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Genetics Model

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, and Glycolate Oxidase, and Malate Synthase were placed in sequence on Backbone 2, Plasmid 2.

Plasmid 1

Repressed System

Sir Richard Henhathel's Activated System

Plasmid 1 uses an AraC and pBAD promoter to regulate 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 it conformation so that transcription can occur [bmcsys]. 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 team in 2012. We assumed fast-equilibrium hypothesis on the formation of the dimer and that there is essentially a constant pool of arabinose in the environment. We can also streamline the binding of the two arabinose 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 the frequent assumption used literature 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

Plasmid 2

Repressed System

Activated System

Plasmid 2 uses a LacI and pTrc promoter is its backbone, which is requires a slightly different model structure from the other promoter. The transcription factor constitutively expressed by the LacI sequence creates a homotetramer and binds to the pTrc sequence repressing transcription of the Reductase, Dehydrogenase, Oxidase, and Synthase genes. We used a similar expression equation for this protein to the repressor protein in plasmid 1. However when IPTG, a lactose analog, is added to the cells, two of these molecule binds to the LacI protein causing it to change conformation and fall off the promoter. This then allows RNA polymerase to bind and start transcription. We used the same assumption as in plasmid 1, grouping the transcription and translation rate into one rate parameter, which simplified to the system on the right. We also grouped the binding of 2 IPTG to the LacI tetramer into one reaction instead of two separate events. Finally, since we are uncertain about the ordering of binding or the rate parameters of the formation of the LacI tetramer, we kept it with separate rate parameter for each subunit binding. This was important to include as the tetramer is the molecule that actually represses the genes. The last thing to note is that for there to be a functional Glycolaldehyde Reductase protein it needs two copies of itself to dimerize. This explains the factor multiplying its transcription rate.

Model Equations: