Combined Actions and Interactions of Chemicals in Mixtures

(Altenburger etal. 1993). Agents that act synergistically at the molecular level (e.g.
receptor binding) may display additivity with endpoints at more complex
functional levels such as cell growth or cell death (Grimme et al. 1996). For this
reason it is important to carry out analysis of combination effects of estrogenic
compounds at different levels of molecular complexity.
7.5.4 The isobole method – a practical approach
Two main reference models for defining expected effects of mixtures of agents
have emerged: the models of concentration addition and response addition. In the
following discussion the model of concentration addition is used. It is by far the
most frequently employed reference model and has sound pharmacological
foundations. Unlike the model of response addition, it is easily applied to the nonfractional
effects yielded by assays employed to quantify estrogenic effects. The
basic idea behind the concept of concentration addition is to compare doses, which
produce effects of equal strength (iso-effective doses). The isobole method, which
is derived from the method of concentration addition and has the advantage of
being illustrative, is widely applied. One of the strengths of the method of isoboles
is that it can be used to analyse combinations of agents, irrespective of the shape of
their dose-response curves (Kortenkamp and Altenburger, 1998). It is possible to
assess mixtures of agents with dissimilar dose-response curves, even when the
maximal effects are not identical.
An analysis using the isobole method is carried out by constructing graphs that
show curves describing combinations of two compounds A and B which produce
the same specified effect (isoboles) (see chapter 2.4.3). The axes of the graph
represent doses of the two compounds on a linear scale. A line joining the isoeffective
doses A and B of the single agents predicts the combination of A and B,
which will yield the same effect, provided the interaction between A and B is
additive. In this case the relationship can be expressed:
dA/DA + dB/DB = 1
where dA and dB are the doses/concentrations of A and B in a mixture that produces
a specified effect and DA and DB are the doses/concentrations of the single agents
which on their own elicit the same effect.
If datapoints lie below the additivity isobole then dA/DA + dB/DB < 1, indicating
synergism. With antagonism concave-down isoboles above the additivity line
appears, as dA/DA + dB/DB > 1. Note that the position of isoboles varies depending
on the effect level chosen for analysis.
The method can also be applied to mixtures where only one of the two agents
produces the effect under consideration. The iso-effective dose of the agent lacking
the effect of interest can be regarded as infinitely large, so that the resulting
additivity isobole runs parallel to the respective dose axis.
Combination of three agents can be analysed by constructing three-dimensional
isobolar surfaces, and combinations of more than three compounds can be assessed
more easily by using a generalisation of the above-mentioned equation:
dA/DA + dB/DB + dC/DC + dD/DD +…………. = 1
Using this approach, valid conclusions on the combination effect of mixtures can
often be drawn on surprisingly few data.
The method of isoboles does not include facilities, which are helpful in deciding
whether deviations from the line of additivity are systematic or simply due to
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