Group biological activity values

Log 1/C = Ea + i (ai are the group contribution of the individual substituents X to the biological activity values and p, is the calculated biological activity of a reference compound, most often the unsubstituted analogue). 

Where G.. is the activity contribution of a substituent in position i, and y represents the overall average of biological activity values. For example, Xjj 1 if the substituent is in position otherwise it is equal to zero. The most convenient way to construct equation 101 is by generating a matrix in which each row represents a specific compound. The columns are divided into as many groups as there are substituted positions on the molecule and each column within a group represents a certain substituent. For a compound in which two sites, a and b, have substituents Xla, X2a,...,Xna, and Ylb,Y2b, >Ymb> the following matrix can be constructed ... 

In the following decades, various a scales were derived for different systems and several attempts were made to derive such relationships also for biological activities of organic compounds. Bruice et al. [10] formulated group contributions to biological activity values in a series of thyroid hormone analogs, which may be considered as a first Free-Wilson-type analysis. Zahradnik and Chvapil [11] and Zahradnik [12,13] tried to apply the concept of the Hammett equation also to biological data (Eq. (5)) ... 

Free-Wilson analysis can be used for a first inspection of biological activity data [30-32]. The values of the group contributions indicate which physicochemical properties might be responsible for the variations in biological activity values and whether nonlinear lipophilicity-activity relationships are involved. Free-Wilson contributions can be derived from Hansch equations (e.g., by Eq. (18) from Eq. (14), or by Eq. (19) from Eq. (15)) [30] ... 

While the success of QSAR analyses may be taken as sufficient evidence for the additivity of group contributions to biological activity values, the following question arises are these group contributions more or less constant from one system to the other or do they depend on the choice of the compounds and/or the biological system ... 

Also the affinity constants of the phosphonamidate analogs (1, Table 1) confirm the additivity concept of group contributions to biological activity values. The different residues R are separated from the bridge atom X by two carbon atoms all affinity values of the three series with X = —NH—, —O —, and — CH2— are closely correlated [137]. 

Indicator variables have also been used to account for other struetural features, e.g. for intramolecular hydrogen bonds, hydrogen bond donor and acceptor properties, ortho effects, cis/trans isomerism, different parent skeletons, different test models, etc. [22, 390]. Some precautions are necessary indicator variables should not describe a single compound (in this case the corresponding group contribution includes the experimental error of this one biological activity value) and the use of indicator variables should be justified from a theoretical point of view otherwise, continuous variables will be mixed with meaningless dummy variables, just to fit the data. 

The version described by Fujita and Ban (eq. 8, chapter 1.1) [20, 390, 391] is a straightforward application of the additivity concept of group contributions to biological activity values. As nowadays only this modification is used, no details of the original formulation of the Free Wilson model and its complicated symmetry equations are discussed here. 

Every substituent which only once occurs in the data set, leads to a single-point determination the corresponding group contribution contains the whole experimental error of this one biological activity value. 

Two extra variables in the first analysis accounted for (+)-enantiomers (aj = —0.97) and (—)-enantiomers (a = 0.17). While the value for the more active (—)-enantiomers is not too far from the theoretical value of 0.3, which results if the (+ )-enantiomers are absolutely inactive, general experience shows that the less active enantiomers cannot be expected to differ from the active ones (or the racemates) by a constant value (problems associated with QSAR analyses of optically active compounds are discussed below and in chapter 9.1). The group contributions of the benzomorphans could be used to predict the biological activity values of structurally related morphinans (49), which are more active than the benzomorphans by some orders of magnitude (eq. 191) [811]. 

As in all other QSAR methods, predictive ability depends on the distances of the compounds to be predicted from the other congeners of the series. One cannot expect reliable predictions of biological activity values for analogs having additional side chains or groups with significantly different eleetronic properties. 

Biological Activity Values and the Additivity of Group Contributions... 

The underlying concept of all QSAR analyses is the additivity of substituent group contributions to biological activity values in the logarithmic scale. This additivity comes from the fact that QSAR models are linear free-energy related. All... 

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