Difference between revisions of "Team:Technion HS Israel/Modelling/Equations"
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− | <h1>Full equations </h1> | + | <h1><font color="#008080">Full equations</font></h1> |
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<h2>1 Notations</h2> | <h2>1 Notations</h2> | ||
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<ul> | <ul> | ||
− | <li> its amount inside a single cell is denoted by | + | <li> its amount inside a single cell is denoted by Y<sub>in</sub></li> |
<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 | + | 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 | + | denoted by Y<sub>out</sub></li> |
</ul> | </ul> | ||
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<li>LA - the complex LuxR and AHL form together.</li> | <li>LA - the complex LuxR and AHL form together.</li> | ||
− | <li> | + | <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> | ||
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<li>aa - Aiia (a AHL-lactonase).</li> | <li>aa - Aiia (a AHL-lactonase).</li> | ||
− | <li> | + | <li>a<sub>1</sub> |
- plasmids with an unactivated LuxR promotor.</li> | - plasmids with an unactivated LuxR promotor.</li> | ||
− | <li> | + | <li>a<sub>2</sub> |
- plasmids with an activated LuxR promotor.</li> | - plasmids with an activated LuxR promotor.</li> | ||
+ | <li>RNA<sub>TetR</sub> | ||
+ | - RNA strands of the TetR gene.</li> | ||
− | <li> | + | <li>TetR - Tet Repressor protein we use.</li> |
− | <li> | + | <li>b<sub>0</sub> |
− | - plasmids with an unactivated Tet promotor.</li> | + | - plasmids with an unactivated Tet promotor.</li> |
− | <li> | + | <li>b<sub>1</sub> |
− | - plasmids with an activated Tet promotor.</li> | + | - plasmids with an activated Tet promotor.</li> |
+ | <li>RNA<sub>ccdb</sub> | ||
+ | - RNA strands of the ccdb gene.</li> | ||
− | < | + | |
+ | <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>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> | ||
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<li>V - volume of the relevant scale. That means, | <li>V - volume of the relevant scale. That means, | ||
<ul> | <ul> | ||
− | <li> | + | <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<sub>sum</sub> | |
− | <li> | + | - the volume of the total space inside all the cells.</li></ul> |
− | - the volume of the total space inside all the cells.</li></ul></li> | + | </li> |
<li>w - width of the cell membrane.</li> | <li>w - width of the cell membrane.</li> | ||
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<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> | ||
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</ul> | </ul> | ||
− | <h2>3 | + | <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/2015/5/54/Technion_HS_2015_eq2.png" alt="equations 10-17 of our model" width="1074px" height="680px" ></img></p> | ||
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<h3>Initial conditions</h3> | <h3>Initial conditions</h3> | ||
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<ul> | <ul> | ||
− | <li> | + | <li>AHL<sub>out</sub> |
- how much AHL we put.</li> | - how much AHL we put.</li> | ||
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<li>b0 - initial number of strands (probably plasmid number). Sounds | <li>b0 - initial number of strands (probably plasmid number). Sounds | ||
− | equal to | + | 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> | ||
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Latest revision as of 00:09, 19 September 2015
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
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.