Timer-SUMO-KillSwitch

From 2013.igem.org

(Difference between revisions)
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 +
<html>
<html>
<div style="margin-top:10px;margin-left:30px;margin-right:30px;float:left;display:inline-block;">   
<div style="margin-top:10px;margin-left:30px;margin-right:30px;float:left;display:inline-block;">   
-
<h2 align="center">Timer-SUMO-KillSwitch</h2>
+
<h2 align="center">Timer Plus Sumo</h2>
<br>
<br>
-
<p align="justify">The separate modules: <a href="https://2013.igem.org/Timer_Plus_Sumo">Timer plus SUMO </a> and  <a href="https://2013.igem.org/KillSwitch">Kill Switch</a> are combined to form the complete model of the system: Timer - SUMO - Kill Switch.  For the final model, the kill switch module is converted in such a way so as the holin and antiholin to be activated by the Pci promoter.
+
<p align="justify">The separate modules: <a href="https://2013.igem.org/Timer_Plus_Sumo">Timer plus SUMO </a> and  <a href="https://2013.igem.org/KillSwitch">Kill Switch</a> are combined to form the complete model of the system: Timer - SUMO - Kill Switch.  For the final model, the kill switch module is converted in such a way so as the holin and antiholin to be activated by the Pci promoter.  
</p>
</p>
 +
<br>
 +
<center>
 +
<img src="https://static.igem.org/mediawiki/2013/9/96/Timer%2Bsumo.png" >
 +
<p>Figure 1: Circuit of the timer including sumo cleaving</p></div>
 +
</center>
 +
 +
<div style="margin-top:40px;margin-left:30px;margin-right:30px;float:left;display:inline-block;"> 
 +
<h2 align="center">Differential Equations</h2>
 +
 +
<p align="justify">
 +
The above circuit can be represented by the following differential equations. We assume a binary
 +
behavior of the T7 promoter. In the presence of IPTG, the T7 promoter will be active. So, we make
 +
the assumption that the T7 is binary variable with two possible states: either active 1 or inactive 0.</p>
 +
<br>
 +
<center>
 +
<img src="https://static.igem.org/mediawiki/2013/b/b0/Equations_SumoUpd.png" >
 +
</center>
<div style="margin-left:30px;margin-right:30px;float:left;display:inline-block;">   
<div style="margin-left:30px;margin-right:30px;float:left;display:inline-block;">   
 +
<h2 align="center">Parameters</h2>
 +
<br>
 +
 +
</html>
 +
<p>
 +
{| align="center" border="1"
 +
|'''Parameter'''
 +
|'''Value'''
 +
|'''Description'''
 +
|'''Units'''
 +
|'''Reference'''
 +
|-
 +
| c<sub>a</sub>
 +
|1020
 +
|Translation rate per amino acid
 +
|min<sup>-1</sup>#<sub>a</sub><sup>-1</sup>
 +
| [[Team:TUDelft/Modeling_References|[7]]]
 +
|-
 +
| c<sub>T7</sub>
 +
|4.16
 +
|Maximum transcription rate of T7
 +
|#m/min
 +
| [[Team:TUDelft/Modeling_References|[2]]]
 +
|-
 +
| c<sub>ptet</sub>
 +
|2.79
 +
