pA2 determination involves measuring drug antagonism through various methods. Sir Heinz Otto Schild developed the pA2 measure in 1947 to quantify antagonism using the dose ratio and affinity constant. The most common methods to determine pA2 values are Schild's plot, which analyzes log dose ratios against antagonist concentrations, and measuring shifts in dose response curves. Higher pA2 values indicate more specific antagonism on the pA scale. The pA2 value is defined as the negative log of the molar antagonist concentration required to double the agonist dose to produce the same effect.

1. pA2 Determination

2. A brief look…….
• Origin of pA2 value
• Drug antagonism & types
• Methods used for determination of drug
antagonism
• Importance of pA2 values and pA scale
• Summary

3. Origin of pA2 value
• Sir Heinz Otto Schild - Quantitative pharmacology
• In 1947 - pA scale, to express drug antagonism.
• Developed methods for assessing & measuring
drug antagonism,like pA2 measure and schild’s
plot
• Introduced the use of term dose ratio

4. Drug Antagonism
• An antagonist is the drug which diminishes or
completely abolishes the effect of agonist in
it’s presence
• For antagonist, efficacy is zero & affinity is
one

5. Experimental estimation of drug
antagonism
• Antagonism of drug induced contractions are of
two types
• Preventive : antagonist first added to the bath
and then agonist added subsequently
• Curative: effect( here contractions) is first
produced by the agonist. Antagonist is then
added to counter it

6. Dose ratio
• Defined as the factor by which the concentration of the
agonist has to be multiplied to produce a response in
the presence of antagonist.
• Higher the dose ratio, more specific is the antagonist.
• Adopt a standard time of exposure to antagonist to rule
out error, as it increases with increase in the exposure
time

7. a = amount of agonist that produces response
A = amount of agonist required in presence of antagonist to
produce response like “a”
B = amount of Antagonist
KB = Affinity constant of the antagonist for the receptors
Then, equilibrium constant for the reaction will be
B + Receptor ↔ B – receptor
Then A/a = 1+ BKB
Dose ratio = EC50 after antagonist
EC50 before antagonist

8. Percentage inhibition
• Antagonism can also be expressed as
• % inhibition =
100- [{height of contraction after exposure to
antagonist/ height of contraction before
exposure to antagonist} x 100]

9. Relative potencies from DRC

10. Mathematical calculation of the potency
• These calculations depends on the assumption
that the response bears a linear relation to log
dose
• Example :
Finding out relative activity of atropine and
methantheline on methacholine induced gastric
acid secretion in the rat by (2+2) dose assay.
Results are as follows

11. Drug
mean
Dose
(µg)
Maximum deflexion of pH in
different groups
Total
Atropine
(S1)
1.52
1.0 1.4 0.9 0.9 1.9 6.1
Methanthaline
(T1)
1.46
0.1 0.9 0.8 0.8 2.35 5.85
Atropine
(S2)
0.52
3.0 0.3 0.25 0.25 1.1 2.1
Methanthaline
(T2)
0.44
0.3 0.3 0.2 0.2 0.55 1.75

12. S1= 1.52, S2=0.52, T1=1.46, T2=0.44
• Log dose ratio (I) = log 3= 0.48
• Dose difference (E) = ½ (T2-T1+S2-S1)
= ½ (0.44-1.46+0.52-1.52)
= -1.01
• Preparation difference (F)= ½ (T1+T2-S1-S2)
(F)=½ (1.46 +0.44-1.52-0.52)
(F)= - 0.07
Slope (b) = E/I = -1.01/ 0.48

13. • Log ratio potency T/S or M = F/b = -0.07/-2.1
M= 0.033
• Potency ratio (antilog M) = 1.08

14. • IC50: concentration that produces 50 percent inhibition
of the effect of agonist.
%
Inhibition
IC50
log dose of antagonist
Determination of IC50 value

15. DRUG
ANTAGONISM
Competitive
Reversible Irreversible
Non
competitive

16. Dose response curve
r
e
s
p
o
n
s
e
Emax
Dose Ratio

17. Dose response curve
r
e
s
p
o
n
s
e
Emax

18. Methods used for determination of drug
antagonism
• Parallel shift of DRC to the right
• Double reciprocal plot of Lineweaver and Burk
• Schild plot
• Difference between pA2 and pA10 values

19. Parallel shift of DRC to right

20. Double reciprocal plot of Lineweaver &
Burk
1/V
1/S

21. Schild plot
• Most commonly used method for estimating
pA2 value
• Plot log(dose ratio-1) against negative log molar
concentration of the antagonist(B) used(or
directly against B)
• When the slope of the line so obtained is unity,
then the antagonism is competitive.

