings

C5010 nM

Shifts the curve along the concentration axis.

Hill slope magnitude1

Controls steepness, not a count of binding sites.

Lower plateau10 units

Upper plateau90 units

Lowest sampled concentration100 pM

Highest sampled concentration1 µM

Noise standard deviation4 response units

Independent normal errors; readings are not clipped to either plateau.

Inspect concentration10 nM

Highlights three replicate readings at one concentration.

50 unitsresponse at the prescribed C50

47.5 unitsmean of three synthetic readings at 10 nM

50 unitsnoise-free response at that concentration

The sampled range covers the midpoint and approaches both plateaus.

This is a coverage check on the known model, not a statistical assessment. Noise, outliers, controls and model suitability still matter when estimating a real curve.

This is a concentration–response simulation with prescribed parameters; no curve is fitted. C50 means halfway between the two plateaus (10 and 90), not necessarily a reading of 50 or 50% of a control. The Hill magnitude controls the shape of this empirical model and does not by itself establish cooperativity. Seed 23; nine log-spaced concentrations, three readings each.

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Quick reference

Four parameters, different roles

A four-parameter logistic curve has two plateaus, a midpoint concentration and a slope. Here C50 is the concentration halfway between the two response plateaus. A smaller C50 shifts the response to lower concentrations without necessarily changing the maximum response. This empirical curve does not identify the biological mechanism.

The range determines what is visible

Logarithmic concentration spacing covers several orders of magnitude. Sampling around the transition helps locate it; sampling near both plateaus helps distinguish the response limits from slope and midpoint. A midpoint outside the tested range requires extrapolation. The tool’s 10% plateau-coverage indicator is an illustrative threshold, not an assay acceptance rule.

Known parameters are not fitted estimates

The line is generated from the settings you choose. Dots are synthetic readings with reproducible, independent normal errors. No regression or confidence interval is calculated. In an experiment, parameters must be estimated from observations, with appropriate controls, replication, uncertainty and checks that the model describes the assay.

Check your understanding Optional

A curve has response plateaus at 20 and 60 units. What is its response at the relative C50?

30 units, half of the upper plateau.40 units, halfway between the plateaus.50 units, by definition.

At the bench

Apply the distinction between observations and estimates when inspecting and fitting your own concentration–response data.

Open Assay Analyser

Sources and model notes

These interactive examples explain selected relationships using the assumptions shown beside their controls. Calculated quantities and illustrative inputs are identified in each tool; use the linked Drybench app to work with your own data.

Wang et al. · Dose-response curve fitting

Primary research describing the four-parameter Hill model and controlled simulations with incomplete curves and noise. This tool uses the equation, not the paper’s fitting algorithm.

NCATS / NIH · Assay Operations for SAR Support

Assay Guidance Manual discussion of relative versus absolute IC50, concentration–response models and interpretation of fitted parameters.