Team:Evry/pop scale

From 2013.igem.org

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Overview of population scale model
 
<h2>Introduction</h2>
<h2>Introduction</h2>
<p>
<p>
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Le modèle de production d'enterobactine nous a montré que celles ci prenaient trop de temps à être produite pour stratégie de flush. Les biologistes ont donc changé de méthode qui met à profit un gel qui bloque les bactéries au niveau du jejunum. Nous avons donc décidé de faire un nouveau modèle similaire au modèle du duodenum.
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The <a href="https://2013.igem.org/Team:Evry/ent_prod">Enterobactin production model</a> showed us that our bacteria take too much time to produce enterobactins, which disables the flush strategy.<br/>
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In response, we changed the strategy, by delivering a gel that would block the bacteria in the jejunum.<br/>
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This model is thus very similar to the flush treatment model, except for the longer time scale, and the computational method.
</p>
</p>
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<h2>Observations</h2>
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<h2>Goal</h2>
<p>
<p>
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This model was made to check if our first strategy was viable. It aims to answer the following question: <br/>
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</p>
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<em>"Is it possible to chelate a significant amount of iron with a flush strategy?"</em>
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<h2>Goals</h2>
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<p>
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</p>
</p>
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<a id="Assumptions"></a>
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<h2>Assumptions</h2>
<ul>
<ul>
<li>No regulation of the patient's iron absorption</li>
<li>No regulation of the patient's iron absorption</li>
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<h2>Materials and methods</h2>
<h2>Materials and methods</h2>
<p>
<p>
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This model is based on cellular automaton algorithm. Les bactéries et les Enterobactines sont des automates cellulaires.  
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This model is based on a cellular automaton algorithm : both the bacteria and the enterobactins are cellular automaton.
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<div align="center">
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<a id="Fig1"></a>
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<div class="captionedPicture" style="width:50%;">
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  <a title="Absorption" href="https://static.igem.org/mediawiki/2013/7/78/Popscalegraph.png">
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    <img alt="Absorption" src="https://static.igem.org/mediawiki/2013/7/78/Popscalegraph.png" class="Picture"/>
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  </a>
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  <div class="caption">
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    <b>Figure 1 : </b> Influence graph.
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  </div>
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</div></div>
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<br/>
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The <a href="#Fig1">Figure 1</a> is a graph representing the influence between the system's variables. <br/>
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<br/>
<table width="100%">
<table width="100%">
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<td width ="50%">
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<a id="Fig2"></a>
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<div class="captionedPicture" style="width:100%;">
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<a id="Fig1"></a>
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<div class="captionedPicture" style="width:60%;">
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   <a title="Absorption" href="https://static.igem.org/mediawiki/2013/9/90/Bacteriaautomaton.png">
   <a title="Absorption" href="https://static.igem.org/mediawiki/2013/9/90/Bacteriaautomaton.png">
     <img alt="Absorption" src="https://static.igem.org/mediawiki/2013/9/90/Bacteriaautomaton.png" class="Picture"/>
     <img alt="Absorption" src="https://static.igem.org/mediawiki/2013/9/90/Bacteriaautomaton.png" class="Picture"/>
   </a>
   </a>
   <div class="caption">
   <div class="caption">
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     <b>Figure 1 : </b> Graph of bacteria automaton.
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     <b>Figure 2 : </b> Graph of bacteria automaton.
   </div>
   </div>
</div>
</div>
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</td>
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<td width="10%">
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</td>
<td>
<td>
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<table width="20%" border="1" style="border-collapse:collapse;">
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<table width="50%" border="1" style="border-collapse:collapse;">
<tr>
<tr>
<td><b>P<sub>growth</sub></b></td>
<td><b>P<sub>growth</sub></b></td>
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<br/>
<br/>
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La Figure 1 représente l'automate qui modélise la bactérie. Cet automate à deux parties : la production d'enterobactines et la croissance. La croissance est décrit dans la Figure 1 par un
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The <a href="#Fig2">Figure 2</a> represents the bacterial automaton. It has two functions : the division and the ennterobactin production.<br/>
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<br/>
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The enterobactin production is ruled by an activator. This activator is a step function (from 0 to 1) with a K<sub>a</sub> threshold, fixed thanks to the <a href="https://2013.igem.org/Team:Evry/Modelmeta1">sensor model</a>:<br/>
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The bacteria produces enterobactins. This production is ruled by a activator. Cette activateur est une fonction palier
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<img src="https://static.igem.org/mediawiki/2013/8/84/Activpopscale.png" width="30%"/></br>
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Where <i>gauss</i> is a gaussian noise.
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and Siderophores chelate iron. Iron arrive in the environment by pulse every second. This pulse is constant. Iron is reduce by body and bacteria absorption. According to the hypothesis, we haven't iron auto-regulation. And the variation of Iron uptake is proportional to the iron quantity.
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</p>
</p>
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<h2>Parameters tuning :</h2>
 
