Team:PKU Beijing/Modeling/Parameters

From 2009.igem.org

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|\gamma_2'||Real Degradation rate of Aa-tRNA||1/40||min^-1||
|\gamma_2'||Real Degradation rate of Aa-tRNA||1/40||min^-1||
|-
|-
-
|\gamma_3||Degradation rate of T7RNAP mRNA||1/4.4||min^-1||Assumption
+
|\gamma_3||Degradation rate of T7RNAP mRNA||1/30+1/4.4||min^-1||Assumption
|-
|-
|\gamma_4||Degradation rate of T7RNAP||1/30+1/40||min^-1||
|\gamma_4||Degradation rate of T7RNAP||1/30+1/40||min^-1||
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Overall, the sensitivity of parameters from trial and error is generally low. The bi-stable-related parameters' sensitivity indicates that the bi-stable model, which is the core in the circuit, is very stable. With all of these facts, we have concluded that this model is reasonable.
Overall, the sensitivity of parameters from trial and error is generally low. The bi-stable-related parameters' sensitivity indicates that the bi-stable model, which is the core in the circuit, is very stable. With all of these facts, we have concluded that this model is reasonable.
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==='''Modeling - P2'''===
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Here's our second model, the one with P2 instead of T3 RNA polymerase
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{|cellpadding=2
 +
|Parameters||Brief Introduction||Value||Unit||Reference/Sensitivity
 +
|-
 +
|k_1||Max Transcription rate of tRNA||46.67||nM/min||Assumption, 1.33
 +
|-
 +
|k_2||Synthesis rate of Aa-tRNA||0.08||min^-1||0.77
 +
|-
 +
|k_3||Max Transcription rate of T7RNAP||1.5625||nM/min||Assumption, 0.00
 +
|-
 +
|k_4||Max Translation rate of T7RNAP||2.68*0.05||min^-1||Assumption, 0.00
 +
|-
 +
|k_5||Max Transcription rate of trigger CI||5.6||nM/min||Assumption, 0.00
 +
|-
 +
|k_6||Transcription rate of bistable CI||5.6||nM/min||Assumption, 0.00
 +
|-
 +
|k_6'||Transcription rate of bistable CI||1||nM/min||0.00
 +
|-
 +
|k_7||Transcription rate of P2||16.8||nM/min||Assumption, 1.15
 +
|-
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|k_7'||Transcription rate of P2||1||nM/min||0.00
 +
|-
 +
|k_8||Translation rate of trigger CI||9.6*0.05||min^-1||Assumption, 0.00
 +
|-
 +
|k_8'||Translation rate of bistable CI||9.6*0.5||min^-1||Assumption, 0.00
 +
|-
 +
|k_9||Max Transcription rate of CI434||5.92||nM/min||Assumption, 0.00
 +
|-
 +
|k_10||Transcription rate of CI434||10.14*1||min^-1||Assumption, 0.00
 +
|-
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|k_11||Max Translation rate of P2||28.8*0.005||min^-1||Assumption, 1.15
 +
|-
 +
|k_12||Max Transcription rate of GFP from Sal||5.25||nM/min||Assumption, 0.00
 +
|-
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|k_12'||Max Trasncription rate of GFP from P2||5.25||nM/min||Assumption, 1.00
 +
|-
 +
|k_13||Translation rate of GFP||9*0.6||min^-1||Assumption, 1.00
 +
|-
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|k_s||rate of AND Gate 1||0.3||nM^-1||0.00
 +
|-
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|k_s'||rate of AND Gate 2||0.01||nM^-1||0.18
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|-
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|K_1||dissociation constant of AraC,tRNA||14||nM||0.19
 +
|-
 +
|K_3||dissociation constant of Sal,T7RNAP||0.5||nM||0.00
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|-
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|K_5||dissociation constant of T7RNAP,trigger CI||3||nM||[http://bionumbers.hms.harvard.edu/bionumber.aspx?s=y&id=103592&ver=1 Ref]
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|-
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|K_6||dissociation constant of CI,bistable CI||40||nM||Ref: iGEM2007 PKU Team
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|-
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|K_6'||dissociation constant of CI434,bistable CI||50||nM||Ref: iGEM2007 PKU Team
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|-
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|K_7||dissociation constant of CI,P2||40||nM||Ref: iGEM2007 PKU Team
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|-
