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

Line 18: Line 18:
  
 
<li> its amount inside all the cells together (its total amount  
 
<li> its amount inside all the cells together (its total amount  
−
   inside the cells) is denoted by Y_{sum}</li>
+
   inside the cells) is denoted by Y<sub>sum</sub></li>
  
 
<li> its amount outside all the cells (its external amount) is  
 
<li> its amount outside all the cells (its external amount) is  
−
   denoted by Y_{out}</li>
+
   denoted by Y<sub>out</sub></li>
  
 
</ul>
 
</ul>
Line 36: Line 36:
 
<li>LA - the complex LuxR and AHL form together.</li>
 
<li>LA - the complex LuxR and AHL form together.</li>
  
−
<li>LA_{2}
+
<li>LA<sub>2</sub>
 
- the dimer we get when two LuxR-AHL complexes bind  
 
- the dimer we get when two LuxR-AHL complexes bind  
 
together.</li>
 
together.</li>
Line 42: Line 42:
 
<li>aa - Aiia (a AHL-lactonase).</li>
 
<li>aa - Aiia (a AHL-lactonase).</li>
  
−
<li>a_{1}
+
<li>a<sub>1</sub>
 
- plasmids with an unactivated LuxR promotor.</li>
 
- plasmids with an unactivated LuxR promotor.</li>
  
−
<li>a_{2}
+
<li>a<sub>2</sub>
 
- plasmids with an activated LuxR promotor.</li>
 
- plasmids with an activated LuxR promotor.</li>
−
<li>RNA_{TetR}
+
<li>RNA<sub>TetR</sub>
 
   - RNA strands of the TetR gene.</li>
 
   - RNA strands of the TetR gene.</li>
  
 
<li>TetR - Tet Repressor protein we use.</li>
 
<li>TetR - Tet Repressor protein we use.</li>
  
−
<li>b_{0}
+
<li>b<sub>0</sub>
 
  - plasmids with an unactivated Tet promotor.</li>
 
  - plasmids with an unactivated Tet promotor.</li>
  
−
<li>b_{1}
+
<li>b<sub>1</sub>
 
  - plasmids with an activated Tet promotor.</li>
 
  - plasmids with an activated Tet promotor.</li>
  
Line 70: Line 70:
 
<li>N - number of bacteria. The bacteria are divided to two groups</li>
 
<li>N - number of bacteria. The bacteria are divided to two groups</li>
  
−
<li>   N^{+}
+
<li>   N<sup>+</sup>
 
  - bacteria with our plasmid.</li>
 
  - bacteria with our plasmid.</li>
  
−
<li>   N^{-}
+
<li>   N<sup>-</sup>
 
  - bacteria without our plasmid (in other words,  
 
  - bacteria without our plasmid (in other words,  
 
bacteria that lost the plasmids we introduced into them).</li>
 
bacteria that lost the plasmids we introduced into them).</li>
Line 79: Line 79:
 
<li>V - volume of the relevant scale. That means,
 
<li>V - volume of the relevant scale. That means,
 
<ul>
 
<ul>
−
<li>   V_{out}
+
<li>   V<sub>out</sub>
 
  - the volume of the space outside the cells.</li>
 
  - the volume of the space outside the cells.</li>
  
−
 <li>  V_{sum}
+
 <li>  V<sub>sum</sub>
 
  - the volume of the total space inside all the cells.</li></ul></li>
 
  - the volume of the total space inside all the cells.</li></ul></li>
  
Line 93: Line 93:
 
<li>C1 - C18 - different reaction constants.</li>
 
<li>C1 - C18 - different reaction constants.</li>
  
−
<li>T^{+}
+
<li>T<sup>+</sup>
 
  - plamid positive generation time.</li>
 
  - plamid positive generation time.</li>
  
−
<li>T^{-}
+
<li>T<sup>-</sup>
 
  - plamid free generation time.</li>
 
  - plamid free generation time.</li>
  
Line 116: Line 116:
 
<ul>
 
<ul>
  
−
<li>AHL_{out}
+
<li>AHL<sub>out</sub>
 
- how much AHL we put.</li>
 
- how much AHL we put.</li>
  
Line 124: Line 124:
  
 
<li>b0 - initial number of strands (probably plasmid number). Sounds  
 
<li>b0 - initial number of strands (probably plasmid number). Sounds  
−
equal to a_{0}(t=0)
+
equal to a<sub>0</sub>(t=0)
 
.</li>
 
.</li>
  
 
<li>b1 - 0.</li>
 
<li>b1 - 0.</li>
  
−
<li>N^{+}
+
<li>N<sup>+</sup>
 
- the number of cells we have at the beginning.</li>
 
- the number of cells we have at the beginning.</li>
  
−
<li>N^{-}
+
<li>N<sup>-</sup>
 
- 0.</li>
 
- 0.</li>
  

Revision as of 20:52, 17 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.
    • 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 Reactions

equations 1-8 of our model

equations 9-13 of our model

equations 14-17 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.