Quantitative analysis of the dynamics in cellular systems is a key aspect of synthetic biology and engineering with the tool of the mathematical model, which not only integrates gene expression data, but also provides an important approach to understanding the dynamics by quantifying the interaction between the regulatory components. At present, the mainstream methods of modeling control network include Petri net, Bayesian network and differential equation model.

In our project, the main idea is to construct certain kinds of recombinant plasmids by selecting the corresponding pollutant ion sensing promoters binding with the reporter genes with T7 amplification systems to decrease the detection limit. It is fairly essential to get the accuracy of experimental data since the experiment of detecting the intensity of signals which is transferred as detectable, is based on the gene circuit, where lays the purport of mathematical modeling.

Our models can be divided into three different aspects. On the gene level, we hope to confirm that the concentration of pollutant ions is positively correlated with the promoter activity. And also we hope to gain insight of the gene expression dynamics of our whole circuit using the differential equation model. Furthermore, we have made a series of regression models about luxAB and tried to explain the surival of freeze dried bacteria with the Boyle van't Hoff relationship. On the aspect of human practices, we manage to investigate the relationship between environmental pollutants and economic, and choose Grossman model to explore the relationship and the amount of GDP emission environment.