Team:PKU Beijing/Modeling/Parameters

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Constructing [[Team:PKU_Bejing/Modeling/ODE|ODEs]] is only the first step of simulating our design. The parameters, actually, play a significant role in the modeling process. Here are two sets of parameters(T3 RNA polymerase and P2) we used.
Constructing [[Team:PKU_Bejing/Modeling/ODE|ODEs]] is only the first step of simulating our design. The parameters, actually, play a significant role in the modeling process. Here are 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.
+
We have done an systematic literature review to select parameters for our model. However, not every parameter can be found from existing data, 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 salicylate(food) and arabinose(bell) to make bistable turn to CI state(have memory). After a period of time, we give the ''E. coli'' arabinose 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.<br>
-
<math>Sensitivity=\frac{c_{max}^{105%}-c_{max}^{95%)}{(105%-95%)*c_{max}^{100%}}</math>
+
[[Image:PKU_Sensi.PNG]]
==='''Assumptions'''===
==='''Assumptions'''===
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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:
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)
Maximum Transcription Rate = Transcription Speed(nt/min)/Gene Length(bp)=4200/Gene Length (nM/min)
 +
Ref: http://gchelpdesk.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi, [https://2008.igem.org/Team:NTU-Singapore/Modelling/Parameter NTU-Singapore iGEM2008 Team]
*'''Translation'''
*'''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:
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)
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.
+
This transformation does not change the degree of freedom of our system. However, this does limit the range of parameters since the strength of RBS can not be too extreme.
 +
Ref: http://gchelpdesk.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi, [https://2008.igem.org/Team:NTU-Singapore/Modelling/Parameter NTU-Singapore iGEM2008 Team]
*'''Cell Division Rate'''
*'''Cell Division Rate'''
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*'''Degradation of mRNA'''
*'''Degradation of mRNA'''
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From Ref:_______________, we have decided that all the mRNA in our system have a half life of 4.4 mins.
+
From Ref1(Belasco 1993) and Ref2(Genome Biology 2006, 7:R99), we have decided that all the mRNA in our system have a half life of 4.4 mins.
==='''Modeling - T3 RNA polymerase'''===
==='''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.
+
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 cooperate to produce T3 RNA polymerase protein.
{|cellpadding=2
{|cellpadding=2
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|K_12||dissociation constant of Sal,GFP||0.5||nM||0.00
|K_12||dissociation constant of Sal,GFP||0.5||nM||0.00
|-
|-
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|K_12'||dissociation constant of T3RNAP,GFP||55||nM||Ref:
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|K_12'||dissociation constant of T3RNAP,GFP||55||nM||Ref: The FEBS journal 2006,273:17 
|-
|-
|n_1||Hill co-effiency of AraC,tRNA||2|| ||  
|n_1||Hill co-effiency of AraC,tRNA||2|| ||  
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|K_12||dissociation constant of Sal,GFP||0.5||nM||0.00
|K_12||dissociation constant of Sal,GFP||0.5||nM||0.00
|-
|-
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|K_12'||dissociation constant of P2,GFP||35||nM||Ref:
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|K_12'||dissociation constant of P2,GFP||35||nM||1.29
|-
|-
|n_1||Hill co-effiency of AraC,tRNA||2|| ||  
|n_1||Hill co-effiency of AraC,tRNA||2|| ||  
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|}
|}
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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.
+
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 construct the circuit with T3 RNA polymerase.
With all necessities prepared, it's time to see the [[Team:PKU_Beijing/Modeling/Result|result]]!
With all necessities prepared, it's time to see the [[Team:PKU_Beijing/Modeling/Result|result]]!
{{PKU_Beijing/Foot}}
{{PKU_Beijing/Foot}}
__NOTOC__
__NOTOC__

Latest revision as of 21:36, 21 October 2009
 
Modeling > Parameters

Parameters

Constructing ODEs is only the first step of simulating our design. The parameters, actually, play a significant role in the modeling process. Here are 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 data, 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 salicylate(food) and arabinose(bell) to make bistable turn to CI state(have memory). After a period of time, we give the E. coli arabinose 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.
PKU Sensi.PNG

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) Ref: http://gchelpdesk.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi, NTU-Singapore iGEM2008 Team

  • 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 strength of RBS can not be too extreme. Ref: http://gchelpdesk.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi, NTU-Singapore iGEM2008 Team

  • 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 Ref1(Belasco 1993) and Ref2(Genome Biology 2006, 7:R99), 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 cooperate 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: The FEBS journal 2006,273:17
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
γ_1Degradation rate of tRNA1/30+1/60min^-1Since half life of tRNA is very long,
we decided to use 60 mins instead
γ_2Degradation rate of Aa-tRNA1/30+1/40min^-1
γ_2'Real Degradation rate of Aa-tRNA1/40min^-1
γ_3Degradation rate of T7RNAP mRNA1/30+1/4.4min^-1Assumption
γ_4Degradation rate of T7RNAP1/30+1/40min^-1
γ_5Degradation rate of trigger CI mRNA1/30+1/4.4min^-1Assumption
γ_6Degradation rate of bistable CI mRNA1/30+1/4.4min^-1Assumption
γ_7Degradation rate of T3RNAP mRNA1/30+1/4.4min^-1Assumption
γ_8Degradation rate of CI1/30+1/44min^-1Ref: iGEM2007 PKU Team
γ_9Degradation rate of CI434 mRNA1/30+1/4.4min^-1Assumption
γ_10Degradation rate of CI4341/30+1/11min^-1Ref: iGEM 2007 PKU Team
γ_11Degradation rate of T3RNAP1/30+1/30min^-1
γ_12Degradation rate of GFP mRNA1/30+1/4.4min^-1Assumption
γ_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, 1.41
k_2Synthesis rate of Aa-tRNA0.08min^-10.81
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, 1.23
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*0.0045min^-1Assumption, 1.23
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^-11.29
K_1dissociation constant of AraC,tRNA14nM0.20
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,GFP35nM1.29
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
γ_1Degradation rate of tRNA1/30+1/60min^-1Since half life of tRNA is very long,
we decided to use 60 mins instead
γ_2Degradation rate of Aa-tRNA1/30+1/40min^-1
γ_2'Real Degradation rate of Aa-tRNA1/40min^-1
γ_3Degradation rate of T7RNAP mRNA1/30+1/4.4min^-1Assumption
γ_4Degradation rate of T7RNAP1/30+1/40min^-1
γ_5Degradation rate of trigger CI mRNA1/30+1/4.4min^-1Assumption
γ_6Degradation rate of bistable CI mRNA1/30+1/4.4min^-1Assumption
γ_7Degradation rate of P2 mRNA1/30+1/4.4min^-1Assumption
γ_8Degradation rate of CI1/30+1/44min^-1Ref: iGEM2007 PKU Team
γ_9Degradation rate of CI434 mRNA1/30+1/4.4min^-1Assumption
γ_10Degradation rate of CI4341/30+1/11min^-1Ref: iGEM 2007 PKU Team
γ_11Degradation rate of P21/30+1/30min^-1
γ_12Degradation rate of GFP mRNA1/30+1/4.4min^-1Assumption
γ_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 construct the circuit with T3 RNA polymerase.

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

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