The DNA coding for the 6 enzymes required for breakdown and assimilation of PET was too long to fit on one plasmid. To rectify this and to be able to test smaller subsystems, the PETase and MHETase genes were placed on Backbone 1, Plasmid 1. The Glycolaldehyde Reductase, Glycolaldehyde Dehydrogenase, Glycolate Oxidase, and Malate Synthase were placed in sequence on Backbone 2, Plasmid 2.

Plasmid 1

Plasmid 1 uses an AraC and pBAD promoter to regulate the expression of PETase and MHETase. The transcription factor made from AraC usually binds and represses the pBAD promoter, halting transcription of the plasmid. The inducer, arabinose, can be added to the media, and this molecule binds to the AraC transcription factor on the DNA strand and changes its conformation so that transcription can occur [1]. The reaction scheme on the left explains a more complete mechanism of the transcription/translation of these proteins. The creation of AraC protein is related to a constitutive promoter which we assume enters the system as a constant rate, K. This method was also used by the UC Davis iGEM team in 2012. We assumed a fast-equilibrium hypothesis on the formation of the dimer and an essentially constant pool of arabinose in the environment. We can also streamline the binding of the two arabinose inducers to the AraC dimer into one reaction determined by the rate parameters k3+ and k3-. Since the amount of RNA polymerase does not change relative to these molecules, and since the frequent assumption used in literature is to group the transcription and translation rate into one overall rate of protein production, we simplify the system further. From these assumptions, we can simplify the system down into the system shown on the right.

Model Equations:

https://bmcsystbiol.biomedcentral.com/articles/10.1186/1752-0509-5-111 useful description and numbers for AraC promoter

Simulations:

Table 1. List of values used in simulation parameters

Figure 1 maps out the expression level of the free repressor protein AraC and Plasmid 1 genes, PETase and MHETase over 12 hours. The population of cells in the simulation was 1e+08. While free AraC protein, which would normally suppress expression, is relatively low there is a high expression of the objective proteins. The MHETase and PETase plots both follow the same trend, although, MHETase does decay slower than PETase and also reaches a higher maximum concentration.

Figure 1. Expression of AraC promoter in presence of Arabinose in Plasmid 1

Sensitivity Analysis:

In Table 1., there are three values that say they are estimated in the calculated column. This is due to the lack of comprehensive material on them, and that these values create realistic behavior of the system. There is a small range in each value where the system remains stable and biologically relevant, so these values were pulled from that range. The behavior of the system throughout the range is consistent with only slight variation on amounts.

References:

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[8] K. Martin, L. Huo, and R.Schleif. “The DNA Loop model for ara repression: AraC Protein occupies the proposed loop sites in vivo and repression-negative mutations lie in these same sites.” In USA Proceedings National Academy of Science. vol. 82, June 1986, pp. 3654-3658. [Available: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC323581/pdf/pnas00315-0095.pdf]
[9] “Part: pSB1C3.”iGEM Registry of Standard Biological Parts. Sept 2008. [Online]. http://parts.igem.org/Part:pSB1C3