<p>
<p>
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The enterobactins chelate iron. For this automoton, we have one rule : <b> One Enterobactin atom can chelate one Iron molecule</b><br/>
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Still, the automaton is ruled by an encounter probability: <img src="https://static.igem.org/mediawiki/2013/3/32/Formulechela.png" width="20%"/><br/>
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Where <i>uniforme(0,1)</i> is the uniform probability function.
</p>
</p>
<h2>Results</h2>
<h2>Results</h2>
<p>
<p>
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<em>"Is it possible to chelate a significant amount of iron with a flush strategy?"</em>
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</p>
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<p>
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We computed the ambient iron and the iron absorbed by the patient on a 5 hour scale, because that is the time our bacterial gel and the chyme will stay in contact.<br/>
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<a id="Fig3"></a>
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<div class="captionedPicture" style="width:80%;">
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  <a title="Absorption" href="https://static.igem.org/mediawiki/2013/5/53/Popscale1.png">
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    <img alt="Absorption" src="https://static.igem.org/mediawiki/2013/5/53/Popscale1.png" class="Picture"/>
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  </a>
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  <div class="caption">
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    <b>Figure 3 : </b> Iron dissolved in jejunum.
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  </div>
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</div>
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<a id="Fig4"></a>
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<div class="captionedPicture" style="width:80%;">
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  <a title="Absorption" href="https://static.igem.org/mediawiki/2013/9/95/Popscale.png">
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    <img alt="Absorption" src="https://static.igem.org/mediawiki/2013/9/95/Popscale.png" class="Picture"/>
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  </a>
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  <div class="caption">
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    <b>Figure 4 : </b> Iron absorbed by the body.
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  </div>
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</div>
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The <a href="#Fig3">Figure 3</a> and <a href="#Fig4">Figure 4</a> show that it is possible to significantly reduce the iron absorption of the patient.
</p>
</p>
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<table width="100%" border="1" style="border-collapse:collapse;">
<table width="100%" border="1" style="border-collapse:collapse;">
<tr>
<tr>
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<td><b>Name</b></td>
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<td><b>Description</b></td>
<td><b>Value</b></td>
<td><b>Value</b></td>
<td><b>Unit</b></td>
<td><b>Unit</b></td>
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<td><b>Description</b></td>
 
<td><b>Reference</b></td>
<td><b>Reference</b></td>
</tr>
</tr>
<tr>
<tr>
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<td>mu</sub></td>
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<td>Iron absorption rate by the body</td>
<td>0.2</td>
<td>0.2</td>
<td>s<sup>-1</sup></td>
<td>s<sup>-1</sup></td>
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<td>Iron absorption rate by the body</td>
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<td>set</td>
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<td><a href="#Ref"></a></td>
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</tr>
</tr>
<tr>
<tr>
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<td>IronQuantity0</td>
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<td>Iron pulse value</td>
<td>4.5.10<sup>-9</sup></td>
<td>4.5.10<sup>-9</sup></td>
<td>mol<sup>-1</sup></td>
<td>mol<sup>-1</sup></td>
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<td>Iron pulse value</td>
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<td>set</td>
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<td><a href="#Ref"></a></td>
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</tr>
</tr>
<tr>
<tr>
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<td>S<sub>act</sub></td>
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<td>Activator threshold</td>
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<td>10**-9</td>
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<td>2*10<sup>-8</sup></td>
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<td>m</td>
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<td>mol</td>
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<td>Duodenum length</td>
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<td><a href="#Ref">[1]</a></td>
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<td><a href="#Ref">[3]</a></td>
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</tr>
</tr>
<tr>
<tr>
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<td>α</td>
 
