1. How effective is an antagonist?
Often find values of pA2 or pKb quoted
The higher the value the more effective the antagonist
pKb = -log Kb (Kb is the equilibrium constant)
i.e an antagonist with a pKb value of 9 would be approximately 1000 times more effective than one with a value of 6 - note log scale
i.e. need a much lower concentration to get an effective block
Of course antagonists are SELECTIVE

2. Calculation of Kb This can be done in 2 ways Using the Schild equation
Using a Schild plot
Produce log concentration curves for the agonist alone and in the presence of a known concentration of antagonist
From these data calculate a DOSE RATIO see graph

3. Calculation of Dose Ratio
CARB
+ ATR 10-7 M
150
“EC50”
100
Response (mm) 50 -2 -1 1 2 3 4
Log conc carbachol (µM)

4. Schild Equation First need to calculate DOSE RATIO (DR)
DR = EC50 (with anagonist)
EC50 (agonist only)
Schild equation: DR = Xb + 1 Kb
Xb = antagonist conc
So Kb = Xb
DR-1

5. Schild Plot
This time need to use a series of antagonist concentrations (at least 3, the more the better)
Again have to calculate DR for each antagonist concentration
Also calculate (DR-1) and log (DR-1)
The Schild plot is a plot of log [antagonist] vs log (DR-1) see graph

6. For competitive antagonism
Schild plot II
For competitive antagonism
slope = 1
2.5
2.0 Kb
Log (DR-1)
1.5
1.0
0.5
0.0
-10.0
-9.5
-9.0
-8.5
-8.0
-7.5
-7.0
Log conc atropine (M)

7. pKb and pA2 pKb is a convenient way of expressing Kb pKb = -log Kb
Note similar to pH
When slope of Schild plot is 1 and ONLY when slope of Schild plot is 1
Then pKb = pA2

8. Recommended Reading pKb and pA2 Pharmacology, 5th Ed: Pages 16 & 17
Basic and Clinical Pharmacology Online Book: Section I, Chapter 2.