OVERVIEW
Modeling is to use mathematical tools to simulate and predict the system. The experiment is restricted by time and cost, which may not be comprehensive. Modeling can solve this problem by establishing mathematical system and improve the whole project. Also, the results of modeling can guide the experiment in turn, and provide clues for the selection of each material in the experiment. Last but not least, modeling can also optimize the production process when satisfying some assumptions.
PURPOSE
We inserted a newly designed quorum sensing system into E. coli and associated this system with major production metabolic pathways so that E. coli growth can be regulated by p-coumaric acid.
QUORUM SENSING
Quorum sensing process
First, lux promoter have basic expression quantity, this will lead to express a small quantity of RpaI, which make p-coumaroyl-CoA (The product of the conversion of p-coumaric acid) into p-coumaroyl-HSL. P-coumaroyl-HSL will combine with RpaR with a constant expression to form a complex, promoting lux promoter expression. Lux promoter controls a toxic protein that stops cells from dividing.
Model hypothesis
1.The lipid solubility of the hyperserine lactone is very good, so it moves in and out of the cell membrane very quickly.
2.The bacteria are evenly distributed in the fermenter.
The ODE model
Because we expect to control the yield of p-coumaric acid by controlling the density of E. coli, our signal factors should be linked to p-coumaric acid. Therefore, based on the quorum sensing model of our team in 2019, we modified and established our own model according to the actual situation.
In the above expression, the meanings of relevant variables are as follows:
The meaning and values of the parameters in the model are as follows:
[1]Marc Weber, Javier Buceta. Dynamics of the quorum sensing switch: stochastic and non-stationary effects. 2013, 7(1):6.
CELL GROWTH
We selected common cell growth models and finally concluded that the Logistic model might be the best suitable for our cell growth experiment. Because we wished that our cell growth model can well show the changes of the population density of E. coli and S. cerevisiae under co-culture conditions, we modified the Logistic model based on our experiment.
In the Logistic model, the ODE model of the growth rate of cells in the growth stage is as follows:
In the expression, X is the population density of E. coli and Y is the population density of S. cerevisiae. The values of relevant parameters are shown in the following table: E. coli and S. cerevisiae were added 1:1:
We get the following image:
E. coli and S. cerevisiae were added 10:1:
We get the following image：
E. coli and S. cerevisiae were added 1:10:
We get the following image：
MOLECULAR TRANSMEMBRANE
In our design, Molecular transmembrane would affect the response efficiency of population density changes in E. coli and S. cerevisiae. Therefore, we thought about it. However, due to the COVID-19, we did not do relevant experiments and further analysis and discussion. Based on some common sense knowledge, we briefly studied the effects of p-coumaric acid and galactose on the transmembrane effects.
The transmembrane mode of p-coumaric acid was passive diffusion, we built the following model:
The transmembrane mode of galactose was active transfer, we built the following model:
In the above expression, the meanings of relevant variables are as follows:
THE OCCUPATION OF SPACE
In the whole co-culture system, With the growth of E. coli and S. cerevisiae, two strains were deposited in the culture space. This results in changes in the growth rates of E. coli and S. cerevisiae. So, in order to make our results more accurate, we took those changes into consideration.
We assume that the fermentation tank is used as the culture space of the co-culture system, and the following model can be obtained:
In the above expression, the meanings of relevant variables are as follows:
