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Team:Paris Bettencourt/tRNA diffusion/Random walker
From 2011.igem.org
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<h4>Random walker model</h4> | <h4>Random walker model</h4> | ||
| - | <p>This model is very similar to the one used in <a href="https://2011.igem.org/Team: | + | <p>This model is very similar to the one used in <a href="https://2011.igem.org/Team:Paris Bettencourt/tRNA diffusion/Random_walker#references">[1]</a>. We consider that the <i>tRNA amber</i> diffusing in the cell is a <em>random walker</em>.</p> |
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<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> | ||
| - | <li><img src='https://static.igem.org/mediawiki/2011/d/d2/Lambda.png' style='width:20px;'/> characteristic size of the particle (1.5x10<sup>-8</<sup>m)</li> | + | <li><img src='https://static.igem.org/mediawiki/2011/d/d2/Lambda.png' style='width:20px;'/> characteristic size of the particle (1.5x10<sup>-8</<sup>m <a href="https://2011.igem.org/Team:Paris Bettencourt/tRNA diffusion/Random_walker#references">[1]</a>)</li> |
| - | <li><i>D</i> diffusion coefficient of the particle (2.57x10<sup>-11</sup>m<sup>2</sup>.s<sup>-1</sup>)</li> | + | <li><i>D</i> diffusion coefficient of the particle (2.57x10<sup>-11</sup>m<sup>2</sup>.s<sup>-1</sup> <a href="https://2011.igem.org/Team:Paris Bettencourt/tRNA diffusion/Random_walker#references">[1]</a>)</li> |
</ul> | </ul> | ||
| - | <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: | + | <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/tRNA diffusion/Random_walker#references">[2]</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> | <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>What really interest us is the probability that two amber codons are successfully translated with the help of <i>tRNA amber</i> by the same ribosome. We have to monitor all the amber codons placed on our <i>mRNA amber</i> present in a cell. We therefore have <em>two occupation sites of interest</em> for each <i>mRNA amber</i> in the cell.</p> | <p>What really interest us is the probability that two amber codons are successfully translated with the help of <i>tRNA amber</i> by the same ribosome. We have to monitor all the amber codons placed on our <i>mRNA amber</i> present in a cell. We therefore have <em>two occupation sites of interest</em> for each <i>mRNA amber</i> in the cell.</p> | ||
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| + | <div id="citation_box"> | ||
| + | <p id="references">References</p> | ||
| + | <ol> | ||
| + | <li><i>Ribosome kinetics and aa-tRNA competition determine rate and fidelity of peptide synthesis.</i> Fluitt A, Pienaar E, Viljoen H. Comput Biol Chem. 2007 Oct;31(5-6):335-46. Epub 2007 Aug 15.</li> | ||
| + | <li><i>Diffusion-based Channel Characterization in Molecular Nanonetworks.</i> Llatser, I., Alarcón, E. and Pierobon, M., to appear in Proc. of the 1st IEEE International Workshop on Molecular and Nano Scale Communication (MoNaCom), held in conjunction with IEEE INFOCOM, Shanghai (China), April 2011</li><!--[http://www.ece.gatech.edu/research/labs/bwn/papers/2011/c6.pdf]--> | ||
| + | <ol> | ||
| + | </div> | ||
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Revision as of 13:03, 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 [1]. 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 (1.5x10-8m [1])- D diffusion coefficient of the particle (2.57x10-11m2.s-1 [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:
[2]
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.
The specificities of our design
What really interest us is the probability that two amber codons are successfully translated with the help of tRNA amber by the same ribosome. We have to monitor all the amber codons placed on our mRNA amber present in a cell. We therefore have two occupation sites of interest for each mRNA amber in the cell.
References
- Ribosome kinetics and aa-tRNA competition determine rate and fidelity of peptide synthesis. Fluitt A, Pienaar E, Viljoen H. Comput Biol Chem. 2007 Oct;31(5-6):335-46. Epub 2007 Aug 15.
- Diffusion-based Channel Characterization in Molecular Nanonetworks. Llatser, I., Alarcón, E. and Pierobon, M., to appear in Proc. of the 1st IEEE International Workshop on Molecular and Nano Scale Communication (MoNaCom), held in conjunction with IEEE INFOCOM, Shanghai (China), April 2011
