Team:ULB-Brussels/Modelling/TA-System

From 2014.igem.org

(Difference between revisions)
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In presence of arabinose, AraC activates the transcription of RNAm (catalysed by RNApoly):
In presence of arabinose, AraC activates the transcription of RNAm (catalysed by RNApoly):
\begin{array}.
\begin{array}.
-
  \hspace{0.06cm}\mathring{\wp} &=& v_{s_{0}} \dfrac{a}{a + K_{0}} - \hspace{0.05cm}v_{d_{0}} \hspace{0.04cm}\wp \\[0.05cm]
+
  \hspace{0.06cm}\mathring{\wp} &=& v_{s_{0}} \dfrac{a}{a + \small\mathcal{K}\normalsize_{0}} - \hspace{0.05cm}v_{d_{0}} \hspace{0.04cm}\wp \\[0.05cm]
-
  \hspace{0.02cm}\mathring{\mathbb{A}} &=&  v_{s_{1}} \dfrac{a}{a + K_{1}} . \dfrac{\wp}{\wp + K_{3}} - \hspace{0.05cm}v_{a} \hspace{0.02cm}(\mathbb{A}\mathbb{B})\hspace{0.02cm} + \hspace{0.05cm}v_{d_{3}}\hspace{0.02cm} \mathbb{C}\hspace{0.03cm} - \hspace{0.05cm}v_{d_{1}} \hspace{0.01cm}\mathbb{A} \\[0.1cm]
+
  \hspace{0.02cm}\mathring{\mathbb{A}} &=&  v_{s_{1}} \dfrac{a}{a + \small\mathcal{K}\normalsize_{1}} . \dfrac{\wp}{\wp + \small\mathcal{K}\normalsize_{3}} - \hspace{0.05cm}v_{a} \hspace{0.02cm}(\mathbb{A}\mathbb{B})\hspace{0.02cm} + \hspace{0.05cm}v_{d_{3}}\hspace{0.02cm} \mathbb{C}\hspace{0.03cm} - \hspace{0.05cm}v_{d_{1}} \hspace{0.01cm}\mathbb{A} \\[0.1cm]
-
  \hspace{0.02cm}\mathring{\mathbb{B}} &=&  v_{s_{2}} \dfrac{a}{a + K_{2}} . \dfrac{\wp}{\wp + K_{4}} - \hspace{0.05cm}v_{a} \hspace{0.02cm}(\mathbb{A}\mathbb{B})\hspace{0.02cm} + \hspace{0.05cm}v_{d_{4}} \hspace{0.02cm}\mathbb{C}\hspace{0.03cm} - v_{d_{2}} \hspace{0.03cm}\mathbb{B} \\[0.15cm]
+
  \hspace{0.02cm}\mathring{\mathbb{B}} &=&  v_{s_{2}} \dfrac{a}{a + \small\mathcal{K}\normalsize_{2}} . \dfrac{\wp}{\wp + \small\mathcal{K}\normalsize_{4}} - \hspace{0.05cm}v_{a} \hspace{0.02cm}(\mathbb{A}\mathbb{B})\hspace{0.02cm} + \hspace{0.05cm}v_{d_{4}} \hspace{0.02cm}\mathbb{C}\hspace{0.03cm} - v_{d_{2}} \hspace{0.03cm}\mathbb{B} \\[0.15cm]
  \mathring{\mathbb{C}} &=& v_{a} \hspace{0.02cm}(\mathbb{A}\mathbb{B}) - (v_{d_{3}}+v_{d_{4}}) \hspace{0.05cm}\mathbb{C}
  \mathring{\mathbb{C}} &=& v_{a} \hspace{0.02cm}(\mathbb{A}\mathbb{B}) - (v_{d_{3}}+v_{d_{4}}) \hspace{0.05cm}\mathbb{C}
\end{array}
\end{array}
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are modificated by the change :
are modificated by the change :
\begin{equation}
\begin{equation}
-
\left(  v_{s_{j}} \dfrac{a}{a + \small\mathcal{K}\normalsize_{j}} \right) \rightarrow \left( v_{s_{j}} \dfrac{K_{j}}{g + K_{j}} \right).
+
\left(  v_{s_{j}} \dfrac{a}{a + \small\mathcal{K}\normalsize_{j}} \right) \rightarrow \left( v_{s_{j}} \dfrac{\small\mathcal{K}\normalsize_{j}}{g + \small\mathcal{K}\normalsize_{j}} \right).
\end{equation}
\end{equation}
NB: We have chosen a Michaelis-Menten kinetics, maybe a higher Hill coefficient would be desirable.</p>
NB: We have chosen a Michaelis-Menten kinetics, maybe a higher Hill coefficient would be desirable.</p>
-
Because we'll preserve some fragment of the population, it's necessary to controle its level. In practical, different parameters are introduced in the mathematical model to describe all the configurations of the biological system (in the equations above, the parameters are the constants $\hspace{0.04cm}K_{j}\hspace{0.02cm}$ and the velocities $\hspace{0.04cm}v_{j}\hspace{0.06cm}$).  
+
Because we'll preserve some fragment of the population, it's necessary to controle its level. In practical, different parameters are introduced in the mathematical model to describe all the configurations of the biological system (in the equations above, the parameters are the constants $\hspace{0.04cm}\small\mathcal{K}\normalsize_{j}\hspace{0.02cm}$ and the velocities $\hspace{0.04cm}v_{j}\hspace{0.06cm}$).
These parameters influence the global dynamics of the TA system, with or without an additional proline with p2A.</p>
These parameters influence the global dynamics of the TA system, with or without an additional proline with p2A.</p>
By modelling and by comparison with experiments, we hope to obtain finally a model close to the reality.</p>
By modelling and by comparison with experiments, we hope to obtain finally a model close to the reality.</p>

