# Endy:Chassis engineering/VM2.0

### From OpenWetWare

Add to My Links# VM2.0 regulation design considerations

- 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)

- Noise
- Self-booting/controlled
- Ability to turn on or off
- Portability

- Tunable
- Pros and cons of DNA copy number, promoter strength, repressor affinities etc.

- Efficient
- Minimizing levels of repressor needed
- Minimizing consumption of small molecules

## Reduced Model

- Two species, RNAP (activator) and repressor
- Continuous differential equations
- MATLAB
- 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

## Species

- T7 RNAP
- Repressor
- Ribosomes
- Repressible T7 promoter
- T7RNAP-promoter complex
- Repressor-promoter complex
- T7 RNAP mRNA
- Repressor mRNA
- Elongating T7 RNAP
- Elongating Ribosomes
- 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?