PHARM/PCS V5 · Procedure 17 Receptor Pharmacology
pA2 Analysis III: Constrained Plot
Estimate pA2 with the Schild slope fixed at −1, the tighter estimate to use once simple competitive antagonism is confirmed.
What it computes
A variant of the Schild plot (Procedure 15) in which the regression line is constrained to have slope = −1, as theory requires for a true competitive antagonist. Only the intercept (= pA2) is estimated, with its standard error computed from a special formula (not from ordinary regression).
Inputs and outputs
You provide
- Antagonist concentration [B] and the agonist dose ratio A′/A, one pair per line
- A confidence level
PHARM/PCS reports
- pA2 with its standard error
- Confidence limits at the level you choose
- The Schild plot with the line constrained to a slope of −1
When to use it
When you've already satisfied yourself the antagonism is simple and competitive (an unconstrained Schild slope near −1 in Procedure 15) and want the most precise pA2 under that assumption. Constraining the slope spends fewer degrees of freedom and tightens the estimate.
Reading the results
Only use this once the unconstrained fit (Procedure 15) justifies the slope = −1 assumption; imposing it on data whose true slope isn't −1 yields a confident but wrong pA2. Because the standard error comes from a special formula rather than ordinary regression, don't compare it head-to-head with the unconstrained SE as if they were the same quantity.
Not ordinary regression
The standard error uses the book's slope-constrained formula (Equation 17.4) rather than ordinary regression, and the t value carries n − 1 degrees of freedom because only the intercept is estimated. Do not compare this standard error head to head with the unconstrained one from Procedure 15.
This page describes the procedure. Calculations run inside the licensed PHARM/PCS V5 application. PHARM/PCS is a trademark of MCS Scientific LLC.