Team:Technion HS Israel/Modelling/Equations

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 Reactions

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.