- Open Access
Mathematical modeling of the effects of glutathione on arsenic methylation
© Lawley et al.; licensee BioMed Central Ltd. 2014
- Received: 13 February 2014
- Accepted: 30 April 2014
- Published: 16 May 2014
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.
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.
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.
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.
- Mathematical model
Arsenic is a naturally occuring metalloid that finds its way into the food chain through water, plants, and animals. In many parts of the world, arsenic is a major health hazard [1–3]. Chronic arsenic exposure has been associated with cancer, heart disease, neuropathies, and with deficits in intelligence in children [4, 5]. Arsenic is mainly ingested as inorganic arsenic, iAs. The metabolism of arsenic in the liver has traditionally been thought to proceed via successive enzymatic methylations to methylarsonic acid, MMAs V, and dimethylarsinic acid DMAs V, with two intervening reduction steps [6–8]. This is known as the Challenger pathway and the methylations are catalyzed by arsenic methyltransferase, AS3MT. The Challenger pathway has been considered a detoxification pathway because reactive oxygens are replaced by methyl groups and DMAs V is readily exported from the liver and excreted in urine. However, there is considerable evidence that the intermediate trivalent MMAs is equally or more toxic than inorganic arsenic or DMAs V [9–11].
In recent years, evidence has been accumulating that the tripeptide glutathione, GSH, plays an important role in the Challenger pathway. Since GSH is a reductant, it increases the rates of the reduction steps [12–14] and glutathione S-transferase has been shown to help convert MMAs V to MMAs III in different tissues [15, 16]. Thomas, Styblo and colleagues [17–19] have studied methylation in the presence of other reductants as well as GSH. Even in the presence of other reductants, GSH increases methylation yield, and Song et al.  suggested that GSH increases the activity of AS3MT. In addition, in the experiments of both  and , it is shown that increasing GSH concentration when the concentration is low increases methylation rate, but increasing GSH concentration when GSH concentration is high decreases methylation rate. Finally, Hayakawa et al.  have proposed an alternate pathway for methylation in which only the arsenicals bound to GSH can be methylated.
Cullen  discusses the current state of knowledge of methylation of arsenic and outlines four different detailed mechanisms. Considerable knowledge is now available on which cysteine residues in AS3MT are necessary for methylation and on the order of the reaction steps [23, 24]. And, it is known  that other thiols besides GSH affect methylation and that there may be an interaction between these thiols and GSH. On the physiological level, GSH is in high concentration in cells and can effect transport processes that control arsenic uptake and removal from cells, as well as the availability of other thiols. Furthermore, GSH is known to bind to xenobiotics, including metals, and, indeed, arsenic-glutathione conjugates appear in the bile of rats fed arsenic containing diets , so arsenic conjugation may be an important arsenic excretion pathway. None of these details is in our model.
There are different kinds of experiments, and corresponding models, that shed light on arsenic methylation and arsenic detoxification. There are studies in humans where arsenic metabolites are measured in urine and blood [8, 26–29]. There are cell culture experiments in which arsenicals are typically measured in the external medium . And, there are experiments in which reaction mixtures of arsenicals, AS3MT, and various other metabolites are prepared [17–21]. A number of pharmacokinetic models have been used to interpret data in these different experimental situations. We have previously constructed a whole body model of arsenic methylation  and compared the results to the clinical results of Buchet et al. [26, 27] and the clinical trial of Gamble et al. in Bangladesh [28, 29]. There are other whole body models [31–35]. We used a reduced version of our whole body model to study the cell culture experiments in . Previous models for these cell culture experiments were created in [37, 38]. In two recent papers, Georgopoulos and coworkers create mathematical models based on the Hayakawa pathway to study hepatocyte culture experiments including GSH conjugation, reactive oxygen species, and DNA damage [39, 40].
Our model, which investigates the three “effects” of GSH described above and depicted in Figure 1, builds on our previous model of arsenic detoxicfication . Although the model simplifies complicated and interesting biochemical and physiological questions that are the object of current investigations, it enables us to understand three important effects of GSH on arsenic methylation. It is vital to understand the effects of GSH on detoxification mechanisms in hepatocytes, because such understanding may give important information on whether substrates like N-acetyl-cysteine that increase liver GSH may be useful supplements in regions of the world where arsenic is endemic in the water or food supply.
