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 What are dose-response curves?

## What are dose-response curves?

Dose-response curves can be used to plot the results of many kinds of experiments. The X axis plots concentration (or dose) of a drug or hormone. The Y axis plots response, which could be almost any measure of biological function.

The term “dose” is often used loosely. In its strictest sense, the term only applies to experiments performed with animals or people, where you administer various doses of drug. You don't know the actual concentration of drug at its site of action—you only know the total dose that you administered. However, the term “dose-response curve” is also used more loosely to describe in vitro experiments where you apply known concentrations of drugs. The term “concentration-response curve” is a more precise label for the results of these types of experiments. The term “dose-response curve” is occasionally used even more loosely to refer to experiments where you vary levels of some other variable, such as temperature or voltage.

## X values are logarithm of doses or concentrations

Dose-response experiments typically use around 5-10 doses of agonist, equally spaced on a logarithmic scale. For example, doses might be 1, 3, 10, 30, 100, 300, 1000, 3000, and 10000 nM. When converted to logarithms (and rounded a bit), these values are equally spaced: 0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0.

All the dose-response curves built in to Prism are provided in two forms. One form assumes that X is the logarithm of concentration or the logarithm of dose. The other form assumes X is concentration or dose. Make sure you pick the form of the equation to match the data you are analyzing.

The uncertainty in the value of the EC50 or IC50 is usually quite asymmetrical. So be sure to choose the profile likelihood method for computing confidence intervals that produces asymmetrical intervals.

## Y values are responses

In a dose-response curve, the Y values are responses. For example, the response might be enzyme activity, accumulation of an intracellular second messenger, membrane potential, secretion of a hormone, change in heart rate, or contraction of a muscle.

You can transform the Y values to new units by multiplying or dividing by a constant. Use Prism's Transform analysis for this. Transforming to new units will not fundamentally change the results of a curve fit.

In some cases, the transform from experimentally observed units to practical units is nonlinear. For example, a nonlinear transform is needed to convert the ratio of two fluorescence values  to concentrations of Ca++. Which Y values should be used when fitting a dose-response curve? Nonlinear regression assumes that all scatter around the curve is Gaussian, so you want to use whatever units make that assumption most true. In many cases, this may be hard to know.