Equations

Here we define the equations and parameters that describe the novel genetic toggle switch that works at the translational level. The switch allows mutually exclusive expression of either green fluorescent protein (GFP) or cyan fluorescent protein (CFP). The synthetic biological circuit is represented in Fig. 1.

Figure 1: Translation of DNA to mRNA.

We can regulate the system when we add galactose or copper. Galactose will bind to the GAL promoter and activate the transcription of M1, allowing the system to express GFP. If we add copper instead of galactose, it will bind to the CUP1 promoter, the transcription of M2 will be activated, leading to the expression of CFP.

From Fig 1 it can be seen that there is mutual inhibition of the translation of the two mRNAs. That is because the translated proteins can bind to the corresponding stem loop structures on the opposing construct.

For our initial conditions, we began with more GFP than CFP and thus the production of CFP was inhibited. When copper was added to the system, the rate of CFP production will increase and decrease for GFP. Eventually, we will see more CFP than GFP so the system will have switched. Once we have more CFP than GFP, galactose can then be added to switch back to an expression of GFP.

The N-Peptide and GFP strand has two MS2-Stem loops as we discovered that one single loop would not inhibit the production of CFP enough to achieve our switch.

Fig. 1 shows the mutual inhibition of the translation of the two mRNAs by the proteins binding to the corresponding stem loop structures on the opposing construct.

This means that if GFP is being expressed, the proteins will bind onto the M2 stem loops, thus preventing M2 from producing CFP. CFP exhibits the same behaviour, inhibiting the production of GFP.

Equation Terms

Each equation is composed of three terms: generation, degradation, and base rate

Generation: There are two forms of the generation term: one for the mRNAs and one for the proteins (GFP and CFP).
For the mRNAs, the generation term is in the form of the Michaelis-Menten equation with Hill coefficients to model the cooperativity of the binding affinities of the stem loops.
For the proteins (GFP and CFP), the Michaelis-Menten equation is modified to take into account the inhibition of one protein on the other. This describes how GFP inhibits the generation of CFP and vice-versa.

Degradation: This term describes the degradation the component within the cell and is a function of the reaction kinetics for the breakdown of the component over time and the dilution that occurs as the cell divides.

Base Rate: This is the concentration of molecules present in the cell when the promoter or inhibitor is not activated.

Equations and Parameters

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