Relative biological response

C is the concentration of drug producing the biological effect being measured, log A, where A is the biological response relative to a standard or lead compound, can also be used, log P is the substituent constant for solubility (i.e., tc), Es is the Taft constant for steric effects, p and a are as previously defined, a, b, and d are constants of the system. 

Our basic methods have been detailed In previous reports (11, 12). In summary, however, our approach Is basically the same as that used by Hansch and co-workers (20-22) A set of compounds, which can reasonably be expected to elicit their carcinogenic response via the same general mechanism. Is chosen, and their relative biological activities, along with a set of molecular descriptors. Is entered Into a computer. The computer, using the relative biological response as the dependent variable, then performs stepwise multiple regression anayses (23) to select... 

R r Multiple correlation coefficient. R indicates the percentage of the variability of the relative biological response that can be accounted for by the selected independent variables. 

As our Index of relative biological response, we chose simply the fraction of liver tumors... 

We consequently became interested in developing a dose-dependent quantitative model using tso as the relative biological response. This model is shown as equation 6. 

It seems that large numbers of chemicals, in equally large numbers of test systems, from mammals to insects, vertebrates to invertebrates, microorganisms to plants, exhibit hormetic dose-response relationships. The relationship is not the same as that described earlier for nutrients, in two ways. First, in the case of hormesis the biological response - the toxicity endpoint - is the same in the protective region and in the region of toxicity (i.e., liver cancer incidence is reduced relative to control incidence over a range of low doses, and then as the NOAEL is exceeded, liver cancer incidence increases above that of controls). This is true hormesis. 

These and other investigators have shown, for many systems where a biological response can be measured quantitatively, that relative biological response can be expressed as functions of various molecular properties by using equations of the same forms as Hammett or Taft relationships ... 

RBR is the relative biological response, tt is defined as log Pg - log P where P is generally the water-octanol partition coefficent for the parent molecule and P is the partition coefficient for the molecule containing substituent S. The a s are standard Hammett or Taft substituent constants (26, 27). 

The most fundamental properties of a chemical substance are those of the substance in pure form, in most cases as a solid or liquid. Molecular mass can be deduced readily from the chemical formula or structure, although a range of values may exist for commercial mixtures. In some cases, the substance may adopt different structural (e.g., cis-trans) or enantiomeric forms, usually with relatively small physical property differences but with potentially substantial differences in ability to induce toxicity or other biological responses. The hexachlorocyclohexane isomers and enantiomers are examples, the insecticide lindane or y HCH being the most active form. 

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