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Team:KULeuven/Modeling
From 2011.igem.org
Modeling Overview
1. Description of the whole system
To 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 Simbiology. A graphical representation of the model was build in the block diagram editor. Afterwards reaction equations and parameters were added to mathematically describe the biological system. For the reactions, a PDF with ordinary differential equations (ODE) is created. There are in total three different kinetic equations we used in the model: Hill equation, Mass equation, Assimiliation reaction. For the parameters, a PDF with parameter values is given below. Also for every subsystem, there are PDF’s with ODE’s. However the equations and parameters used for the full model, should be the most accurate.
2. Full Model
There are in total 5 different kinetic equations we used in the model Transcription equation For most promoters, hill kinetics is used, it is a way of quantitatively describing cooperative binding processes, it was developed for hemoglobin in 1913. A Hill coefficient (n) is a measure for the cooperativity. Translation equation RNA degradation Protein degration Assimiliation
3. Simulation tests
Simulations 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 second
4. Sensitivity Analysis and parameter scan
In our works, sensitivity analysis (SA) is used to examine how the activity of the gene expression in the output of each model can be attributed to different kinetic parameters in the inputs of the model. We can also use this technique to determine the effects of changing variable in the models. The results of sensitivity analysis for each model are shown in subsystem pages.In the model of cell death, we do the simulation test with each parameter changing within the certain range with the value incremented by the certain interval.
5. Kinetic Constants
Kinetic parameters Reference
