pA2 value, Schild plot and pD2 values- applications in pharmacology

seminar presentation on pA2 values and pD2 values

1. Dr. Deepak Daniel

2. 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 .

3. 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

4. A characteristic di ff erence between competitive and noncompetitive antagonists is that competitive antagonists reduce agonist potency , whereas noncompetitive antagonists reduce agonist efficacy .

5. 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. This “r” can be found out from the extent of the rightward shift of DRC.

6. EC50  concentration of a drug required to produce a response that is 50% of the maximum response achievable. Higher the Dose Ratio , more specific is the antagonist.  

7. pAx Value pA scale proposed by Schild to express drug antagonism . pA x : 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).

8. pA 2 value pA 2 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 in the absence of antagonist.

9. Example Drug with concentration A  0.4 ml response recorded 16 mm Drug with concentration 2A  0.8 ml response recorded 28 mm As per definition, pA2 Negative log of molar concentration of antagonist required to reduce response of 2A  A.

10. Methods used for determination of types of drug antagonism

11. Parallel Shift Plot Simplest form of experimental approach of identifying an antagonist in which the shift of DRC is parallel towards right after addition of competitive antagonist is seen. 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.

12. Parallel shift of DRC to right The extent of the rightward shift tells us by what ratio we have to increase the dose of agonist to get the same effect.

13. 2) Lineweaver-Burk Plot or Woolf-Lineweaver-Burk Plot/graph This method was developed by Hans Lineweaver and Dean Burk in 1934 for the assessment of enzyme kinetics. Inverse response is plotted against the inverse of dose concentration of agonist, which was invented to analyze how fast a drug can produce its response, against a present antagonist. This method is applied to distinguish between competitive and noncompetitive antagonists.

14. Schild plot Most commonly used method for estimating pA2 values for pharmacological competitive antagonists is to plot (DR-1) against negative log molar concentration of the antagonist. DR  agonist dose ratio When the schild plot gives a statistically acceptable straight line with a slope, then the antagonism is competitive.

15. Steps for schild plot

16. Schild plot

17. 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

18. Calculate pA2 value of Prazosin using Noradrenaline as agonist in rat anococcygeus muscle preparation

19. Applications of pA2 Quantifying Antagonist Potency: The pA2 value provides a measure of how potent a competitive antagonist is in blocking the effects of an agonist. Higher pA2 values indicate greater potency in inhibiting the agonist's effects. 2. Comparing Antagonists: pA2 values allow for a direct comparison of different antagonists targeting the same receptor. Antagonists with higher pA2 values are more effective at blocking the receptor.

20. 3. Understanding Mechanisms of Antagonism: By comparing pA2 values of various antagonists, insights into the mechanisms of action and binding affinities of these compounds at specific receptors can be gained. 4. Predicting Clinical Effects : The pA2 value can aid in predicting the clinical efficacy of competitive antagonists. Higher pA2 values suggest that lower doses of the antagonist might be required for therapeutic effects. 5. Selecting Antagonists for Specific Situations: When designing treatment regimens, selecting an antagonist with an appropriate pA2 value can be crucial. For example, if rapid and reversible blockade is desired, an antagonist with a lower pA2 value might be chosen.

21. 6. Studying Receptor Pharmacology: The pA2 value is widely used in receptor pharmacology research to investigate the interactions between agonists and competitive antagonists, providing insights into receptor kinetics and binding properties. 7. Drug Development: Determining the pA2 value during the preclinical stage of drug development helps in selecting lead compounds with optimal antagonistic properties for further development. 8. Understanding Dose-Response Relationships: The pA2 value contributes to understanding dose response relationships by quantifying the concentration at which antagonists effectively inhibit the agonist response.

22. pA2 scale High values: high specificity Horizontal lines: non specific antagonism Steep lines: highly specific antagonists pA2 values of four antagonists against histamine and acetylcholine as measured on guinea pig ileum. Points on the two scales referring to the same antagonist are joined.

23. pD2 The pD2 value represents the negative logarithm of the concentration of a drug required to produce 50% of the maximum response (EC50). pD2=−log(EC50) pD2 value allows for a standardized comparison of the potency of different drugs or the same drug under varying conditions. By converting the EC50 values into logarithmic scale, it becomes easier to compare the potencies of drugs with different EC50 values.

24. Applications of pD2 : Drug Development : Researchers use pD2 values to compare the potencies of different compounds during drug development. This helps in selecting the most potent compounds for further study. Therapeutic Dosing : Understanding the pD2 value aids in determining appropriate dosages of drugs for therapeutic use. Drugs with lower pD2 values require lower concentrations to achieve the desired effect. Drug Interaction Studies : pD2 values can be used to assess potential drug interactions. If two drugs have similar pD2 values, they might compete for the same receptor or enzyme, potentially leading to interactions.

25. pD2’ Measures the affinity of a reversible 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.

26. Determined by the equation pD2’= pDx + log[ (E AM \E ABM ) – 1] where, pDx is negative molar concentration of the antagonist employed. E AM and E ABM are the maximal contraction heights in the absence and presence of antagonist respectively.

27. References Fundamentals of experimental pharmacology: M.N Ghosh Practical Manual Of Experimental and Clinical Pharmacology: Bikash Medhi

28. Thank you