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VM2.0 regulation design considerations
- 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)
- Ability to turn on or off
- Pros and cons of DNA copy number, promoter strength, repressor affinities etc.
- Minimizing levels of repressor needed
- Minimizing consumption of small molecules
- Two species, RNAP (activator) and repressor
- Continuous differential equations
- Dimensionless variables, lumped parameters.
- Parameterized for T7 RNAP, "typical" repressor
= dimensionless concentration of T7 RNAP
= dimensionless concentration of repressor
If I assume that the two species are expressed in a constant ratio (i.e polycistronic expression or under promoters of proportional strength and have similar degradation rates) then the two equations can be reduced to one -
Big questions to answer
- What are the steady state levels of RNAP/Repressor as a function of parameters?
- Setting the LHS of Equation 3 to 0 and solving for the steady state level, with and ignoring small terms, the (single) fixed point, is
- What is the material usage like?
- What happens when RNAP level drops suddenly (e.g. when another T7 reporter in the cell is derepressed.)
Reduced model results
- T7 RNAP
- Repressible T7 promoter
- T7RNAP-promoter complex
- Repressor-promoter complex
- T7 RNAP mRNA
- Repressor mRNA
- Elongating T7 RNAP
- Elongating Ribosomes
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?