Difference between revisions of "Team:Technion HS Israel/Modelling/Equations"

 
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<h1>Full equations </h1>
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<h1><font color="#008080">Full equations</font></h1>
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<h2>1 Notations</h2>
 
<h2>1 Notations</h2>
  
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<li>b<sub>1</sub>
 
<li>b<sub>1</sub>
 
  - plasmids with an activated Tet promotor.</li>
 
  - plasmids with an activated Tet promotor.</li>
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<li>RNA<sub>ccdb</sub>
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  - RNA strands of the ccdb gene.</li>
  
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</li>ccbd - Toxin we use to kill the cell.</li>
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<li>ccbd - Toxin we use to kill the cell.</li>
  
 
<li>X - any gene we want to measure the amount of it that will be  
 
<li>X - any gene we want to measure the amount of it that will be  
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<li>   V<sub>out</sub>
 
<li>   V<sub>out</sub>
 
  - the volume of the space outside the cells.</li>
 
  - the volume of the space outside the cells.</li>
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 <li>  V<sub>sum</sub>
 
 <li>  V<sub>sum</sub>
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  - the volume of the total space inside all the cells.</li></ul></li>
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  - the volume of the total space inside all the cells.</li></ul>
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<li>w - width of the cell membrane.</li>
 
<li>w - width of the cell membrane.</li>
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<h2>3 Reactions</h2>
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<h2>3 Equations</h2>
  
 
<p><img src="https://static.igem.org/mediawiki/2015/2/25/Technion_HS_2015_eq1.png" alt="equations 1-9 of our model" width="1074px" height="641px" ></img></p>
 
<p><img src="https://static.igem.org/mediawiki/2015/2/25/Technion_HS_2015_eq1.png" alt="equations 1-9 of our model" width="1074px" height="641px" ></img></p>
  
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<p><img src="https://static.igem.org/mediawiki/2015/5/54/Technion_HS_2015_eq2.png" alt="equations 10-17 of our model" width="1074px" height="567px" ></img></p>
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<p><img src="https://static.igem.org/mediawiki/2015/5/54/Technion_HS_2015_eq2.png" alt="equations 10-17 of our model" width="1074px" height="680px" ></img></p>
  
  

Latest revision as of 00:09, 19 September 2015

Technion 2015 HS Team's Wiki

Full equations

1 Notations

1.1 Notation principles

Every relevant substance in the cell is denoted with uppercase letters which describes the substance, and a subscript which encodes the scale in which the amount of the substance is measured by the variable. For example, if we have a substance Y,

  • its amount inside a single cell is denoted by Yin
  • its amount inside all the cells together (its total amount inside the cells) is denoted by Ysum
  • its amount outside all the cells (its external amount) is denoted by Yout

2 A list of all the notations we used

Substances:

  • A - AHL (The auto inducer, a short for N-Acyl homoserine lactone).
  • L - LuxR (a transciptional activator protein)
  • LA - the complex LuxR and AHL form together.
  • LA2 - the dimer we get when two LuxR-AHL complexes bind together.
  • aa - Aiia (a AHL-lactonase).
  • a1 - plasmids with an unactivated LuxR promotor.
  • a2 - plasmids with an activated LuxR promotor.
  • RNATetR - RNA strands of the TetR gene.
  • TetR - Tet Repressor protein we use.
  • b0 - plasmids with an unactivated Tet promotor.
  • b1 - plasmids with an activated Tet promotor.
  • RNAccdb - RNA strands of the ccdb gene.
  • ccbd - Toxin we use to kill the cell.
  • X - any gene we want to measure the amount of it that will be produced by the bacteria colony. For example, it might represent the amount of a certain drug the bacteria produce.

Other quantitie of interest:

  • N - number of bacteria. The bacteria are divided to two groups
  •    N+ - bacteria with our plasmid.
  •    N- - bacteria without our plasmid (in other words, bacteria that lost the plasmids we introduced into them).
  • V - volume of the relevant scale. That means,
    •    Vout - the volume of the space outside the cells.
      •  
    •   Vsum - the volume of the total space inside all the cells.
  • w - width of the cell membrane.

Constants

  • C1 - C18 - different reaction constants.
  • T+ - plamid positive generation time.
  • T- - plamid free generation time.
  • p - the chance to loose a plasmid.
  • D- AHL diffusion constant.

3 Equations

equations 1-9 of our model

equations 10-17 of our model

Initial conditions

  • AHLout - how much AHL we put.
  • a0 - initial number of strands (probably plasmid number).
  • a1 - 0.
  • b0 - initial number of strands (probably plasmid number). Sounds equal to a0(t=0) .
  • b1 - 0.
  • N+ - the number of cells we have at the beginning.
  • N- - 0.
  • all the rest - 0.