Team:TUDelft/Modeling Cascade

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{{Template:TUDelftiGEM2009}}
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=Modeling Negative Cascade=
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=Modeling the Transcriptional Cascade=
[[Image:Negative_Feedforward.jpg|center| <center> Negative cascade assembly and overview </center> | thumb | 550px]]<br>
[[Image:Negative_Feedforward.jpg|center| <center> Negative cascade assembly and overview </center> | thumb | 550px]]<br>
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A full description of the Transcriptional Cascade can be found [https://2009.igem.org/Team:TUDelft/Synthetic_Transcriptional_Cascade here].
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==ODEs==
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The kinetic equations were written out in a Matlab script for both transcription and translation.
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[[Image:TUD_eq_cas.png]]
[[Image:TUD_eq_cas.png]]
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[[Image:TUD_symboltable_cas.png]]
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{| border="1" align="center"
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| <b>Symbol</b> || <b>Definition</b>
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|- align="left"
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| k<sub>IPTGin</sub>, k<sub>IPTGout</sub> || rate constants
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|- align="left"
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| k<sub>50IPTG</sub>, k<sub>50LacI</sub>, k<sub>50TetR</sub>, k<sub>50CI</sub> || dissociation constants
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|- align="left"
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| d<sub>mRNA</sub> || mRNA degradation rate
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|- align="left"
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| d<sub>TetR</sub>, d<sub>CI</sub>, d<sub>RFP</sub>, d<sub>GFP</sub> || protein degradation rates
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|- align="left"
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| a<sub>pLac</sub>, a<sub>pTet</sub>, a<sub>&lambda;p</sub> || transcription leakage (%)
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|- align="left"
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| c<sub>pLac</sub>, c<sub>pTet</sub>, c<sub>&lambda;p</sub> || maximum transcription rates
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|- align="left"
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| &alpha;<sub>1</sub>, &alpha;<sub>2</sub>, &alpha;<sub>3</sub>, &alpha;<sub>4</sub> || translation rates
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|- align="left"
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| n<sub>IPTG</sub>, n<sub>LacI</sub>, n<sub>TetR</sub>, n<sub>CI</sub> || Hill coefficients
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|- align="left"
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| [X]<sub>mRNA</sub> || concentration of X mRNA
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|- align="left"
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|}
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==Sensitivity==
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{| border="1" align="center"
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| <b>Parameter</b> || <b>Normalized Sensitivity</b>
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|- align="left"
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| k<sub>IPTGin</sub>, k<sub>IPTGout</sub> ||
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|- align="left"
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| k<sub>50IPTG</sub>, k<sub>50LacI</sub>, k<sub>50TetR</sub>, k<sub>50CI</sub> ||
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|- align="left"
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| d<sub>mRNA</sub> ||
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|- align="left"
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| d<sub>TetR</sub>, d<sub>CI</sub>, d<sub>RFP</sub>, d<sub>GFP</sub> ||
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|- align="left"
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| a<sub>pLac</sub>, a<sub>pTet</sub>, a<sub>&lambda;p</sub> ||
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|- align="left"
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| c<sub>pLac</sub>, c<sub>pTet</sub>, c<sub>&lambda;p</sub> ||
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|- align="left"
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| &alpha;<sub>1</sub>, &alpha;<sub>2</sub>, &alpha;<sub>3</sub>, &alpha;<sub>4</sub> ||
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|- align="left"
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| n<sub>IPTG</sub>, n<sub>LacI</sub>, n<sub>TetR</sub>, n<sub>CI</sub> ||
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|- align="left"
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| [X]<sub>mRNA</sub> ||
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|- align="left"
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|}
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==Parameter Sweeps==
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{|border = "0"
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|-
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|rowspan="2"|
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<gallery>
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Image:test.jpg|'''1111 :''' parameter vs parameter
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Image:test.jpg|'''1111 :''' parameter vs parameter
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Image:test.jpg|'''1111 : ''' parameter vs parameter
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</gallery><gallery>
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Image:test.jpg|'''1111 : ''' parameter vs parameter
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Image:test.jpg|'''111 : ''' parameter vs parameter
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Image:test.jpg|'''1111 : ''' parameter vs parameter
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</gallery>
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|}
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==Stability==
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Jacobian
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{|border = "0"
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|-
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|rowspan="2"|
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<gallery>
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Image:test.jpg|'''1111 :''' parameter vs parameter
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Image:test.jpg|'''1111 :''' parameter vs parameter
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Image:test.jpg|'''1111 : ''' parameter vs parameter
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</gallery><gallery>
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Image:test.jpg|'''1111 : ''' parameter vs parameter
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Image:test.jpg|'''111 : ''' parameter vs parameter
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Image:test.jpg|'''1111 : ''' parameter vs parameter
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</gallery>
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|}
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==Design Recommendations==
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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.
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# Significant transcription leakages greatly shorten the delay time. Attempt to minimize leakages. Leakage of &lambda;p is a far bigger problem than pTet leakage.
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# Use a weak promoter and a weak RBS on the last stage (&lambda;p) of the cascade.
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# A weak pLac promoters is favorable.
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# A strong pTet promoter is favorable.
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# A strong RBS on CI gene is favorable.
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# A weak RBS on TetR gene is favorable.
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# A weak RBS on the endonuclease is favorable although a strong RBS can be used for the GFP gene.
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# When choosing RBS and promoter strengths avoid the red areas on the stability plots.
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{{Template:TUDelftiGEM2009_end}}
{{Template:TUDelftiGEM2009_end}}

Revision as of 16:43, 29 September 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


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

Test.jpg

1111 : parameter vs parameter

Test.jpg

1111 : parameter vs parameter

Test.jpg

1111 : parameter vs parameter

Test.jpg

1111 : parameter vs parameter

Test.jpg

111 : parameter vs parameter

Test.jpg

1111 : parameter vs parameter

Stability

Jacobian

Test.jpg

1111 : parameter vs parameter

Test.jpg

1111 : parameter vs parameter

Test.jpg

1111 : parameter vs parameter

Test.jpg

1111 : parameter vs parameter

Test.jpg

111 : parameter vs parameter

Test.jpg

1111 : parameter vs parameter

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.


Retrieved from "http://2009.igem.org/Team:TUDelft/Modeling_Cascade"