Hansch equation

Once parameters modeling various properties have been defined, equations predicting activity may be constructed. Classically, Hansch equations take the form of Equation 12.18,1 

At this point, a considerable amount of theory on Hansch analysis has been presented with almost no examples of practice. The next three Case Studies will hopefully solidify ideas on Hansch analysis that have already been discussed. Each Case Study introduces a different idea. The first is an example of a very simple Hansch equation with a small data set. The second demonstrates the use of squared parameters in Hansch equations. The third and final Case Study shows how indicator variables are used in QSAR studies. If you are unfamiliar with performing linear regressions, be sure to read Appendix B on performing a regression analysis with the LINEST function in almost any common spreadsheet software. A section in the appendix describes in great detail how to derive Equations 12.20 through 12.22 in the first Case Study. 

In a study by Hansch, five mete-substituted diethyl phosphonate esters (12.14) showed cholinesterase inhibition in fruit flies. Correlations between cr-values, ),-values, and both parameters together were explored. The relevant data are included in Table 12.5. 

The first Hansch equation (Equation 12.20) relates biological activity (log 1/ho) to the electronic effect of the R-group (o-m). 

Once both steric and electronic parameters are included in the regression, Equation 12.22 accommodates nearly 99% (0.994 X 0.994) of the variance in the data. 

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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. 

This quadratic dependence has been observed in many systems, and the dominance of lipophilicity in controlling activity reflects its importance in transport [74]. Nevertheless, the biological response (BR) of a series of compounds (which is often expressed by the inverse of the drug concentration) may also involve an electronic ( ) and/or a steric (5) contribution. Hence, QSARs have been mostly constructed using the generalized Hansch equation [337] ... 

Handylab, 26 976 Hanford N reactor, 17 572-573 Hanford production reactors, 17 570 Hanksite, 5 785t Hansa yellows, 14 317 Hansch equation, 10 329 Hansenula polymorpha, 12 479 Hantaviruses, 3 137 Hantzsch pyridine synthesis, 16 550 Hantzsch-Widman nomenclature system, 17 399... 

DOUBLE-RECIPROCAL PLOT HANSCH CONSTANT HANSCH EQUATION HANSCH S CORRELATION ANALYSIS Hapten,... 

Know how to construct a Hansch equation from activity and property data... 

Be able to critically evaluate the validity of a Hansch equation... 

The Hansch equations that are available from the data in Table 12.5 have been covered, but there are still a few topics that deserve specific mention. All the topics revolve around the correlation coefficient—its generation, significance, and reliability. 

As always, the compounds included in the training set are vital for obtaining a useful Hansch equation. If only the... 

A second problem for Hansch analysis and any other predictive method is combinatorial chemistry. As methods in combinatorial chemistry continue to be refined and advanced, directed combinatorial libraries constructed around the scaffold of a lead have become a more standard practice. The availability of hundreds of lead analogues greatly diminishes the potential contribution from a Hansch equation. Why predict a structure s activity when one can make a library of essentially all interesting analogues, screen the library, and know the activity for certain ... 

The criticisms in the previous paragraphs lead to a question If Hansch analysis is of such questionable value, then why has an entire chapter of this textbook been devoted to the subject Despite the fading utility of classical QSAR methods such as Hansch analysis, the logic behind Hansch analysis is invaluable to medicinal chemistry. Synthetic chemists in the pharmaceutical industry intuitively consider the ideas used to construct Hansch equations. Ideas such as electronics, sterics, and lipophilicity underlie traditional SAR approaches in the laboratory. Critical analysis of activity data and emphasis on seeking holes in R-group selection are also fundamental to successful SAR on a lead. Through the study of Hansch analysis, all these crucial ideas are presented in a rational framework that helps demonstrate their relevance. Just as importantly, Hansch analysis provides the foundation for the next generation of QSAR comparative molecular field analysis. 

To continue the comparison, Martin prepared an additional set of 12 analogues of 12.18 and determined their activity against the 5-HT2 receptor. Both Nelson s Hansch equation and Martin s CoMFA model were used to generate calculated activities of the 12 new compounds. The summary of the findings is shown in Table 12.8. 

The root mean square (RMS) of the differences between the experiment and predicted values for the Hansch equation was 0.75, while the CoMFA gave 0.65. A smaller value for the RMS of the differences indicates CoMFA afforded a more accurate model. 

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