Team:TU-Munich/Modeling/Kill Switch

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Revision as of 14:39, 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:

siRNA method: When some trigger is activated, siRNA is expressed inhibiting the expression of a vital gene
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:

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

Defining

we get the following quadratic equation for the stable point of V

If α = 1, the unique stable point is

To analyze the stability of these the eigenvalues of the Hessian matrix H

must be computed. The eigenvalues are

If α ≠ 1, the stable points are

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

for α > 1:
for α < 1:

Nuclease Modell

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.

@@ Line 27: / Line 27: @@
 Defining [[File:TUM13_siRNA_alpha_beta_def.png]] we get the following quadratic equation for the stable point of V [[File:TUM13_siRNA_stable_quadratic.png|center]]
-If [[File:TUM13_siRNA_alpha_eq_1.png]], the unique stable point is [[File:TUM13_siRNA_alphaIS1_stable.png|center]]
+If &alpha; = 1, the unique stable point is [[File:TUM13_siRNA_alphaIS1_stable.png|center]]
 To analyze the stability of these the eigenvalues of the Hessian matrix  H [[File:TUM13_siRNA_alphaIS1_Hessian.png|center]]
@@ Line 33: / Line 33: @@
 must be computed. The eigenvalues are [[File:TUM13_siRNA_alphaIS1_EV.png|center]]
-&alpha;
+If &alpha; ≠ 1, the stable points are
-[[File:TUM13_siRNA_alpha_neq_1.png|center]]
 [[File:TUM13_siRNA_stable_points.png|center]]
-[[File:TUM13_siRNA_alpha_gt_1.png|center]]
+Now only one of these is in the sensible range, because
+*for &alpha; > 1: [[File:TUM13_siRNA_alphaGT1_lowerbound.png]]
+*for &alpha; < 1: [[File:TUM13_siRNA_alphaLT1_lowerbound.png]]
-[[File:TUM13_siRNA_alphaGT1_lowerbound.png|center]]
-[[File:TUM13_siRNA_alpha_lt_1.png|center]]
-[[File:TUM13_siRNA_alphaLT1_lowerbound.png|center]]
 [[File:TUM13_siRNA_stable_realistic_point.png|center]]