Variables in the model ( μ M)
Rate constants in the model ( μ M/hr)
k 1 = 10-11
k -1 = 375
k 2 = 10-5
k -2 = .25
k 3 = 10-3
k -3 = 10-3
k 4 = ln(2)/2.5
k 5 = 100
k 6 = .1
Reduction of MMAsV
k 7 = 5
k 8 =.1
Reduction of DMAsV
K m = 4.6
K m for [iAs]
K m = 4.6
K m for [iAs]
We use the value K m = 4.6 μ M for the Michaelis-Menten constant for AS3MT for iAsIII as found in . The reaction has substrate inhibition by iAsIII; we take the inhibition constant to be M as found in . It is known that this reaction is inhibited by the product MMAsV and we take the inhibition constant, M from  and . We note that it is not certain that the enzyme investigated in  is identical to AS3MT.
As above we take K m = 4.6 μ M and we set M as in  and . The inhibition of V 2 by MMAsIII is proposed in this paper; the inhibition constant M was obtained by fitting the data in . It is reasonable that the second methylation reaction be inhibited by MMAsIII since the first methylation reaction is inhibited by MMAsV [35, 43], though this doesn’t seem to have been remarked on before. We were driven to include this inhibition by the data in , their Figure six, which is discussed in detail under Results. The square gave a much better fit of the data, which suggests that the inhibition is cooperative.
Glutathione as a reductant
It has been known since [12, 44, 45] that GSH acts to reduce pentavalent to trivalent arsenicals. In cells or in vivo other thiols can also act as reductants. We take the rate of the reaction from MMAsV to MMAsIII to be k 5 + k 6[GSH], the k 5 term representing the reduction by other endogenous thiols and the second term representing the reduction by GSH. The concentration of GSH is varied in some of the experiments in [19, 20] and in some of our simulations. We take the rate of the reaction from DMAsV to DMAsIII to be k 7 + k 8[GSH] for similar reasons.
Glutathione affects arsenic methyltransferase
It has been known for a long time that the presence of GSH helps the reduction steps in the methylation chain. The importance of the Styblo data, in , Figure six, is that both DMAsIII and total DMAs go up by a factor of about four in the presence of GSH. This shows conclusively that GSH increases substantially the activity of AS3MT. We chose a Hill function for the effect of GSH on AS3MT, and the rate constants because they gave a good fit of the data in [19, 20].
Glutathione sequesters arsenic
Arsenic has an affinity for sulfur , so it is not surprising that it binds to GSH, especially since a major role of GSH in the liver is to remove xenobiotics including metals. Indeed, arsenic-glutathione compounds can be found in the bile of rats fed arsenic diets . We include in our model the formation of arsenic triglutathione, AsTG, monomethylarsenic diglutathione, MMAsG, and dimethylarsenic glutathione, DMAsG, from iAs III, MMAs III, and DMAs III, respectively. We assume mass-action kinetics and that the reactions are reversible; rate constants are given in Table 2.
The Styblo experiments on MMAsIII
It has been known for a long time that the presence of GSH helps the reduction steps in the methylation chain. The importance of the data in , Figure six is that both DMAsIII and total DMAs go up by a factor of about four in the presence of GSH. This shows conclusively that GSH increases substantially the activity of AS3MT.
The model curves fit the data points in each panel very well. Note that in the presence of 1 mM GSH more total DMAs is formed and also that there is almost no DMAsV present because, in this experimental context, it is immediately reduced to DMAsIII, most of which is conjugated with GSH.
The influence of GSH on methylation
In silico experiments
Temporal variation of GSH
In hepatocytes, GSH has concentrations in the mM range but is exported rapidly and turns over with a half-life of 1.5 to 2.5 hours . The solutions in which cells are maintained typically contain the amino acids (cysteine, glycine, and glutamate or glutamine) necessary for the cells to resynthesize GSH. Nevertheless, the GSH concentration may vary considerably. For example, in the human hepatocytes used in , the cellular GSH concentration increased by 80% from day 1 to day 7. The experiments in  and  that we discussed above were conducted with purified enzymes in solution and not with living cells in vitro. The half-life of GSH in solution was found to vary from.2 to 70 hours depending on pH and temperature . This raises the question of whether GSH degradation might play a role in experiments with purified enzyme in solution.
