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

The system for capturing of ions Hg²⁺ into the cell and it consequent reduction for Hg⁰ it is a complex process that has several steps for its realization. Such procedure aims to transform mercury ion in a volatile element (Hg⁰) capable of passive diffusion through membrane to cell’s exterior.

According to Picture 1, the capturing and reduction system work, basically, with proteins merP, merT, merC, merF and merA, where the first one a periplasmic protein, that binds to mercury ion to carry it to one of the transporters (merT, merC ou merF), that are localized at the inner membrane, and release Hg²⁺ to intracellular. Then it will get under MerA enzyme action that is capable of reduce Hg2+ into Hg0, making it possible to get out passively through cell membrane.

Figure 01: Mer genes action in bacterial cell

In order to simplify such processes, those were written as a sequence of chemical reactions where it was considered that the formation of complexes enzyme-substrate and mer proteins were in balance.

• 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

As stated before, all this supposing that the reaction I is in balance.

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: