Modelling

Quorum Sensing

Quorum sensing mechanism was used to form biofilm of E.coli strain Top10, BL21 and DH5α that used in labwork. We have modeled growth curve of E.coli to determine when we must move E.coli colony from inoculum flask to reaction flask that contains PET. Besides growth curve, we have modeled some coupled ODEs to model growth curve, AI-2 production that affects signaling, and biofilm formation. AI-2 production in E.coli was used as colony signal of quorum sensing until it reaches specific points and finally form biofilm that affected by its quorum sensing by AI-2 signaling. We use Hill kinetics function as our approach to model AI-2 production and biofilm formation. Based on model that we built and confirmation from wetlab team, we found inoculation time until E.coli reaches quorum sensing condition is 10 hours. Not only time that necessary for quorum sensing condition, we found from model, parameter that affect significantly to biofilm formation was specific growth rate (μ) and initial amount of bacteria that will be inoculated.

Here ODEs that we used :

Growth curve

AI-2 Production

Biofilm Formation

PETase Transcription

After we have inoculated bacteria until biofilm was formed, process that we focused is PETase production in bacterium body, or usually called transcription. The illustration of transcription of PETase is given below.

We define M(t) and C(t) as functions versus time (in further discussions will be just written as M and C). Before going to differential equations that illustrate rate of mRNA (symbolized as M) and PETase production (symbolized by C), we made several assumptions for the model:

1. No inclusion body is produced during the transcription. Consecutively, there’s also no TetR produced during the transcription.

2. Initally, there are 0.05 μM of mRNA and zero amount of PETase.

There, the differential equation of each parameter obtained through the analysis of mass balance are We choose αm = 0.011 μmin-1, γm= 0.009 μmin-1, γC= 0.04 μmin-1. Each of the differential equation is solved analytically using the MATLAB. Through the graph, we can see that at the steady state, the rate of production is 1.220 mg/(liter∙h) which attained at 600/60 = 10 h. This datum will be used as the boundary condition in mass transfer modelling of PETase through the biofilm.

Rate of PET Degradation with Biofilm

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