Team:Exeter/Modelling

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Exeter | ERASE

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Project Design

Modelling

Biological modelling has been used for a variety of purposes. We sought to build a model which would help us to analyse and debug our biological design . Furthermore, we wanted a method of visualising our bacterium. Specifically, our aims were that:

• the model should inform the biological design • the model should inform the choice of experiments • the model should be receptive to empirical observations • the model should help explain how our biological system works Many iGEM teams have modelled their bacteria at the biochemical level using systems of differential equations. We started in the same manner, and then built a stochastic model on top of this to make the simulation more realistic. We then created a model of the diffusion of TNT across the cell membrane. Another model was created for the growth of the bacteria and the inclusion of a kill switch. Finally, we tried to bring these models together to create as accurate a model of our system as possible. The Biochemical Level We reasoned that the primary determinant of TNT degradation within the cell would be the activity of the introduced enzyme, either XenB or NemA. The degradation of the TNT by these enzymes can be modelled by Michaelis-Menten kinetics. A simple set of ordinary differential equations which would describe the system then would be: 𝑑𝐶𝑒𝑙𝑙𝑑𝑡=𝑔𝐶𝑒𝑙𝑙−𝑑𝑇𝑁𝑇 𝑑[𝑇𝑁𝑇]𝑑𝑡= −𝑘𝑐𝑎𝑡𝑇𝑁𝑇[𝐶𝑒𝑙𝑙]𝐾𝑚+ 𝑇𝑁𝑇 where: ‘[Cell]’ is the number of cells in the colony ‘[TNT]’ is the number of TNT molecules ‘g’ is the growth rate of the cells ‘d’ is the rate at which TNT kills the cells ‘kcat’, ‘km’ are arbitrary constants of the Michaelis-Menten equations Data for the Kcat and Km of XenB and NemA was not available, and so we initially ran the simulation using different arbitrary values. These yielded different distinct cases depending on the initial conditions. When the TNT was started at 20, if the amount of cells was started at 5, then the cells would ‘die out’. If the amount of cells was started at 10 for the same amount of TNT, though, the cells would increase indefinitely and the amount of TNT would be reduced to 0.

Exeter | ERASE