Team:UFMG Brazil/modeling

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TMAO - Modeling

Labels and conventions

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

C_TS: Complex formed by TorT and TorS

C_TSM: Complex formed by TorT+TorS and one molecule of TMAO C_TM: 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.

Imposing the equilibrium in the first reaction we have:

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

Regarding the enzymatic reaction:

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

With Ce = E0 - C

Solving for C:

with

.

In conclusion, we find

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 '''Labels and conventions'''
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+<!-- MathJax (LaTeX for the web) -->
-  \operatorname{erfc}(x) =
+<script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
-  \frac{2}{\sqrt{\pi}} \int_x^{\infty} e^{-t^2}\,dt =
-  \frac{e^{-x^2}}{x\sqrt{\pi}}\sum_{n=0}^\infty (-1)^n \frac{(2n)!}{n!(2x)^{2n}}
- </math>
 : The enzymatic complex formed by TorT+TorS+TMAO, which reacts with TorR