Timer Plus Sumo

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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

The parameters used in the specific model are listed below. In particular, the parameters


Transcription rates of T7

For the T7 promoter a transcription rate of 50 bp/sec [2] is converted to per minute using an average base pair length of 720 bp:

Relative promoter strength

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].


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