In order to predict the protein expression rate and amount under different nisin concentrations, we treated the bacteria in isolation, which means at the single cell level. This prediction will be incorporated into the equation to calculate the total protein amount at the community level.
In the NICE system, the PnisZ or PnisA promoter controlled gene expression rate depends on the concentration of nisin. We try to predict the gene expression rate under different nisin concentrations. In one research, the quantitative relationship between the extracellular concentrations of nisin and the efficiency of PnisZ were measured (Guo et al., 2013). We retrieved the data (Table 1) to get a fitting equation, which will be used in the protein production model.
Table 1 Data used in the fitting
The log-sigmoid function was used to fit, because the nisin receptors on the cell membrane is limited, and this function value will not continue to increase as x reach to a certain value. This is suit for the characteristics of our promoter.
In the NICE system, the protein of interest production process is shown as below：
We tried to use Michaelis-Mentin kinetics to predict the protein production rate. We made several modifications on the equation to accommodate the transcriptional regulatory mode of the PnisZ promoter.
The Michaelis-Mentin kinetics equations:
Attention：We replaced [PnisZ] in the Michaelis-Mentin kinetics by F(X) that we obtain by fitting, and we try to transform this typical math model to describe the direct proportion relationship between [PnisZ] and the concentrate of extracellular nisin.
[PnisZ], [mRNA] and [P] represent the concentrations of PnisZ, mRNA and product protein respectively. Coefficient k was got by the experimental result.
The remaining symbols are defined in Table 2.
Table 2 Definition of symbols used in the Michaelis-Mentin kinetics
Analysis and Results
Using the model we established, we predict the protein production rate under different nisin concentrations as shown in Figureure 1.1. The higher concentrations of nisin will lead to higher expression levels of protein of interest.
Figure 1.1 Simulated protein production levels under different nisin conditions
To test whether our model can be applied to the real situation, we compared the expression levels of mCherry proteins and the simulated results. As shown in Figureure 1.2, the two curves are well matched.
Figure 1.2 The fluorescence intensity levels produced by mCherry proteins along with the simulated protein levels under different concentrations of nisin.
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