Quantitative structure-activity relationships. 3. A comparison of different Free-Wilson models

The Fujita-Ban model and the classical Free-Wilson model are shown to be linearly related: the de novo group contributions obtained by one model are linear transformations of those obtained by the other model. An example is given to illustrate this linear dependence. The Fujita-Ban model is characterized by a number of advantages as compared with the classical Free-Wilson model: no transformation of the structural matrix and no symmetry equations are necessary; all group contributions are based on an arbitrarily chosen reference compound, preferably the unsubstituted compound; the constant term, which is the theoretically predicted activity value of the reference compound, and the values of the group contributions are not markedly influenced by addition or elimination of a compound; the problem of linear dependence (the singularity problem) sometimes can be circumvented by preparation of a contracted matrix; if the unsubstituted compound is chosen as reference compound, the group contributions are numerically equivalent to Hansch-derived group contributions; therefore, the Hansch approach and the Fujita-Ban model can be combined to a mixed approach. Taking all these facts into consideration, the Frujita-Ban model is recommended as the most suitable approach for the calculation of de novo group contributions.