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A Kinetic Model in MATLAB

The creation of our electrochemical sensor presented us with an interesting question: How fast will it be? Instead of trying many timecourses in the lab we turned to modelling to give us an answer. We have created a kinetic model for one of our systems, the uidA system, to give us an estimate of the time needed to observe a result.

How did we build it?

Using the SimBiology toolbox for MATLAB we created a framework of the electrochemical reporter system. We started at the genetic level, modelling transcription, translation, and the enzyme catalysis. We also included the transport of the substrate into the cell and the diffusion of the product out of the cell. The degradation reactions for the RNA transcript and the enzyme were also included. The reaction scheme is shown below in figure 1.

Figure 1: Diagrammatic representation of the reactions involved in converting the PNPG substrate into the electrochemical analyte PNP. This was created in the SimBiology toolbox for MATLAB

After creating the basic framework for the model we needed to create mathematical equations for each reaction with appropriate rate constants. These equations and the corresponding values are shown below in tables 1 and 2.

Table 1: Mathematical representation of electrochemical reporter gene expression and the subsequent production of the electrochemical analyte. Constants are described in Table 2.
Table 2: Values assigned to kinetic parameters described in Table 1.

What did it show?

Before running the model we needed to decide what an appropriate endpoint would be. As we were trying to determine how quickly we could get a result we chose 2µM as our endpoint. This was chosen because initial electrochemical testing of PNP showed strong responses at concentrations as low as this. With our endpoint chosen the model was run and the data is shown below in figure 2.

Figure 2: PNP produced by a cell expressing uidA according to our mathematical model. The 2µM endpoint is reached in just over 4 minutes.

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