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As a trace element, mercury is present in all natural systems, and thus all organisms have some small
amount of tolerance for this substance in minute doses. In larger concentrations, however, mercury
can be quite harmful or even fatal. Throughout the world mercury has come under widespread use in
industry, agriculture, and medicine, increasing the risk for people to become ill or die due to the
ingestion of fish tainted with mercury. In recent years much work has been done to assess the effects
of mercury on both fish and their predators, including humans.
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For this project, applied mathematicians
at MathEcology developed a physiologically based toxicokinetic model to predict the uptake and
distribution of methyl mercury in fish, with specific focus on species of freshwater fish commonly used
for human consumption.
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Physiologically based toxicokinetic models for organic chemicals divide the fish into five tissue
compartments: liver, kidney, fat, richly perfused (stomach, intestines, spleen, and gonads), and poorly
perfused (white muscle, skin, and fins) tissue groups. The uptake and elimination of the chemical at
the gills was modeled as countercurrent exchange processes, parametrized for trout.
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Methyl mercury has a very low octanol-water partition coefficient, which impedes its uptake by
biological cells (though it can bind with organic matter in the water column before entering the fish’s
system and thus be more readily absorbed and retained be tissues, and less readily excreted). There
are several methods of movement of solutes across membranes, however here we were concerned with
passive diffusion down the activity gradient, which can be described by Fick’s Law in combination with
flow-limited uptake. In developing the system, we modeled the gill area as a function of body size,
and thus included growth effects.
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At high initial concentrations of methyl mercury, the fish epithelium can become damaged or a mucous
layer can form on the outside of the lamellae, effectively increasing the thickness of the epithelium
and decreasing the flux of chemical across the gills. In extreme cases, this damage can be so severe
that the gills fail entirely and the fish essentially "drowns". We modeled the uptake of methyl
mercury by the fish as being governed by both passive diffusion and flow-limited uptake, in that the
most restricted method of uptake became the limiting case.
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To model the rate of change of concentration of methyl mercury in the various compartments for the
model, it is important to understand the partitioning of the chemical in the different biological
phases of the organism. For partition coefficients less than one, the concentration in venous blood is
greater than the concentration in the tissues in the compartment; for coefficients greater than one,
the concentration in the tissues is greater than that in the venous blood. When the venous blood has a
higher concentration of methyl mercury than does the arterial blood entering the compartment, the
amount of toxicant in the compartment is decreasing and the tissues are eliminating the chemical. When
the arterial blood has a higher concentration than the venous blood, bioaccumulation is occurring
within the compartment.
Extrabranchial elimination was quantified by first order and Michaelis-Menten elimination, which is
limited by Vmax, the maximum chemical uptake rate.
One of the assumptions of the model was a constant environmental concentration of methyl mercury, which
was not represented per se by the experimental data. The equilibria predicted by the theoretical model
indicated that long-term concentrations in kidney and muscle should be highest, followed by
concentrations in the liver. The experimental data, however, exhibited higher long-term concentrations
in the liver than in the muscle. This may have been due to several factors: the partition coefficients
in the model neglected binding of mercury compounds to proteins in the tissues; extrabranchial
elimination was not included in the equilibrium values calculated for both liver and kidneys; and
chemical elimination and demethylation was neglected in the differential equations for all compartments.
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