Endy:Chassis engineering/VM2.0: Difference between revisions

From OpenWetWare
Jump to navigationJump to search
No edit summary
 
(4 intermediate revisions by 2 users not shown)
Line 1: Line 1:
__NOTOC__
__NOTOC__
<showhide><h1>VM2.0 regulation design considerations</h1>__HIDER__
<h1>VM2.0 regulation design considerations</h1>{{hide|1=
<hide>
[[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 19: Line 18:


What are the metrics for each of the design considerations?
What are the metrics for each of the design considerations?
</hide></showhide>
}}
<br style="clear:both" />
<br style="clear:both" />


Line 39: Line 38:
<br>
<br>


<math>[u]</math> = dimensionless concentration of T7 RNAP
<math>\displaystyle [u]</math> = dimensionless concentration of T7 RNAP
<br>
<br>


<math>[v]</math> = dimensionless concentration of repressor
<math>\displaystyle [v]</math> = dimensionless concentration of repressor
<br>
<br>
<br style="clear:both" />
<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===
===Reduced model results===
[[Image:BC-VM20TimeCourse.jpg|thumb|300px|left|Time Course for RNAP and repressor species in reduced model]]
[[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]]
[[Image:BC-VM20FixedPoint.jpg|thumb|300px|right|Nullclines and fixed point for plausible parameter values]]
<br style="clear:both" />
<br style="clear:both" />
<showhide><h2>Species</h2>__HIDER__
<h2>Species</h2>{{hide|1=
<hide>
#T7 RNAP
#T7 RNAP
#Repressor
#Repressor
Line 65: 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?
</hide></showhide>
}}

Latest revision as of 07:07, 3 May 2007

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


[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

  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, [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]
  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?
Retrieved from "https://openwetware.org/mediawiki/index.php?title=Endy:Chassis_engineering/VM2.0&oldid=114136"