|Maximum transcription rate of Ptet
 +
|#m/min
 +
| [[Team:TUDelft/Modeling_References|[4]]]
 +
|-
 +
| c<sub>ci</sub>
 +
|1.79
 +
|Maximum transcription rate of Pci
 +
|#m/min
 +
| [[Team:TUDelft/Modeling_References|[3]]]
 +
|-
 +
| d<sub>mRNA</sub>
 +
|0.231
 +
|Degradation rate of mRNA
 +
|min<sup>-1</sup>
 +
| [[Team:TUDelft/Modeling_References|[8]]]
 +
|-
 +
| d<sub>TET</sub>
 +
|0.1386
 +
|Degradation rate of TET
 +
|min<sup>-1</sup>
 +
| [[Team:TUDelft/Modeling_References|[9]]]
 +
|-
 +
| d<sub>CI</sub>
 +
|0.042
 +
|Degradation rate of CI
 +
|min<sup>-1</sup>
 +
| [[Team:TUDelft/Modeling_References|[9]]]
 +
|-
 +
| d<sub>PEP</sub>
 +
|6.3*10<sup>-3</sup>
 +
|Degradation rate of the peptide
 +
|min<sup>-1</sup>
 +
|Assumed the same as GFP
 +
|-
 +
| d<sub>PSU</sub>
 +
|6.3*10<sup>-3</sup>
 +
|Degradation rate of the peptide plus SUMO
 +
|min<sup>-1</sup>
 +
|Assumed the same as GFP
 +
|-
 +
| d<sub>Ulp</sub>
 +
|1.263*10<sup>-2</sup>
 +
|Degradation rate of Ulp
 +
|min<sup>-1</sup>
 +
|Assumed the same as GFP
 +
|-
 +
|l<sub>t7</sub>
 +
|0.002
 +
|Leakage factor of T7
 +
|  -
 +
|Assumption
 +
|-
 +
|l<sub>ptet</sub>
 +
|0.002
 +
|Leakage factor of Ptet
 +
|  -
 +
|Assumption
 +
|-
 +
|l<sub>ci</sub>
 +
|0.002
 +
|Leakage factor of Pci
 +
|  -
 +
|Assumption
 +
|-
 +
|k<sub>tet</sub>
 +
|6
 +
|Dissociation constant of Ptet
 +
|#m
 +
|[[Team:TUDelft/Modeling_References|[10]]]
 +
|-
 +
|k<sub>ci</sub>
 +
|20
 +
|Dissociation constant of Pci
 +
|#m
 +
|[[Team:TUDelft/Modeling_References|[10]]]
 +
|-
 +
|k<sub>cUlp</sub>
 +
|3
 +
|Turnover rate of Ulp
 +
|min<sup>-1</sup>
 +
|[[Team:TUDelft/Modeling_References|[6]]]
 +
|-
 +
|n<sub>ci</sub>
 +
|3
 +
|Hills coefficient
 +
|  -
 +
|[[Team:TUDelft/Modeling_References|[11]]]
 +
|-
 +
|n<sub>tet</sub>
 +
|3
 +
|Hills coefficient
 +
|  -
 +
|[[Team:TUDelft/Modeling_References|[11]]]
 +
|-
 +
|s
 +
|0 or 1
 +
|Activation/Inactivation of T7 promoter
 +
|Binary
 +
|Assumption
 +
|-
 +
|s<sub>ci</sub>
 +
|228
 +
|Length of CI
 +
|amino acids
 +
|[[Team:TUDelft/Modeling_References|[12]]]
 +
|-
 +
|s<sub>PSU</sub>
 +
|18 + 110
 +
|Length of peptide plus SUMO
 +
|amino acids
 +
|[[Team:TUDelft/Modeling_References|[12]]]
 +
|-
 +
|s<sub>TET</sub>
 +
|206
 +
|Length of TET
 +
|amino acids
 +
|[[Team:TUDelft/Modeling_References|[13]]]
 +
|-
 +
|s<sub>Ulp</sub>
 +
|233
 +
|Length of Ulp1
 +
|amino acids
 +
|[[Team:TUDelft/Modeling_References|[13]]]
 +
|-
 +
|}
 +
</p>
 +
 +
<br>
 +
<html>
 +
 +
 +
<div style="margin-left:30px;margin-right:30px;float:left;display:inline-block;"> 
 +
<h2 align="center">Results</h2>
 +
<p align="justify">
 +
TET and ULP must be set equal to zero (or a numerical equivalent). For CI the steady state value is
 +
