Difference between revisions of "Team:Aix-Marseille/Model"

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[[File:T--Aix-Marseille--Toulouse_logo.jpg|link=https://2016.igem.org/Team:Toulouse_France|300px|350px|center]]
 
[[File:T--Aix-Marseille--Toulouse_logo.jpg|link=https://2016.igem.org/Team:Toulouse_France|300px|350px|center]]
  
====Introduction====
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==Introduction==
 
We conceived a model in order to handle questions concerning the following situation:
 
We conceived a model in order to handle questions concerning the following situation:
 
A bacterial growth is carried out in a bioreactor, continually supplied in substrate.
 
A bacterial growth is carried out in a bioreactor, continually supplied in substrate.
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As a plasmids can be a disadvantage for growth (energy spent into replicating processes) or a advantage (protection against a toxin) this question is hard to answer. But in this situation, where  one type of plasmid can influence on the  presence of the other type of plasmid in (and reciprocally) in the same bacteria, the question become too tough to answer and only a mathematical model can resolve such a interrogation!
 
As a plasmids can be a disadvantage for growth (energy spent into replicating processes) or a advantage (protection against a toxin) this question is hard to answer. But in this situation, where  one type of plasmid can influence on the  presence of the other type of plasmid in (and reciprocally) in the same bacteria, the question become too tough to answer and only a mathematical model can resolve such a interrogation!
  
====Equations====
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==Equations==
  
=====Development of the model=====
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===Development of the model===
  
 
In 1967 Fredrickson et al. <ref name="Fredrickson1967">[https://pdfs.semanticscholar.org/1873/0fa936b17078cfe2b0ab1f74d44eae002758.pdf Fredrickson AG, Ramkrishna D, Tsuchiya H (1967) Statistics and dynamics of correct pro- caryotic cell populations. Mathematical Biosciences 1: 327–374.]</ref> studied mathematically
 
In 1967 Fredrickson et al. <ref name="Fredrickson1967">[https://pdfs.semanticscholar.org/1873/0fa936b17078cfe2b0ab1f74d44eae002758.pdf Fredrickson AG, Ramkrishna D, Tsuchiya H (1967) Statistics and dynamics of correct pro- caryotic cell populations. Mathematical Biosciences 1: 327–374.]</ref> studied mathematically
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</nowiki>
 
</nowiki>
  
=====Objectives=====
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===Objectives===
  
 
The aim of studying the behaviour of this model is to investigate how  
 
The aim of studying the behaviour of this model is to investigate how  
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the culture progresses, and how this depends on the various parameters in the model.
 
the culture progresses, and how this depends on the various parameters in the model.
  
=====Proposition: Adding contention=====
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===Proposition: Adding contention===
  
 
We need to introduce a modification to equation 3 (the state dependant
 
We need to introduce a modification to equation 3 (the state dependant
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gene copy and without anti-toxin to the $IC_{50}$.
 
gene copy and without anti-toxin to the $IC_{50}$.
  
====Program====
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==Program==
  
 
We made a program to simulate the model corresponding to these equations, using a bayesian algorithm.
 
We made a program to simulate the model corresponding to these equations, using a bayesian algorithm.
  
For speed of execution, is programmed in C, using the GNU scientific library.  
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It is programmed in C to maximize performance, using the GNU scientific library.  
  
 
Plots were made using R with ggplot2.
 
Plots were made using R with ggplot2.
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[[https://static.igem.org/mediawiki/2016/f/f8/T--Aix-Marseille--program-toulouse.zip download]]
 
[[https://static.igem.org/mediawiki/2016/f/f8/T--Aix-Marseille--program-toulouse.zip download]]
  
====Results====
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==Results==
 
[[File:T--Aix-Marseille--model-plot-d20-70.png|300px|350px|left|thumb]]
 
[[File:T--Aix-Marseille--model-plot-d20-70.png|300px|350px|left|thumb]]
  
We can see that with D growing, corresponding to more bacterias growing, more bacterias tend to lose their plasmids.
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We can see that with D increasing, corresponding to more bacteria growing, more bacteria tend to lose their plasmids and to have various numbers of plasmid.
Plasmids do not have enough time to be replicated
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These results can be interpreted by the fact that if D is increasing, thus $µ$ also increases, then bacteria grow faster, and divide faster.
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With small values of D, bacteria grow slowly and all plasmids have time to be replicated between each cell division.
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That is why for these values, most bacteria still have maximum values of plasmids and are all in the same situation hence the focusing of the plot for small values of D.
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If D is higher time for each bacteria to replicate their plasmids between each division is reduced, and the situation of each individual bacteria becomes different, explaining the scattering on the plot.
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This show that one of the main factor influencing the loss of plasmid is the growth of bacteria. Of course other factor have shown impact as replication rate of plasmids and the relative toxicity of each toxin.
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<div style="clear:both"></div>
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==Bibliography==
  
====Bibliography====
 
 
<references/>
 
<references/>
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Latest revision as of 01:19, 20 October 2016