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Team:ULB-Brussels/Modelling
From 2014.igem.org
$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \newcommand{\MyColi}{{\small Mighty\hspace{0.12cm}Coli}} \newcommand{\Stabi}{\small Stabi}$ $\newcommand{\EColi}{\small E.coli} \newcommand{\SCere}{\small S.cerevisae}\\[0cm] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \newcommand{\PI}{\small PI}$ $\newcommand{\Igo}{\Large\mathcal{I}} \newcommand{\Tgo}{\Large\mathcal{T}} \newcommand{\Ogo}{\Large\mathcal{O}} ~$
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Population Dynamics ModelThe growth of bacteria involves ... a Population Dynamics Model can be fitted in our system. Theorically, two approaches have been planned:
$1.1)$ $By$ $Probabilities$When some new plasmids are introduced into the cytoplasm of E.Coli bacteria, it does not garantee that the daughter cells will contain it. Indeed, these plasmids can be lost after cell division or replication. In this regard, it is interesting to study a model based on the different possibilities of plasmid combinations in bacteria, as in the study of mutations in animals. A typical example of a similar case is found if we study the mutations of the eyes color in a family, by vertical genes transfer. IOf course, in the case of plasmids, one must also take horizontal genes transfer into account. A Probabilistic Model is useful because easily undertstandable, but requires some assumptions.$1.2)$ $By$ $Logistic$ $\small\&\normalsize$ $Lotka$ $Equations$The Logistic Equation was initially introduced during the beginning of the XIXth Century, by the belgian mathematician P.F. Verhulst. Now, this equation is mainly used in Population Dynamics Models, especially in Biological Sciences. Mathematicians currently finish Ph.D thesis using it, and the analytical Lotka-Volterra model is directly associated with the Verhulst theory. Another interesting model is obtained from Euler-Lotka equation to the Leslie matrix coefficients. Other models exist, f.e. by Monod equation, but these ideas are less consistent with our global and partial systems.Toxin-Antitoxin SystemsTwo type II TA systems are investigating in our $\MyColi$ project. The $\hspace{0.12cm}\small\mathtt{1}\normalsize^{st}$ consists of ccdB (the toxin, T) and ccdA (the antitoxin, A) and for the $\hspace{0.12cm}\small\mathtt{2}\normalsize^{nd}$ these are Kid (T) and Kis (A): $\newcommand{\AA}{\mathbb{A}} \newcommand{\CC}{\mathbb{C}} \newcommand{\TT}{\mathbb{T}} \newcommand{\GG}{\mathbb{G}} \newcommand{\KK}{\mathcal{K}}$$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 is not protected by a mutation (such events are possible, but excessively rare) or if the antidote is degraded (very frequent because ccdA is unstable in comparison with ccdA), the death of a bacterium in unavoidable. This TA system will be implemented for $\EColi$ bacteria.$2.2)$ $Kis/Kid$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. This TA system will be implemented for $\SCere$ yeasts. By modelling and by comparison with experiments, we would obtain finally a model that correctly describes our TA system.Bioreactor and 2A PeptideThe p2A peptide is an important building block in our system. We think that its use can enhance the production of bioreactors.Bibliography
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- Université Libre de Bruxelles -
