Model's Assumption

The effect of the endogenous Kdp system of E.coli was neglected.

In our engineered E.coli, it contains the inserted plasmid of PKdpF plus green fluorescence protein generator (BBa_E0240) in pSB3K3 backbone as well as the endogenous Kdp operon, and both operons have the same promoter, PKdpF. As a matter of fact, titration by the endogenous kdp operon of the transcription inducer, phosphorylated KdpE which binds to PKdpF was expected initially. And the titration of phosphorylated KdpE is anticipated to lower the expression of GFP. However, when the DNA copy number of both endogenous and the inserted operons were determined, it was found that the number of endogenous kdp operon is 10 times smaller than that of the inserted one:

This implied that the number of endogenous promoter PKdpF is ten times smaller than that of the inserted operon and accounts only 8.33% of the total number of promoter PKdpF in the engineered E.coli. Therefore, the titration effect of phosphorylated KdpE becomes insignificant. As a result, the effect of endogenous Kdp system was negligible.

Level of KdpD, KdpE and KdpF were assumed to be constant

In accordance to [Kremling A. 04], in the potassium ions concentration range which we were studying, from 0mM to 0.02 mM, the fluctuation of the concentration KdpF as well as KdpD and KdpE was only within 10 µM and 3 µM respectively. Due to the small fluctuation range compared to the gene expression of GFP reporter, it was reasonable to assume the concentration of KdpD, KdpE and KdpF to be constant in the model.

It was assumed that the initial concentration of mRNA for GFP, immature GFP and mature GFP equal to zero.

It was assumed that all reactions below were in steady state such that:

Equations of the Model:

Phosphorylation of KdpD: