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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 | [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 the same as 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] |
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
