# Endy:Chassis engineering/VM2.0

(diff) ←Older revision | Current revision (diff) | Newer revision→ (diff)

# VM2.0 regulation design considerations

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?

## 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

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

$\displaystyle [u]$ = dimensionless concentration of T7 RNAP

$\displaystyle [v]$ = 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 -

$\dot{[u]} = \frac{a_{0}+a_{1}[u]}{1+[u]+r[u]^{n}}-[u]\qquad(3)$

1. 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, $\displaystyle u_{ss}$ with $\scriptstyle n=2$ and ignoring small terms, the (single) fixed point, is $u_{ss} = \frac{\sqrt{a_{1}}}{r}$
2. What is the material usage like?
3. What happens when RNAP level drops suddenly (e.g. when another T7 reporter in the cell is derepressed.)

### Reduced model results

Time Course for RNAP and repressor species in reduced model
Nullclines and fixed point for plausible parameter values

## Species

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?