EC50

The term half maximal effective concentration (EC50) refers to the concentration of a drug, antibody or toxicant which induces a response halfway between the baseline and maximum after some specified exposure time. It is commonly used as a measure of drug's potency.

The EC50 of a graded dose response curve therefore represents the concentration of a compound where 50% of its maximal effect is observed. The EC50 of a quantal dose response curve represents the concentration of a compound where 50% of the population exhibit a response, after a specified exposure duration.

It is also related to IC50 which is a measure of a compound's inhibition (50% inhibition). For competition binding assays and functional antagonist assays IC50 is the most common summary measure of the dose-response curve. For agonist/stimulator assays the most common summary measure is the EC50.

Responses to concentration typically follow a sigmoidal curve, increasing rapidly over a relatively small change in concentration. The inflection point at which the increase in effectiveness with increasing concentration begins to slow is the EC50. This can be determined mathematically by derivation of the best-fit line. While relying on a graph for estimation is more convenient, it yields less precise and less accurate results.

Equation
Many different equations can be used to derive an EC50. One possible function is:

$$Y = Bottom + \frac{Top - Bottom}{1 + (\frac{X}{EC_{50}})^{\mathrm{Hill coefficient}} }$$

where Y is the observed value, Bottom is the lowest observed value, Top is the highest observed value, and the Hill coefficient gives the largest absolute value of the slope of the curve.

Limitations
The effects of a stressor or drug generally depend on the exposure time. Therefore, the EC50 (and similar statistics) will be a function of exposure time. The exact shape of this time function will depend upon the stressor (e.g., the specific toxicant), its mechanism of action, the organism exposed, et cetera. This time dependency hampers the comparison of potency or toxicity between compounds and between different organisms.