Team:PKU Beijing/Modeling/Parameters

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Latest revision as of 21:36, 21 October 2009

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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.

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.

Parameters	Brief Introduction	Value	Unit	Reference/Sensitivity
k_1	Max Transcription rate of tRNA	46.67	nM/min	Assumption, 0.19
k_2	Synthesis rate of Aa-tRNA	0.08	min^-1	0.09
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 T3RNAP	1.75	nM/min	Assumption, 1.34
k_7'	Transcription rate of T3RNAP	1	nM/min	0.00
k_8	Translation rate of trigger CI	9.6*0.045	min^-1	Assumption, 0.00
k_8'	Translation rate of bistable CI	9.6*0.3	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*0.5	min^-1	Assumption, 0.00
k_11	Max Translation rate of T3RNAP	3*0.15	min^-1	Assumption, 1.34
k_12	Max Transcription rate of GFP from Sal	5.25	nM/min	Assumption, 0.00
k_12'	Max Trasncription rate of GFP from T3RNAP	5.25	nM/min	Assumption, 1.00
k_13	Translation rate of GFP	9*0.6	min^-1	Assumption, 1.00
k_s	rate of AND Gate 1	0.3	nM^-1	0.00
k_s'	rate of AND Gate 2	0.3	nM^-1	0.18
K_1	dissociation constant of AraC,tRNA	14	nM	0.03
K_3	dissociation constant of Sal,T7RNAP	0.5	nM	0.00
K_5	dissociation constant of T7RNAP,trigger CI	3	nM	[http://bionumbers.hms.harvard.edu/bionumber.aspx?s=y&id=103592&ver=1 Ref]
K_6	dissociation constant of CI,bistable CI	40	nM	Ref: iGEM2007 PKU Team
K_6'	dissociation constant of CI434,bistable CI	50	nM	Ref: iGEM2007 PKU Team
K_7	dissociation constant of CI,T3RNAP	40	nM	Ref: iGEM2007 PKU Team
K_7'	dissociation constant of CI434,T3RNAP	50	nM	Ref: iGEM2007 PKU Team
K_9	dissociation constant of CI,CI434	40	nM	Ref: iGEM2007 PKU Team
K_12	dissociation constant of Sal,GFP	0.5	nM	0.00
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_3	Hill co-effiency of Sal,T7RNAP	2
n_5	Hill co-effiency of T7RNAP,CI	2
n_6	Hill co-effiency of CI,bistable CI	4		Ref: iGEM2007 PKU Team
n_6'	Hill co-effiency of CI434,bistable CI	2		Ref: iGEM2007 PKU Team
n_7	Hill co-effiency of CI,T3RNAP	4		Ref: iGEM2007 PKU Team
n_7'	Hill co-effiency of CI434,T3RNAP	2		Ref: iGEM2007 PKU Team
n_9	Hill co-effiency of CI,CI434	4		Ref: iGEM2007 PKU Team
n_12	Hill co-effiency of Sal,GFP	2
n_12'	Hill co-effiency of T3RNAP,GFP	2
γ_1	Degradation rate of tRNA	1/30+1/60	min^-1	Since half life of tRNA is very long, we decided to use 60 mins instead
γ_2	Degradation rate of Aa-tRNA	1/30+1/40	min^-1
γ_2'	Real Degradation rate of Aa-tRNA	1/40	min^-1
γ_3	Degradation rate of T7RNAP mRNA	1/30+1/4.4	min^-1	Assumption
γ_4	Degradation rate of T7RNAP	1/30+1/40	min^-1
γ_5	Degradation rate of trigger CI mRNA	1/30+1/4.4	min^-1	Assumption
γ_6	Degradation rate of bistable CI mRNA	1/30+1/4.4	min^-1	Assumption
γ_7	Degradation rate of T3RNAP mRNA	1/30+1/4.4	min^-1	Assumption
γ_8	Degradation rate of CI	1/30+1/44	min^-1	Ref: iGEM2007 PKU Team
γ_9	Degradation rate of CI434 mRNA	1/30+1/4.4	min^-1	Assumption
γ_10	Degradation rate of CI434	1/30+1/11	min^-1	Ref: iGEM 2007 PKU Team
γ_11	Degradation rate of T3RNAP	1/30+1/30	min^-1
γ_12	Degradation rate of GFP mRNA	1/30+1/4.4	min^-1	Assumption
γ_13	Degradation rate of GFP	1/30+1/60	min^-1	Since 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

