Page 53 - The Toxicology of Fishes

Bioavailability of Chemical Contaminants in Aquatic Systems 33

When just the free form of the toxic metal (M) binds to the gill sites (X), this model can be expressed
as follows:

   m   n 
∑
EC =  f EX  ⋅1 + ( K CX ⋅[ C j ) ]  ⋅  ∑ R i  (2.7)
+
1
(  1 − f EX)⋅ K MX     j j    i 
where EC is the total concentration of metal in the exposure water required to elicit a specified effect
and is a product of the three mathematical expressions on the right side of the equation. The first
expression is a baseline effect concentration that is expected in the absence of any cation competition
and ligand complexation. It is a function of (1) f , the fraction ([MX EFF ]/[X TOT ]) of the gill sites that
EX
must be occupied by the toxic metal to elicit the effect of concern, and (2) K MX , the association
constant for the binding of the toxic metal to the gill sites.
The second expression provides the factor by which the EC increases (bioavailability decreases) due
to cations that compete with the toxic metal for the gill sites. This factor increases with increasing
products of [C ], the free concentration of the j-th of m competing cations, and K CjG , the association
j
constant for the binding of this cation to the gill sites.
The third expression provides the factor by which the EC increases (bioavailability decreases) due to
ligands that complex the toxic metal in the exposure water. This factor increases with increasing
concentration ratios (R ) of each metal complex to the free metal. For single-ligand complexes, this
i
ratio is simply the product of the free concentration of the ligand and the association constant for
this complex; however, in general, calculation of the R values requires a chemical speciation model
i
that can address more complicated speciation relationships and relate calculations to total chemical
concentrations, because free concentrations generally are unknown.
When only one competing cation or complexing ligand is varied, this model predicts a linear rela-
tionship between the EC and the free concentration of that cation or ligand, with the intercept equal to
the baseline EC. De Schamphelaere and Janssen (2002) provided good examples of such linear relation-
ships for copper toxicity to a cladoceran and also addressed how this mathematical framework can be
expanded to address the toxicity of species other than free metal.
Recent efforts have demonstrated that this bioavailability modeling approach can be useful for describ-
ing the toxicity of various metals to fish and other aquatic organisms (see review by Paquin et al., 2002a).
Santore et al. (2001) and Di Toro et al. (2001) accounted for a high percentage of the variation of toxicity
within a large dataset for acute copper lethality to fathead minnows, nearly always predicting toxicity
to within a factor of two. Figure 2.12 shows a subset of these data consisting of a series of test waters
with the same pH, low organic matter content, and similar relative amounts of major cations and anions
but different total ion concentrations. The large range of copper toxicity in this dataset primarily reflects
the combined effects of changes in alkalinity, calcium, and sodium. The model is very successful in
predicting relative changes in toxicity and underestimates LC values by only about 30% on average.
50
This underestimation of LC values might be due to uncertainties in model parameterization and sample
50
characterization (especially regarding the organic complexation in these samples) or to uncertainties in
model formulation discussed below.
One strength of this modeling approach is that parameters can be primarily, or even entirely, estimated
independently of the toxicity relationships of interest. Estimation of metal speciation in exposure water
does not depend at all on toxicity data, and association constants for binding of metal to gill sites can
be estimated from accumulation experiments. Only the gill accumulation associated with the toxic effect
has to be determined under toxic conditions, and it does not have to involve any consideration of the
effects of exposure conditions on toxicity (MacRae et al., 1999). If such independent parameter estimates
are not feasible or are uncertain, this model can also be used to estimate or refine parameter values from
the toxicity relationships (De Schamphelaere and Janssen, 2002); however, to the extent that model
parameters are derived from toxicity data, there is less confidence that the model truly describes the
processes regulating bioavailability rather than just providing a reasonable framework for data-fitting.
Despite the successes of this approach for modeling metal bioavailability, certain uncertainties and
limitations in the model formulation must be noted: