Outline

We are now interested in applying peptide-based quorum-sensing systems from gram-positive bacteria in some new fields, and we would like to demonstrate how to engineer multicellular biological systems that are capable of expressing spatial patterns of gene expression, such as GFP, on a bacterial lawn. Instead of using GFP in our patterns, we use inserted genes that reflect with the number of bacterial to express protein in order to complete a specific function.

Mathematical modeling and experimental research are relatively complementary to each other. Biology have gradually became a qualitative field of research. In the following content, we made three models to quantify the peptide accumulation with bacterial proliferation under the abovementioned types of agr systems to predict the gene expression pattern of different type of agr systems and to simulate the gene expression of AimR-AimP system. To help readers understand our modeling theory, we also wrote notes for all the modeling techniques. At last, we expect to improve mathematical modeling to make it more convenient to use.

Model 1. peptide concentration accumulation model

Introduction:

In order to quantify the peptide concentration accumulation with bacterial proliferation under different conditions, we regarded the bacteria 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. It relies on the signaling peptide AIP (auto-inducing peptide) that is produced by the cell and activating the quorum-sensing system.

Modeling:

In the agr system, the protein of interest production process is shown as below：

We tried to use Michaelis-Mentin kinetics to predict the peptide production rate. We made several modifications on the equation to accommodate the transcriptional regulatory mode of the P2 promoter[1, 2].

Attention:

We replaced [agr] 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 [agr] and bacterial flora quantity stimulus. [agr], [mRNA] and [P] represent the concentrations of agr, mRNA and product protein respectively. Coefficient k was got by the experimental result. 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, 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

Reference:
[1].Guo, T., S. Hu, and J. Kong, Functional analysis and randomization of the nisin-inducible promoter for tuning gene expression in Lactococcus lactis. Current Microbiology, 2013. 66(6): p. 548.
[2].Selinger, D.W., et al., Global RNA Half-Life Analysis in Escherichia coli Reveals Positional Patterns of Transcript Degradation. Genome Research, 2003. 13(2): p. 216.

Model 2. the gene expression model of different type of agr systems

Introduction:

To be surface displayed, proteins should be secreted after translation and then anchored to the cell wall, which is really a long journey. In order to predict the peptide, the gene expression model of different type of agr systems, in this section, we try to simulate the secretion process in bacteria, and to predict the amount of protein can be surface displayed at a given time[3].

Figure 3. the gene expression model of agr system

In fact, in the agr-QS system of Staphylococcus aureus that we are going to model the p2 promoter seems to exhibit a significant increase. In a high-density environment the bacteria will exhibit novel behavior such as virulence or sporulation (both biologically costly but critical and advantageous).

Modeling:

A recursion equation was used to calculate the amount of protein that on the cell wall. The value of was determined by reference (Lin et al., 2016)[4], the definition of symbols are listed in Table 2.

Table 2 Definition of symbols used in the recursion equation

Analysis and Results:

The gene expression of different type of agr systems was shown in figure 2. At the beginning of the experiment, the extracellular signal molecule concentration was always at a fairly low level, and after 0.6 the critical point, the signal molecules began to increase rapidly, and we found that the signal growth trend was delayed but not stopped, and the growth rate of the curves were different due to different type.

Figure 4. the gene expression of different type of agr systems

Reference:
[3].Borrero, J., et al., Use of the usp45 lactococcal secretion signal sequence to drive the secretion and functional expression of enterococcal bacteriocins in Lactococcus lactis. Applied Microbiology & Biotechnology, 2011. 89(1): p. 131.
[4].Lin, J., et al., Construction and characterization of three protein-targeting expression system in Lactobacillus casei. FEMS Microbiol Lett, 2016. 363(7).

Model 3. the gene expression model of AimR-AimP systems

Introduction:

This models, which can predict the gene expression of AimR-AimP systems, is practical for many research. In this model, the genetic circuit describes the biochemical reactions taking place inside the cell(Figure5). The intracellular model describes the fluctuations in concentrations of each substance by modelling each chemical reaction.

Figure 5.the gene expression model of AimR-AimP system

This QS system of AimR-AimP remains to be further studied for potential application. The QS response is quite tightly regulated as expression occurs only once the local bacterial density passes a fixed threshold value, similar unlike a switch.

Modeling:

Let us now consider the complete AimR-AimP system as illustrated in the 5th figure. For the rate equation involving [P], we need to add both contributions from the sender and receiver systems and only take a single decay. In the lab one can "simply" (Biologists clearly agree with this statement) put the sender and receiver to recreate the AimR-AimP system with biobricks[5-6].

Table 3 Definition of symbols used in the recursion equation

Analysis and Results:

As it’s shown, in the early stages of the experiment, extracellular signal molecules increased with time, but soon the signal molecules increased to a bottleneck. Into the late experiment, the signal molecules continue to decrease, and ultimately reach a fairly low level, making the signal molecular curve to form a first increase after the trend.

Figure 6. the gene expression of different type of AimR-AimP systems

Reference:
[5].https://2008.igem.org/Team:Cambridge/Modeling
[6].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