Use Math to Explain and Simulate!
This year, we constructed two models to simulate the bacteria quorum sensing process and Kill Switch. For the quorum-sensing model, we used the Gillespie algorithm in random simulation to simulate the physiological processes at macro and micro levels. Specifically, we described Acyl-homoserine lactone's concentration accurately by monitoring both production and diffusion, which is first-of-its-kind to reveal details of the process, and developed originally by us. We further improved the model from 19Fudan team to better model the quorum sensing process for various bacteria growing stages. For the stage change caused by the anti-microbial peptide (mcbA), we provided explanations to its observed dynamic stability. For the Kill Switch model, based on the experimental data from 19BNU team, we improved the logistic equation, adjusted the promoter properties according to more suitable literature references, and made sensitivity analysis – and we obtain better and more insightful results.
Model one:Bacteria Quorum Sensing Process
In the first model, we describe the quorum sensing process in three parts. In Model 1.1, we discuss the change of AHL concentration in a single cell. AHL is produced in bacteria and transported to the surrounding environment through free diffusion. Since the number of molecules in a single section is small and random, we adopted Gillespie algorithm to simulate the trend of molecule numbers under the random process. In model 1.2, we followed the discussion in 3.1. To know when the quorum sensing switch is turned on, it is necessary to know polymer concentration formed by AHL and LuxR when AHL concentration is high enough. Our results demonstrate that polymer concentration remains dynamically stable even in a single cell, which guarantees our system's stable operation. In Model 1.3, we discuss the role of antimicrobial peptide circuits. Since the loop will open when the concentration of AHL increases and will close when the concentration is low enough, it forms a dynamic equilibrium. We use a phase diagram to describe this steady state.
1.1 AHL in a cell
In this model, we simulate changes in the number of AHL in a cell. As mentioned above, AHL is generated inside the cell and transported out by free diffusion. In the initial stage, for AHL's concentration outside the bacteria is approximately 0, free diffusion is basically not inhibited and only related to AHL's concentration inside the cell. We believe that the main physiological processes about AHL are as follows:
Firstly,the expression of LuxI and LuxR:
Then,the degradation of LuxI and LuxR:
The production of AHL and its diffusion outside the cell:
Lastly,the combination and dissociationof AHL and LuxR:
