Team:TU-Munich/Modeling/Kill Switch

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If α = 1, the unique stable point is [[File:TUM13_siRNA_alphaIS1_stable.png|70px]]  
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If α = 1, the unique stable point is [[File:TUM13_siRNA_alphaIS1_stable.png]].
To analyze the stability of these the eigenvalues of the Hessian matrix  H [[File:TUM13_siRNA_alphaIS1_Hessian.png|center]]
To analyze the stability of these the eigenvalues of the Hessian matrix  H [[File:TUM13_siRNA_alphaIS1_Hessian.png|center]]
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must be computed. The eigenvalues are [[File:TUM13_siRNA_alphaIS1_EV.png|center]]
must be computed. The eigenvalues are [[File:TUM13_siRNA_alphaIS1_EV.png|center]]
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So these
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These are both negative, so this is a stable point.

Revision as of 14:48, 3 October 2013


Kill Switch Modeling

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 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

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 tested method the concentration of siRNA R and nuclease N as appropriate. Both concentrations are normalized to the unit interval [0,1].

siRNA Model

We determined the governing equations of this model to be the following:

TUM13 siRNA formula.png

with initial conditions V(0) = 1 and R(0) = 0, where at the time t=0 the trigger is activated.

The stable points V* and R* of this system have to satisfy
TUM13 siRNA stable satisfy.png
Defining TUM13 siRNA alpha beta def.png we get the following quadratic equation for the stable point of V
TUM13 siRNA stable quadratic.png


If α = 1, the unique stable point is TUM13 siRNA alphaIS1 stable.png.

To analyze the stability of these the eigenvalues of the Hessian matrix H
TUM13 siRNA alphaIS1 Hessian.png
must be computed. The eigenvalues are
TUM13 siRNA alphaIS1 EV.png

These are both negative, so this is a stable point.


If α ≠ 1, the stable points are

TUM13 siRNA stable points.png


Now only one of these is in the sensible range, because

  • for α > 1: TUM13 siRNA alphaGT1 lowerbound.png
  • for α < 1: TUM13 siRNA alphaLT1 lowerbound.png


TUM13 siRNA stable realistic point.png


TUM13 siRNA expandby.png
TUM13 siRNA V rewritten.png
TUM13 siRNA V in01.png
TUM13 siRNA Hessian.png
TUM13 siRNA EigVals b.png
TUM13 siRNA EigVals.png
TUM13 siRNA END.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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