Team:Paris Bettencourt/Modeling

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<h1>Modeling</h1>
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<br>
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<h2>Modeling in our project</h2>
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= Modeling =
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<p>Our modeling was organized around two main questions:
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<ul>
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<li>Can we <em>explain the transfer</em> through nanotubes?</li>
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<li>What will be the <em>behaviour of our constructs</em> and how will it impact our experimental designs?</li>
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</ul></p>
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== Direct observation ==
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<p>Answering those two questions was essential for our project. We needed to know <em>what to expect in order to design our experiments</em> properly and to know what kind of restults we should obtain.</p>
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== Characterization ==
 
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[[File:Parameters.png|thumb|center|upright=3.0|Relevant parameters for modeling]]
 
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[[File:Equations.png|thumb|center|upright=3.0|Allosteric equations for modeling]]
 
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=== T7 system ===
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<h2>Investigating nanotube transfer</h2>
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[[File:0711_Modelling_T7_without_delay.jpg|thumb|center|upright=3.0|First T7 model without delay between receptor and amplifier]]
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[[File:0711_Modelling_T7_with_delay.jpg|thumb|center|upright=3.0|T7 model with delay between receptor and amplifier]]
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<p>In order to answer the first question, we investigated the <em>physical properties of cell membrane</em> and <em>passive diffusion</em> to comprehend how the transfer could occur. We came up with two different ideas that could explain molecule transfer through the nanotubes, and based our original models on these assumptions, done in Java for passive diffusion and in Matlab for assisted diffusion.These two novel models show that transfer through the nanotubes, whether happening by passive diffusion or the so-called assisted diffusion, is happening too quickly to be accurately measured by fluorescent microscopy. As nanotube transfer is too fast compared to genetic response to allow us to measure its time span correctly, our conclusion was that our designs would not allow us to determine which one of these two processes (passive or assisted diffusion) is dominant during the transfer. Even though this makes it impossible to create a definitive model of molecule transfer through the nanotubes, the information provided by our two alternative models gave us an <em>insight on the time scale of the transfer</em>.</p>
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<table>
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<tr>
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  <td style="width:200px; text-align:center"><a href="https://2011.igem.org/Team:Paris_Bettencourt/Modeling/Diffusion"><img style="width:150px; margin-top:20px;" src="https://static.igem.org/mediawiki/2011/1/1a/Passive-diff-button.png"></a>
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  </td>
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  <td><b><a href="https://2011.igem.org/Team:Paris_Bettencourt/Modeling/Diffusion">Passive diffusion in nanotubes</a></b> We investigate here the hypothesis of passive diffusion through nanotubes.
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  </td>
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</tr>
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<tr>
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  <td style="width:200px; text-align:center"><a href="https://2011.igem.org/Team:Paris_Bettencourt/Modeling/Assisted_diffusion"><img style="width:150px; margin-top:20px;" src="https://static.igem.org/mediawiki/2011/b/b9/Active-diff-button.png"></a>
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  </td>
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  <td><b><a href="https://2011.igem.org/Team:Paris_Bettencourt/Modeling/Assisted_diffusion">Assisted diffusion</a></b> We propose here a model explaining how diffusion through nanotubes could be "assisted" by the tension differential between cell walls.
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  </td>
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</tr>
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</table>
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=== tRNA amber system ===
 
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[[Team:Paris_Bettencourt/tRNA_diffusion|The amber suppressor tRNA diffusion.]] The idea of the system is to pass tRNA amber molecules through the nanotubes. At every moment of time in the receiver cell there is a certain amount of transcripted mRNA-T7 among the others mRNA. The behavior of tRNA amber arrived to a receiver cell is random, so to describe its interaction with mRNA-T7 and its futher translation we can reason in terms of probability.
 
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<h2>Predicting the behaviour of our designs</h2>
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<p>The second question was a crucial step in the design of our experiments. Taking into account the predicted time scale and other information provided by our two general models, we were able to build <em>models of each of our genetic networks</em>. These models are an improvement of Uri Alon's approach in <i>An Introduction to Systems Biology: Design Principles of Biological Circuits</i> and were done in Matlab. With these models we showed that some designs might work better that the others. For instance, we prioritized the T7 RNA polymerase diffusion and tRNA diffusion systems and decided to concentrate our wet lab experiments and characterizatons in these systems. The ComS system, on the other hand, was less developed because of some disadvantages that our model predicted (high background even without induction, very high activation threshold mainly). Moreover, our models let us <em>evaluate the response time of each of our our constructs</em>. With these estimations, were able to prepare protocols for our <a href ="https://2011.igem.org/Team:Paris_Bettencourt/Experiments/Microscopy">microscopic experiments</a> (by evaluating the characteristic response time of our system, the activation thresholds, etc.).</p>
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We can consider two types of events : a tRNA amber molecule gets close to a mRNA molecule and once it is close, it fits its anti-codon to some codon of the mRNA. The way of reasoning is chosen because there is an easy analogy to this problem : the problem of boxes and balls. There are two types of boxes, a of the first type and b of the second(that corresponds to the set of mRNA-T7 and mRNA-non-T7), and there are t balls(tRNA amber). All the balls are randomly distributed in the boxes. If there is two or more balls in some box of the first type(two or more tRNA amber per mRNA-T7) then a T7 molecule will be produced with a chance <math> $ \Delta = \Delta_1 + \Delta_2 $ </math>
 
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This system can be modelled after making some important assumptions :
 
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* All the molecules in the cell are uniformly distributed.
 
