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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.
Parameters
| Parameter | Value | Description | Units | Reference |
| ca | 1020 | Translation rate per amino acid | min-1#a-1 | [1] |
| cpTet | 1.5e-7 | maximum transcription rate (M/min) | [2] | |
| cpλ | 1.5e-7 | maximum transcription rate (M/min) | estimate | |
| K50IPTG | 1.3e-6 | dissociation constant (M) | [3] | |
| K50LacI | 800e-9 | dissociation constant (M) | [3] | |
| K50TetR | 179e-12 | dissociation constant (M) | [3] | |
| K50CI | 8e-12 | dissociation constant (M) | [3] | |
| nIPTG | 2 | Hills coefficient | [3] | |
| nLacI | 2 | Hills coefficient | [3] | |
| nTetR | 3 | Hills coefficient | [3] | |
| nCI | 2 | Hills coefficient | [3] | |
| dLacI | 0.1386 | degradation rate (M/min) | [3] | |
| dTetR | 0.1386 | degradation rate (M/min) | [3] | |
| dCI | 0.042 | degradation rate (M/min) | [3] | |
| dRFP | 6.3e-3 | degradation rate (M/min) | [3] | |
| dGFP | 6.3e-3 | degradation rate (M/min) | [3] | |
| dmRNA | 0.029 | degradation rate (M/min) | [4] | |
| α | 16 - 57 | translation rate (translations/min/mRNA), depends on growth rate (a default value of 30 is used) | [5] | |
| kIPTG | 0.92 | rate constant for IPTG diffusion into cell | [6] |
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
Figure 2: Simulation Results
