Timer Plus Sumo

From 2013.igem.org

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<h2 align="center">Timer Plus Sumo</h2>
<h2 align="center">Timer Plus Sumo</h2>
<br>
<br>
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<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
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<p align="justify">In this section the system of Figure 1 is modeled. The structure of the timer has two repressing promoters (PcI and Ptet) and the input is the T7 promoter and the output is the protease Ulp-1. This Ulp-1 cleaves off the SUMO from the produced SUMO-peptide.
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T7 promoter and the output to Ulp-1. Furthermore, the Ulp-1 cleaves off the SUMO from the peptide
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combined with the SUMO.  
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</p>
</p>
<br>
<br>
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The above circuit can be represented by the following differential equations. We assume a binary
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
behavior of the T7 promoter. In the presence of IPTG, the T7 promoter will be active. So, we make
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the assumption that the T7 is binary variable with two possible states: either active 1 or inactive 0,
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the assumption that the T7 is binary variable with two possible states: either active 1 or inactive 0.</p>
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this is the variable s.
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</p>
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<br>
<br>
<center>
<center>
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<img src="https://static.igem.org/mediawiki/2013/f/f9/Equations_Sumo.png" >
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<img src="https://static.igem.org/mediawiki/2013/b/b0/Equations_SumoUpd.png" >
</center>
</center>
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<div style="margin-top:30px;margin-left:30px;margin-right:30px;float:left;display:inline-block;">   
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<div style="margin-left:30px;margin-right:30px;float:left;display:inline-block;">   
<h2 align="center">Parameters</h2>
<h2 align="center">Parameters</h2>
<br>
<br>
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<b> Transcription rates of T7</b>
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<br>
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</html>
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<p align="justify">
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<p>
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For the T7 promoter an transcription rate of 50 bp/sec [2] converted to per minute using an average
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{| align="center" border="1"
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base pair length of 720 bp:
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|'''Parameter'''
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<br>
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|'''Value'''
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<center>
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|'''Description'''
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<img src="https://static.igem.org/mediawiki/2013/8/8c/Equations.png" >
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|'''Units'''
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</center>
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|'''Reference'''
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|-
 +
| c<sub>a</sub>
 +
|1020
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|Translation rate per amino acid
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|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
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|Maximum transcription rate of Ptet
 +
|#m/min
 +
| [[Team:TUDelft/Modeling_References|[4]]]
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|-
 +
| c<sub>ci</sub>
 +
|1.79
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|Maximum transcription rate of Pci
 +
|#m/min
 +
| [[Team:TUDelft/Modeling_References|[3]]]
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|-
 +
| d<sub>mRNA</sub>
 +
|0.231
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|Degradation rate of mRNA
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|min<sup>-1</sup>
 +
| [[Team:TUDelft/Modeling_References|[8]]]
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|-
 +
| d<sub>TET</sub>
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|0.1386
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|Degradation rate of TET
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|min<sup>-1</sup>
 +
| [[Team:TUDelft/Modeling_References|[9]]]
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|-
 +
| d<sub>CI</sub>
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|0.042
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|Degradation rate of CI
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|min<sup>-1</sup>
 +
| [[Team:TUDelft/Modeling_References|[9]]]
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|-
 +
| d<sub>PEP</sub>
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|6.3*10<sup>-3</sup>
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|Degradation rate of the peptide
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|min<sup>-1</sup>
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|Assumed the same as GFP
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|-
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| d<sub>PSU</sub>
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|6.3*10<sup>-3</sup>  
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|Degradation rate of the peptide plus SUMO
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|min<sup>-1</sup>
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|Assumed the same as GFP
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|-
 +
| d<sub>Ulp</sub>
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|1.263*10<sup>-2</sup>
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|Degradation rate of Ulp
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|min<sup>-1</sup>
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|Assumed twice the rate of GFP
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|-
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|l<sub>t7</sub>
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|0.002
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|Leakage factor of T7
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|  -
 +
|Assumption
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|-
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|l<sub>ptet</sub>
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|0.002
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|Leakage factor of Ptet
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|  -
 +
|Assumption
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|-
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|l<sub>ci</sub>
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|0.002
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|Leakage factor of Pci
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|  -
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|Assumption
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|-
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|k<sub>tet</sub>
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|6
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|Dissociation constant of Ptet
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|#m
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|[[Team:TUDelft/Modeling_References|[10]]]
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|-
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|k<sub>ci</sub>
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|20
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|Dissociation constant of Pci
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|#m
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|[[Team:TUDelft/Modeling_References|[10]]]
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|-
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|k<sub>cUlp</sub>
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|3
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|Turnover rate of Ulp
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|min<sup>-1</sup>
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|[[Team:TUDelft/Modeling_References|[6]]]
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|-
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|n<sub>ci</sub>
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|3
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|Hills coefficient
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|  -
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|[[Team:TUDelft/Modeling_References|[11]]]
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|-
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|n<sub>tet</sub>
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|3
 +
|Hills coefficient
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|  -
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|[[Team:TUDelft/Modeling_References|[11]]]
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|-
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|s
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|0 or 1
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|Activation/Inactivation of T7 promoter
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|Binary
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|Assumption
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|-
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|s<sub>ci</sub>
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|228
 +
|Length of CI
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|amino acids
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|[[Team:TUDelft/Modeling_References|[12]]]
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|-
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|s<sub>PSU</sub>
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|18 + 110
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|Length of peptide plus SUMO
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|amino acids
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|[[Team:TUDelft/Modeling_References|[12]]]
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|-
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|s<sub>TET</sub>
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|206
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|Length of TET
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|amino acids
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|[[Team:TUDelft/Modeling_References|[13]]]
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|-
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|s<sub>Ulp</sub>
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|233
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|Length of Ulp1
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|amino acids
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|[[Team:TUDelft/Modeling_References|[13]]]
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|-
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|}
</p>
</p>
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<b>Relative promoter strength</b>
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<br>
<br>
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<html>
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<div style="margin-left:30px;margin-right:30px;float:left;display:inline-block;"> 
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<h2 align="center">Results</h2>
<p align="justify">
<p align="justify">
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The promoter strengths of cI and Tet are taken as a factor of T7. PcI is found to be approximatly
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Here the results are given of the simulation upon activating the T7 promoter. For starting conditions the steady state values of the concentrations are used when T7 is switched off.  
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0.43 times the strength of T7 [1] and Ptet is approximatly 2.79. [2].
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</p>
</p>
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<b>Turnover rate Ulp</b><br>
 
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<p>
 
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The parameter kcUlp is the turnover rate. It can be calculated based on in vitro specifications [5]. It is
 
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stated that  10<sup>-5 mg of Ulp1 cleaves 85% of 100 μg of SUMO combined with GFP in 1 hr. Furthermore
 
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the molecular weight of Ulp1 is 28 kDa and the molecular weight of SUMO is 11 kDa and the molecular
 
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weight of GFP is 27 kDa.
 
<br>
<br>
<center>
<center>
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<img src="https://static.igem.org/mediawiki/2013/e/ea/Equation2.png" >
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<img src="https://static.igem.org/mediawiki/2013/5/5d/Sumo.png">
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<p>Figure 2: Simulation Results</p></div>
</center>
</center>
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However a second company dictates a very dierent value. Here they specify one unit as cleaving 85%
 
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of 2 �g. This results in a kcUlp of around 3 min<sup>-1</sup> which is significantly different. [6] We assume the
 
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latter value in the model.
 
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<center>
 
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<img src="https://static.igem.org/mediawiki/2013/c/cf/TABLE.png" width=700 >
 
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</center>
 
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</p>
 
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<h2 align="center">Simulation</h2>
 
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<br>
 
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<b>Initial Conditions</b>
 
<br>
<br>
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<h2 align="center">Discussion</h2>
<p align="justify">
<p align="justify">
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TET and ULP must be set equal to zero (or a numerical equivalent). For CI the steady state value is
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In the graph the effect of the timer is clearly observed, at first the peptide+SUMO is produced, and after approximatly 80 minutes more Ulp is produced leading to an increased cleaving of the SUMO. Also note that there is cleaving of the SUMO already from the start, as the promoters are somewhat leaky.  
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assumed as a starting condition as this is expressed before activation.
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</p>
</p>
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<b>Results</b>
 
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</html>
</html>

Latest revision as of 07:51, 20 August 2013

Timer Plus Sumo


In this section the system of Figure 1 is modeled. The structure of the timer has two repressing promoters (PcI and Ptet) and the input is the T7 promoter and the output is the protease Ulp-1. This Ulp-1 cleaves off the SUMO from the produced SUMO-peptide.


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 twice the rate of 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

Here the results are given of the simulation upon activating the T7 promoter. For starting conditions the steady state values of the concentrations are used when T7 is switched off.


Figure 2: Simulation Results


Discussion

In the graph the effect of the timer is clearly observed, at first the peptide+SUMO is produced, and after approximatly 80 minutes more Ulp is produced leading to an increased cleaving of the SUMO. Also note that there is cleaving of the SUMO already from the start, as the promoters are somewhat leaky.

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