Improvement, Hansch equations

Hansch analysis is useful not only for drug discovery. A study of insecticides and related nonpolar compounds has shown that the bioconcentration of these compounds (log BC) in trout muscle is related to log P. Create a Hansch equation based on the following data. Does including a (log P)2 term improve the fit Is this surprising Explain. (Neely, W. B., Branson, D. R., Blau, G. E. Partition Coefficient to Measure Bioconcentration Potential of Organic Chemicals in Fish. Environ. Sci. Technol. 1974,8, 1113-1115.)... 

For reasons discussed below, data points for the 4-SCH3 and 3-SCH3 derivatives were omitted from the fits of Equations 10-12. Hence n, the number of data points included in the fits, equals 13 instead of 15. Examination of Equations 10-12 indicates, however, that even though log (I/LD90) exhibits a fairly strong dependence on <7, the data are not particularly well correlated by the Hansch equation. Addition of r2 and tt terms to Equation 10 raises the percent correlation (r2) from 61 to 67%, but F is decreased and the standard error SE increased in the process. Hence, the correlation is not statistically improved. 

The statistical parameters in Equations 13—15 for the 4-substituted TFMS series members and Equations 16-18 for the 3-substituted compounds demonstrate that the fit of the biological data to the Hansch equation is significantly improved when the TFMS herbicides are separated into two classes (cf. Equations 10-12). Both the 3- and 4-series exhibit a strong dependence not only on o-, but also on tt. For the 4-sub-... 

Placement of the Parent Compound. Separation of the TFMS herbicides into two classes consisting of meta- and para-substituted derivatives which were fitted separately resulted in significantly improved correlations via the Hansch equation. It was not readily apparent, however, into which of the two herbicidal categories the H-substituted parent com-... 

TFMS derivative in the presence of surfactant (cf. also Figures 2a and 2c). Thus, the loss in Foxtail activity which results from the deleterious effect of surfactant on the pa term in the Hansch equation is compensated by the improved partitioning characteristics (large Bn term) of the 4-methylsulfonyl derivative in the presence of surfactant. The net result is that the overall pre-emergence Foxtail activity is not greatly affected by Tween 80. As illustrated in Table XIII, however, this effect is only apparent since significant changes in both ir and a dependence have taken place. 

Equations (9) and (10) constitute the fundament of all QSAR studies. Since 1964, they have remained essentially unchanged, with the exception of two minor modifications. Improvements resulted from the combination of Hansch equations with indicator variables [22], which may be considered as a mixed Hansch/Free-Wilson model (Eq. (11)) [23], and from the formulation of a theoretically derived nonlinear model for transport and distribution of drugs in a biological system, the bilinear model (Sec. 4 Eq. (30)) [24] ... 

Both models remained unchanged over the past three decades. Some improvements resulted from the combination of Hansch equations with indicator variables... 

An example, how a Hansch equation can be improved by comparing the group contributions with those obtained from Free Wilson analysis, is given below. Eq. 75 was derived for the antifungal activities of phenyl ethers (13, X, Y = H, OH) [426]. Eq. 76 results if all members of the series are included, giving an even worse fit [393] in both equations the a term is not significant. 

Some other examples of the stepwise derivation of Hansch equations and of the improvement of Hansch equations from the interpretation of Free Wilson analyses have been published (compare eqs. 75 — 77, chapter 4.3) [22, 390, 393],... 

Hansch formulated a parabolic model (eq. 7, chapter 1.1) [15, 17—19] for the mathematical description of nonlinear relationships. He was aware that the sides of a parabola are always more or less curved, while in most cases at least the left side of the structure-activity relationship (i.e. the lipophilicity dependence of the more hydrophilic analogs) is strictly linear equations including a third-order lipophilicity term did not produce much improvement [19]. A computer simulation of the transport of drugs in a biological system, using hypothetical rate constants,... 

Equations (17) and (18) cannot be used directly for predictive purposes since they only describe and identify the components and not the original p/50 values directly. They clearly show, however, what the physical nature of the components is and in what direction stracture / has to be varied in order to arrive at more potent derivatives. True equations in the sense of a QSAR could have been obtained by the already mentioned special target rotation of Weiner and Malinowski, which would lead to a direct replacement of the abstract P j by molecule parameters according to equation (15). This, however, would not add new information in the present case, at least not for the three enzyme systems. For the ascites test the situation is a little different since here a small contribution of the first component in addition to the second component is present. If a Hansch analysis is directly applied to the experimental data of ascites inhibition alone a relation with % very similar to equation (18) is again obtained which can, however, be improved slightly by adding an electronic term. 

In addition to the log P, other physico-chemical parameters were investigated as to their relationship with the observed toxicities of both the subgroups and the entire set of 1,4-di-substituted benzene derivatives. Parameters so used include w for each of the subset functional groups (R = NO2, NHj, Cl, OH, NMOj), and the substituents (X) molar refractivity (AMR), cTp, and field and resonance contributions, as listed by Hansch and Leo (1979). While some of the correlation coefficients improved and slightly lower s values were obtained, all these derived equations fail to satisfy the demand for an explanation of all the data with an acceptable standard error of, say, s = 0.3 to 0.4 log units. It can be concluded then, that one or more of the following conditions prevail ... 

The addition of the discrete variable Hd, the ability of the substituent to donate hydrogen, further improves the model, as demonstrated by equation 5. Again, all included molecular descriptors contribute to the model at the P = 0.05 level of significance. Because the hydroxy substituent, common to all phenols, is a hydrogen donor substituent (Hansch and Leo 1979), the addition of the Hd descri ptor helps account for the toxicity of compounds with two para-oriented hydrogen donor groups. For the most part these are the less toxic compounds. 

A further improvement came from the combination of Hansch and Free-Wilson analysis in a mixed approach, which widens the applicability of both QSAR methods. In equation (5), physicochemical parameters describe parts of the molecules with broad structural variation, whereas indicator variables encode structural variations which cannot be included otherwise (the lipophilicity parameter tx may be used instead of log P) ... 

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