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：

At the initial induction concentration of OD0.8, and the Induction time is 2 hours. Under this condition, the nickel ion concentration has a significant function relationship with the fluorescence intensity.

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.

Each cell has the same state.

The reaction in the process satisfies the first-order kinetic reaction.

Then we got 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:

We found that a high concentration of nickel ions will reduce the expression of fluorescence, because nickel ions have cytotoxicity.

The July 20 experimental data is as follows:

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

Where