Shapes of the biological response curves

The most common curves are bell-shaped, the peak activity corresponding to a given value of the number n of carbon 

The activity can increase, without any particular rule, with the number of carbon atoms (curve B). 

In other series, the activity increases first with the number of carbon atoms and then reaches a plateau (curve D). 

The activity can also decrease regularly, starting with the first member of the series (curve E). This was found for the toxicity of aliphatic nitriles or for the antiseptic properties of aliphatic aldehydes. 

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FIGURE 14.9 Shapes of the biological response curves in homologous series. 

All of these considerations indicate that the biology behind the shape of the tumor dose-response curve is much more complex than a simple conclusion that mutagenic activity = linear dose-response. Ultimately, biologically based dose-response models and use of biomarker data may make it possible to extend the tumor dose-response curve to low doses based on biological data, rather than presumptions about the shape of the dose-response curve. In the shorter term, it is important to recognize that the biology is complex, and linear extrapolation from tumor data is a health-protective science policy decision. 

There have been several mathematical models developed for estimating the effects of exposures at dosage levels below those for which test data are available. It is beyond the scope of this chapter to review these models in any detail and for a more detailed discussion the reader is referred to reviews such as those by Schneiderman et al. Cranmer, and Hoel et al. What will be discussed here are the biological bases and implications of some of these models, and a recently conducted, large-scale experiment which attempted to determine the shape of the dose response curve for mice fed low levels of the carcinogen 2-acetylaminofluorene (2-AAF). 

The biological response line for acute respiratory disease is a dose-response curve, which for a constant concentration becomes a duration-response curve. The shape of such a curve reflects the ability of the human body to cope with short-term, ambient concentration respiratory exposures and the overwhelming of the body s defenses by continued exposure. 

As mentioned above, the cannabimimetic SAR does not necessarily parallel the SAR of cannabinoids for other biological or therapeutic effects. Indeed, we have found now that enantiomer (33), which (as noted above) does not cause cannabimimetic effects, is a potent analgetic particularly in the presence of cupric ions. In table 4, we present the results of several analgetic tests. In all tests, (33) shows activity at (or above) the potency level of morphine. However, as previously noted with delta-1-THC and other cannabinoids, the dose-response curve is not sharp (as with morphine) but flat. Surprisingly, the level of analgetic potency is retained over a period of 3 to 4 days. In some tests, activity actually falls beyond a certain concentration, the dose-response curve assuming an inverted U shape. 

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