Revision as of 09:51, 13 August 2014

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \newcommand{\MyColi}{{\small Mighty\hspace{0.12cm}Coli}} \newcommand{\Stabi}{\small Stabi}$ $\newcommand{\EColi}{\small E.coli} \newcommand{\SCere}{\small S.cerevisae}\\[0cm] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \newcommand{\PI}{\small PI}$ $\newcommand{\Igo}{\Large\mathcal{I}} \newcommand{\Tgo}{\Large\mathcal{T}} \newcommand{\Ogo}{\Large\mathcal{O}} ~$ Example of a hierarchical menu in CSS

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Retrieved from "http://2014.igem.org/Team:ULB-Brussels/Modelling/TA-System"




- Université Libre de Bruxelles -


mv to Intro page: [1] Previous page: [2] Concl page: [3]

Toxin-Antitoxin Systems

Two type II TA systems are investigating in our project. The first consists of ccdB (the toxin, T) and ccdA (the antitoxin, A) and these are Kid (T) and Kis (A) for the second:

2.1) CcdBA

One of the most studied and characterized TA systems, CcdBA involves two principal components : ccdB and its antidote ccdA. As we explained in the introduction page of our project, ccdB is an inhibitor of the DNA gyrase, so it binds the subunit A of the DNA gyrase complex when it's bound to DNA. When DNA double strand is broken, there is activation of emergency signals (SOS system blocks cellular division in bacteria). If the DNA gyrase cannot protect itself by a mutation (some events are possible, but very rare) or if the antidote is degraded (very frequent because ccdA is unstable in comparison with ccdA), the death of a bacterium in unavoidable.

\begin{equation} \hspace{-0.12cm}\wp\hspace{0.02cm}\equiv[p2A]\\ \mathbb{A}\hspace{0.02cm}\equiv[ccdA]\\ \mathbb{B}\hspace{0.02cm}\equiv[ccdB]\\ \mathbb{C}\hspace{0.02cm}\equiv[(ccdA)_{2}-(ccdB)_{2}]\\ a\equiv[ara] \hspace{0.12cm}|\hspace{0.12cm} g\equiv[glu]\\[0.12cm] \mathring{x}= \dfrac{dx}{dt} \end{equation} In presence of arabinose, AraC activates the transcription of RNAm (catalysed by RNApoly): \begin{array}. \hspace{0.06cm}\mathring{\wp} &=& v_{s_{0}} \dfrac{a}{a + \small\mathcal{K}\normalsize_{0}} - \hspace{0.05cm}v_{d_{0}} \hspace{0.04cm}\wp \\[0.05cm] \hspace{0.02cm}\mathring{\mathbb{A}} &=& v_{s_{1}} \dfrac{a}{a + \small\mathcal{K}\normalsize_{1}} . \dfrac{\wp}{\wp + \small\mathcal{K}\normalsize_{3}} - \hspace{0.05cm}v_{a} \hspace{0.02cm}(\mathbb{A}\mathbb{B})\hspace{0.02cm} + \hspace{0.05cm}v_{d_{3}}\hspace{0.02cm} \mathbb{C}\hspace{0.03cm} - \hspace{0.05cm}v_{d_{1}} \hspace{0.01cm}\mathbb{A} \\[0.1cm] \hspace{0.02cm}\mathring{\mathbb{B}} &=& v_{s_{2}} \dfrac{a}{a + \small\mathcal{K}\normalsize_{2}} . \dfrac{\wp}{\wp + \small\mathcal{K}\normalsize_{4}} - \hspace{0.05cm}v_{a} \hspace{0.02cm}(\mathbb{A}\mathbb{B})\hspace{0.02cm} + \hspace{0.05cm}v_{d_{4}} \hspace{0.02cm}\mathbb{C}\hspace{0.03cm} - v_{d_{2}} \hspace{0.03cm}\mathbb{B} \\[0.15cm] \mathring{\mathbb{C}} &=& v_{a} \hspace{0.02cm}(\mathbb{A}\mathbb{B}) - (v_{d_{3}}+v_{d_{4}}) \hspace{0.05cm}\mathbb{C} \end{array} In presence of glucose, AraC becomes a repressor of the promotor pBAD, so the three first differential equations (for $\hspace{0.1cm}\wp\hspace{0.04cm}$, $\hspace{0.04cm}\mathbb{A}\hspace{0.04cm}$ $\small\&\normalsize$ $\hspace{0.04cm}\mathbb{B}\hspace{0.1cm}$) are modificated by the change : \begin{equation} \left( v_{s_{j}} \dfrac{a}{a + \small\mathcal{K}\normalsize_{j}} \right) \rightarrow \left( v_{s_{j}} \dfrac{\small\mathcal{K}\normalsize_{j}}{g + \small\mathcal{K}\normalsize_{j}} \right). \end{equation} NB: We have chosen a Michaelis-Menten kinetics, maybe a higher Hill coefficient would be desirable.

Because we'll preserve some fragment of the population, it's necessary to controle its level. In practical, different parameters are introduced in the mathematical model to describe all the configurations of the biological system (in the equations above, the parameters are the constants $\hspace{0.04cm}\small\mathcal{K}\normalsize_{j}\hspace{0.02cm}$ and the velocities $\hspace{0.04cm}v_{j}\hspace{0.06cm}$). These parameters influence the global dynamics of the TA system, with or without an additional proline with p2A.

By modelling and by comparison with experiments, we hope to obtain finally a model close to the reality.

2.2) Kis/Kid

The same is relevant about the second TA system studied. In this case, the two principal components are Kid and its antidote Kis and the parameters are chosen a little bit different than in the first system.