1.Introduction
According to our design of E.coli detector，we can know the mechanism of com system in E.coli detector is as the below : when the CSP ,which is secreted by Streptococcus mutans, reaches a certain threshold, it will bind to the comD of the engineered bacteria E.coli BL21, then comE will be phosphorylated. Once the comE phosphorylated ,the inducible promoter nlmC will be turned on and the downstream gene green fluorescent protein will be expressed . So,If the reaction can proceed to comE phosphorylation, the subsequent reaction will proceed smoothly. Therefore, whether comE can be successfully phosphorylated is the key of our project.For this reason,a model need to established for analysis.
2.Model building
Use the mathematical model to roughly simulate the entire experimental process, and then compare whether the simulation results of the model are consistent with the experimental results.
Use the law of mass action to describe the first step of the combined reaction of CSP and ComD：
Due to thermodynamic reasons, it should be a two-way reversible reaction in theory：
But because the reverse reaction rate is too small, it can be ignored.
Next, describe the changes from ComDCSP to ComE~P. X is the amount of various substances,β，α，γ，ρ，K, , are the rate constants, is the maximum cell synthesis rate, is the cell volume, is the local cell density, and is the phosphoric acid. The transformation rate is established as follows.
3. Parameter
From the theoretical model above , it can be known that CSP can successfully react with ComD and then phosphorylate ComE. So the subsequent reaction will proceed smoothly. Is this theoretical model work? The experiments need to design and test.
4.Test Results
The result is showed in Fig.1.By analyzing the changes of fluorescence intensity and CSP concentration with OD600=0.8, it can be seen that the fluorescence intensity increases with the increase of CSP concentration, and the fluorescence intensity increases faster after 12 hours of culture, indicating that the system needs 12 hours to express the green fluorescent protein.
Fig.1 The test result of model
5. Comprehensive evaluation
From the experimental results, it can be seen that the experimental process has completed the reaction, that is, ComE is successfully phosphorylated, so that the subsequent reaction can proceed smoothly. The agreement between the model and the experimental results further illustrates the accuracy of the experimental process design. It can be regarded as a relatively complete model and experimental design.
6.Reference
- Zhang Xiaocui. Dynamics of a constructed Bacterial quorum sensing system [D]. Xiamen University,2018.
- Wang Ru. Qualitative research on the discontinuous model of signal molecular concentration regulation by quorum sensing [D].Xi 'an University of Science and Technology,2019