Parameters	Brief Introduction	Value	Unit	Reference/Sensitivity
k_1	Max Transcription rate of tRNA	46.67	nM/min	Assumption, 1.41
k_2	Synthesis rate of Aa-tRNA	0.08	min^-1	0.81
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, 1.23
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
k_11	Max Translation rate of P2	28.8*0.0045	min^-1	Assumption, 1.23
k_12	Max Transcription rate of GFP from Sal	5.25	nM/min	Assumption, 0.00
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
k_s	rate of AND Gate 1	0.3	nM^-1	0.00
k_s'	rate of AND Gate 2	0.01	nM^-1	1.29
K_1	dissociation constant of AraC,tRNA	14	nM	0.20
K_3	dissociation constant of Sal,T7RNAP	0.5	nM	0.00
K_5	dissociation constant of T7RNAP,trigger CI	3	nM	[http://bionumbers.hms.harvard.edu/bionumber.aspx?s=y&id=103592&ver=1 Ref]
K_6	dissociation constant of CI,bistable CI	40	nM	Ref: iGEM2007 PKU Team
K_6'	dissociation constant of CI434,bistable CI	50	nM	Ref: iGEM2007 PKU Team
K_7	dissociation constant of CI,P2	40	nM	Ref: iGEM2007 PKU Team
K_7'	dissociation constant of CI434,P2	50	nM	Ref: iGEM2007 PKU Team
K_9	dissociation constant of CI,CI434	40	nM	Ref: iGEM2007 PKU Team
K_12	dissociation constant of Sal,GFP	0.5	nM	0.00
K_12'	dissociation constant of P2,GFP	35	nM	1.29
n_1	Hill co-effiency of AraC,tRNA	2
n_3	Hill co-effiency of Sal,T7RNAP	2
n_5	Hill co-effiency of T7RNAP,CI	2
n_6	Hill co-effiency of CI,bistable CI	4		Ref: iGEM2007 PKU Team
n_6'	Hill co-effiency of CI434,bistable CI	2		Ref: iGEM2007 PKU Team
n_7	Hill co-effiency of CI,P2	4		Ref: iGEM2007 PKU Team
n_7'	Hill co-effiency of CI434,P2	2		Ref: iGEM2007 PKU Team
n_9	Hill co-effiency of CI,CI434	4		Ref: iGEM2007 PKU Team
n_12	Hill co-effiency of Sal,GFP	2
n_12'	Hill co-effiency of P2,GFP	2
γ_1	Degradation rate of tRNA	1/30+1/60	min^-1	Since half life of tRNA is very long, we decided to use 60 mins instead
γ_2	Degradation rate of Aa-tRNA	1/30+1/40	min^-1
γ_2'	Real Degradation rate of Aa-tRNA	1/40	min^-1
γ_3	Degradation rate of T7RNAP mRNA	1/30+1/4.4	min^-1	Assumption
γ_4	Degradation rate of T7RNAP	1/30+1/40	min^-1
γ_5	Degradation rate of trigger CI mRNA	1/30+1/4.4	min^-1	Assumption
γ_6	Degradation rate of bistable CI mRNA	1/30+1/4.4	min^-1	Assumption
γ_7	Degradation rate of P2 mRNA	1/30+1/4.4	min^-1	Assumption
γ_8	Degradation rate of CI	1/30+1/44	min^-1	Ref: iGEM2007 PKU Team
γ_9	Degradation rate of CI434 mRNA	1/30+1/4.4	min^-1	Assumption
γ_10	Degradation rate of CI434	1/30+1/11	min^-1	Ref: iGEM 2007 PKU Team
γ_11	Degradation rate of P2	1/30+1/30	min^-1
γ_12	Degradation rate of GFP mRNA	1/30+1/4.4	min^-1	Assumption
γ_13	Degradation rate of GFP	1/30+1/60	min^-1	Since 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!

^Top

@@ Line 7: / Line 7: @@
 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 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.
+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'''===
@@ Line 17: / Line 17: @@
 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, [https://2008.igem.org/Team:NTU-Singapore/Modelling/Parameter NTU-Singapore iGEM2008 Team]
 *'''Translation'''
@@ Line 22: / Line 23: @@
 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, [https://2008.igem.org/Team:NTU-Singapore/Modelling/Parameter NTU-Singapore iGEM2008 Team]
 *'''Cell Division Rate'''
@@ Line 27: / Line 29: @@
 *'''Degradation of mRNA'''
-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'''===
@@ Line 92: / Line 94: @@
 |K_12||dissociation constant of Sal,GFP||0.5||nM||0.00
 |-
-|K_12'||dissociation constant of T3RNAP,GFP||55||nM||Ref:
+|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|| ||
@@ Line 208: / Line 210: @@
 |K_12||dissociation constant of Sal,GFP||0.5||nM||0.00
 |-
-|K_12'||dissociation constant of P2,GFP||35||nM||Ref:
+|K_12'||dissociation constant of P2,GFP||35||nM||1.29
 |-
 |n_1||Hill co-effiency of AraC,tRNA||2|| ||
@@ Line 259: / Line 261: @@
 |}
-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]]!
 {{PKU_Beijing/Foot}}
 __NOTOC__