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 | + | 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> | ||
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> | + | <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> | + | <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> | + | <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> | + | <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> | ||
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> | + | <li> V<sub>out</sub> |
- the volume of the space outside the cells.</li> | - the volume of the space outside the cells.</li> | ||
− | <li> | + | <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> | + | <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 | + | 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
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
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.