Free-Wilson substituent constants

Cammarata compared the Free-Wilson constants derived for a series of tetracycline analogs with some physical constants, and found a relationship which involved two parameters (4). In as yet unpublished work on antimalarial compounds I have found good linear relationships to exist between certain Free-Wilson substituent constants (S.C.) and Hansch s pi or Hammett s sigma constants for the same substituents. These relationships are shown in Table I. 

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 ... 

It should be pointed out here that the Hansch method, too, assumes that each substituent plays a constant and additive role from compound to compound, and it, too, is limited by the almost irreducible standard deviation of about 0.2 or 0.25 log 1/C units (8). In a recently published paper, Cammarata treats the relationships and assumptions involved in the Hansch and Free-Wilson methods from a systematic point of view (8). 

Free-Wilson model The Free-Wilson model is a mathematical approach for QSAR and is based on the hypothesis that the biological activity within a series of molecules arises from the constant and additive contributions of the various substituents, without determining their physicochemical basis. 

Free Wilson Analysis is an alternative procedure to the Hansch analysis (Free and Wilson, 1964). The assumption made here is that in a group of related compounds (i.e., a series having substitutions at more than one position), the effect of any given substituent is not dependent on the effects of a substituent at other positions. Measurement of physical properties are not necessary since substituent constants are based on biological activities. Equation 1.27 is the mathematical representation, where A is the log potency of a reference compound,... 

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. 

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... 

The second method, which was applied in the field of QSAR of corrosion inhibitors, is the Free-Wilson approach (Free and Wilson, 1964). Although by this method it has also been assumed that all the molecules are derivatives of a common parent structure, it is not necessary to collect substituent constant values to derive a regression equation. With this assumption, that inhibition efficiency is the dependent variable to be accounted for the Free-Wilson method is based on the following equation... 

An entirely different approach was taken by Free and Wilson (198). They assumed that the biological activity of a molecule can be represented as the sum of the activity contributions of a definite substructure and the corresponding substituents. This implies that the contributions of the parent fragment (a hypothetical structure that has no substituents) and of the substituents are constant and independent of substituents at other positions on the fragment. This can be expressed mathematically as... 

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