Endy:Chassis engineering/VM2.0: Difference between revisions
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__NOTOC__ | __NOTOC__ | ||
<h1>VM2.0 regulation design considerations</h1>{{hide|1= | |||
[[Image:BC-VM20Regulation.png|thumb|right|500px|Regulation scheme for VM2.0]] | [[Image:BC-VM20Regulation.png|thumb|right|500px|Regulation scheme for VM2.0]] | ||
#Stability | #Stability | ||
Line 7: | Line 7: | ||
#**parameter sensitivity analysis | #**parameter sensitivity analysis | ||
#*Response time | #*Response time | ||
#**Better to have this fast or slow (slow response time averages out short time scale fluctuations) | |||
#Self-booting/controlled | #Self-booting/controlled | ||
#*Ability to turn on or off | #*Ability to turn on or off | ||
Line 17: | Line 18: | ||
What are the metrics for each of the design considerations? | What are the metrics for each of the design considerations? | ||
}} | |||
<br style="clear:both" /> | <br style="clear:both" /> | ||
==Model== | ==Reduced Model== | ||
Continuous differential | [[Image:BC-VM20RegulationReduced Model.jpg|thumb|400px|right|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 | |||
<br> | |||
<math> | |||
\dot{[u]} = \frac{a_{0}+a_{1}[u]}{1+[u]+[v]^{n}}-[u]\qquad(1) | |||
</math> | |||
<br> | |||
<math> | |||
\dot{[v]} = \frac{b_{0}+b_{1}[u]}{1+[u]+[v]^{n}}-[v]\qquad(2) | |||
</math> | |||
<br> | |||
<math>\displaystyle [u]</math> = dimensionless concentration of T7 RNAP | |||
<br> | |||
<math>\displaystyle [v]</math> = dimensionless concentration of repressor | |||
<br> | |||
<br style="clear:both" /> | |||
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 - | |||
<math> | |||
\dot{[u]} = \frac{a_{0}+a_{1}[u]}{1+[u]+r[u]^{n}}-[u]\qquad(3) | |||
</math> | |||
===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, <math>\displaystyle u_{ss}</math> with <math>\scriptstyle n=2</math> and ignoring small terms, the (single) fixed point, is <math>u_{ss} = \frac{\sqrt{a_{1}}}{r}</math> | |||
#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=== | |||
[[Image:BC-VM20TimeCourse.jpg|thumb|300px|left|Time Course for RNAP and repressor species in reduced model]] | |||
[[Image:BC-VM20FixedPoint.jpg|thumb|300px|right|Nullclines and fixed point for plausible parameter values]] | |||
<br style="clear:both" /> | |||
<h2>Species</h2>{{hide|1= | |||
#T7 RNAP | #T7 RNAP | ||
#Repressor | #Repressor | ||
Line 36: | Line 77: | ||
===Model analysis notes=== | ===Model analysis notes=== | ||
*A cooperative autogene network can exhibit bistability or monostability depending on parameter values ([http://web.mit.edu/biophysics/sbio/ 7.81]). Does this apply if there is no cooperativity? | *A cooperative autogene network can exhibit bistability or monostability depending on parameter values ([http://web.mit.edu/biophysics/sbio/ 7.81]). Does this apply if there is no cooperativity? | ||
}} |
Latest revision as of 07:07, 3 May 2007
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
[math]\displaystyle{
\dot{[u]} = \frac{a_{0}+a_{1}[u]}{1+[u]+[v]^{n}}-[u]\qquad(1)
}[/math]
[math]\displaystyle{
\dot{[v]} = \frac{b_{0}+b_{1}[u]}{1+[u]+[v]^{n}}-[v]\qquad(2)
}[/math]
[math]\displaystyle{ \displaystyle [u] }[/math] = dimensionless concentration of T7 RNAP
[math]\displaystyle{ \displaystyle [v] }[/math] = 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 -
[math]\displaystyle{ \dot{[u]} = \frac{a_{0}+a_{1}[u]}{1+[u]+r[u]^{n}}-[u]\qquad(3) }[/math]
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, [math]\displaystyle{ \displaystyle u_{ss} }[/math] with [math]\displaystyle{ \scriptstyle n=2 }[/math] and ignoring small terms, the (single) fixed point, is [math]\displaystyle{ u_{ss} = \frac{\sqrt{a_{1}}}{r} }[/math]
- 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?