assumed as a starting condition as this is expressed before activation.
 +
</p>
 +
<br>
 +
<center>
 +
<img src="https://static.igem.org/mediawiki/2013/5/5d/Sumo.png">
 +
<p>Figure 2: Simulation Results</p></div>
 +
</center>
 +
<br>
 +
 +
 +
</html>
 +
{{:Team:TU-Delft/Templates/Navigation}}
 +
{{:Team:TU-Delft/Templates/Style}}
 +
{{:Team:TU-Delft/Templates/Frog}}
 +
{{:Team:TU-Delft/Templates/Logo}}
 +
<html>
 +
 +
<div style="margin-top:10px;margin-left:30px;margin-right:30px;float:left;display:inline-block;"> 
 +
<h2 align="center">Timer Plus Sumo</h2>
 +
<br>
 +
<p align="justify">In this section the system of Figure 1 is modeled. The structure of the timer is very similar version of the timer compared to the construct of iGEM TU Delft team 2009. Here the input is changed to a
 +
T7 promoter and the output to Ulp-1. Furthermore, the Ulp-1 cleaves off the SUMO from the peptide
 +
combined with the SUMO.
 +
</p>
 +
<br>
 +
<center>
 +
<img src="https://static.igem.org/mediawiki/2013/9/96/Timer%2Bsumo.png" >
 +
<p>Figure 1: Circuit of the timer including sumo cleaving</p></div>
 +
</center>
 +
 +
<div style="margin-top:40px;margin-left:30px;margin-right:30px;float:left;display:inline-block;"> 
<h2 align="center">Differential Equations</h2>
<h2 align="center">Differential Equations</h2>
 +
 +
<p align="justify">
 +
The above circuit can be represented by the following differential equations. We assume a binary
 +
behavior of the T7 promoter. In the presence of IPTG, the T7 promoter will be active. So, we make
 +
the assumption that the T7 is binary variable with two possible states: either active 1 or inactive 0.</p>
 +
<br>
<center>
<center>
-
<img src="https://static.igem.org/mediawiki/2013/8/87/Combined_equations.png" >
+
<img src="https://static.igem.org/mediawiki/2013/b/b0/Equations_SumoUpd.png" >
</center>
</center>
 +
 +
<div style="margin-left:30px;margin-right:30px;float:left;display:inline-block;"> 
<h2 align="center">Parameters</h2>
<h2 align="center">Parameters</h2>
 +
<br>
 +
 +
</html>
 +
<p>
 +
{| align="center" border="1"
 +
|'''Parameter'''
 +
|'''Value'''
 +
|'''Description'''
 +
|'''Units'''
 +
|'''Reference'''
 +
|-
 +
| c<sub>a</sub>
 +
|1020
 +
|Translation rate per amino acid
 +
|min<sup>-1</sup>#<sub>a</sub><sup>-1</sup>
 +
| [[Team:TUDelft/Modeling_References|[7]]]
 +
|-
 +
| c<sub>T7</sub>
 +
|4.16
 +
|Maximum transcription rate of T7
 +
|#m/min
 +
| [[Team:TUDelft/Modeling_References|[2]]]
 +
|-
 +
| c<sub>ptet</sub>
 +
|2.79
 +
|Maximum transcription rate of Ptet
 +
|#m/min
 +
| [[Team:TUDelft/Modeling_References|[4]]]
 +
|-
 +
| c<sub>ci</sub>
 +
|1.79
 +
|Maximum transcription rate of Pci
 +
|#m/min
 +
| [[Team:TUDelft/Modeling_References|[3]]]
 +
|-
 +
| d<sub>mRNA</sub>
