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Barium toxicity by disruption of normal K + and Na + /K + channel functioning
(Das  et  al. 1988; Delfino et  al. 1988; Taglialatela et  al. 1993; Bradberry and Vale
1995) is a particularly informative example of the role played by binding tendencies
on effects in metazoans. In this case, it is the class (a) metal ion binding charac-
teristics that emerge as important. Tatara et  al. (1998) determined LC 50 values for
nematodes ( Caenorhabditis elegans ) exposed to a series of mono-, di-, and trivalent
metal ions including Ba 2+ . They produced a QSAR with χ 2 r and |Log of K OH |, but
found that Ba 2+ was much more toxic than predicted from the general QSAR model.*
Tatara et al. explained this difference using the relative charge densities of K + and
Ba 2+ . The atomic radii of K + and Ba 2+ are 1.38 and 1.36 Å, respectively, but these very
similar radii are associated with ions of different charge. The result is very different
ion charge densities as reflected in the metric, Z 2 r −1 . The bonding to the K + channel
is much more stable for Ba 2+ than K + , resulting in a blocking of the essential passage
of K + through membrane ionophores of excitable tissues. Nervous and muscle tis-
sue could not function properly. This explained the atypical toxicity of Ba 2+ to the
nematode.
In summary, differences in metal coordination chemistries produce differences in
the bioaccumulation and effects of single metals. Associated trends can be predicted
with basic metrics of metal-ligand interactions.
1.3.3 m etAl i interActions in m ixtures
Quantitative means of coping with joint action of metals in mixture have lagged
behind those used to quantify effects of single metals. This has produced a body of
mixture publications that are more descriptive or graphical than those for single met-
als. In some extreme cases, they are insufficient for quantifying joint effects despite
common use. Typical studies include the toxic unit approach in research such as that
implemented by Sprague and Ramsay (1965) and Brown (1968), and also the iso-
bole graphical approach taken by Nash (1981), Broderius (1991), or Christensen and
Chen (1991). Some approaches, such as the rudimentary concentration additivity con-
text of toxic units, can be misinformative, tending to confuse as much as advance
understanding. The classic quantitative models based on independent and similar joint
action provide the best chance of exploring metal ion mixture effects as correlated
with coordination chemistry.
Joint action of mixtures is quantified differently depending on whether the mixed
toxicants are thought to be acting independently or by a similar mode of action
(Finney 1947). In practice, independently acting chemicals are notionally those
acting by different modes. In other instances, similar joint action is assumed: the
mixed toxicants share a dominant mode of action and display similar toxicokinetics.
Mixed toxicants can result in potentiation in which the presence of one chemical
at nonlethal levels makes another toxic or more toxic. Mixed toxicants can also be
synergistic. In that case, the two or more toxicants together at the specified levels
are more toxic than would be predicted by simply summing the effect expected for
each alone at those concentrations. The opposite (antagonism) can also occur if the
* Lewis et al. (1999) later found similar outlier behavior for barium mouse and rat toxicities.
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