Hansch analysis

The above Hansch equations are also generally referred to as linear free energy relationships (LFER) as they are derived from the free energy concept of the drug-receptor complex. They also assume that biological activity is linearly related to the electronic and lipophilic contributions of the various substituents on the parent molecule. 

A typical Hansch analysis has been applied to the 50% inhibitory concentrations (ICjo) of oxidative phosphorylation of 11 doubly substituted salicylanilides (Table 37.1) as reported by Williamson and Metcalf [17]. Multiple linear regression leads to the following model  

Lipophilicity (log P), Hammett electronic parameter (a) and inhibitory concentration (ICj,) for oxidative phosphorylation of 11 doubly substituted salicylanilides [17], The two substitution positions are labeled A and B. 

Frequently, the relationship between biological activity and log P is curved and shows a maximum [ 18]. In that case, quadratic and non-linear Hansch models have been proposed [19]. The parabolic model is defined as  

Note that the lipophilicity parameter log P is defined as a decimal logarithm. The parabolic equation is only non-linear in the variable log P, but is linear in the coefficients. Hence, it can be solved by multiple linear regression (see Section 10.8). The bilinear equation, however, is non-linear in both the variable P and the coefficients, and can only be solved by means of non-linear regression techniques (see Chapter 11). It is approximately linear with a positive slope (/ ,) for small values of log P, while it is also approximately linear with a negative slope b + b for large values of log P. The term bilinear is used in this context to indicate that the QSAR model can be resolved into two linear relations for small and for large values of P, respectively. This definition differs from the one which has been introduced in the context of principal components analysis in Chapter 17. 

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Kubinyi, H. QSAR Hansch Analysis and Related Approaches, VCH, Weinheim, 1993. 

This is already the 37th volume in our series on Methods and Principles in Medicinal Chemistry which started in 1993 with a volume on QSAR Hansch Analysis and Related Approaches, written by Hugo Kubinyi. An average release of roughly three volumes per year indicates the increasing appreciation of the series in the MedChem world. 1 want to express my sincere thanks to my editor friends Hugo Kubinyi and Gerd Folkers for their continuous and precious contributions to the steady development of our series. 

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... 

A difficulty with Hansch analysis is to decide which parameters and functions of parameters to include in the regression equation. This problem of selection of predictor variables has been discussed in Section 10.3.3. Another problem is due to the high correlations between groups of physicochemical parameters. This is the multicollinearity problem which leads to large variances in the coefficients of the regression equations and, hence, to unreliable predictions (see Section 10.5). It can be remedied by means of multivariate techniques such as principal components regression and partial least squares regression, applications of which are discussed below. 

The fundamental assumption of Hansch analysis is that substituent values are additive. This implies that substituents are mutually independent, i.e. that the effect of a substitution group at one position in the parent molecule is independent of substitution groups at other positions. The assumption of additivity is violated, for example, when hydrogen bonding occurs between two adjacent substituents. 

The second extrathermodynamic method that we discuss here differs from Hansch analysis by the fact that it does not involve experimentally derived substitution constants (such as o, log P, MR, etc.). The method was originally developed by Free and Wilson [29] and has been simplified by Fujita and Ban [30]. The subject has been extensively reviewed by Martin [7] and by Kubinyi [8]. The method is also called the de novo approach, as it is derived from first principles rather than from empirical observations. The underlying idea of Free-Wilson analysis is that a particular substituent group at a specific substitution site on the molecule contributes a fixed amount to the biological activity (log 1/C). This can be formulated in the form of the linear relationship ... 

The interpretation of the result of a Free-Wilson analysis is somewhat different from that of a Hansch analysis. The coefficients in the Hansch model represent absolute contributions to the biological activity of a compound from the various... 

The Free-Wilson analysis provides more site-specific information than a Hansch analysis. It is recommended to carry out a Free-Wilson analysis first in order to obtain an idea of the importance of the substituent groups and of the sensitivity of the substitution sites. This type of analysis can be regarded as being qualitative, as it points to the important pharmacophores in the molecule. The information thus obtained may guide the selection of the appropriate physicochemical, topological... 

The method of PCA can be used in QSAR as a preliminary step to Hansch analysis in order to determine the relevant parameters that must be entered into the equation. Principal components are by definition uncorrelated and, hence, do not pose the problem of multicollinearity. Instead of defining a Hansch model in terms of the original physicochemical parameters, it is often more appropriate to use principal components regression (PCR) which has been discussed in Section 35.6. An alternative approach is by means of partial least squares (PLS) regression, which will be more amply covered below (Section 37.4). 

The selection of the number of PLS-components to be included in the model was done according to the PRESS criterion (Section 36.3). Note that the result is comparable to the one which we obtained earlier by means of the simple Hansch analysis (Section 37.1.1). Hence, in this case, there is no obvious benefit to include a quadratic term of log P in the model. 

The same assumptions apply to CoMFA as to ordinary Hansch analysis. These are additivity of effects and the availability of structurally similar (congeneric) molecules. The method does not account for pharmacokinetic effects, such as distribution, elimination, transport and metabolization. A prospective drug may appear to bind well to the receptor or enzyme, but may not reach the target site due to undesirable pharmacokinetic properties [8]. 

Y.C. Martin, Quantitative Drug Design. A Critical Introduction. Marcel Dekker, New York, 1978. H. Kubinyi, QSAR Hansch Analysis and Related Approaches. VCH, Weinheim, 1993. 

HT(la) /alpha( 1)-adrenergic receptor affinity by classical Hansch analysis, artificial neural networks, and computational simulation of ligand recognition. Journal of Medicinal Chemistry, 44, 198-207. 

Lopez-Rodriguez, M.L., Morcillo, M.J., Fernandez, E., Rosado, M.L., Pardo, L. and Schaper, K.-f. (2001) Synthesis and structure-activity relationships of a new model of arylpiperazines. 6. Study of the 5-HTiA/ai-adrenergic receptor affinity by classical Hansch analysis, artificial neural networks, and computational simulation of ligand recognition. Journal of Medicinal Chemistry, 44, 198-207. 

Kubinyi, H. Methods and principles in medicinal chemistry. In QSAR Hansch Analysis and Related Approaches, Mannhofd, R., Keogsgaaed-iaesen, P., and Timmeeman, H. (Eds.). VCH, Weinheim, New York, 1993. 

H. Kubinyi (1993). Hansch analysis and related approaches. In R. Mannhold (Ed.). Methods and... 

Historically, this is the most popular mathematical approach to QSAR. The major contribution of Hansch analysis is in recognizing the importance of logP, where P is the octanol-water partition coefficient. LogP is perhaps the most important measure of a... 

Introduced by Corwin Hansch in the early 1960s, Hansch analysis considers both the physicochemical aspects of drug distribution from the point of application to the point of effect and the drug-receptor interaction. In a given group of drugs that have analogous structures and act by the same mechanism, three parameters seem to play a major role ... 

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. 

PLS was advantageous when studying the relationship of the toxicity of thiify triazines on Daphnia magna (25), and in a comparison between Hansch analysis and PLS analysis, using the same data set, it was shown that tiie multivariate approach of PLS provided more useful models than the Hansch type approach (26). 

A general theory of quantitatively comparing molecular shapes using common overlap steric volume(33-36) and, more recently, descriptors derived from superimposed molecular potential energy fields of pairs of molecules(37) has been derived and tested. This theory allows a "marriage between Hansch analysis and conformational analysis. 

Principles and practice of Hansch Analysis A guide to structure-activity correlation for the medicinal chemist, 6, 83... 

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