Modified Free-Wilson method for the analysis of biological activity data

Abstract

Abstract A general approach to the analysis of biological activity data in terms of molecular constitution has been proposed. The algorithm is closely related to that of Free & Wilson [ J. Med. Chem. 7 , 395 (1964)]. The biological activity or its transform is split into the sum of contributions characteristic of different positions (segments) of the molecule, the segment contributions , the contributions characteristic of pairs of segments, the interaction contributions , and possibly higher order terms. The contributions are to be determined from a given set of biological activity data by a linear least-squares method. The analysis of the solution space of the resulting system of linear equations reveals that additional constraints must be imposed on the contributions in order that the problem be well-defined. One of the possible choices is to assign a standard substituent to each position in the molecule and define the segment (interaction) contributions relative to those of the standard substituents (pairs of substituents). This choice assures that the values obtained do not change formally when particular compounds are added or removed from the data set. In contrast to this, in the traditional Free-Wilson approach the segment contributions are defined relative to the average of all the segment contribution in a given position over the data set analyzed and therefore are shifted when the data set is changed. An algorithm has also been developed which handles cases when additional linear dependences occur between the contributions. A numerical example is presented.