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|K_7'||dissociation constant of CI434,P2||50||nM||Ref: iGEM2007 PKU Team
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|-
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|K_9||dissociation constant of CI,CI434||40||nM||Ref: iGEM2007 PKU Team
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|-
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|K_12||dissociation constant of Sal,GFP||0.5||nM||0.00
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|-
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|K_12'||dissociation constant of P2,GFP||35||nM||Ref:
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|-
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|n_1||Hill co-effiency of AraC,tRNA||2|| ||
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|-
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|n_3||Hill co-effiency of Sal,T7RNAP||2|| ||
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|-
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|n_5||Hill co-effiency of T7RNAP,CI||2|| ||
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|-
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|n_6||Hill co-effiency of CI,bistable CI||4|| ||Ref: iGEM2007 PKU Team
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|-
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|n_6'||Hill co-effiency of CI434,bistable CI||2|| ||Ref: iGEM2007 PKU Team
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|-
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|n_7||Hill co-effiency of CI,P2||4|| ||Ref: iGEM2007 PKU Team
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|-
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|n_7'||Hill co-effiency of CI434,P2||2|| ||Ref: iGEM2007 PKU Team
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|-
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|n_9||Hill co-effiency of CI,CI434||4|| ||Ref: iGEM2007 PKU Team
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|-
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|n_12||Hill co-effiency of Sal,GFP||2|| ||
 +
|-
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|n_12'||Hill co-effiency of P2,GFP||2|| ||
 +
|-
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|\gamma_1||Degradation rate of tRNA||1/30+1/60||min^-1||Since half life of tRNA is very long,<br>we decided to use 60 mins instead
 +
|-
 +
|\gamma_2||Degradation rate of Aa-tRNA||1/30+1/40||min^-1||
 +
|-
 +
|\gamma_2'||Real Degradation rate of Aa-tRNA||1/40||min^-1||
 +
|-
 +
|\gamma_3||Degradation rate of T7RNAP mRNA||1/30+1/4.4||min^-1||Assumption
 +
|-
 +
|\gamma_4||Degradation rate of T7RNAP||1/30+1/40||min^-1||
 +
|-
 +
|\gamma_5||Degradation rate of trigger CI mRNA||1/30+1/4.4||min^-1||Assumption
 +
|-
 +
|\gamma_6||Degradation rate of bistable CI mRNA||1/30+1/4.4||min^-1||Assumption
 +
|-
 +
|\gamma_7||Degradation rate of P2 mRNA||1/30+1/4.4||min^-1||Assumption
 +
|-
 +
|\gamma_8||Degradation rate of CI||1/30+1/44||min^-1||Ref: iGEM2007 PKU Team
 +
|-
 +
|\gamma_9||Degradation rate of CI434 mRNA||1/30+1/4.4||min^-1||Assumption
 +
|-
 +
|\gamma_10||Degradation rate of CI434||1/30+1/11||min^-1||Ref: iGEM 2007 PKU Team
 +
|-
 +
|\gamma_11||Degradation rate of P2||1/30+1/30||min^-1||
 +
|-
 +
|\gamma_12||Degradation rate of GFP mRNA||1/30+1/4.4||min^-1||Assumption
 +
|-
 +
|\gamma_13||Degradation rate of GFP||1/30+1/60||min^-1||Since half life of GFP is very long,<br>we use 60 mins instead
 +
|}
 +
 +
Overall, the sensitivity of parameters from trial and error is also low. The bi-stable is also shows great stability. However, we consider the value in AND Gate 2 is too extreme. Although this fact doesn't indicate that the circuit design is wrong or we can't finish the weblab project theoretically, we decided that it's very necessary to do the circuit with T3 RNA polymerase.
 +
 +
With all necessities prepared, it's time to see the [[Team:PKU_Beijing/Modeling/Result|result]]!
{{PKU_Beijing/Foot}}
{{PKU_Beijing/Foot}}
__NOTOC__
__NOTOC__

Revision as of 22:48, 16 October 2009
 
Modeling > Parameters

Parameters

Constructing ODEs is only the first step of simulating our design. The parameters, actually, play a bigger role in the modeling process. Here's two sets of parameters(T3 RNA polymerase and P2) we used.

