Chemistry Reference
In-Depth Information
mixed toxicants produce an effect less than predicted from simply summing the
expected effect of each one alone. Functional, dispositional, or receptor-based modes
for antagonism exist. Functional antagonism occurs if the toxicants change the pro-
cess leading to adverse effect in opposite directions, neutralizing each other's effect.
Dispositional antagonism occurs if the toxicant influences the uptake, movement,
deposition, or elimination of the other(s). Receptor antagonism occurs if the toxi-
cants block or compete in a material way with the other from a receptor. A relevant
example might be the competition of metal ions for movement through ion channels,
such as that described by Vijverberg et al. (1994). A quick review of the discussions
above should reveal the capacity of metals to interact in these manners and for these
interactions to be related to intermetal binding trends.
Again, modeling joint action of mixed toxicants is based on whether the mixed
chemicals are thought to be predominately independent or similar in action for an
adverse effect. The joint effect (
P
M
1
+M
2
) of two independently acting metals (
M
1 and
M
2) combined at concentrations
C
M
1
and
C
M
2
that alone would produce
P
M
1
and
P
M
2
proportions (or probabilities) of effect would be predicted with the model,
P
M
1 +
M
2
=
P
M
1
+
P
M
2
(1 −
P
M
1
) or
P
M
1
+
P
M
2
−
P
M
1
P
M
2
(1.3)
As discussed in Chapter 8, any deviation from ideal independence might be
detected by inserting a parameter (ρ) to be estimated into Equation (1.3) in place
of the implied 1 and then testing for significant deviation from 1 for the parameter
estimate (Newman and Clements 2008).
P
M
1 +
M
2
=
P
M
1
+
P
M
2
− ρ
P
M
1
P
M
2
(1.4)
Depending on study goals, a general linear modeling approach might be applied
to these kinds of data. If there are more metals in the mixture, the independent joint
action model can be expanded to Equation (1.5).
P
M
1 +
M
2 +
M
3...
= 1 − (1 −
P
M
1
) (1 −
P
M
2
) (1 −
P
M
3
)…
(1.5)
The approach is different for mixed metals that are assumed to have a material
degree of interaction due to a similar mode of action. Such situations produce toxi-
cant effect-concentration relationships for each of the toxicants alone that have the
same slopes (
Slope
Common
) (Finney 1947). Extending the notation above to the case of
similar joint action,
Pr
obit
(
P
M
1
) =
Intercept
M
1
+
Slope
Common
(
Log
C
M
1
)
(1.6)
Pr
obit
(
P
M
2
) =
Intercept
M
2
+
Slope
Common
(
Log
C
M
2
)
(1.7)
The logarithm of the relative potency of these mixed toxicants (e.g., ρ
M
2
) can
then be estimated (Equation [1.8]) and used to predict the combined effects of these
mixed toxicants (Equation [1.9]).
