QSAR applications: Hansch analysis and Free Wilson analysis, CADD

This presentation gives information on Physicochemical parameters and their role in Hansch analysis and Free Wilson analysis of QSAR.

1. COMPUTER AIDED DRUG DESIGN SEMINAR ON QUANTITATIVE STRUCTURE ACTIVITY RELATIONSHIPS: “ APPLICATIONS” GAGAN S Govt. College of Pharmacy, Bengaluru Dept. of Pharmaceutical Chemistry.

2. CONTENTS : Definition of Hansch analysis Physicochemical parameters Hansch analysis Free-Wilson analysis Relation between Hansch and Free-Wilson analysis

3. What is “HANSCH ANALYSIS” ? Hansch analysis make attempts to mathematically relate drug activity to measurable chemical properties. It is a statistical method used to correlate physicochemical parameters (also called descriptors)with biological activity.

4. Physicochemical parameters : LIPOPHILICITY/PARTITION PARAMETERS : Partition coefficient Lipophilic substituent constants STERIC EFFECTS : Taft steric parameter Molar refractivity ELECTRONIC EFFECTS : Hammett constant

5. LIPOPHILICITY FACTORS: Partition coefficient : (log P) Refers to the whole molecules. Linear relationship between P and drug activity. Log 1/C = K 1 log P + K 2 Parabolic form over large ranges.

6. Log P0 represents the optimum partition coefficient for biological activity. Parabolic relationships could be represented by log (1/C) = - k 1 (log P ) 2 + k 2 logP + k 3 Where K1, K2 and K3 are constants that are normally determined by regression analysis.

7. Lipophilic substituent constants: (  ) Lipophilicity of substituent groups not of the whole molecule.  = log P RH - log P RX PRH = Partition coefficient of the standard compound. PRX = Partition coefficient of the monosubstituted derivative. What is its value in case of several substituents?

8. ELECTRONIC EFFECTS : The Hammett constant (  ): The distribution of electrons within a molecule depends on the nature of the electron withdrawing and donating groups found in that structure. Hammett used this concept to calculate what are now known as Hammett constants ( x ) for a variety of monosubstituted benzoic acids.

9.  X = log ( K BX /K B )  X = log K BX – log K B Where KB and KBX are the equilibrium constants for benzoic acid and mono substituted benzoic acids respectively. What the values of  X tell about?

10. STERIC EFFECTS : The Taft steric parameter (Es): Taft (1956) used the relative rate constants of the acid catalysed hydrolysis of a-substituted methyl ethanoates to define his steric parameter. He used methyl ethanoate as his standard and defined Es as: Es = log(k(XCH2COOCH3))/(k(CH3COOCH3)) Es= logk (XCH2COOCH3) - logk (CH3COOCH3)

11. Molar refractivity : The molar refractivity is a measure of both the volume of a compound and how easily it is polarized. Where n is the refractive index, M the relative mass and ρ the density of the compound.

12. HANSCH ANALYSIS Hansch postulated that the biological activity of a drug could be related to three parameters by simple mathematical relationships based on the general format: Log 1/C = k1 (partition parameter) + k2(electronic parameter) + K3(steric parameter) + K4

13. If the range of hydrophobicity values are limited to a small range then the equation will be linear as follows Log 1/C = K1 log P + K2  + K3Es + k4 If the log P values are spread over a large range then the equation will be parabolic Log 1/C = - K1 log P 2 + K2 log P + K3  + K4Es + k5. The constants K1 – K5 are determined by computer software in order to get the best fitting equation. 2

14. Not all the parameters will necessarily be significant. For example, the adrenergic blocking activity of 13-Halo-arylamines was related to  and  and did not include a steric factor. 2 The accuracy of a hansch equation may be assured from the values of the standard deviations (s) and the regression constant (r). The value of the correlation coefficient (r) is a measure of how closely the data matches the equation. It varies from zero to one. A value of r=1 indicates a perfect match.

15. Examples : This equation tells us that biological activity increase if the substituents have a positive  value and a negative  value. In other words, the substituents be hydrophobic and electron donating.

16. Hansch equations may be used to predict the activity of an as yet un-synthesized analogue. This enables the medicinal chemist to make an informed choice as to which analogues are worth synthesizing. Limitations : Conformational changes in receptor are ignored. Metabolism of drug is not considered. The potency – lipophilicity relationship may be parabolic or linear.

17. Advantages: The use of descriptors collected from simple chemical systems can be utilized for prediction of biological activity in complex systems. The predictions are quantitative with statistical confidence limits. The method is easy to use and inexpensive.

18. CRAIG PLOTS : Craig plots are two dimensional plots of one parameter against another. The plot is divided into four sections corresponding to the positive and negative values of the parameters. They are used, in conjunction with an already established Hansch equation to select the aromatic substituents that are likely to produce highly active analogues.

19. For example, suppose that a Hansch analysis carried out on a series of aromatic compounds yields the Hansch equation: Log 1/C = 2.67  - 2.56  + 3.92 To obtain a high value for the activity (1/C) it is necessary to pick substituents with a positive  value and a negative  value.

20. FREE-WILSON ANALYSIS It is a true structure activity relationship model in which biological activity of a compound is the sum of the contribution of all the substituents and the parent moiety.

21. It is based on the following assumptions: The entire drug list should have the same parent structure. The substitution pattern in various derivatives has to be same. The substitutions have to contribute to the biological activity additively.

22. Therefore, Free Wilson Analysis (FWA) is additive mathematical model in which a particular substituent in a specific position is assumed to make an additive and constant contribution to the biological activity of a molecule in a series of chemically related molecules. 3

23. Log 1/C = Σ (ai Ii ) + µ I = The substituent ai = Contribution of the substituent Ii = Contribution of the parent structure µ = Average activity

24. Example:

25. Advantages of FWA : It is simpler, faster and cheaper method where no substituent constants  ,  , Es are not required. Efficiency of the method is high with greater complexity of the structure. The substituent which can or cannot fulfil the principle of additively can be recognised .

26. RELATIONSHIP BETWEEN HANSCH AND FREE WILSON ANALYSIS : Hansch analysis uses different physicochemical properties to correlate structure activity relationships in a quantitative way. Free Wilson uses different substituents at different positions and their individual effect on the biological activity. Comparatively, Free Wilson method is simple, fast method as there is no need to calculate physicochemical parameters.

27. But, in free Wilson analysis, prediction of activity for other substituents is not possible. Secondly, the assumed independence of the influence of the substituens on total activity is often not seen in practice. One can use either Hansch or Free Wilson analysis or both to predict the activity of new molecules before their synthesis.

28. Reference : Fundamentals of Medicinal Chemistry, Gareth Thomas, WILEY Publication, Pg. No. 78-89. QSAR Hansch analysis, NPTEL, IIT Madras. https://youtu.be/3CvH9tHBji8