Timer-SUMO-KillSwitch

From 2013.igem.org

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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 Plus Sumo</h2>
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<h2 align="center">Timer-SUMO-KillSwitch</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>
<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/b/b0/Equations_SumoUpd.png" >
+
<img src="https://static.igem.org/mediawiki/2013/8/87/Combined_equations.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>
</html>
 +
 +
<p>
<p>
  {| align="center" border="1"
  {| align="center" border="1"
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|'''Reference'''
|'''Reference'''
|-
|-
-
| c<sub>a</sub>
+
|a
|1020
|1020
|Translation rate per amino acid
|Translation rate per amino acid
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|min<sup>-1</sup>
|min<sup>-1</sup>
| [[Team:TUDelft/Modeling_References|[9]]]
| [[Team:TUDelft/Modeling_References|[9]]]
-
|-
 
-
| d<sub>PEP</sub>
 
-
|6.3*10<sup>-3</sup>
 
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|Degradation rate of the peptide
 
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|min<sup>-1</sup>
 
-
|Assumed the same as GFP
 
|-
|-
| d<sub>PSU</sub>
| d<sub>PSU</sub>
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|Degradation rate of Ulp
|Degradation rate of Ulp
|min<sup>-1</sup>
|min<sup>-1</sup>
-
|Assumed the same as GFP
+
|Assumed twice the rate of GFP
|-
|-
|l<sub>t7</sub>
|l<sub>t7</sub>
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|  -
|  -
|Assumption
|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>
|k<sub>ci</sub>
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|min<sup>-1</sup>
|min<sup>-1</sup>
|[[Team:TUDelft/Modeling_References|[6]]]
|[[Team:TUDelft/Modeling_References|[6]]]
-
|-
 
-
|n<sub>ci</sub>
 
-
|3
 
-
|Hills coefficient
 
-
|  -
 
-
|[[Team:TUDelft/Modeling_References|[11]]]
 
|-
|-
|n<sub>tet</sub>
|n<sub>tet</sub>
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|  -
|  -
|[[Team:TUDelft/Modeling_References|[11]]]
|[[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}}
 
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{{:Team:TU-Delft/Templates/Style}}
 
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{{:Team:TU-Delft/Templates/Frog}}
 
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{{:Team:TU-Delft/Templates/Logo}}
 
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<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>
 
-
 
-
<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;"> 
 
-
<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>
|n<sub>ci</sub>
Line 347: Line 118:
|  -
|  -
|[[Team:TUDelft/Modeling_References|[11]]]
|[[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>
|s<sub>ci</sub>
|228
|228
-
|Length of CI
+
|Length of Ci
-
|amino acids
+
| amino acids
|[[Team:TUDelft/Modeling_References|[12]]]
|[[Team:TUDelft/Modeling_References|[12]]]
|-
|-
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<br>
<br>
 +
<html>
<html>
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<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">Results</h2>
<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>
<br>
<center>
<center>
-
<img src="https://static.igem.org/mediawiki/2013/5/5d/Sumo.png">
+
<img src="https://static.igem.org/mediawiki/2013/f/f6/Combined_simulation.png" width="700">
-
<p>Figure 2: Simulation Results</p></div>
+
<p>Figure 1: Simulation Results</p></div>
</center>
</center>
<br>
<br>

Latest revision as of 07:52, 20 August 2013

Timer-SUMO-KillSwitch


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.

Differential Equations

Parameters


Parameter Value Description Units Reference
a 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]
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 twice the rate of GFP
lt7 0.002 Leakage factor of T7 - Assumption
lptet 0.002 Leakage factor of Ptet - Assumption
kci 20 Dissociation constant of Pci #m [10]
kcUlp 3 Turnover rate of Ulp min-1 [6]
ntet 3 Hills coefficient - [11]
nci 3 Hills coefficient - [11]
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


Figure 1: Simulation Results


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