Team:TU-Munich/Modeling/Kill Switch

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Kill Switch Modelling

Purpose

The idea of our kill switch is to kill off our moss, as soon as it leaves the filter system. For this purpose two methods were proposed:

  1. siRNA method: When some trigger is activated, siRNA is expressed to inhibiting the expression of a vital gene
  2. nuclease method: When some trigger is activated, a nuclease is released destroying the DNA of the cell

Model

To decide between these two methods we modelled the vitality V of the cell (a number between 0 and 1, so a perfectly functional cell has V=1, a dead cell V=0) and depending on the test method the concentration of siRNA and nuclease as appropriate. Both concentrations were assumed to be normalized to the unit interval [0,1].

siRNA Modell

We determined the governing equations to be the following:

TUM13 siRNA formula.png
TUM13 siRNA initial.png
TUM13 siRNA stable satisfy.png

Defining TUM13 siRNA alpha beta def.png


TUM13 siRNA stable quadratic.png
TUM13 siRNA alpha eq 1.png
TUM13 siRNA alphaIS1 stable.png
TUM13 siRNA alphaIS1 Hessian.png
TUM13 siRNA alphaIS1 EV.png
TUM13 siRNA alpha neq 1.png
TUM13 siRNA stable points.png
TUM13 siRNA alpha gt 1.png
TUM13 siRNA alphaGT1 lowerbound.png


TUM13 siRNA alpha lt 1.png
TUM13 siRNA alphaLT1 lowerbound.png
TUM13 siRNA stable realistic point.png


Nuclease Modell

TUM13 nuc formula.png
TUM13 nuc initial.png
TUM13 nuc stable satisfy.png
TUM13 nuc hessian ev.png

Conclusion

For a functional kill-switch it is necessary, that the cells are actually killed completely and not just live on with reduced vitality. So based on our modelling results the siRNA approach is not satisfactory, while the nuclease satisfies the requirement. As a result the team pursued the nuclease approach leading to our final kill-switch.

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