Mathematical modeling of the effects of glutathione on arsenic methylation

Abstract

Background: Arsenic is a major environmental toxin that is detoxified in the liver by biochemical mechanisms that are still under study. In the traditional metabolic pathway, arsenic undergoes two methylation reactions, each followed by a reduction, after which it is exported and released in the urine. Recent experiments show that glutathione plays an important role in arsenic detoxification and an alternative biochemical pathway has been proposed in which arsenic is first conjugated by glutathione after which the conjugates are methylated. In addition, in rats arsenic-glutathione conjugates can be exported into the plasma and removed by the liver in the bile.

Methods: We have developed a mathematical model for arsenic biochemistry that includes three mechanisms by which glutathione affects arsenic methylation: glutathione increases the speed of the reduction steps; glutathione affects the activity of arsenic methyltranferase; glutathione sequesters inorganic arsenic and its methylated downstream products. The model is based as much as possible on the known biochemistry of arsenic methylation derived from cellular and experimental studies.

Results: We show that the model predicts and helps explain recent experimental data on the effects of glutathione on arsenic methylation. We explain why the experimental data imply that monomethyl arsonic acid inhibits the second methylation step. The model predicts time course data from recent experimental studies. We explain why increasing glutathione when it is low increases arsenic methylation and that at very high concentrations increasing glutathione decreases methylation. We explain why the possible temporal variation of the glutathione concentration affects the interpretation of experimental studies that last hours.

Conclusions: The mathematical model aids in the interpretation of data from recent experimental studies and shows that the Challenger pathway of arsenic methylation, supplemented by the glutathione effects described above, is sufficient to understand and predict recent experimental data. More experimental studies are needed to explicate the detailed mechanisms of action of glutathione on arsenic methylation. Recent experimental work on the effects of glutathione on arsenic methylation and our modeling study suggest that supplements that increase hepatic glutathione production should be considered as strategies to reduce adverse health effects in affected populations.

Figure 1

The reaction diagram. The diagram depicts the traditional Challenger pathway [6] augmented by three effects of glutathione. V ₁and V ₂are the velocities of the methylation steps. GSH and other reductants increase the velocity of the reduction reactions. GSH increases the activation of AS3MT. GSH conjugates and sequesters the arsenicals iAs, MMAs ^III, and DMAs ^III. Although not indicated, the half-life of GSH in reaction mixtures is taken into account. The various inhibitions of iAs and MMAs ^III are indicated. The kinetics of V₁ and V₂ and the functional form, U (GSH) by which GSH affects AS3MT are given in the Methods.

Figure 2

MMAs ^III inhibits the second methylation step. The red dots are data regraphed from Panels C and D (WT) in Figure six of [19]. The blue curves were computed from the mathematical model. For both the data and model curves, the reaction mixture had either 0 mM GSH (left panel) or 1 mM GSH (right panel).

Figure 3

Time course experiments. 1 μM iAs was introduced into a reaction mixture containing 0 mM GSH (upper panels) or 1 mM GSH (lower panels). The red and green dots are data points taken from [19]; the curves are the result of model computations. The experimental measurements did not distinguish between arsenicals and arsenicals bound to GSH, so, likewise, the model curves represent the named arsenicals plus their GSH conjugates. For more detail, see the text.

Figure 4

The influence of GSH on methylation. 1 μM iAs was introduced into reactions mixtures with the indicated amount of GSH. MMAs and DMAs (and their GSH conjugates) were measured after two hours. The green dots and red dots are redrawn data from the experiments in [19], Figure two and [20], Figure six, respectively. The connected blue dots, which are the predictions of our mathematical model, capture the qualitative features of the experimental data.

Figure 5

Removing influences of GSH on methylation. The left and right panels both reproduce the experimental data, [20] red and [19] green, and blue model curve for MMAs + DMAs with varying amounts of GSH from the right panel of Figure 4. The black curve in the left panel shows what the model fit would be if we removed from the model the excitatory influence of GSH on AS3MT. The black curve in the right panel shows what our model fit would be if we removed the binding of arsenicals to GSH from the model. Clearly, neither black curve fits the data. Both influences of GSH (blue curve) are necessary to explain the experimental data.

Figure 6

The effect of the half-life of GSH. The reactions mixture starts with 20 mM GSH and 1 μM iAs. We assume the half-life of GSH in the mixture is 2.5 hours. The rates of the first methylation step, V₁, the second methylation step, V₂, and total methylation vary dramatically throughout an 8 hour period. For explanations, see the text.