This document explains how to calculate the potency of antagonists in pharmacology using two key values: pa2 for competitive reversible antagonists and pd2' for competitive irreversible or non-competitive antagonists. It details the formulas and steps necessary to derive these values, highlighting the importance of distinguishing between pd2 and pd2' values. Accurate measurement of these potencies helps in achieving effective treatment and improving drug efficacy.

1. Calculating pA2 and pD2'
Values
In pharmacology, pA2 and pD2' values are used to measure
the potency of antagonists.
Here's how to calculate them.
Dr. Shivankan Kakkar, M.D.

2. Two Types of Antagonists
1. Competitive Reversible
Antagonist
The potency of a competitive reversible
antagonist is expressed as a pA2 value.
2. Competitive Irreversible or Non-
Competitive Antagonist
The potency of an competitive Irreversible
or Non-competitive antagonist is expressed
as a pD2' value.

3. pD2 vs. pD2' Values
pD2
Measures the potency of an agonist.
pD2'
Measures the potency of an antagonist.
Remember, it's important not to confuse *pD2 and pD2' values. They measure different
things!
Note:-
*pD2=the negative logarithm of an **EC50
**EC50= the concentration (or dose) effective in producing 50% of the maximal
response

4. Exercise 1: pA2 Calculation
Potency of a Competitive Reversible
Antagonist

5. pA2 Calculation
The potency of a competitive reversible antagonist is expressed as a pA2 value.
The pA2 value is the negative logarithm of the molar concentration of antagonist
which causes a twofold shift of the concentration-response curve for agonist.
The larger the pA2 value, the more potent the antagonist.
We derive the pA2 value using the following formula:
pA2
= pAx + log(x-1)

6. pA2 Calculation Formula
pA2 = pAx + log(x-1)
Here,
x = Concentration Ratio
pAx = —log[antagonist conc]
Using the formula and the dose-response curves, we'll calculate the pA2 value of the
antagonist.

7. Calculating Concentration Ratio
The concentration ratio of the antagonist is derived from the ratio of the concentration of
agonist that gives the same response in the presence and absence of the antagonist.We
can derive the concentration ratio using either *pD2 or **EC50 values:
Concentration-ratio 'x'= Antilog [ pD2 (absence) — pD2 (presence) ]
or
Concentration-ratio 'x'= EC50 (presence) / EC50 (absence)
Note:-
*pD2=the negative logarithm of an **EC50
**EC50= the concentration (or dose) effective in producing 50% of the maximal response

8. Calculating pA2 Values
1 Step 1
Determine the pD2/EC50 values in the presence and absence of antagonist.
2 Step 2
Calculate the concentration ratio using the concentration values.
3 Step 3
Calculate pAx using the antagonist concentration.
4 Step 4
Calculate the pA2 value using the formula.
Now, let's see how we can calculate pA2 values using these steps.

9. Steps in pA2 Value Calculation
Step 1
From this graph, we can see that:
Presence of antagonist: pD2 = 5.5 & EC50 = 3 x 10-6M
Absence of antagonist: pD2 = 6.5 & EC50 = 3 x 10-7M

10. Steps in pA2 Value Calculation
Step 2
The next step is to calculate the concentration-ratio using either the pD2 or EC50 values.
Concentration-ratio "x" = Antilog (6.5 – 5.5) = Antilog (1) = 10

11. Steps in pA2 Value Calculation
Step 3
pAx = — log antagonist conc = — log (1 x 10-6) = 6
Step 4
pA2 = pAx + log (x—1) = 6 + log (10—1) = 6 + 0.95 = 6.95

12. Exercise 2: pD2' Calculation
Potency of a Competitive Irreversible or
Non- Competitive Antagonist

13. pD2' Calculation
The pD2' value is a measure of the potency of a competitive irreversible or non-
competitive antagonist.
The pD2’ value is the negative logarithm of the molar concentration of antagonist which
causes a halving of the maximal response of the agonist.
The larger the pD2’ value, the more potent the antagonist. The formula we use to derive a
pD2' value is:
pD2' = pDx + log(x-1)

14. pD2' Calculation Formula
pD2’ = pDx + log(x-1)
Here,
x = Depression of Maximal Response
pDx = —log[antagonist conc]
To calculate the pD2' value, we'll follow the formula and calculate the depression of the
maximal response in the presence and absence of the antagonist.

15. Calculating pD2' Value
Using the above concentration-response curves, the first step is to determine the maximum
responses in the presence and absence of antagonist.
Maximal response in absence of antagonist: 100%
Maximal response in presence of antagonist: 50%

16. Calculating pD2' Value
We can now work out x:
x = Maximal response in absence of antagonist / Maximal response in presence of antagonist
x = 100 / 50 = 2

17. Calculating pD2' Value
We can now work out pDx:
pDx = —log antagonist conc = —log (3 x 10-6) = 5.5

18. Calculating pD2' Value
We can now work out pD2':
pD2' = pDx + log (x – 1) = 5.5 + log (2 – 1) = 5.5

19. The Importance of Measuring Potency
Accurate Dosage
Measuring potency can
help us achieve the desired
effect using the lowest
possible dose of the drug.
Improving Efficacy
Measuring potency can
help us improve the
efficacy of drugs by
tinkering with the
concentration ratios or the
drug dose.
Effective Treatment
Measuring potency can
help us identify the right
treatment or drug for a
given disease or condition.