We have done an systematic literature review to select parameters for our model. However, not every parameter can be found from existing works, which means we have to guess part of the parameters from trial and error. To check whether we have guessed correctly, we do the sensitivity test. The sensitivity test works like this: We first give both Sal(food) and AraC(bell) to make bistable turn to CI state(have memory). After a period of time, we give the E. coli AraC stimulus and GFP output will raise after a short while. We select the highest concentration point of GFP in the second procedure. The sensitivity of a parameter is calculated by using the following equations. The closer the sensitivity is to zero, the more reasonable the parameter is. <math>Sensitivity=\frac{c_{max}^{105%}-c_{max}^{95%)}{(105%-95%)*c_{max}^{100%}}</math>

Assumptions

Our model consists of 53 parameters, which makes the modeling process very difficult. To reduce the amount of work without losing quality, we proposed the following assumptions.

  • Transcription

The average transcription speed in E.coli is 70nt/s. Assuming all the transcription in our circuit works in such speed, we can calculate the maximum transcription rate for each transcription equation by using this formula: Maximum Transcription Rate = Transcription Speed(nt/min)/Gene Length(bp)=4200/Gene Length (nM/min)

  • Translation

The average translation speed in E.coli is 40Aa/s. Also assuming all the translation in our circuit works in the same speed, we can calculate the theoretical transcription rate. However, in wetlab, we can use different rbs to regulate the translation process, thus, the translation rate can be written as: Translation Rate = RBS * Translation Speed(Aa/min)/Protein Length(Aa) = 2400RBS/Protein Length (min^-1) This transformation does not change the degree of freedom of our system. However, this does limit the range of parameters since the concentration of RBS can not be too extreme.

  • Cell Division Rate

We have assume the period of cell division is 30 mins, which means the "degradation rate" in our model is actually the sum of degradation rate of the substance(1/half life) and cell division rate(1/30 mins).

  • Degradation of mRNA

From Ref:_______________, we have decided that all the mRNA in our system have a half life of 4.4 mins.

Modeling - T3 RNA polymerase

We have construct two models, the difference of which is in the AND Gate 2 module. In this section, we'll demonstrate the parameters of our first model, in which T3 RNA polymerase mRNA with amber mutation and Aa-tRNA will be consumed to produce T3 RNA polymerase protein.

