Team:UCSF/Modeling Results

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.

To test the robustness of this dynamic system, we sampled the parameters using Latin-cubic sampling, and searched the suitable groups of parameters which could make the population ratio of the two strains (x=n1/n2) get to a constant number, and at the same time could also enable the final steady ratio to be neither too large nor too small, say, not larger than 10, and not smaller than 0.1.

Finally we found 261 out of 10000 groups of parameters that meet our requirement. This number gives an evaluation of the robustness.

What’s more, to give guidance on how to tune parameters to make experiments work out, we should find out which parameter is sensitive, say, which one to tune and how to tune it to make an experiment successful.

Due to the reasons above, we did sensitivity analysis using C++, the results are as following:
k_1 and k_2 are more sensitive than other parameters;
k_1 and k_2 are more sensitive when they are enlarged than they are reduced.

The result of sensitivity analysis indicates that k_1 or k_2 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.

Result of Simulation