 +
|0.231
 +
|Degradation rate of mRNA
 +
|min<sup>-1</sup>
 +
| [[Team:TUDelft/Modeling_References|[8]]]
 +
|-
 +
| d<sub>TET</sub>
 +
|0.1386
 +
|Degradation rate of TET
 +
|min<sup>-1</sup>
 +
| [[Team:TUDelft/Modeling_References|[9]]]
 +
|-
 +
| d<sub>CI</sub>
 +
|0.042
 +
|Degradation rate of CI
 +
|min<sup>-1</sup>
 +
| [[Team:TUDelft/Modeling_References|[9]]]
 +
|-
 +
| d<sub>PEP</sub>
 +
|6.3*10<sup>-3</sup>
 +
|Degradation rate of the peptide
 +
|min<sup>-1</sup>
 +
|Assumed the same as GFP
 +
|-
 +
| d<sub>PSU</sub>
 +
|6.3*10<sup>-3</sup>
 +
|Degradation rate of the peptide plus SUMO
 +
|min<sup>-1</sup>
 +
|Assumed the same as GFP
 +
|-
 +
| d<sub>Ulp</sub>
 +
|1.263*10<sup>-2</sup>
 +
|Degradation rate of Ulp
 +
|min<sup>-1</sup>
 +
|Assumed the same as GFP
 +
|-
 +
|l<sub>t7</sub>
 +
|0.002
 +
|Leakage factor of T7
 +
|  -
 +
|Assumption
 +
|-
 +
|l<sub>ptet</sub>
 +
|0.002
 +
|Leakage factor of Ptet
 +
|  -
 +
|Assumption
 +
|-
 +
|l<sub>ci</sub>
 +
|0.002
 +
|Leakage factor of Pci
 +
|  -
 +
|Assumption
 +
|-
 +
|k<sub>tet</sub>
 +
|6
 +
|Dissociation constant of Ptet
 +
|#m
 +
|[[Team:TUDelft/Modeling_References|[10]]]
 +
|-
 +
|k<sub>ci</sub>
 +
|20
 +
|Dissociation constant of Pci
 +
|#m
 +
|[[Team:TUDelft/Modeling_References|[10]]]
 +
|-
 +
|k<sub>cUlp</sub>
 +
|3
 +
|Turnover rate of Ulp
 +
|min<sup>-1</sup>
 +
|[[Team:TUDelft/Modeling_References|[6]]]
 +
|-
 +
|n<sub>ci</sub>
 +
|3
 +
|Hills coefficient
 +
|  -
 +
|[[Team:TUDelft/Modeling_References|[11]]]
 +
|-
 +
|n<sub>tet</sub>
 +
|3
 +
|Hills coefficient
 +
|  -
 +
|[[Team:TUDelft/Modeling_References|[11]]]
 +
|-
 +
|s
 +
|0 or 1
 +
|Activation/Inactivation of T7 promoter
 +
|Binary
 +
|Assumption
 +
|-
 +
|s<sub>ci</sub>
 +
|228
 +
|Length of CI
 +
|amino acids
 +
|[[Team:TUDelft/Modeling_References|[12]]]
 +
|-
 +
|s<sub>PSU</sub>
 +
|18 + 110
 +
|Length of peptide plus SUMO
 +
|amino acids
 +
|[[Team:TUDelft/Modeling_References|[12]]]
 +
|-
 +
|s<sub>TET</sub>
 +
|206
 +
|Length of TET
 +
|amino acids
 +
|[[Team:TUDelft/Modeling_References|[13]]]
 +
|-
 +
|s<sub>Ulp</sub>
 +
|233
 +
|Length of Ulp1
 +
|amino acids
 +
|[[Team:TUDelft/Modeling_References|[13]]]
 +
|-
 +
|}
 +
</p>
 +
 +
<br>
 +
<html>
 +
 +
 +
<div style="margin-left:30px;margin-right:30px;float:left;display:inline-block;"> 
 +
<h2 align="center">Results</h2>
 +
<p align="justify">
 +
TET and ULP must be set equal to zero (or a numerical equivalent). For CI the steady state value is
 +
assumed as a starting condition as this is expressed before activation.
 +
</p>
 +
<br>
 +
<center>
 +
<img src="https://static.igem.org/mediawiki/2013/5/5d/Sumo.png">
 +
<p>Figure 2: Simulation Results</p></div>
 +
</center>
 +
<br>
 +
</html>
</html>

