Team:Calgary/Modelling/MC/Results

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Membrane Computing Modelling

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Differential Equation Modelling

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For complete results, please review our paper (A Model of the Quorum Sensing System in Genetically Engineered E.Coli Using Membrane Computing).






Figure 1: Distribution of AI-2 Molecules between newborn cells from parent cells. On X-axis, time steps are aligned, and on Y-axis number of AI-2 molecules are placed. This graph shows that the simulation is ran for 3000 time steps and started with one cell (blue line) and other cells are generated over time by divisions (red, green, and yellow lines). This graph demonstrates that number of AI-2 molecules changes logarithmically between divisions, and suddenly drops at each division.




Figure 2: As concentration of AI2 is high in the environment, the LuxPQ complex detects the signal and switches off the production of GFP proteins. As seen in the figure, at the beginning of the simulation there was a massive production of GFP protein however as time evolves this production decreases and existing GFPs degrades.





Figure 3: Comparison of production and degradation of GFP proteins in parent cells and newborn cells. The First graph shows that the number of AI-2 molecules in the environment is continuously increasing over the 7000 steps. The second graph shows the number of GFP proteins within one of the parent cells (indicated by ”P”) in the simulation. This cell keeps producing GFP proteins up to the division point. After that the newborn daughter cell (indicated by ”D”) continues the production of GFPs, however it does not last very long as this cell reaches to the point (indicated by red line) that recognizes the high concentration of AI-2 in the environment and cancel the production of GFPs. After this point, the degradations of GFPs occur. Graph 3 demonstrates the number of GFP proteins in one of the newborn cells in the simulation and implies that the production of GFP proteins occurs once (indicated by black line) in this cell. However after very soon the cell changes its biological cascade and hence the inherited GFP proteins and the produced one are degraded. The reason for observing this behavior is since the concentration of AI-2 molecules in the environment is high by the birth time of daughter cells, they switches to the second biological cascade faster than their parent cells that keep producing GFPs for more than 2000 time steps.





Figure 4: AI-2 Binding to the LuxP-LuxQ Protein Complex. Each column represents one of twenty E.coli bacteria. The state of the modelled bacteria over a period of 50 simulated time steps is depicted along the vertical axis. The color of each cell indicates the binding degree between AI-2 and the LuxP-Q complex. The color spectrum spans from red (no binding) over white to blue (complete binding). As time progresses an increasing amount of AI-2 is produced by LuxS and gets bound to the LuxPQ complex.





Figure 5: Distributions of Applied Rules. For each rule r0 to r16 the number of its application is charted. Charts like this help to understand which rules, i.e. which interactions, are more or less important within the simulated system or how changes in the rates of reactions affect the rule distributions.





Figure 6: This figure compares the change of concentration of four different objects namely AI-2, GFP, LuxU.p, and LuxO.p within one of the simulated cells to the change of concentration of AI-2 molecules in the environment. First graph demonstrates the change of concentration of AI-2 molecules within the cell. At the be- ginning, number of AI-2s is continuously increasing and these molecules are accumulated in the cell, without any transportation to the environment. However, after around 2500 steps the cell reaches to the point that it starts to transport AI-2 molecules to the environment (indicated by yellow line). As it could be seen in graph 5 in this figure, the number of AI-2 molecules are exponentially increasing in the environment after some steps between 2000 and 3000 (indicated by red arrow in the figure). After the massive increase in the concentration of AI-2s in the environment, the LuxPQ complex of the cell (which was adding phosphate groups to the cytoplasmic protein, LuxU) changes its behavior from being kinase to being phosphatase. Therefore, after this point, this complex starts removing phosphate groups from LuxU. This circumstance could be observed in graph 2, where the number of LuxU.p increases exponentially at the beginning of the simulation, and then this number drops suddenly at some step around 3000 (shown by green line), as the LuxPQ complex start dephosphorylating these proteins. When LuxU.p is dephosphorylated, the LuxO.p complex will be degraded by housekeeping phosphates as shown in the third graph. Without the LuxO.p complex, GFP proteins could not be produced anymore, and therefore their number decreases as they start to be degraded some step after 3000 (shown by black line in graph 5). These proteins will be completely degraded over the time, and that is the reason why the cell turn dark after a while.