Question

Advantage and disadvantage of free willsion analysis

Answer 1

Free and Wilson reasoned that the biological activity for a set of analogues could be described by the contributions that substituents or structural elements make to the activity of a parent structure.
Free-Wilson equations do not require the use of substituent constants such as ,  m,  p, F, R, ES, and MR, and are represented by the general equation:

where aj is the group contribution of the structural feature X in position j in molecule i and  is the theoretical biological activity value of a reference or parent compound. The descriptor Xijhas a value of 1 if the feature is present in position j in moleculei and 0 in the absence of that feature. There are advantages and disadvantages of Free-Wilson type analyses that are discussed in Exploring QSAR.
The presence and absence of structural elements is indicated by the values 1 and 0, respectively. It is possible to add indicator variables to the Hansch equation as a combination of Free-Wilson analysis and Hansch analysis. The indicator variables can be used to describe a variety of structural features, such as substructures, chiral centers and special substituents.
A typical tabulation for a set of compounds is shown in the following table:

metaparameta-para-log 1/C log 1/C (X)(Y)FClBrIMeFClBrIMeobsd.calc.a)HH          7.467.82HF     1    8.168.16HCl      1   8.688.59HBr       1  8.898.84HI        1 9.259.25HMe         19.309.08FH1         7.527.52ClH 1        8.168.03BrH  1       8.308.26IH   1      8.408.40MeH    1     8.468.28ClF 1   1    8.198.37BrF  1  1    8.578.60MeF    11    8.828.62ClCl 1    1   8.898.80BrCl  1   1   8.929.02MeCl     1  1   8.969.04ClBr 1     1  9.009.05BrBr  1    1  9.359.28MeBr    1  1  9.229.30MeMe    1    19.309.53BrMe  1      19.529.51
MLR can be performed on data in the above table, resulting in the regression equation that follows. Notice that the independent variables are the various groups shown in square brackets and are simply indicating the status of those groups. A negative coefficientindicates that the presence of that group is unfavourable to activity; a positive coefficientindicates that the presence of that group is favourable to activity.