Team:UFMG Brazil/TMAO



Modeling TMAO system

The TMAO system requires several reactions steps. Thus, we modeled it in order to obtain the production rate of activated TorR. Since the activated TorR enables the reporter's protein transcription, our model could be simplified in just one equation.

thumb TMAO system schema

Labels and conventions

CE: The enzymatic complex formed by TorT+TorS+TMAO, which reacts with TorR

C: intermediate component of the final enzymatic process

P: Product of the enzymatic reaction

CTS: Complex formed by TorT and TorS

CTSM: Complex formed by TorT+TorS and one molecule of TMAO

CTSM: Complex formed by TorT and TMAO

First Modeling

This is the simplest modeling process to be considered in our study. The product of the enzymatic process is collapsed in only one reaction that was placed at equilibrium.

Eq1 tmao.png

Imposing the equilibrium in the first reaction we have:

Eq2 tmao.png

The value of CE is the initial enzyme concentration for the subsequent enzymatic reactions.

Eq3 tmao.png

Regarding the enzymatic reaction:

Eq4 tmao.png

The following relation holds E0 = CE + C. And as usual imposing the steady state condition:

Eq5 tmao.png

With CE = E0 - C

Solving for C:

Eq6 tmao.png
Eq7 tmao.png

In conclusion, we find:

Eq8 tmao.png

Tmao firstModeling.png

Second Modeling

It was used the same pattern of reactions as before, but with a standpoint of "essential activation" (the first reaction is no longer considered to equilibrium). Some enzymes need to be activated to bind the substrate. In our case, the enzyme is activated by TorS and activators are TMAO and TorT. The rate of product P appearance depends on the activators concentration. The equation that varies with respect to the previous case is:

Eq9a tmao.png

The total concentration of the enzyme is:

Eq9 tmao.png

Then we considered Eq10 tmao.png and imposed Eq11 tmao.png and Eq12 tmao.png

The system of equations also comes from:

Eq13 tmao.png

Defining Eq14 tmao.png and replacing we have:

Eq15 tmao.png

In conclusion the rate of product appearance results

Eq16 tmao.png

We have made simulations in order to see if our model can distinguish between different concentrations of TMAO (input) and how would be the activation of the transcription factor TorR (output). In general, it seems that the system will reach a saturation limit, except for very low concentrations of TMAO, but the appearing of the product is faster for higher concentrations of TMAO.

Tmao simulations.jpeg

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