Optimization Hansch Analysis

In contrast to the qualitative better and worse approach of traditional SAR, many researchers have sought to develop a method that is able to quantitatively link molecular structure changes to biological activity, a quantitative structure-activity relationship (QSAR). As a method, QSAR strives to develop a mathematical formula to relate biological activity as a function of molecular or substituent properties. 

The benefit of QSAR is a more efficient lead optimization process. If a good QSAR formula can be derived, the activity of leads can be approximated by calculation without 

In an assay or screen, biological activity is often reported as ED50, /C50, or a similar term. From the discussion of receptor theory in Chapter 4, ED50 is equivalent to KD, the equilibrium constant for dissociation of a drug-receptor complex (Equation 12.2). 

Furthermore, the logarithm of equilibrium constants is directly proportional to the process associated standard free energy changes (Equations 12.3 and 12.4). 

Therefore, by substitution of Equation 12.2 into Equation 12.4, changes in the standard free energy of binding (AG°) are directly proportional to the logarithm of an activity measure (ED5o) (Equation 12.5). 

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The simplicity of Hansch analysis also means that experienced medicinal chemists may be able to identify trends in activity without the assistance of a QSAR equation. Making individual new lead analogues is generally a slow process, and a medicinal chemist has ample time to examine SAR data. While a chemist will not be able to quantify a structure-activity relationship, just knowing the approximate trend of the relationship is usually adequate for lead optimization. Hansch analysis is valuable only if it can reveal something that is not already known about the compounds being tested. 

Hansch analysis marked the breakthrough of QSAR. The method was soon extended with additional parameters with the aim of improving the fit between biological and physicochemical data and for the prediction of drugs with optimal... 

Nevertheless, Hansch analysis revolutionized drug molecule optimization and directly led to two other strategies for molecule optimization the Free-Wilson method and the Topliss decision tree. 

On the basis of the origin of molecular descriptors used in calculations, QSAR methods can be divided into three groups. One group is based on a relatively small number (usually many times smaller than the number of compounds in a data set) of physicochemical properties and parameters describing,for example, hydrophobic, steric, and electrostatic effects. Usually, these descriptors are used as independent variables in multiple regression approaches (18) Jn the literature, these methods are typically referred to as Hansch analysis (8).These types of descriptors and corresponding linear optimization methods used in traditional QSAR analyses are discussed extensively in the chapter by Celassie (7) and therefore is not reviewed here. 

The OASIS method is based on the same assumption as -+ Hansch analysis and can be regarded as an extended and optimized version of the Hansch approach [Mekenyan and Bonchev, 1986 Mekenyan et al, 1990a]. 

Objectives Optimize biological activity of drugs Find new active lead compounds Characteristics Response in isolated systems Effects are specific and well defined Specific mechanism of action Receptor is known in most cases Techniques Hansch Approach Multivariate Analysis Computerized molecular modeling Estimate rates of fate processes Analyze Processes Whole organism response Net effects (mortality growth, etc.) Specific nonspecific mechanisms Receptor unknown in most cases Hansch Approach Multivariate Analysis Molecular modeling not applied... 

Another major reason for plotting factors is the possibility that an optimum will be observed. This is illustrated genetically in Figure 16. It is clear that optimal behavior occurs often in the relationship of tr or log P to activity (Hansch and Fujita Takemoto et al. ). It is thus reasonable to include a term as a faaor in an analysis of biodata. However, the inclusion of squared terms for all factors in a design would be a problem relative to the probability of chance correlations. Since examples of optimal behavior for other faaors have been reported (e.g., for or a ), this possibility must be considered. 

The most appropriate and widely used method for extracting information from large data sets is QSAR and its relatives, quantitative structure-property relationships (QSPR) for property modeling, and quantitative structure-toxicity relationships (QSTR) for toxicity modeling. QSAR is a simple, well validated, computationally efficient method of modeling first developed by Hansch and Fujita several decades ago (30). QSAR has proven to be very effective for discovery and optimization of drug leads as well as prediction of physical properties, toxicity, and several other important parameters. QSAR is capable of accounting for some transport and metabolic (ADMET) processes and is suitable for analysis of in vivo data. 

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