Mathematical modeling and experimental research are relatively complementary to each other. Biology have gradually became a qualitative field of research. In our study, we made respectively three models to quantify the peptide accumulation with S. aureus proliferation under the four types of Agr system, to predict the gene expression pattern of the four types of Agr system, and to simulate the gene expression of AimR-AimP system. To help readers understand our modeling theory, we also wrote attentions for all the modeling process. At last, we expect to improve mathematical modeling to make it more convenient to use.

Introduction:

In order to quantify the peptide concentration accumulation with S. aureus proliferation under different conditions, we regarded the each S. aureus as isolated unit. This prediction will be incorporated into the equation to calculate（simulate） the total protein amount at the community level.

Figure 1. The agr-Quorum Sensing System of S.aureus

The Agr-QS system is a quorum-sensing system in S. aureus and typical for Gram-positive bacteria. As shown in figure 1, when the transcription factor from AgrA phosphorylation binds with P2 promoter, agrB and agrD were continuously promoted to express AgrB and AgrD respectively[2]. In the Agr system, the protein of interest production process is briefly shown as below：

Modeling:

Our study is based on the quorum-sensing system of Gram-positive bacteria. In order to model the biological law of S. aureus, the prioritized task is to quantify the peptide accumulation with S. aureus proliferation under the four types of Agr system.

Assumption:

1. P2 promoter is always in large quantity and that its binding to the transcription factor from AgrA phosphorylation happens on a faster time scale to promote the genes downstream to express.

2. The product never binds with the free enzyme.

3. The conversion between enzyme-substrate and enzyme-product is much faster than that of association and dissociation events.

We tried to use Michaelis-Mentin kinetics equation[3] to predict the peptide production rate. We made several modifications on the equation to accommodate the transcriptional regulatory mode of the P2 promoter.

Attention:

1. [P2:F], [mRNA] and [P] represent the concentrations of P2 promoter and the transcription factor from AgrA phosphorylation, mRNA and product protein respectively.

2. The rate K is not just a simple constant and is given as the Hill function in the equations.

The remaining symbols are defined in Table 1.

Table 1 Definition of symbols used in the Michaelis-Mentin kinetics

Analysis and Results:

Using the model we established with MATLAB, we quantified the peptide concentration accumulation with bacterial proliferation under different type of agr systems as shown in Figure 2. As it’s shown, the higher of the bacterial flora quantity, the higher expression levels of protein of interest. After a period of time, the peptide concentration was in a platform period.

Figure 2. the peptide concentration accumulation with bacterial proliferation

The advantage of our model with Michaelis-Mentin kinetics equation is that we have not had to directly measure data for all of our enzymes, which is a difficult process. The results of our forecasting model matches well with previous relative researches. In addition, we can make the parameters of the equation much closer to the reality with experiment data.

Reference:
[1].https://2008.igem.org/Team:Cambridge/Modeling
[2] James, E.H., A.M. Edwards, and S. Wigneshweraraj, Transcriptional downregulation of agr expression in Staphylococcus aureus during growth in human serum can be overcome by constitutively active mutant forms of the sensor kinase AgrC. FEMS Microbiol Lett, 2013. 349(2): p. 153-62
[3]. https://2015.igem.org/Team:Oxford/Modeling