PA2 and PD2 VALUES

Dr.Shamshi AzmiJRDept. of Pharmacology

INTRODUCTION

• In 1947, Sir Heinz Otto Schild devised a scale , known as 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.

Drug antagonism

• An antagonist is the drug which completely or partially blocks the

effect of agonist in its presence.

• Antagonist have only affinity but no intrinsic activity or efficacy,

i.e. efficacy is zero & affinity is one.

Competitive antagonism

• Antagonist competes with the agonist for the same binding site on

receptor.

Reversible competitive antagonism• Here binding between antagonist and receptor is reversible.

• Antagonism can be overcome by increasing concentration of the

agonist and vice-versa.

• There is parallel shift of dose response curve to right with increasing concentration of antagonist but maximal response remains same.

Dose Ratio(r)

Emax

response

Dose Ratio• The dose ratio(r) is the factor by which the concentration of the

agonist has to be multiplied to produce a given response in

presence of antagonist.

• Higher the dose ratio more specific is the antagonist.

• This “r” can be found out from the extent of the rightward shift of

DRC.

• Dose ratio(r) = EC’50/EC50

• EC’50 means the dose of agonist at which 50% of effect is produced

in presence of antagonist.

Irreversible competitive antagonist

• Antagonist binds to receptor irreversibly by forming covalent

bond.

• As the dose of antagonist is increased, the slope as well as

maximal response of the agonist decreases.

• With sufficiently high dose of antagonist, no amount of agonist

will produce response.

response

Non competitive antagonist

• Antagonist binds to different site of the receptor such that

agonist is unable to combine with the receptor or is unable to

produce response.

• Its effect is similar to irreversible competitive antagonist, where

antagonist cannot be displaced even with higher concentration

of agonist.

PA2 value

pA2 is the measure of the affinity of a reversible competitive antagonist

for a specific receptor.

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 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)

Experimental estimation of drug antagonism

Antagonism of drug induced contractions are of two types-

• Preventive: antagonist is first added into the bath to

prevent the effect of agonist added subsequently.

• Curative: effect (here contractions) is first produced by

the agonist and then, antagonist is added to counter it.

Methods used for determination of types of drug antagonism

• Parallel shift of DRC to the right

• Double reciprocal plot of Lineweaver and Burk

• Difference between pA2 and pA10 values

• Schild’s plot

Parallel shift of DRC to right

• If the DRC of agonist shifts to the right without any depression

of maximal response following an antagonist, it is likely that the

antagonist is of a competitive nature. However, it needs further

confirmation.

• The extent of the rightward shift tells us by what ratio we have

to increase the dose of agonist to get the same effect.

Dose Ratio(r)

Emax

response

Double reciprocal plot of Lineweaver and Burk (Chen and Russell,1950)

• If the points lie on straight line and if the stragiht lines

determined in the presence and absence of antagonist

intersect on the line corresponding to infinite dose then

the antagonism is said to be competitive.

Difference between pA2 & pA10 values

• By this method competitive and non competitive nature of

antagonist can be determined.

• Both pA2 and pA10 values for agonist- antagonist pair is

determined on the same tissue.

• If the difference between them is approximately 0.95 (0.8-1.2):

Competitive antagonism

Method of determination of PA2

• Organ bath is connected with two bottles one containing only

physiological salt solution and other containing antagonist

solution.

• A number of sub maximal

contractions are first obtained

with an agonist at regular

intervals till a constant

response is produced.

• Then organ bath is filled with

solution containing antagonist

and dose of agonist is doubled

in its presence

• The response some times increases initially but gradually

diminishes and reaches steady level.

• Concentration of antagonist that produces a response slightly

greater than the original response to single dose of agonist is

first used.

• Then the bath is connected to the bottle containing the salt

solution to allow for complete recovery of its effect.

• The assay is concluded by producing series of maximal

contractions.

• Then the experiment is repeated with the concentration of

antagonist that produces slightly smaller response then the

original response to a single dose of agonist.

Plotting of pA2 values

• The contraction height of the single dose of agonist in the

absence of antagonist and contraction height of double dose

agonist following two concentrations of antagonist are

expressed as percentage of maximal contraction .

• Later, two percentage contraction are then plotted against the

two doses of antagonist on log scale.

• The concentration of antagonist that produces response equal

to single dose of agonist is found by interpolation.

Schild’s plot

• Most commonly used method for estimating pA2 value

• 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 this logarithmically, we get schild’s equation

• Log( r-1) = log Xb- log Kb

• Very simple & useful equation

Thus, plot of log(r-1) on the y-axis and –logXb on the x–axis gives

us SCHILD’S PLOT

pA2 value is directly read out at the point where line intersects x-axis at zero level

of y-axis

Intercept (E)- pA2 value for the antagonist

Applications of pA2 measurements

• Principle advantage: gives us simple numbers

• Helps us differentiate between competitive & non competitive

antagonism.

• Drugs that act on the same receptors can be expected to be antagonized

by the same concentration of a competitive antagonist, even though they

themselves may differ considerably in activity.

• If the given agonist-antagonist pair gives similar pAx values on different

preparations, it is suggestive that receptors are identical.

• On other hand, different pAx values are indicative of different receptors.

pA scale

High values: high specificity

Horizontal lines: non specific antagonism

Steep lines: highly specific

antagonists

pD2’ value

• Measures the affinity of a non competitive as well as

irreversible competitive antagonist for a specific receptor.

• Defined as negative logarithm of the molar concentration of

non competitive antagonist which will reduce the effect of an

agonist to one-half (50%) its maximum.

• Determined by the equation

pD2’= pDx + log[ (E1\E2) – 1]

where,

• pDx is negative molar concentration of the antagonist

employed.

• E1 and E2 are the maximal contraction heights in the absence

and presence of antagonist respectively.

• 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 drug antagonism.

Thank you…