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Timer Plus Sumo
From 2013.igem.org
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, this is the variable s.
Parameters
Transcription rates of T7
For the T7 promoter an transcription rate of 50 bp/sec [2] converted to per minute using an average
base pair length of 720 bp:
The promoter strengths of cI and Tet are taken as a factor of T7. PcI is found to be approximatly 0.43 times the strength of T7 [1] and Ptet is approximatly 2.79. [2].
Turnover rate Ulp
The parameter kcUlp is the turnover rate. It can be calculated based on in vitro specifications [5]. It is
stated that 10-5 mg of Ulp1 cleaves 85% of 100 μg of SUMO combined with GFP in 1 hr. Furthermore
the molecular weight of Ulp1 is 28 kDa and the molecular weight of SUMO is 11 kDa and the molecular
weight of GFP is 27 kDa.
Simulation
Initial Conditions
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.
Results
