We will show our results from three aspects：

Qualitative analysis：

After 12 hours of incubation(LB，37℃，200r/min), we observed the bacteria on a fluorescence microscope.

In the medium with the addition of nickel ions, we can see visible red fluorescence.

In other media, there is no such phenomenon. The whole vision is black.

So our device only responds to nickel ions.

Quantitative analysis：

The initial induction concentration was OD0.8, and the induction time was 2 hours. Under these conditions, the nickel ion concentration had a significant fucntional relationship with the fluorescence itensity.

Especially in the nickel ion concentration of 10-6mmol / L to 10-4mmol / L between.

model：

At first, we made some assumptions.

Assumptions:

The degradation of and other substances are linear.

Every cell has the same state.

The reaction in the process satisifies the requirements of the first-order kinetic reaction.

Then we reached some conclusions through modeling.

Incomplete Repression:

Under incomplete repression, the bacteria express red fluorescent proteins without the presence of nickel ions.

The incomplete repression of promoters is a major issue in our fluorescence system. This issue was particularly observed in following diagram.

The solution of this differential equation is as follows：

Cytotoxicity:

Or experiment is designed to induce the expression fo fluorescent proteins in the presence of nickel ions, however, we found that above a certain concentration of nickel ions, the expression of fluorescent proteins will be reduced due to nickel ion cytotoxicity.

The July 20 experimental data is as follows:

The different equation of the red fluorescent protein is then modified to:

Where