Revision as of 13:03, 16 August 2013

Timer Plus Sumo


The separate modules: Timer plus SUMO and Kill Switch are combined to form the complete model of the system: Timer - SUMO - Kill Switch. For the final model, the kill switch module is converted in such a way so as the holin and antiholin to be activated by the Pci promoter.


Figure 1: Circuit of the timer including sumo cleaving

Differential Equations

The above circuit can be represented by the following differential equations. We assume a binary behavior of the T7 promoter. In the presence of IPTG, the T7 promoter will be active. So, we make the assumption that the T7 is binary variable with two possible states: either active 1 or inactive 0.


Parameters


Parameter Value Description Units Reference
ca 1020 Translation rate per amino acid min-1#a-1 [7]
cT7 4.16 Maximum transcription rate of T7 #m/min [2]
cptet 2.79 Maximum transcription rate of Ptet #m/min [4]
cci 1.79 Maximum transcription rate of Pci #m/min [3]
dmRNA 0.231 Degradation rate of mRNA min-1 [8]
dTET 0.1386 Degradation rate of TET min-1 [9]
dCI 0.042 Degradation rate of CI min-1 [9]
dPEP 6.3*10-3 Degradation rate of the peptide min-1 Assumed the same as GFP
dPSU 6.3*10-3 Degradation rate of the peptide plus SUMO min-1 Assumed the same as GFP
dUlp 1.263*10-2 Degradation rate of Ulp min-1 Assumed the same as GFP
lt7 0.002 Leakage factor of T7 - Assumption
lptet 0.002 Leakage factor of Ptet - Assumption
lci 0.002 Leakage factor of Pci - Assumption
ktet 6 Dissociation constant of Ptet #m [10]
kci 20 Dissociation constant of Pci #m [10]
kcUlp 3 Turnover rate of Ulp min-1 [6]
nci 3 Hills coefficient - [11]
ntet 3 Hills coefficient - [11]
s 0 or 1 Activation/Inactivation of T7 promoter Binary Assumption
sci 228 Length of CI amino acids [12]
sPSU 18 + 110 Length of peptide plus SUMO amino acids [12]
sTET 206 Length of TET amino acids [13]
sUlp 233 Length of Ulp1 amino acids [13]


Results

TET and ULP must be set equal to zero (or a numerical equivalent). For CI the steady state value is assumed as a starting condition as this is expressed before activation.


Figure 2: Simulation Results


Timer Plus Sumo


In this section the system of Figure 1 is modeled. The structure of the timer is very similar version of the timer compared to the construct of iGEM TU Delft team 2009. Here the input is changed to a T7 promoter and the output to Ulp-1. Furthermore, the Ulp-1 cleaves off the SUMO from the peptide combined with the SUMO.


Figure 1: Circuit of the timer including sumo cleaving

Differential Equations

The above circuit can be represented by the following differential equations. We assume a binary behavior of the T7 promoter. In the presence of IPTG, the T7 promoter will be active. So, we make the assumption that the T7 is binary variable with two possible states: either active 1 or inactive 0.


Parameters


Parameter Value Description Units Reference
ca 1020 Translation rate per amino acid min-1#a-1 [7]
cT7 4.16 Maximum transcription rate of T7 #m/min [2]
cptet 2.79 Maximum transcription rate of Ptet #m/min [4]
cci 1.79 Maximum transcription rate of Pci #m/min [3]
dmRNA 0.231 Degradation rate of mRNA min-1 [8]
dTET 0.1386 Degradation rate of TET min-1 [9]
dCI 0.042 Degradation rate of CI min-1 [9]
dPEP 6.3*10-3 Degradation rate of the peptide min-1 Assumed the same as GFP
dPSU 6.3*10-3 Degradation rate of the peptide plus SUMO min-1 Assumed the same as GFP
dUlp 1.263*10-2 Degradation rate of Ulp min-1 Assumed the same as GFP
lt7 0.002 Leakage factor of T7 - Assumption
lptet 0.002 Leakage factor of Ptet - Assumption
lci 0.002 Leakage factor of Pci - Assumption
ktet 6 Dissociation constant of Ptet #m [10]
kci 20 Dissociation constant of Pci #m [10]
kcUlp 3 Turnover rate of Ulp min-1 [6]
nci 3 Hills coefficient - [11]
ntet 3 Hills coefficient - [11]
s 0 or 1 Activation/Inactivation of T7 promoter Binary Assumption
sci 228 Length of CI amino acids [12]
sPSU 18 + 110 Length of peptide plus SUMO amino acids [12]
sTET 206 Length of TET amino acids [13]
sUlp 233 Length of Ulp1 amino acids [13]


Results

TET and ULP must be set equal to zero (or a numerical equivalent). For CI the steady state value is assumed as a starting condition as this is expressed before activation.


Figure 2: Simulation Results


Retrieved from "http://2013.igem.org/Timer-SUMO-KillSwitch"