Free-Wilson analyses

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 number of compounds must at least be equal to n. 

In the above expression the indicator variable I(X) takes the value 0 or 1, depending upon the absence or presence of the substituent X in a particular compound. The overall result of the regression is not significant at the 0.05 level of probability. This may be due to the unfavorable proportion of the number of compounds to the number of parameters in the regression equation (10 to 6). Only the indicator variable for substituent NHj at position W in the tetracycline molecule reaches significance (p = 0.02). This can be confirmed by looking at Table 37.4 

Complete indicator table and bacteriostatic activities of 10 triply substituted tetracyclines. The three substitution positions are labeled U, V and W [31]. 

In a broad sense, one may include the Free-Wilson equation within the class of linear free energy relationships (LFER). It is also subjected to the assumption of additivity of the contributions to the biological activity by substituent groups at different substitution sites. The assumption requires, for example, that there is no hydrogen bonding interaction between the various substitution groups. 

The additivity assumption holds that the contribution of any group to activity is dependent on position but is constant as long as the group is in that position. This assumption holds regardless of what other substituents are present in the molecule. 

If one takes the contribution of a hydrogen to activity as 0.0, then one can calculate the group contribution for a derivative by simply subtracting the activity of the parent from the activity of that derivative. For example, for the series of N-phenylsuccinimides reported by Takayama and Fujinami, we would find that the 3-Cl contribution was 

The reliability of a group contribution calculated in this way is low since the value contains the error of measurement for both the parent molecule and the derivative. Bruice et al. were the first to recognize that the additivity assumption could be expressed mathematically. Free and Wilson carried this 

Here the biological response, as in regression analysis techniques, should be expressed as the log of the inverse of the concentration required to elicit a desired response, i.e., biological response = log(l/C). This is done as a matter of convention so that a larger number will correspond to a more active compound. 

This equation can be solved by a least-squares fit to a straight line, in which case the group contributions G, become the regression coefficient for the parameters A FORTRAN program to run Free-Wilson anaijrsis has been provided by Purcell et al. However, any least-squares analysis program can be used for the analysis provided sufficient observations are available. The minimum number of observations required to solve this equation is given by 

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The work by Hammett and Taft in the 1950s had been dedicated to the separation and quantification of steric and electronic influences on chemical reactivity. Building on this, from 1964 onwards Hansch started to quantify the steric, electrostatic, and hydrophobic effects and their influences on a variety of properties, not least on the biological activity of drugs. In 1964, the Free-Wilson analysis was introduced to relate biological activity to the presence or absence of certain substructures in a molecule. 

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... 

Craig, P. N. (1972) Structure-activity correlations of antimalarial compounds. 1. Free-Wilson analysis of 2-phenylquinoline-4-carbinols. J Med Chem 15(2), 144-149. 

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]. 

Free Wilson analysis is easy to apply. No physio-chemical properties are needed to describe biological activity, just values of 1 or 0, to indicate the presence or absence of a certain position. 

On the other hand, Free Wilson analysis is much more restricted than Hansch analysis, because of its many parameters and the corresponding decrease on the number of degrees of freedom of the statistical analysis (Kubinyi 2002). 

This represents 3X3X3X6X6X3 = 2916 possible compounds. A good Free-Wilson analysis was obtained from only 42 of the possible analogs the preparation of these 42 compounds enables one to predict with a fair assurance the approximate antimalarial activity to be expected for almost 2900 unprepared analogs. 

In preparing the matrix for a Free-Wilson analysis, one must be careful to avoid situations which lead to singularities and hence cannot give a unique solution. The problem to be avoided is illustrated in Table IV in its simplest form. 

The similarity in approaches of Hansch analysis and Free-Wilson analysis allows them to be used within the same framework. This is based on their theoretical consistency and the numerical equivalencies of activity contributions. This development has been called the mixed approach and can be represented by the following equation ... 

Bocek-Kopecky analysis -> Free-Wilson analysis... 

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. 

Related to the Free-Wilson analysis is the -> DARC/PELCO analysis, which is an extension of the former to the hyperstructure concept [Duperray et al, 1976a]. 

Although the predictive power of a model is considered to be a criterion for the relevance of QSAR models, the main purpose of Hansch analysis and related approaches such as Free-Wilson analysis concerns not prediction, but a better understanding of the chemical problem. 

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