Team:TUDelft/Modeling Cascade

From 2009.igem.org

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Image:test.jpg|'''1111 :''' parameter vs parameter
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Image:3d Clamp vs alpha4 regions.png| Maximum Transcription Rate of &lambda;p vs Translation Rate &alpha;4 (of GFP mRNA).
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Image:3d CpLac vs Clamp regions.png| Maximum Transcription Rate of pLac vs Maximum Transcription Rate of &lambda;p.
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Image:3d CpLac vs CpTet regions.png| Maximum Transcription Rate of pLac vs Maximum Transcription Rate of pTet.
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Image:3d CpTet vs alpha2 regions.png| Maximum Transcription Rate of pTet vs Translation Rate &alpha;2 (of CI mRNA).
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Image:3d CpTet vs Clamp regions.png| Maximum Transcription Rate of pTet vs Maximum Transcription Rate of &lambda;p.
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Image:3d leakage a2 vs a4 regions.png| Transcription Leakage of &lambda;p vs Transcription Leakage of pTet.
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Revision as of 14:52, 1 October 2009

Modeling the Transcriptional Cascade

Negative cascade assembly and overview

A full description of the Transcriptional Cascade can be found here.

ODEs

The kinetic equations were written out in a Matlab script for both transcription and translation.

TUD eq cas.png

Symbol Definition
kIPTGin, kIPTGout rate constants
k50IPTG, k50LacI, k50TetR, k50CI dissociation constants
dmRNA mRNA degradation rate
dTetR, dCI, dRFP, dGFP protein degradation rates
apLac, apTet, aλp transcription leakage (%)
cpLac, cpTet, cλp maximum transcription rates
α1, α2, α3, α4 translation rates
nIPTG, nLacI, nTetR, nCI Hill coefficients
[X]mRNA concentration of X mRNA

The default solution of the system of ODEs can be seen below:

TUD ODE default solution.png

Sensitivity

Parameter Normalized Sensitivity
kIPTGin, kIPTGout
k50IPTG, k50LacI, k50TetR, k50CI
dmRNA
dTetR, dCI, dRFP, dGFP
apLac, apTet, aλp
cpLac, cpTet, cλp
α1, α2, α3, α4
nIPTG, nLacI, nTetR, nCI
[X]mRNA

Parameter Sweeps

In the following plots the delay time of the cascade is shown as a function of two different parameters. A delay time off 500 is used to represent an infinite delay (maroon colour). The delay is considered to be over once the concentration of the final product (in this case GFP) goes above 10nM.

Delay Time vs Transcription Leakage of λp.

Translation Rate α1 (of TetR mRNA) vs Translation Rate α4 (of GFP mRNA).

Maximum Transcription Rate of λp vs Translation Rate α4 (of GFP mRNA).

Maximum Transcription Rate of pLac vs Maximum Transcription Rate of λp.

Maximum Transcription Rate of pLac vs Maximum Transcription Rate of pTet.

Maximum Transcription Rate of pTet vs Translation Rate α2 (of CI mRNA).

Maximum Transcription Rate of pTet vs Maximum Transcription Rate of λp.

Transcription Leakage of λp vs Transcription Leakage of pTet.

Stability

Jacobian

Maximum Transcription Rate of λp vs Translation Rate α4 (of GFP mRNA).

Maximum Transcription Rate of pLac vs Maximum Transcription Rate of λp.

Maximum Transcription Rate of pLac vs Maximum Transcription Rate of pTet.

Maximum Transcription Rate of pTet vs Translation Rate α2 (of CI mRNA).

Maximum Transcription Rate of pTet vs Maximum Transcription Rate of λp.

Transcription Leakage of λp vs Transcription Leakage of pTet.

Design Recommendations

Based on the results of the simulations, a series of recommendations were given to the delay team to aid them in choosing parts which would maximize the delay time.

  1. Significant transcription leakages greatly shorten the delay time. Attempt to minimize leakages. Leakage of λp is a far bigger problem than pTet leakage.
  2. Use a weak promoter and a weak RBS on the last stage (λp) of the cascade.
  3. A weak pLac promoters is favorable.
  4. A strong pTet promoter is favorable.
  5. A strong RBS on CI gene is favorable.
  6. A weak RBS on TetR gene is favorable.
  7. A weak RBS on the endonuclease is favorable although a strong RBS can be used for the GFP gene.
  8. When choosing RBS and promoter strengths avoid the red areas on the stability plots.


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