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<td>0.3</td>
 
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<td>s<sup>-1</sup></td>
 
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<td>Duodenum absorption rate</td>
 
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<td><a href="#Par">tuned</a></td>
 
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</tr>
 
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<tr>
 
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<td>σ</td>
 
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<td>0.72</td>
 
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<td>s<sup>-1</sup></td>
 
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<td>Regulation coefficient</td>
 
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<td><a href="#Par">tuned</a></td>
 
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</tr>
 
</table>
</table>
</p>
</p>
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<h2>Conclusion</h2>
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<p>
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The combination of the two graphs shows that the bacteria would be able to <b>neutralize some of the incoming iron</b> before it is absorbed by the duodenum.<br/>
 +
The next modeling step could be more oriented towards risk assessment based on a cellular automaton approach.
 +
</p>
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<h2>Models and scripts</h2>
 +
<p>
 +
This model was made using the Python language. You can <a href="https://static.igem.org/mediawiki/2013/9/9e/Popscale.zip"> download the python script here</a>.
 +
</p>
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Latest revision as of 03:59, 29 October 2013

Iron coli project

Introduction

The Enterobactin production model showed us that our bacteria take too much time to produce enterobactins, which disables the flush strategy.
In response, we changed the strategy, by delivering a gel that would block the bacteria in the jejunum.
This model is thus very similar to the flush treatment model, except for the longer time scale, and the computational method.

Goal

This model was made to check if our first strategy was viable. It aims to answer the following question:
"Is it possible to chelate a significant amount of iron with a flush strategy?"

Assumptions

  • No regulation of the patient's iron absorption
  • Constant iron flow in the intestine
  • Homogeneous fluid
  • The bacterial natural absorption is insignificant compared to the chelation
  • The patient ingests 20mg of iron per day (Guideline Daily Amounts)

Materials and methods

This model is based on a cellular automaton algorithm : both the bacteria and the enterobactins are cellular automaton.

Absorption
Figure 1 : Influence graph.

The Figure 1 is a graph representing the influence between the system's variables.

Absorption
Figure 2 : Graph of bacteria automaton.
Pgrowth Division Probability
Pdeath Death probability
age variable rate of bacteria ageing

The Figure 2 represents the bacterial automaton. It has two functions : the division and the ennterobactin production.
The enterobactin production is ruled by an activator. This activator is a step function (from 0 to 1) with a Ka threshold, fixed thanks to the sensor model:

Where gauss is a gaussian noise.

The enterobactins chelate iron. For this automoton, we have one rule : One Enterobactin atom can chelate one Iron molecule
Still, the automaton is ruled by an encounter probability:
Where uniforme(0,1) is the uniform probability function.

Results

"Is it possible to chelate a significant amount of iron with a flush strategy?"

We computed the ambient iron and the iron absorbed by the patient on a 5 hour scale, because that is the time our bacterial gel and the chyme will stay in contact.

Absorption
Figure 3 : Iron dissolved in jejunum.
Absorption
Figure 4 : Iron absorbed by the body.
The Figure 3 and Figure 4 show that it is possible to significantly reduce the iron absorption of the patient.

Parameter values

Description Value Unit Reference
Iron absorption rate by the body 0.2 s-1 set
Iron pulse value 4.5.10-9 mol-1 set
Activator threshold 2*10-8 mol [1]

Conclusion

The combination of the two graphs shows that the bacteria would be able to neutralize some of the incoming iron before it is absorbed by the duodenum.
The next modeling step could be more oriented towards risk assessment based on a cellular automaton approach.

Models and scripts

This model was made using the Python language. You can download the python script here.

References:

Retrieved from "http://2013.igem.org/Team:Evry/pop_scale"