Endy:Chassis engineering/VM2.0

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VM2.0 regulation design considerations

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Regulation scheme for VM2.0

1. Stability
   • Noise
     • analytical stability analysis on very simple model or Routh-Hurwitz analysis for full model
     • parameter sensitivity analysis
   • Response time
     • Better to have this fast or slow (slow response time averages out short time scale fluctuations)
2. Self-booting/controlled
   • Ability to turn on or off
   • Portability
3. Tunable
   • Pros and cons of DNA copy number, promoter strength, repressor affinities etc.
4. Efficient
   • Minimizing levels of repressor needed
   • Minimizing consumption of small molecules

What are the metrics for each of the design considerations? </hide></showhide>

Reduced Model

Reduced network for VM2.0

• Two species, RNAP (activator) and repressor
• Continuous differential equations
• MATLAB
• Dimensionless variables, lumped parameters.
• Parameterized for T7 RNAP, "typical" repressor

[math]\displaystyle{ \dot{[u]} = \frac{a_{0}+a_{1}[u]}{1+[u]+[v]^{n}}-[u]\qquad(1) }[/math]
[math]\displaystyle{ \dot{[v]} = \frac{a_{0}+a_{1}[u]}{1+[u]+[v]^{n}}-[v]\qquad(2) }[/math]

[math]\displaystyle{ [u] }[/math] = dimensionless concentration of T7 RNAP

[math]\displaystyle{ [v] }[/math] = dimensionless concentration of repressor

Reduced model results

Nullclines and fixed point for plausible parameter values

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Species

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1. T7 RNAP
2. Repressor
3. Ribosomes
4. Repressible T7 promoter
5. T7RNAP-promoter complex
6. Repressor-promoter complex
7. T7 RNAP mRNA
8. Repressor mRNA
9. Elongating T7 RNAP
10. Elongating Ribosomes
11. etc.

Model analysis notes

• A cooperative autogene network can exhibit bistability or monostability depending on parameter values (7.81). Does this apply if there is no cooperativity?

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