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Team:Paris Bettencourt/tRNA diffusion/Random walker
From 2011.igem.org
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<h1>Effective translation of mRNA amber and tRNA amber diffusion</h1> | <h1>Effective translation of mRNA amber and tRNA amber diffusion</h1> | ||
| - | <p>This model is very similar to the one used in <a href="https://2011.igem.org/Team:Paris_Bettencourt/Hypothesis#references">[2]</a>. We consider that the | + | <p>We already justified the hyptothesis of neglecting the time in takes for a molecule to reach any given point in a cell (see <a>Modeling hypotheses</a>). However in this design we want to have <em>two <i>tRNA amber</i></em> reaching the amber codons on the same mRNA, <em>exactly when the ribosome is on the first and second amber codon</em>. This requires a little more analysis before validating the possibility of the translation of the <i>mRNA amber</i> into a fully functional T7 RNA polymerase.</p> |
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| + | <h4>Random walker model</h4> | ||
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| + | <p>This model is very similar to the one used in <a href="https://2011.igem.org/Team:Paris_Bettencourt/Hypothesis#references">[2]</a>. We consider that the <i>tRNA amber</i> diffusing in the cell is a <em>random walker</em>.</p> | ||
<br> | <br> | ||
| - | <p>We want to see how long it takes for a | + | <p>We want to see how long it takes for a tRNA to diffuse to any point of a cell. We use the following parameters:</p> |
<ul> | <ul> | ||
<li><i>V</i> volume of the cell (10<sup>-18</sup> m<sup>3</sup>)</li> | <li><i>V</i> volume of the cell (10<sup>-18</sup> m<sup>3</sup>)</li> | ||
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<p>We divide the cytoplasm volume <i>V</i> into <img src='https://static.igem.org/mediawiki/2011/7/72/Occupation_sites_general.png' style='width:80px;'/> occupation sites for the walker. The characteristic time <img src='https://static.igem.org/mediawiki/2011/8/84/Tau.png' style='width:20px;'/> associated with the transition from one site to another is:<img src='https://static.igem.org/mediawiki/2011/8/81/Characteristic_time_general.png' style='width:90px;'/> <a href="https://2011.igem.org/Team:Paris_Bettencourt/Hypothesis#references">[3]</a></p> | <p>We divide the cytoplasm volume <i>V</i> into <img src='https://static.igem.org/mediawiki/2011/7/72/Occupation_sites_general.png' style='width:80px;'/> occupation sites for the walker. The characteristic time <img src='https://static.igem.org/mediawiki/2011/8/84/Tau.png' style='width:20px;'/> associated with the transition from one site to another is:<img src='https://static.igem.org/mediawiki/2011/8/81/Characteristic_time_general.png' style='width:90px;'/> <a href="https://2011.igem.org/Team:Paris_Bettencourt/Hypothesis#references">[3]</a></p> | ||
| - | <p>If we have <i>R</i> walkers of this type, the probability that a molecule arrives at a given occupation site during the time interval <img src='https://static.igem.org/mediawiki/2011/8/84/Tau.png' style='width:20px;'/> is: <img src='https://static.igem.org/mediawiki/2011/b/bb/Probability_general.png' style='width:80px;'/>. | + | <p>If we have <i>R</i> walkers of this type, the probability that a molecule arrives at a given occupation site during the time interval <img src='https://static.igem.org/mediawiki/2011/8/84/Tau.png' style='width:20px;'/> is: <img src='https://static.igem.org/mediawiki/2011/b/bb/Probability_general.png' style='width:80px;'/>.</p> |
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| + | <p>Until this point, the model does not differ from what we used to do. But let's dive into the additions we had to make to explore the possibility of functional T7 RNA polymerase production.</p> | ||
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| + | <h4>The specificities of our design</h4> | ||
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| + | <p></p> | ||
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Revision as of 12:27, 11 September 2011
Effective translation of mRNA amber and tRNA amber diffusion
We already justified the hyptothesis of neglecting the time in takes for a molecule to reach any given point in a cell (see Modeling hypotheses). However in this design we want to have two tRNA amber reaching the amber codons on the same mRNA, exactly when the ribosome is on the first and second amber codon. This requires a little more analysis before validating the possibility of the translation of the mRNA amber into a fully functional T7 RNA polymerase.
Random walker model
This model is very similar to the one used in [2]. We consider that the tRNA amber diffusing in the cell is a random walker.
We want to see how long it takes for a tRNA to diffuse to any point of a cell. We use the following parameters:
- V volume of the cell (10-18 m3)
characteristic size of the particle (m)- D diffusion coefficient of the particle (m2.s-1)
We divide the cytoplasm volume V into 
occupation sites for the walker. The characteristic time 
associated with the transition from one site to another is:
[3]
If we have R walkers of this type, the probability that a molecule arrives at a given occupation site during the time interval is: 
.
Until this point, the model does not differ from what we used to do. But let's dive into the additions we had to make to explore the possibility of functional T7 RNA polymerase production.
