# Team:UCSF/Modeling Results

### From 2012.igem.org

Though we don’t know the exact parameters in the experiments, and sometimes even cannot tune every parameter in reality, the more robust a dynamic system is, the easier the experiments could succeed.

k1 and k2 are more sensitive when they are enlarged than they are reduced.

The result of sensitivity analysis indicates that k1 or k2 should be tuned if we fail to get a steady population ratio of the two strains. But this result leaves us a dilemma in tuning the parameters in reality in experiments, because k_1 and k_2, the maximum growth rates of Escherichia coli (gDM/(Ls)), are the natural characteristics of the cells, which makes this situation intractable. We could tune α and β to get the final steady population ratio we want, but if the system couldn’t even go to a steady ratio, that doesn’t make sense in reality. That’s why a new approach should be proposed.

To test our analytical result and the robustness of this system, we simulated the system in Matlab with different groups of parameters:

Setting the initial values to [0.1, 0.2, 0, 0], [0.1, 0.5, 0, 0], [0.1, 1.0, 0, 0], [0.3, 0.2, 0, 0], [0.3, 0.5, 0, 0], [0.3, 1.0, 0, 0], [0.7, 0.2, 0, 0], [0.7, 0.5, 0, 0], [0.7, 1.0, 0, 0] respectively, we follow the values of x of each line as time goes on, and a phase plane is shown below

However, when the population ratio of the two strains gets to a steady state, y (c_1/c_2 ) doesn’t necessarily be constant. As an example, with another group of parameters