# Relative vs. absolute IC50

The definition of an IC50 can be ambiguous.

The difference between the relative and absolute IC50

This figure (from a longer article on IC50 values)  shows a situation where the IC50 can be defined two ways.

Clearly, a single value cannot summarize such a curve. You'd need at least two values, one to quantify the middle of the curve (the drug's potency) and one to quantify how low it gets (the drug's maximum effect).

The middle of the curve, the IC50, can be ambiguous as is sometimes defined in two alternative ways:

• Relative IC50. This is by far the most common definition, and is usually what people mean by "the IC50". It is the concentration required to bring the curve down to point  half way between the top and bottom plateaus of the curve. This is not the value that corresponds to 50% on the right Y axis.
• Absolute IC50. The concentration that provokes a response halfway between the Blank and the NS value (half way between the two sets of green data points on the graph) is sometimes called the "absolute IC50". This is the value that corresponds to 50% on the right axis. This term is not very standard, and is a bit misleading as there is nothing absolute about an "absolute EC50". I don't think this value is useful, and suggest it not be used.

Note that this definition of absolute IC50 requires that the inhibitor brings the binding or response down to less than 50% (where 0% is defined by a large dose of a standard inhibitor). If the inhibitor only brings the response down to (say) 60%, then the curve never crosses the Y=50% line, so the absolute IC50 is undefined.

The terminology is used inconsistently. The EPA (Environmental Protection Agency of the US) defines log(IC50) to mean what I called the absolute IC50 above, and defines log(EC50) to mean the relative IC50.

When are the relative and absolute IC50s the same?

The relative and absolute IC50 values are the same when the curve descends to a Y value of 0. In many cases, you have reliable control data to define 0. In other cases, 0 is defined in a logical way. For experiments where Y is the rate of cell growth, then if you inhibit cell growth completely, Y will be 0. In these kinds of experiments, the concentration that gives a Y value of 50% of maximum is called the GI50, for Growth Inhibition 50%. The value of the GI50 is identical to the relative or absolute IC50.

Fitting a dose-response curve to find the absolute IC50

I don't find the concept of an absolute IC50 to be useful. But if you do, it is not hard to fit a curve to determine it. Appendix A of this EPA  document, give the needed equation (which I have generalized a bit, so not require that the data already be normalized).

`Fifty=(Top+Baseline)/2`

`Y= Bottom + (Top-Bottom)/(1+10^((LogIC50-X)*HillSlope + log((Top-Bottom)/(Fifty-Bottom)-1))) `

Note the distinction between the parameter Bottom and Baseline. Bottom is the Y value of the bottom plateau of the curve itself. Baseline is the Y value that defines 0% -- maximal inhibition by a standard drug. You'll definitely want to constrain Baseline to be a constant value based on controls. You may also want to constrain Top.

Download the Prism file that fits that equation to make the graph shown above. When fitting data to that equation, don't forget to constrain Baseline and Top to appropriate values determined by controls.  Additionally, this file contains another graph where the data are already normalized to run from 0 to 100%. These data are fit to a simpler equation where Baseline is set to equal zero, and Top is set to equal 100. These are hard wired into the equation, so you don't have to remember to constrain those two parameters to constant values.

An alternative approach for normalized data

Here is an alternative approach you can use if your data are normalized. It does not require entering a user-defined equation.

1. Make sure that your data are normalized to some controls. That means the response at the left end (low concentrations) is near 100%, and the response at higher concentrations is above 0%. If the response plateaus at 0%, then an absolute and relative IC50 are the same, and  you can just fit the usual dose-response curve to find the IC50.
2. At the bottom of the data table, add a new row of data. Enter 50 into each Y column. Leave X blank for this row.
3. Use nonlinear regression to fit the data to the log(inhibitor) vs. response (variable slope) curve.
4. On the first (fit) tab of the nonlinear regression dialog, check the option: " Interpolate unknowns from standard curve." Of course, these data are not a standard curve, and there are unknowns. But this option asks Prism to interpolate the X value of the curve when Y=50.
5. On the Constrain tab, consider constraining Top to have a constant value of 100. If you have used good controls to normalize your data, then you know the top plateau of the curve has to be Y=100, so should tell Prism to use that constraint.
6. The IC50 reported as part of the main results table will be the relative IC50.
7. Look on the additional results page of interpolated results to see the value of X when Y=50. This is the absolute IC50.
8.

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