Free-Wilson descriptor

The Free-Wilson descriptors of the i th compound are indicator variables Ij s where I, = 1 if the kth substituent is present in the ith site and = 0 otherwise. These descriptors are usually collected in a table called the Free- Wlson matrix (Table F-1), where the rows represent the data set molecules and each column represents a substituent in a specific site. 

Free-Wilson descriptors -> Free-Wilson analysis... 

Moreover, molecular descriptors different from Free-Wilson descriptors were calculated by transformation of the Free-Wilson matrix through Fourier analysis [Flolik and Halamek, 2002], In this case, Fourier analysis is used to change site- and substituent-oriented binary variables into a few real numbers [Holik and Halamek, 2002]. 

A key advantage of the Free-Wilson method over standard descriptors-based QSAR techniques is the estimation of activity contribution for individual R-group structures that are readily interpretable to medicinal chemists. 

A large combined data set of 48 propafenones was then analyzed by both Free-Wilson analysis and a combined Hansch/Free-Wilson approach using an artificial neural network (ANN). With this approach it was possible, in contrast to conventional MLR analysis, to correctly predict the MDR-reversing activity of 34 compounds of the data set after the ANN was trained by only 14 compounds. Best results were obtained using those descriptors showing the highest statistical significance in MLR analysis [150]. 

The epoch of QSAR (Quantitative Structure-Activity Relationships) studies began in 1963-1964 with two seminal approaches the a-p-7i analysis of Hansch and Fujita " and the Free-Wilson method. The former approach involves three types of descriptors related to electronic, steric and hydrophobic characteristics of substituents, whereas the latter considers the substituents themselves as descriptors. Both approaches are confined to strictly congeneric series of compounds. The Free Wilson method additionally requires all types of substituents to be suflficiently present in the training set. A combination of these two approaches has led to QSAR models involving indicator variables, which indicate the presence of some structural fragments in molecules. 

Fujita-Ban analysis is a modified Free-Wilson analysis where the activity contribution of each substituent is relative to the activity of a - reference compound [Fujita and Ban, 1971]. Any compound can be chosen as the reference, but usually the H-sub-stituted compoimd (all R = H) is adopted. The Free-Wilson matrix in the Fujita-Ban analysis does not contain the descriptors corresponding to the substituents of the reference compound, i.e. the number of indicator variables is diminished by the number of sites S with respect to the corresponding original Free-Wilson approach. Moreover the row vector corresponding to the reference compound is characterized by all the descriptor binary values equal to zero. 

The most well-known approaches based on substituent descriptors are the Hansch analysis and - Free-Wilson analysis in the latter technique, the substituents are defined by - indicator variables representing their presence/absence in the substitution sites of the parent molecule. 

There are numerous examples of traditional Hansch QSAR studies in the literature. " Some include large sets of descriptors, while others explore just a few. If physicochemical descriptor values are not readily available, indicator variables, denoting presence or absence of a certain structural feature, may be of help. This is the basis of the Free-Wilson (FW) method. 

The total number of indicator descriptors (i.e., the Free-Wilson matrix columns) is... 

Hansch bilinear models —> Hansch analysis Hansch descriptors —> Hansch analysis Hansch-Free-Wilson mixed models Hansch analysis... 

Binary descriptors are also used in Free-Wilson analysis and DARC/PELCO analysis. 

Structure/Response Correlations, Hansch analysis, Hammett equation, Free-Wilson analysis. Linear Solvation Energy Relationships, Linear Free Energy Relationships, group contribution methods, substituent descriptors, extrathermodynamic approach, and biological activity indices. 

The Free-Wilson method has the advantage that one does not need to estimate physical property descriptors for the compounds. This property also makes it difficult, if not impossible, to forecast the bioactivity of untested substituents. Moreover, the assumption of a constant effect on the potency of a particular substituent at a particular position breaks down in the case of a nonlinear relationship of potency with log P. 

We have successfully applied LOGANA and LOGON in a number of cases [122-126, 171] and use both methods routinely. As a simple example we shall present here results [122] obtained for a series of fungicidal carboxamides as inhibitors of succinate dehydrogenase (experimental data from [172]). The series comprises 89 compounds of the general stractuie presented in Fig. 5. Stmctuial variations are so extensive that QSAR methods of the Hansch or Free-Wilson type do not lead to meaningful results. Tables 6 and 7 summarize the topological descriptors used in the analysis. 

To comply with good statistical practice, several criteria have to be met for a significant regression model based on either the physico-chemical descriptors (Hansch approach) or the indicator variables (Free-Wilson method) ... 

Like the continuous physico-chemical descriptor Z variables, indicators of the presence or absence of certain substructures have also been treated by multiple regression analysis. As modified by Fujita and Ban (Seydel and Schaper, 1979), this group contribution method can be a useful alternative to the LFER approach, if only limited knowledge is available about the relevant molecular properties or no uniform physico-chemical descriptors for the various compounds in the data set are accessible. For activities and properties of compounds that may be attributed to the occurrence of certain substructures in the molecules (e.g. biodegradation section 4.8), Free-Wilson-type substructure models have their major application in environmental sciences. 

One of the disadvantages of the Free-Wilson method is that— unlike regression equations based on physicochemical parameters— it cannot be used to make predictions for substituents not included in the original analysis. The technique may break down when there are linear dependencies between the structural descriptors, for example, when two substituents at two positions always occur together, or where interactions between substituents occur. Advantages of the technique include its ability to handle data sets with a small number of substituents at a large number of positions, a situation not well handled by other analytical methods, and its ability to describe quite unusual substituents since it does not require substituent constant data. A number of variations and improvements have... 

QSARs include statistical methods to relate biological activities (most often expressed by logarithms of equipotent molar activities) with structural elements (Free Wilson analysis), physicochemical properties (Hansch analysis), or fields (3D QSAR). The parameters used in a QSAR model are also called (molecular) descriptors. Classical QSAR analyses (Hansch and Free Wilson analyses) consider only 2D structures. Their main field of application is in substituent variation of a common scaffold. 3D-QSAR analysis (CoMFA) has a much broader scope. It starts from 3D structures and correlates biological activities with 3D-property fields (McKinney et al. 2000). 

George R. Famini and Leland Y. Wilson, Linear Free Energy Relationships Using Quantum Mechanical Descriptors. 

Famini, G.R. and Wilson, L.Y. (1999) Using theoretical descriptors in linear free energy relationships characterizing several polarity, acid and basicity scales./. Phys. Org. Chem., 12, 645. 

The classical QSAR methodology started 1964 with the publications of Hansch and Fujita (1964) and Free and Wilson (1964) and the statement of Hansch (1969) resulted from a proposal by Fujita. They proposed to combine several physiochemical parameters (tt, a), also called descriptors, in a quantitative model. This Hansch-type analysis is very flexible and describes many different kinds of biological activities, e.g. in vitro data such as enzyme inhibition (Kubinyi 2002) ... 

---