22. Schild plot
B(molar concentration)

23. -log(B)
Schild plot

24. Schild’s equation
Let’s say:
Drug A is an agonist; drug B is an competitive antagonist
Xb :concentration of antagonist used
Kb : equilibrium constant for the antagonist
Addition of B will shift the DRC 0f A towards right
The extent of shift / dose ratio(r ) = (Xb/Kb) +1
“r”will help in determining Kb for B
Expressing the above equation logarithmically, we get
schild’s equation

25. Schild’s equation
Log( r-1) = log Xb- log Kb
Thus,plot of log(r-1) on the y-axis and –logXb
on the x – axis gives us SCHILD’S PLOT

26. Estimation of Pa2 from Schild’s plot
• pA2 value can be directly calculated from the
Schild’s plot for a particular antagonist.
• Firstly graph is plotted using the required values
for different antagonist concentrations used
• The point at which the line intersects x- axis is the
pA2 value of that antagonist for that particular
receptor

28. Percentage response
• The response to a particular dose of agoinst
before adding antagonist is taken as 100%
• The response to the same dose in the
presence of antagonist is taken as the
percentage of the normal 100% response

29. pA2 value
• Measure for the equilibrium dissociation constant of
the antagonist
• Defined as the negative log of molar concentration of
the antagonist which will reduce the effect of double
dose of the agonist drug to that of a single dose
• pAx: x denotes the the number by which the agonist
dose has to be increased to get the effect of single
dose in the presence of antagonist
• X can be 2 or 10( pA2 and pA10)

30. • Thus, if the presence of a molar concentration
of 10-9.4 mepyramine in the bath reduces the
effect of 2mg histamine on guinea pig ileum to
that produced by 1µg in the absence of
mepyramine, the pA2 of mepyramine-
histamine on guinea pig ileum will be ______

31. Methods
pA2 determination on isolated guinea pig
ileum

32. Methods
pA2 determination

33. Plotting of pA2 value
• Plot the negative log of molar concentration of
antagonist on the x-axis and percentage
response on the y-axis
• The point on the x axis corresponding to the
50% response gives the pA2 value directly

35. pA scale
High values: high
specificity
Horizontal lines: non
specific antagonism
Steep lines: highly
specific antagonists

36. Difference between pA2 & pA10 values
• Determine both pA2 and pA10 values for
agonist- antagonist pair on the same tissue
• It the difference between them is approx 0.95
( 0.8 -1.2):Competitive antagonism
• Both the values can be interpolated from
Schild’s plot

37. Applications of pA2 measurements
• Helps us differentiate between competitive & non
competitive antagonism
• If the same agonist antagonist pair is gives similar
pAx values on different preparation, it suggests that
receptors are identical
• Drugs that act on the same receptor can be
expected to be antagonised by the same
concentration of a competitive antagonist, even
though they themselves may differ considerably in
activity

38. pD2’ value
• Measures the affinity of either non competitive
or irreversible competitive antagonist for a
specific receptor
• Defined as –log(B) which will decrease the
maximum effect of agonist by 50%
• Higher the pD2 value ,higher the potency

39. To summarize…..
Pharmacological drug antagonism can be assessed and
measured practically by different methods
Most commonly used methods : pA2 value estimation
and Schild’s plot
Dose ratio is the most important factor which needs to
be determined in antagonism

40. Refrences
• Medhi B, Prakash A. Practical manual of
experimental and clinical pharmacology.
Jaypee Brothers, Medical Publishers Pvt.
Limited; 2010.
• Ghosh M. Fundamentals of experimental
pharmacology. 2015 ; 118-31
• Pharmacological experiments in isolated
preprations; edinburg university: 1970
• S.K. Kulkarni. Handbook of experimental
pharmacology. Vallabh prakashan;2004:95-7