IGEM:IMPERIAL/2009/M2/Modelling/Analysis

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The E.ncapsulator: the disease killer



Contents

Preliminary Model 1: Genetic circuit

Hypothesis

  • When glucose concentrations are above threshold, there would not be any activation of production of colanic acid or trehalose.
  • When glucose concentrations decrease below threshold, there will be strong activation of M2 and there will be an increase in protein production in the system.
  • For decreased concentration of glucose, there will be increased amounts of colanic acid and trehalose produced.

Equations


\begin{alignat}{2}
\frac{d[m_i]}{dt}  =  \frac{km_i^{n_i}}{{[g]}^{n_i}+ km_i^{n_i}} - dm_i*[m_i] \qquad (1)\\
\frac{d[p_i]}{dt}  = [m_i]*kp_i - dp_i*[p_i] \qquad (2)\\
where\ i = 1, 2, 3, 4, 5 
\end{alignat}

Legend

Term Variable/Parameter Meaning/description
1 - RcsB
2 - B3023
3 - Waal Ligase
4 - OtsA
5 - OtsB
g Variable Concentration of glucose
mi Variable Concentration of ith mRNA
pi Variable Concentration of ith protein
ni Parameter Hill coefficient of ith mRNA


Explanation of equations

  • In equation (1), we have used a repressing hill function of glucose. This is because glucose, represses CRP, which activates our system. A decrease in [glucose] below threshold will activate M2 strongly.
  • The genes are produced in parallel, hence the repressing hill function will appear in the mRNA equations, for all our proteins.


Simulations

Simulation 1: Effects of increasing glucose concentrations on production of protein

Image:m2.0.jpg

Explanations

  • When there is a decrease in glucose concentration beyond threshold, there is a great increase in amount and rate of protein production.
  • A short time delay is seen as transcription and translation takes time.

Data Fitting

Matlab files

References









































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