The main point of this study was to explore the different ways that GSH could affect the Challenger pathway  for oxidative methylation of inorganic arsenic. Three effects were included: (i) reduction of arsenicals with valence 5 to valence 3; (ii) activation of AS3MT; (iii) sequestration of arsenicals by binding to GSH. We used the model to analyze the experimental data in  and . First we showed that experiments with MMAs as a substrate in  show clearly that MMAs III is an inhibitor of the second methylation step. Next we showed that the model predictions, Figure 3, match well the experiments in  where the amounts of iAs, MMAs, and DMAs were followed over time. Both  and  show that methylation proceeds slowly at low GSH and high GSH, but quite quickly at intermediate GSH ranges. This important finding is reproduced by the model, Figure 4, and we show that the reason for this is the combined effect of AS3MT activation by GSH and the sequestration of arsenicals by GSH. Finally, we pointed out that temporal variation in the amount GSH in reaction mixtures or cells needs to be taken into account in interpreting experimental data.
An important consequence of these findings is that recent experimental data can be explained well by the Challenger pathway augmented with these effects of GSH. This does not prove that the Hayakawa pathway , in which only GSH-conjugated arsenicals are methylated, is wrong. It just shows that the methylation of GSH-conjugated arsenicals is not necessary to explain the effects of GSH seen in  and . Indeed, it is possible that both GSH free arsenicals and GSH bound arsenicals can be methylated, perhaps at different rates. There is some evidence that for a methyl transferase that is orthologous to AS3MT that GSH-conjugated arsenicals are preferred substrates for binding to the enzyme’s active site .
Easterling et al.  created a pharmacokinetic model to study the hepatocyte data in . In order to fit the data, they needed to introduce a storage compartment for arsenicals in cells. Likewise, in our whole body model and hepatocyte model  we needed to introduce cellular storage compartments. It is tempting to speculate that the binding of arsenicals to GSH was an important part of the“storage mechanism” in both cases.
S-adenosylmethionine (SAM) is the methyl group donor in the methylation reactions. It is not included explicitly in our model because SAM was not varied in the experiments that we were trying to explain. The SAM concentration occurs implicitly in the V max values of the first and second methylation reactions. The K m of AS3MT for SAM was measured as 11.8 μM in , but the data in  imply that the K m is 50 μM. This is an important issue for the applications of arsenic biochemistry to human toxicity studies. Gamble and coworkers [28, 29] showed that folate supplementation of folate-deficient individuals in Bangladesh lowers blood arsenic levels. Raising folate levels can raise SAM concentrations in folate deficient individuals , so the presumed mechanism was that SAM levels were raised, thus making more methyl groups available for the methylation reactions. However, once SAM levels are back into the normal range (50 – 100 μM for rats), raising SAM more by further folate supplementation won’t help if the K m = 11.8 because the reaction will already be saturated, whereas if the K m = 50 μM then further supplementation should help.
The binding of GSH to arsenicals may be a significant detoxification mechanism as there is evidence that arsenic binds to GSH and then is removed in the bile [25, 51] and sequestration might also reduce the toxicity of trivalent arsenicals. Thus, whole body models of arsenic detoxification need to take into account this removal mechanism as well as the removal of arsenic-GSH conjugates from the liver to the blood and urine. This will be the subject of future work.
The effects of GSH on arsenic methylation discussed in this study and the removal of arsenic-GSH complexes in the bile and urine imply that increasing GSH might be a way to reduce As toxicity. GSH levels are under strong regulatory control in the liver . Nevertheless, supplementation strategies have proven useful in several circumstances where GSH liver levels are low. N-acetyl cysteine is the antidote given in emergency departments in cases of acetaminophen overdose [53, 54] and glutamine is often given after surgery or other trauma to decrease inflammation [55, 56]. In both cases the intent is to increase GSH production in the liver. Plasma GSH levels in Bangladesh are quite low, 2.6 μM  as compared to the normal range, 2 – 20 μM [47, 58, 59]. This suggests that supplementation by N-acetyl-cysteine may be a viable strategy for reducing arsenic toxicity.
The Challenger pathway, supplemented by three effects of glutathione, is sufficient to explain recent data on arsenic methylation.
Monomethylarsonous acid inhibits the second methylation step.
The three different effects of glutathione on arsenic methylation make the interpretation of experimental results difficult.
Mathematical modeling of arsenic methylation can aid in the interpretation of experimental data.
Supplementation by N-acetyl-cysteine may be a viable strategy for reducing arsenic toxicity.
This research was partially supported by NSF EF-1038593 (HFN,MR), and NIH grants R01 ES019876 (D. Thomas), R01 ES011601 (MVG), RO1 CA133595, and R00ES018890 (MNH).
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