Team:UFAM Brazil/Modeling

The Hg²⁺ ions uptake and entrance from the cell exterior to the interior system and its subsequent reduction to Hg⁰ species is a complex process that has several steps for its realization. This procedure aims to transform the mercury ion in a volatile element (Hg⁰), able to passively diffuse through the membranes to the cell exterior.

According to Figure 1, the uptake and reduction system operates basically with merP, merT, merC, merF and merA proteins, being the first a periplasmic protein that binds to mercury ion for carrying to one of its transporters (merT, merC or merF), which are located in the inner membrane, and release Hg²⁺ inside the cells. Then, Hg²⁺ undergoes the merA enzyme action, which can reduce Hg²⁺ to Hg⁰, thereby enables its passive exist by membrane.

Figure 01: Mer genes action in bacterial cell

For the purpose of simplifying such processes, these are written in a sequence of chemical reactions, considering the enzyme complexes formation of mer substrates and proteins were always in equilibrium.

• Hg²⁺ OUT – Mercury concentration outside the cell

• CI – Complex concentration Hg2+-merP

• CII – Complex concentration Hg2+-merP-merT

• CIII – Complex concentration Hg2+-merP-merC

• CIV – Complex concentration Hg2+-merP-merF

So, as discussed earlier, assuming the reaction I in equilibrium:

Simplifing, it was assumed that only one Hg2+ transporter was active, for this example, the merT protein. Calculating the elements formation speeds involved in the mercury ions transport into the cell:

Assuming CII complex formation in equilibrium, again:

However,

Therefore,

Thus, Hg²⁺ uptake into the cell speed, assuming functionality of only merT, is given by:

Similarly, for exclusive functionality to merC or merF it is given:

Now taking into account the reduction process of Hg2+ to Hg0, we have this general equation:

Assuming CV complex formation in equilibrium:

Finally, the reduction rate of mercury ion is given by: