Timer Plus Sumo

From 2013.igem.org

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<div style="margin-top:10px;margin-left:30px;margin-right:30px;float:left;display:inline-block;"> 
<h2 align="center">Timer Plus Sumo</h2>
<h2 align="center">Timer Plus Sumo</h2>
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<div style="margin-left:50px;margin-right:50px;float:left;display:inline-block;"> 
 
<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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<center>
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<img src="https://static.igem.org/mediawiki/2013/9/96/Timer%2Bsumo.png" >
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<p>Figure 1: Circuit of the timer including sumo cleaving</p></div>
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</center>
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<div style="margin-top:40px;margin-left:30px;margin-right:30px;float:left;display:inline-block;"> 
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<h2 align="center">Differential Equations</h2>
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<p align="justify">
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The above circuit can be represented by the following differential equations. We assume a binary
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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.</p>
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<br>
<center>
<center>
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<img src="https://static.igem.org/mediawiki/2013/9/96/Timer%2Bsumo.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-left:30px;margin-right:30px;float:left;display:inline-block;"> 
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<h2 align="center">Parameters</h2>
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<br>
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<p>
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{| align="center" border="1"
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|'''Parameter'''
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|'''Value'''
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|'''Description'''
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|'''Units'''
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|'''Reference'''
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|-
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| c<sub>a</sub>
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|1020
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|Translation rate per amino acid
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|min<sup>-1</sup>#<sub>a</sub><sup>-1</sup>
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| [[Team:TUDelft/Modeling_References|[7]]]
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|-
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| c<sub>T7</sub>
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|4.16
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|Maximum transcription rate of T7
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|#m/min
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| [[Team:TUDelft/Modeling_References|[2]]]
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|-
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| c<sub>ptet</sub>
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|2.79
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|Maximum transcription rate of Ptet
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|#m/min
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| [[Team:TUDelft/Modeling_References|[4]]]
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|-
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| c<sub>ci</sub>
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|1.79
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|Maximum transcription rate of Pci
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|#m/min
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| [[Team:TUDelft/Modeling_References|[3]]]
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|-
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| d<sub>mRNA</sub>
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|0.231
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|Degradation rate of mRNA
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|min<sup>-1</sup>
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| [[Team:TUDelft/Modeling_References|[8]]]
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|-
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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>
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| [[Team:TUDelft/Modeling_References|[9]]]
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|-
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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>
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| [[Team:TUDelft/Modeling_References|[9]]]
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|-
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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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|-
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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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|  -
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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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|  -
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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
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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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|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
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|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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|}
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</p>
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<b><font color="#330000" size="3">Timer</font></b>
 
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<p align="justify" margin: 20px >The most important aspect here is the modeling of the ‘time delay’: What is the difference in time between inducing and the output. In our case we have two outputs, a small delay must also be present between those two.
 
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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>
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At the moment only one output is currently modeled, the ULP-1 protease.  Results of this simulation are shown in Figure 1, here the time delay is about …  minutes. Next to add is the interaction with the peptide tagged with SUMO and the ULP-1 protease. The second output will be added later (the kill switch cassette).  
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<p align="justify">
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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.  
</p>
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<b><font color="#330000" size="3">SUMO fusion</font></b>  
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<center>
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<p align="justify" margin: 20px >The peptide is expressed with a SUMO tag added to it, expressing the protease will cleave of the SUMO. It is important to accurately know this cleavage rate in order to describe the rate of ‘free’ peptide production.
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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>
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</center>
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<h2 align="center">Discussion</h2>
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<b><font color="#330000" size="3">Kill switch</font></b>  
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<p align="justify">
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<p align="justify" margin: 20px >
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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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The kill switch contains two important parts the expression of holin and the antiholin. These two are important tuning parameters to make the system stable and robust. It will be essential to make sure that the ‘free’ peptide reaches a steady state before lysis of the cell. Making sure of this yields the most efficient system, lysis before the cleavage is done yields less active peptides. The tuning parameters will be the respective RBS and the const. promoter, a thorough sensitivity analysis will be performed on this model to derive the optimal conditions and robustness.  
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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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