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* The number of tRNA amber diffused through the nanotubes is much more smaller than the one of the mRNA.
 
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== Master/Slave ==
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<table>
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<tr>
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  <td style="width:200px; text-align:center"><a href="https://2011.igem.org/Team:Paris_Bettencourt/what_is_modeling"><img style="width:150px" src="https://static.igem.org/mediawiki/2011/2/2b/Question_mark_button.png"></a>
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  </td>
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  <td><b><a href="https://2011.igem.org/Team:Paris_Bettencourt/what_is_modeling">The basics about genetic networks modeling</a></b> You can find here an introduction to our methods and the general idea behind most gene network models.
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  </td>
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</tr>
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<tr>
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  <td style="width:200px; text-align:center;"><a href="https://2011.igem.org/Team:Paris_Bettencourt/Hypothesis"><img style="width:150px; margin-top:20px;" src="https://static.igem.org/mediawiki/2011/2/21/Hypotheses_button.png"></a>
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  </td>
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  <td><b><a href="https://2011.igem.org/Team:Paris_Bettencourt/Hypothesis">Our assumptions</a></b> Because of the specificities of our project, we had to adapt the "classic" model to better represent our current situation. On top of that we made and justified a few other hypotheses detailed in this section.
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  </td>
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</tr>
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<tr>
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  <td style="width:200px; text-align:center"><a href="https://2011.igem.org/Team:Paris_Bettencourt/Modeling/Designs"><img style="width:150px; margin-top:20px;" src="https://static.igem.org/mediawiki/2011/a/ac/Graph-button.png"></a>
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  </td>
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  <td><b><a href="https://2011.igem.org/Team:Paris_Bettencourt/Modeling/Designs">Modeling our designs</a></b> Models predicting the behaviour of our designs are detailled in this section.
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  </td>
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</tr>
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</table>
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Latest revision as of 03:14, 29 October 2011

Team IGEM Paris 2011

Modeling

Modeling in our project

Our modeling was organized around two main questions:

  • Can we explain the transfer through nanotubes?
  • What will be the behaviour of our constructs and how will it impact our experimental designs?

Answering those two questions was essential for our project. We needed to know what to expect in order to design our experiments properly and to know what kind of restults we should obtain.

Investigating nanotube transfer

In order to answer the first question, we investigated the physical properties of cell membrane and passive diffusion to comprehend how the transfer could occur. We came up with two different ideas that could explain molecule transfer through the nanotubes, and based our original models on these assumptions, done in Java for passive diffusion and in Matlab for assisted diffusion.These two novel models show that transfer through the nanotubes, whether happening by passive diffusion or the so-called assisted diffusion, is happening too quickly to be accurately measured by fluorescent microscopy. As nanotube transfer is too fast compared to genetic response to allow us to measure its time span correctly, our conclusion was that our designs would not allow us to determine which one of these two processes (passive or assisted diffusion) is dominant during the transfer. Even though this makes it impossible to create a definitive model of molecule transfer through the nanotubes, the information provided by our two alternative models gave us an insight on the time scale of the transfer.

Passive diffusion in nanotubes We investigate here the hypothesis of passive diffusion through nanotubes.
Assisted diffusion We propose here a model explaining how diffusion through nanotubes could be "assisted" by the tension differential between cell walls.

Predicting the behaviour of our designs

The second question was a crucial step in the design of our experiments. Taking into account the predicted time scale and other information provided by our two general models, we were able to build models of each of our genetic networks. These models are an improvement of Uri Alon's approach in An Introduction to Systems Biology: Design Principles of Biological Circuits and were done in Matlab. With these models we showed that some designs might work better that the others. For instance, we prioritized the T7 RNA polymerase diffusion and tRNA diffusion systems and decided to concentrate our wet lab experiments and characterizatons in these systems. The ComS system, on the other hand, was less developed because of some disadvantages that our model predicted (high background even without induction, very high activation threshold mainly). Moreover, our models let us evaluate the response time of each of our our constructs. With these estimations, were able to prepare protocols for our microscopic experiments (by evaluating the characteristic response time of our system, the activation thresholds, etc.).

The basics about genetic networks modeling You can find here an introduction to our methods and the general idea behind most gene network models.
Our assumptions Because of the specificities of our project, we had to adapt the "classic" model to better represent our current situation. On top of that we made and justified a few other hypotheses detailed in this section.
Modeling our designs Models predicting the behaviour of our designs are detailled in this section.