Hansch and free wilson analysis

QSAR Models
Hansch, Free wilson and Bilinear models

1. QSAR MODELS HANSCH AND FREE WILSON ANALYSIS By Dr SK. ARIFA BEGUM HOD, AVANTHI INSTITUTE OF PHARMACEUTICAL SCIENCES

2. Various QSAR approaches have been developed gradually over a time span of more than a hundred years and served as a valuable predictive tool, particularly in the design of pharmaceuticals and agrochemicals. It is sometime used in more sense as a hansch analysis. The introduction of the Hansch model in 1964 enabled medicinal chemists to formulate their hypothesis of structure activity relationships in quantitative terms and to check these hypotheses by means of statistical methods. Hansch Analysis Linear equation In general, biological activity for a group of ‘ congeneric ’ chemicals can be described by a comprehensive model:   Log 1/C 50= aπ + b ε+ c S+ d Π hydrophobicity parameter, ε electronic parameter and S steric parameter

3. Hansch proposed that the action of a drug as depending on two processes. Journey from point of entry in the body to the site of action which involves passage of series of membranes and therefore it is related to partition co-efficient log P ( lipophilic ) and can be explained by random walk theory. 2. Interaction with the receptor site which in turn depends on, a ) Bulk of substituent groups ( steric ) b) Electron density on attachment group (electronic). He suggested linear and non-linear dependence of biological activity on different parameters. log (1/C) = a (log P) + b σ + cES + d .......................linear log (1/C) = a (log P)2+ b(log P) + c σ + dES + e ........nonlinear Where a-e are constants determined for a particular biological activity by multiple regression analysis. Log P, σ, ES etc, are independent variables whose values are obtained directly from experiment or from tabulations. Other parameters than those shown may also be included.

4. The biological activity is normally expressed as 1/C so a graph is drawn by plotting log 1/C versus log P values to correlate the activity and partition coefficient or hydrophobicity . In studies where the range of the log P values are ranges between 1 to 4 and a straight-line graph is obtained i.e. there is an existence of relation between hydrophobicity and biological activity. As per this, the equation is log (1/C) = K1 log P + K2 Eg . Binding of drug to serum albumin. It can be determined by their hydrophobicity, in study of 40 compounds they resulted in the following equation: log (1/C) = 0.75 log P + 2.30 Conclusions Serum albumin binding increases as log P increases that mean hydrophobic drugs bind more strongly to serum albumin than hydrophilic drug can be important in estimating effective dose levels for that drug and drugs of similar structure

5. Hansch Non linear equation Due to the curvilinear, or bilinear, relationship between log1/C 50 and hydrophobicity normally found in single dose tests the quadratic π 2 term was later introduced to the model. Hansch (1969) Developed the parabolic Hansch equation for dealing with extended hydrophobicity ranges. Log 1/C= - a (log P) 2 + b.log P + c σ+ k Eg drugs which are independent of cell target action like General Anaesthetics . These are related to the log P factor alone to operate in cell membrane only These function by entering the central nervous system (CNS) and ‘dissolving’ into cell membranes where they affect membrane structure and nerve function.

6. Conclusion:- Anaesthetic activity increases with increasing hydrophobicity (ii) they depend upon lipophilicity only (iii) There is an optimum value for log P (log P0), beyond which increasing hydrophobicity causes a decrease in anaesthetic activity. Finally, hydrophobic drugs are often more susceptible to metabolism and subsequent elimination. Lipophilicity has a relationship with concentration and indirectly with biological activity .It can be concluded by graph [Transition of linear equational effect of “log P” into parabolic eq uational effect “log P 2 ”]. The value of log P at the maximum (log P0) represents the optimum partition coefficient for biological activity. Beyond that point, an increase in log P results in a decrease in biological activity.

7. Free and Wilson Mathematical model Free and Wilson (1964) formulated an additive model, where the activity is expressed as a simple sum of contributions from different substituents. BA = ­ aixi + u BA is the biological activity, u is the average contribution of the parent molecule, and ai is the contribution of each structural feature; xi denotes the presence Xi = 1 or absence Xi = 0 of a particular structural fragment. Fujita and Ban (1971) simplified the Free-Wilson equation estimating the activity for the non-substituted compound of the series and postulated Fujita-Ban equation that used the logarithm of activity, which brought the activity parameter in line with other free energy-related terms. Log BA = Gi Xi+ u In this equation, u is defined as the calculated biological activity value of the unsubstituted parent compound of a particular series. Gi represents the biological activity contribution of the substituents, whereas Xi is ascribed with a value of one when the substituent is present or zero when it is absent .  

8. The Free Wilson model is a simple and efficient method for the quantitative description of structure activity relationships. It is the only numerical method which directly relates structural features with biological properties, in contrast to Hansch analysis, where physicochemical properties are correlated with biological activity values. Nevertheless both approaches are closely interrelated, not only from a theoretical point of view, but also in their practical applicability. Free-Wilson equations do not require the use of substituent constants such as  ,   m ,   p , F, R, E S , and MR In many cases both models can be combined to a mixed approach which includes Free Wilson type parameters to describe the activity contributions of certain structural modifications and physicochemical parameters to describe the effect of some other substituents on the biological activity.

9. BILINEAR MODEL The interactions of drugs with their biological counterparts are determined by intermolecular forces, i.e . by hydrophobic, polar, electrostatic, and steric interactions. Quantitative structure-activity relationships (QSAR) derive models which describe the structural dependence of biological activities either by physicochemical parameters ( Hansch analysis), by indicator variables encoding different structural features (Free Wilson analysis), or by three-dimensional molecular property profiles of the compounds (comparative molecular field analysis, CoMFA ). Both models remained unchanged over the past three decades. Some improvements resulted from the combination of Hansch equations with indicator variables , which may be considered as a mixed Hansch and Free Wilson model , and from the formulation of theoretically derived nonlinear models for transport . Introduction and distribution of drugs in a biological system, e.g. the bilinear model . log 1jC = a log P - b log ( β P + 1) + c

10. Kubinyi (1976) Investigated the transport of drugs via aqueous and lipoidal compartment systems And further refined the parabolic equation of Hansch to develop a superior bilinear (non-linear) QSAR model. Log 1/C =a. log P- b.log (β. P + 1) + k β is the connectivity term