Team:ULB-Brussels/Modelling/Population-Dynamics

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When some new plasmids are genetically introduced into the cytoplasm of E.Coli bacteria, this doesn't garantee that the future copies will contain it. Indeed, these plasmids can be lost after cell division or replication, so it's interesting to study a model based on the different possibilities of plasmid combinations in bacteria, like in the studies of mutations in animals. A typical example of a similar way is found if we study the mutations of the eyes or hair color in a family, by vertical genes transfer. In this case, there's a horizontal genes transfer too, originated by the plasmids. </p>
When some new plasmids are genetically introduced into the cytoplasm of E.Coli bacteria, this doesn't garantee that the future copies will contain it. Indeed, these plasmids can be lost after cell division or replication, so it's interesting to study a model based on the different possibilities of plasmid combinations in bacteria, like in the studies of mutations in animals. A typical example of a similar way is found if we study the mutations of the eyes or hair color in a family, by vertical genes transfer. In this case, there's a horizontal genes transfer too, originated by the plasmids. </p>
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Revision as of 20:00, 4 September 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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- Université Libre de Bruxelles -



Population Dynamics Model

A Population Dynamics Model can be fitted in our system. Theoretically, two approaches have been planned:

$1.1)$ $By$ $Probabilities$

When some new plasmids are genetically introduced into the cytoplasm of E.Coli bacteria, this doesn't garantee that the future copies will contain it. Indeed, these plasmids can be lost after cell division or replication, so it's interesting to study a model based on the different possibilities of plasmid combinations in bacteria, like in the studies of mutations in animals. A typical example of a similar way is found if we study the mutations of the eyes or hair color in a family, by vertical genes transfer. In this case, there's a horizontal genes transfer too, originated by the plasmids.

Figure M.2 : A first example of bacteria generations at same acceptation plasmid rate for a Toxin (T), an Antitoxin (A), the two (T&A) or no plasmid (-).

We remark in [Fig M.2] that we'll converge to obtain bacteria without Toxin or Antitoxin. A Probabilistic Model is useful because easily undertsood, but necessits some assumptions to makesense.

$1.2)$ $By$ $Logistic$ $Equation$

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 this, and the analytical Lotka-Volterra model is directly associated with the Verhulst theory.

Other models exist, f.e. by Monod equation, but this idea cannot be consistent with our global system.
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