Team:Calgary/Modelling/Results

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Membrane Computing Modelling

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Differential Equation Modelling

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The following is the graph produced by our differential equation based model under five different levels of LuxPQ (1, 10, 100, 1000, 10000):


Figure 1: The rate of GFP degradation for different LuxPQ levels with respect to time.

Green fluorescent protein (GFP) degradation rate remain relatively constant from one LuxPQ to 100 LuxPQ. This may be due to the amplifying effect of LuxPQ phosphatase activity. Since one LuxPQ have the potential to de-phosphorylate large amount of LuxU, having more LuxPQ around does not necessarily translate into faster de-phosphorylation of LuxU. Beyond 1,000 LuxPQ, however, the GFP degradation rate starts to fall. The reason behind this phenomenon could be that because the binding of AI-2 to LuxPQ is not 100%, not all of 1,000 LuxPQ are bound to 1,000 AI-2 molecules, leading to slower de-phosphorylation of LuxU. Having a slower de-phosphorylation rate of LuxU means that there are more than enough LuxU:pi and LuxO:pi to initiate the production of GFP, and therefore the degradation rate of GFP is slow or remain constant.

The following is the graph produced by our differential equation based model under five different levels of AI-2 (1, 10, 100, 1000, 10000):


Figure 2. The rate of GFP degradation for different AI-2 levels with respect to time. The LuxPQ level was kept at 100 because as shown in figure 1, LuxPQ at 1, 10, and 100 seemed to produce a consistent rate of GFP degradation.

At AI-2 levels of 1 and 10, the degradation rate of GFP remain constant due to lack of [AI-2:LuxPQ] complex to carry out the de-phosphorylation of LuxU. At 100 AI-2 molecules, we start to see some degradation of GFP due to increase in the [AI-2:LuxPQ] phosphotase. However, as the binding of AI-2 to LuxPQ is not 100%, not all of 100 AI-2 are bound to LuxPQ molecules, and therefore the GFP degradation does not reach 0. Finally, beyond AI-2 levels of 1000, we see a significant decrease in GFP, almost reaching 0. This phenomenon possibly suggests that the AI-2 level have to be at least a fold higher than the level of LuxPQ in order to see a significant difference between system on and off.