Team:UFMG Brazil/modeling

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Imposing the equilibrium in the first reaction we have:
Imposing the equilibrium in the first reaction we have:
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Revision as of 14:52, 27 September 2013

Contents

Modeling TMAO system

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. 

2TMAO + 2TorT + TorS ⇆ CE     k1,k-1

CE + TorR ⇆ C → CE + P     k2,k-2,k3,

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 with 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
Tmao secondModeling.png

Modeling IMA System

First Reaction - Cobalt ions bind to albumin

The cobalt ion binds to albumin protein, originating the cobalt-albumin complex. If the albumin is derived from a healthy patient, it will bind more cobalt ions than a albumin derived from a patient with heart disease. It happens because patients with heart conditions will have a isquemic modified albumin (IMA), which has less capability of binding to cobalt. Thus, the amount of free cobalt in the system will be determined by the presence of a normal or ischemic albumin in the sample.

Eq1 cobalt.png

Second Reaction - The entry of cobalt in the cell

There are four cobalt transporters in the cell. The rcnA (Uniprot code: P76425) and zntA (Uniprot code: P37617) transport the cobalt to outside the cell. The corA (Uniprot code: P0ABI4) and zupT (Uniprot code: P0A8H3) transport the cobalt to inside the cell.

Eq3 cobalt.png

The equation for the cobalt flux through these transporters is:

Eq2 cobalt.png

Third Reaction - Transcription

In our modeling, we considered the cobalt acting as a transcriptional activator in order to simplify our model.

The transcriptional activation are accessed by the equation:

Eq4 cobalt.png

The transcription and translation are accesed by the equations:

Eq5 cobalt.png

Cobalt experiments

Figure - Modeling simulation of IMA system


Ufmg 2013 yfp appearing time.png

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