ParametersBrief IntroductionValueUnitReference/Sensitivity
k_1Max Transcription rate of tRNA46.67nM/minAssumption, 0.19
k_2Synthesis rate of Aa-tRNA0.08min^-10.09
k_3Max Transcription rate of T7RNAP1.5625nM/minAssumption, 0.00
k_4Max Translation rate of T7RNAP2.68*0.05min^-1Assumption, 0.00
k_5Max Transcription rate of trigger CI5.6nM/minAssumption, 0.00
k_6Transcription rate of bistable CI5.6nM/minAssumption, 0.00
k_6'Transcription rate of bistable CI1nM/min0.00
k_7Transcription rate of T3RNAP1.75nM/minAssumption, 1.34
k_7'Transcription rate of T3RNAP1nM/min0.00
k_8Translation rate of trigger CI9.6*0.045min^-1Assumption, 0.00
k_8'Translation rate of bistable CI9.6*0.3min^-1Assumption, 0.00
k_9Max Transcription rate of CI4345.92nM/minAssumption, 0.00
k_10Transcription rate of CI43410.14*0.5min^-1Assumption, 0.00
k_11Max Translation rate of T3RNAP3*0.15min^-1Assumption, 1.34
k_12Max Transcription rate of GFP from Sal5.25nM/minAssumption, 0.00
k_12'Max Trasncription rate of GFP from T3RNAP5.25nM/minAssumption, 1.00
k_13Translation rate of GFP9*0.6min^-1Assumption, 1.00
k_srate of AND Gate 10.3nM^-10.00
k_s'rate of AND Gate 20.3nM^-10.18
K_1dissociation constant of AraC,tRNA14nM0.03
K_3dissociation constant of Sal,T7RNAP0.5nM0.00
K_5dissociation constant of T7RNAP,trigger CI3nM[http://bionumbers.hms.harvard.edu/bionumber.aspx?s=y&id=103592&ver=1 Ref]
K_6dissociation constant of CI,bistable CI40nMRef: iGEM2007 PKU Team
K_6'dissociation constant of CI434,bistable CI50nMRef: iGEM2007 PKU Team
K_7dissociation constant of CI,T3RNAP40nMRef: iGEM2007 PKU Team
K_7'dissociation constant of CI434,T3RNAP50nMRef: iGEM2007 PKU Team
K_9dissociation constant of CI,CI43440nMRef: iGEM2007 PKU Team
K_12dissociation constant of Sal,GFP0.5nM0.00
K_12'dissociation constant of T3RNAP,GFP55nMRef:
n_1Hill co-effiency of AraC,tRNA2
n_3Hill co-effiency of Sal,T7RNAP2
n_5Hill co-effiency of T7RNAP,CI2
n_6Hill co-effiency of CI,bistable CI4 Ref: iGEM2007 PKU Team
n_6'Hill co-effiency of CI434,bistable CI2 Ref: iGEM2007 PKU Team
n_7Hill co-effiency of CI,T3RNAP4 Ref: iGEM2007 PKU Team
n_7'Hill co-effiency of CI434,T3RNAP2 Ref: iGEM2007 PKU Team
n_9Hill co-effiency of CI,CI4344 Ref: iGEM2007 PKU Team
n_12Hill co-effiency of Sal,GFP2
n_12'Hill co-effiency of T3RNAP,GFP2
\gamma_1Degradation rate of tRNA1/30+1/60min^-1Since half life of tRNA is very long,
we decided to use 60 mins instead
\gamma_2Degradation rate of Aa-tRNA1/30+1/40min^-1
\gamma_2'Real Degradation rate of Aa-tRNA1/40min^-1
\gamma_3Degradation rate of T7RNAP mRNA1/30+1/4.4min^-1Assumption
\gamma_4Degradation rate of T7RNAP1/30+1/40min^-1
\gamma_5Degradation rate of trigger CI mRNA1/30+1/4.4min^-1Assumption
\gamma_6Degradation rate of bistable CI mRNA1/30+1/4.4min^-1Assumption
\gamma_7Degradation rate of T3RNAP mRNA1/30+1/4.4min^-1Assumption
\gamma_8Degradation rate of CI1/30+1/44min^-1Ref: iGEM2007 PKU Team
\gamma_9Degradation rate of CI434 mRNA1/30+1/4.4min^-1Assumption
\gamma_10Degradation rate of CI4341/30+1/11min^-1Ref: iGEM 2007 PKU Team
\gamma_11Degradation rate of T3RNAP1/30+1/30min^-1
\gamma_12Degradation rate of GFP mRNA1/30+1/4.4min^-1Assumption
\gamma_13Degradation rate of GFP1/30+1/60min^-1Since half life of GFP is very long,
we use 60 mins instead

Overall, the sensitivity of parameters from trial and error is generally low. The bi-stable-related parameters' sensitivity indicates that the bi-stable model, which is the core in the circuit, is very stable. With all of these facts, we have concluded that this model is reasonable.

