Free-Wilson model

Table 37.3 shows the complete table of eight indicator variables for 10 triply substituted tetracyclines [31 ] that have been tested for bacteriostatic activity (1/Z), which is defined here as the ratio of the number of colonies grown with a substituted and with the unsubstituted tetracycline. In this application we have three substitution positions, labelled U, V and W. The number of substituents at the three sites equals 2,3 and 3, respectively. Arbitrarily, we chose the compound with substituents H, NOj and NO2 at the sites U, V and W as the reference compound. This leads to a reduction of the number of indicator variables from eight to five, as shown in Table 37.4. The solution of the Free-Wilson model can be obtained directly by means of multiple regression ...

Principal components analysis can also be used in the case when the compounds are characterized by multiple activities instead of a single one, as required by the Hansch or Free-Wilson models. This leads to the multivariate bioassay analysis which has been developed by Mager [9]. By way of illustration we consider the physicochemical and biological data reported by Schmutz [41] on six oxazepines... 

Kubinyi, H., Kehrhahn, . H. (1976) Quantitative structure-activity relationships. 3. A comparison of different Free-Wilson models. JMed Chem 19(8), 1040-1049. 

The Free-Wilson model (also called additivity model) is defined as ... 

The Fujita-Ban model is a linear transformation of the classical Free-Wilson model indeed, group contributions of the Free-Wilson model can be transformed to Fujita-Ban group contributions by subtracting the group contributions of the corresponding substituents of the reference compound. 

Free-Wilson model Free-Wilson analysis... 

In regard to the representation of biological activity in the various Free-Wilson models there has been discussion (221,... 

Given the number of substitution sites S and the number of substituents for each site Nj, the maximum number of structurally diverse compounds that can be studied by a Free-Wilson model is... 

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] ... 

Free-Wilson models are appropriate if certain chemical features are responsible for changes in biological activities. The corticosteroid-binding globulin affinities of steroids are a standard data set for 3D QSAR analyses [103,104], However, the whole data set can be described with just one Free-Wilson parameter 4.5 > C=C< (value is 1 if a double bond is present in the 4,5-position of ring A value is 0 if there is a single bond or an aromatic bond Eq. (66)), with about the same quality of fit and predictivity [105] ... 

A closer inspection of the individual group contributions shows that there are some nonlinear effects. The exchange of hydrogen in the X group against phenyl or cyclohexyl or the exchange of phenyl to cyclohexyl and vice versa depends on the groups that are already present in X (Table 3). A much simpler Free-Wilson model... 

Free-Wilson model The Free-Wilson model is a mathematical approach for QSAR and is based on the hypothesis that the biological activity within a series of molecules arises from the constant and additive contributions of the various substituents, without determining their physicochemical basis. 

In Equations 8-11 a, b, c, and d represent the substituent contribution to the total activity of the compounds while the subscripts x and y denote the substituent positions on the parent molecule. Neither the additive model (noticeably similar to the Free-Wilson model) (Equation 8), the multiplicative model (Equation 9), nor the combined model (Equation 10) described the biological activity significantly. The combined expression (Equation 11), however, gave a statistically significant correlation between substituent activity and biological response for both the m- (35) and p- (34) disubstituted series. 

This is otherwise known as the Free-Wilson models especially in structure-activity studies. The models are shown graphically in figure 2.1. 

REFERENCE STATE PRESENCE-ABSENCE MODEL (FREE-WILSON) MODEL... 

The LFER models based on the same 22 compounds as in the de novo analysis were derived from all three bacterial systems in an attempt to see if physicochemical parameters would complement the results obtained from the Free-Wilson models. Again, series of statistically equivalent models were obtained. This probably was due to the distribution of values for these parameters. 

The Free Wilson model was in its original formulation [16] not as simple. No reference compound was selected and so-called symmetry equations were generated to avoid the problem of linear dependences between the variables. 

The version described by Fujita and Ban (eq. 8, chapter 1.1) [20, 390, 391] is a straightforward application of the additivity concept of group contributions to biological activity values. As nowadays only this modification is used, no details of the original formulation of the Free Wilson model and its complicated symmetry equations are discussed here. 

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