1. Description of the whole systemTo predict and optimize the behaviour of E.D. Frosti, we constructed a model to mathematical describe the biological system. The system can be divided into three subsystems, representing the freeze, antifreeze and cell death mechanism of the bacterial cell. Lactose will induce the freeze system, resulting in the production of the ice nucleating protein (INP). In addition, lactose will repress the antifreeze system, preventing the formation of the antifreeze protein (AFP). On the other hand, L-arabinose is the inducing compound of the antifreeze system and the repressing compound of the freeze system. Upon application in the environment, a cell death mechanism will kill the cells when low temperatures are applied. We designed one model for the whole system and 3 models for 3 subsystems. The 3 subsystems are antifreeze, freeze and cell death. For more information about these 3 subsystems, we refer to the extended project description and the 3 modelling pages: freeze, antifreeze and cell death.
To make predictions for the E.D. Frosti system, a structured segregated model is designed in the MATLAB Simbiology Toolbox . The kinetic actions (transcription, translation, complexation, ...) that take place in the subsystems can be described by Ordinary Differential Equations (ODEs) like Mass-Action laws, Hill Kinetic laws,  and so on. An extensive search for parameters involved in these ODEs has resulted in the discovery of almost all necessary quantities for the simulations. To summarize the model, we made a PDF-file containing all the ODEs involved in modeling the subsystem, and a file with a clear overview of the used parameters .
2. Full Model
3. Simulation testsSimulations with different initial amounts of lactose and arabinose were done to check the efficiency of the dual inhibition system. When both arabinose and lactose are present, AFP production as well as INP production should be inhibited. However, the results reveal that there is no inhibition of AFP when the concentration of lactose and arabinose are both set to 1. The production rates of AFP and CeaB are much higher than that of INP formation (Figure 1). The main reason for the difference in protein production is the formation of LuxR-AHL complex, which is a fast reaction compared to other reactions in the system. The LuxR-AHL complex stimulates AFP production and inhibits INP production. Therefore, the rate of AFP production is much higher than the rate of INP production. In addition, the inhibition of AFP production is much lower than the inhibition of INP production.
The dual inhibition system can be improved by further parameter optimization or structural system changes based on simulations by the model. At the moment, this problem has no effect on the proper working of the E.D. Frosti system, which is the production of AFP or INP when one stimulus is present. We never want to create AFP and INP at the same time.
Figure 1: amount of lactose-arabinose 1-1, huge difference between production of AFP and INP
Figure 2: amount of lactose-arabinose 100-1 after 100 seconds