Modeling - P2

Here's our second model, the one with P2 instead of T3 RNA polymerase

ParametersBrief IntroductionValueUnitReference/Sensitivity
k_1Max Transcription rate of tRNA46.67nM/minAssumption, 1.33
k_2Synthesis rate of Aa-tRNA0.08min^-10.77
k_3Max Transcription rate of T7RNAP1.5625nM/minAssumption, 0.00
k_4Max Translation rate of T7RNAP2.68*0.05min^-1Assumption, 0.00
k_5Max Transcription rate of trigger CI5.6nM/minAssumption, 0.00
k_6Transcription rate of bistable CI5.6nM/minAssumption, 0.00
k_6'Transcription rate of bistable CI1nM/min0.00
k_7Transcription rate of P216.8nM/minAssumption, 1.15
k_7'Transcription rate of P21nM/min0.00
k_8Translation rate of trigger CI9.6*0.05min^-1Assumption, 0.00
k_8'Translation rate of bistable CI9.6*0.5min^-1Assumption, 0.00
k_9Max Transcription rate of CI4345.92nM/minAssumption, 0.00
k_10Transcription rate of CI43410.14*1min^-1Assumption, 0.00
k_11Max Translation rate of P228.8*0.005min^-1Assumption, 1.15
k_12Max Transcription rate of GFP from Sal5.25nM/minAssumption, 0.00
k_12'Max Trasncription rate of GFP from P25.25nM/minAssumption, 1.00
k_13Translation rate of GFP9*0.6min^-1Assumption, 1.00
k_srate of AND Gate 10.3nM^-10.00
k_s'rate of AND Gate 20.01nM^-10.18
K_1dissociation constant of AraC,tRNA14nM0.19
K_3dissociation constant of Sal,T7RNAP0.5nM0.00
K_5dissociation constant of T7RNAP,trigger CI3nM[http://bionumbers.hms.harvard.edu/bionumber.aspx?s=y&id=103592&ver=1 Ref]
K_6dissociation constant of CI,bistable CI40nMRef: iGEM2007 PKU Team
K_6'dissociation constant of CI434,bistable CI50nMRef: iGEM2007 PKU Team
K_7dissociation constant of CI,P240nMRef: iGEM2007 PKU Team
K_7'dissociation constant of CI434,P250nMRef: iGEM2007 PKU Team
K_9dissociation constant of CI,CI43440nMRef: iGEM2007 PKU Team
K_12dissociation constant of Sal,GFP0.5nM0.00
K_12'dissociation constant of P2,GFP35nMRef:
n_1Hill co-effiency of AraC,tRNA2
n_3Hill co-effiency of Sal,T7RNAP2
n_5Hill co-effiency of T7RNAP,CI2
n_6Hill co-effiency of CI,bistable CI4 Ref: iGEM2007 PKU Team
n_6'Hill co-effiency of CI434,bistable CI2 Ref: iGEM2007 PKU Team
n_7Hill co-effiency of CI,P24 Ref: iGEM2007 PKU Team
n_7'Hill co-effiency of CI434,P22 Ref: iGEM2007 PKU Team
n_9Hill co-effiency of CI,CI4344 Ref: iGEM2007 PKU Team
n_12Hill co-effiency of Sal,GFP2
n_12'Hill co-effiency of P2,GFP2
\gamma_1Degradation rate of tRNA1/30+1/60min^-1Since half life of tRNA is very long,
we decided to use 60 mins instead
\gamma_2Degradation rate of Aa-tRNA1/30+1/40min^-1
\gamma_2'Real Degradation rate of Aa-tRNA1/40min^-1
\gamma_3Degradation rate of T7RNAP mRNA1/30+1/4.4min^-1Assumption
\gamma_4Degradation rate of T7RNAP1/30+1/40min^-1
\gamma_5Degradation rate of trigger CI mRNA1/30+1/4.4min^-1Assumption
\gamma_6Degradation rate of bistable CI mRNA1/30+1/4.4min^-1Assumption
\gamma_7Degradation rate of P2 mRNA1/30+1/4.4min^-1Assumption
\gamma_8Degradation rate of CI1/30+1/44min^-1Ref: iGEM2007 PKU Team
\gamma_9Degradation rate of CI434 mRNA1/30+1/4.4min^-1Assumption
\gamma_10Degradation rate of CI4341/30+1/11min^-1Ref: iGEM 2007 PKU Team
\gamma_11Degradation rate of P21/30+1/30min^-1
\gamma_12Degradation rate of GFP mRNA1/30+1/4.4min^-1Assumption
\gamma_13Degradation rate of GFP1/30+1/60min^-1Since half life of GFP is very long,
we use 60 mins instead

Overall, the sensitivity of parameters from trial and error is also low. The bi-stable is also shows great stability. However, we consider the value in AND Gate 2 is too extreme. Although this fact doesn't indicate that the circuit design is wrong or we can't finish the weblab project theoretically, we decided that it's very necessary to do the circuit with T3 RNA polymerase.

With all necessities prepared, it's time to see the result!

^Top


 

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