Why does fitting data to the allosteric EC50 shift model sometimes lead to 'ambiguous' results?
The allosteric EC50 shift model described by Christopoulos and Kenakin (Pharmacol Rev, 54: 323-374, 2002) is built in to Prism 5. It fits a family of curves, to determine the EC50 of the control curve as well as two parameters (Kb and alpha) that describe the allosteric interaction of a modulator.
We know of two reasons why it won't converge on a reasonable fit:
Incorrect initial value of logKb
The equation built in to Prism (up to 5.03 and 5.0c) has the wrong initial value for logKb. The rule should be that the initial value equals
1*log(mean of column titles)
Instead, it is programmed in as
-1*log(mean of column titles)
There are two ways to fix this. One is to clone the equation, and make your own version with the correct initial value. The other is to override the initial value in the initial value tab of nonlinear regression.
Must have at least three data sets
The description in the Prism help neglects one important "detail": You must have at least three curves, and preferably more.
If you only have one control curve and one curve in the presence of modulator, the values of Kb and alpha are simply not defined. An infinite combination of Kb's and alpha's can give you the same shift. The fit will be ambiguous.
For the fit to actually converge and not be ambiguous, it is necessary to define the value of the allosteric cooperativity parameter, alpha. This requires enough curves such that the progressive shifts of the agonist concentration-response curve starts to approach a limit.