Team:UFAM Brazil/Modeling

For better comprehension and organization of the mathematics modeling, each experimental situation of our will be analyzed separately: Biosensoring, Bioaccumulation e Bioremediation.

BIOACCUMULATION AND BIOREMEDIATION

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: