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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  <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 transcribed mRNA-T7 among the others mRNA. The behavior of tRNA amber that arrived in a receiver cell is random, so in order to describe its interaction with mRNA-T7 and its further 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 reason in two steps : first a tRNA amber molecule gets close to a mRNA molecule. Then, it binds it's anti-codon with a codon of the mRNA. This reasoning is similar to the problem of boxes and balls. There are two types of boxes: 'a' of the first type and 'b' of the second (which 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 are 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 P_0.
 
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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. Thus the chance that three or more tRNA amber will "find" one mRNA-T7 is negligible comparing to the one of two tRNA amber (finding a mRNA-T7). In our model we will consider that at one moment of time each mRNA interacts with 0, 1 or 2 tRNA amber.
 
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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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</table>
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== Bi-directional communication ==
 
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== Brownian motion and diffusion ==
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A significant part of our designs relies on diffusion of very few molecules to activate the amplification and reporter systems. For instance, we know that in the T7 design, we need less than 10 T7 RNA polymerase to trigger the amplification. Knowing how a molecule moves in a cell just after its transport through nanotubes was necessary. To model this kind of behaviour we had to look into the mechanisms of diffusion for single molecules in cells. This meant studying the motions of diffusion.<br>
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Please note that we are ''not'' talking here about the movement of molecules inside the nanotubes, which requires other types of model.<br>
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=== Diffusion without boundary conditions ===
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        <div id="footer-wrapper">
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The first step was to study the general principle of diffusion and to apply them to a single molecule. We expected to estimate the order of magnitude for diffusion time of molecules with this model, not to have a precise understanding of the movement of molecules in a cell. Most of our experimental designs rely on time measurement to characterize the nanotubes, it was therefore crucial to see if diffusion time could add a significant delay to the response of receiver cells.<br>
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The principle of this first model is quite simple. We use the statistical diffusion equation with a new normalisation constant so that it describes the behaviour of one molecule. Rather than obtaining a concentration field, we end up for each spatial position with a distribution of the probability of the presence of the molecule. We did not use any kind of limit conditions, we therefore only have the "movements" of one molecule floating in an infinite water medium.<br>
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The equation of diffusion is the following:<br>
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[[File:diffusion_equation.png|thumb|center]]
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Where ''c'' is the concentration of particles in the cell, function of <math>\vec{x}</math> (position) and ''t'' (time). ''D'' is the diffusion coefficient.<br>
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The solution for such an equation is:<br>
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[[File:Diffusion_solution_form.png‎ |thumb|center]]
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The star * represents the convolution of the two functions. The first part represents the initial conditions which are in our case a Dirac function centered on the origin of space (there is only one molecule at (0,0,0) at t=0). the second part of this solution is the so-called fundamental solution.
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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.

Retrieved from "http://2011.igem.org/Team:Paris_Bettencourt/Modeling"