PHARMACOLOGY

 pAx and pD2 scale ::

It is the pharmacological scale used to express drug antagonism This was proposed by H.O.Schild (1947) 

pAx is defined as the negative log of the molar concentration of antagonist in the presence of which x multiple dose of agonist is required to produce the same effect as produced in the absence of antagonist Usually pA2 scale is used to compare the potency of two antagonists 

    pA2 can be defined as the negative logarithm of the molar concentration of antagonist in the presence of which double the dose of agonist is required to produce the same effect as produced in the absence of antagonist 

    Histamine contracts guineapig uterus and these contractions are blocked by mepyramine if the pA2 Value of mepyramine is 10 then in the presence of 1.0 x 10-10 M  dose of mepyramine double the dose of histamine will be required to produce the same effect as produced in its absence if 3 ug/ml histamine is required to produce 50% response then in presence of mepyramine (10-10 M) dose 6 ug/ml histamine will be required to produce 50 % response To calculate pA2 value the dose response curves to agonists are constructed in absence and presence of various doses of antagonist The EC50 value of each is determined and the dose ratio (x) is determined for each as follows ::

        Dose ratio = EC50 in presence of antagonist 

                            ---------------------------------------

                            EC50 in absence of antagonist 

From the above plot one can also determine pA10 (x=10) if the difference between pA2 and pA10 is 0.95 then antagonism is considered to be competitive The value may be approximately around 0.95 if it is 0.5 or less then the type of antagonism is certainly not competitive Thus pA2-pA10 is a method of confirming the competitive antagonism 

    The pA2 can also be calculated by following formula :

        pA2= _ log[B] +log [A2] --1

                                         -------

                                         [A1]

Where [B]=Molar concentration of antagonist 

            [A2]= EC50 of agonist in the presence of antagonist 

            [A1] = EC50 of agonist in absence of antagonist 

    The pA2 scale is useful in differentiating the nature of receptors involved in particular drug action The pA2 Value is always same for a particular antagonist irrespective of the preparation used in other words if the pA2 Value obtained for particular drug is the same in different preparation one can say that the same receptors are involved in each preparation if pA2 values are different in different tissues then it is suggestive of different receptors involved in the action e.g. pA2 obtained with ACh- atropine in rectus abdominis is 4.0 whereas it is 8.1 in guinea pig ileum and 8.3 in frog auricle it suggests that receptors of guinea pig ileum and frog auricle are the same whereas they are different in rectus abdominis 

                The pA2 value for a particular antagonist is always the same irrespective of the agonist used for e.g pA2 for mepyramine will be same when 2-(2-pyridyl) ethylamine (PEA) is used instead of histamine 

            The agonist antagonist relation has also been explained on the basis of association dissociation of drug with receptor This was explained by Paton (1961) under the rate theory According to the rate theory a response is not the function of occupancy of receptor but it is the function of drug receptor complex formation The respone is produced only when the complex is formed for further response it has to be dissociated i.e. hit and run away Thus all drugs have high rates of association but difference between agonist and antagonist is on the basis of rate of dissociation Agonists have high dissociation whereas antagonists have low dissociation rates 

        The pD2 a pharmacological scale proposed by Ariens and colleagues to represent non competitive antagonism it is defined as negative log of molar concentration of antagonist which reduces the maximum effect obtainable with the agonist to half it can be determined from the following equation : 

                pD2=pDx+log X-l 

Where pDx is the negative log of molar concentration of antagonist in the presence of which the maximum response of agonist is reduced by x concentration of antagonist 

        X= Ratio of maximum response to a given dose of agonist in the absence and presence of antagonist 

            pD2 value obtained with different dose of antagonist will not change significantly if the antagonism is non competitive