Team:Worldshaper-XSHS/Model
Nicotine detection model
To detect the existence of nicotine better, we made the first and second versions of system. Built on the pSB1C3 backbone, the former version contains a nicA2 promoter and a GFP gene, while the latter adds a T7 RNA polymerase gene and a T7 promoter in the middle of the former design, so as to enhance the expression of the fluorescence. Via experiments, we learnt that the activity of the nicA2 promoter is regulated by the concentration of nicotine, so we applied different concentrations on both designs for test, and used the results to build the following math models using MATLAB (R2018b). Correlation of the growth of first detection system with nicotine concentration
(A) Assumptions for the model:
1. The growth of the E. coli strain can be regarded as exponential within 4 hours
2. The concentration of nicotine in the environment is constant
3. The nicotine concentration is beyond the detection limit of the promoter
4. The fluorescent protein shows no significant sign of degradation
(B) Model used:
Where t stands for time; k is the assumed index of the bacteria growth, which is related to the concentration of nicotine; k_c is the index of fluorescence expression
(C)Time-varying fluorescence intensity under different concentrations of nicotine
（1) When the concentration of nicotine equals to 0.001 g/L, the fluorescence can be detected by the plate reader. With the passage of time, the fluorescence expression increases, which is significant at the 4-hour timepoint. The function is fitted as following:
In this model, the growth index is positive, indicating that this concentration of nicotine did show no significant toxicity to the bacteria.
(2) When the concentration of nicotine equals to 0.01 g/L, the plate reader can still detect fluorescence, but the fluorescence intensity is lower than that of 0.001 g/L, and the whole curve tends to be gentle. The fitted function is
The growth index is 1.205, which is significantly less than that of 0.001 g/L. We conjecture that under this concentration, nicotine shows toxicity to bacteria.
(3) When the concentration of nicotine equals to 0. 1 g/L, the fluorescence detected at several time points are substantially lower than those of the blank control, with negative values. We conjecture that 0.1 g / L of nicotine shows significant toxicity to the strain, which will trigger a large number of damage or death of the bacteria, resulting in a decrease in fluorescence value. At 4-hour timepoint, a peak of fluorescence expression appeared, probably because the strongest induction effect of nicotine is shown at the certain time, offsetting some of the variation in fluorescence intensity caused by bacterial damage. The fitted function is:
The growth index here is -3.65, indicating that this concentration of nicotine has seriously affected bacteria growth.
When the concentration of nicotine equals to 1 g/L, the fluorescence intensity is basically negative. We suppose that this concentration of nicotine causes great damage to the bacteria. The fitted function is:
In this model, the growth index is -71.06, indicating that the bacteria growth is significantly inhibited.
5) We analyzed the correlation of k (growth index) with the concentration of nicotine, and the results showed that k and pC (-lg c) showed a significant positive correlation. The higher concentration of nicotine, the smaller k it results in, that is, the stronger the inhibition of growth. The fitted function is
When the concentration of nicotine is around 〖10〗^(-1.5) g/L (approximately 0.032 g/L), the growth of bacteria begins to be inhibited. As the concentration increases, the inhibition increases. When it comes to 〖10〗^(-1) g/L (0.1 g/L), the bacteria growth is inhibited to a certain degree, where k is calculated as -3.62038186. When concentration increases to 〖10〗^(-0.5) g/L (approximately 0.32 g/L), the inhibition is significant, and k is calculated as -17.56950279.
(6) Conclusion: Nicotine exhibits two properties for the strain. On one hand, it can activate the promoter and induce the fluorescence expression; on the other hand, nicotine has a toxic effect on the bacteria. Under the combined effect of these two properties, our detection system exhibits different fluorescence intensities and variations in it. According to the analysis of the above model, when the concentration of nicotine is lower than 0.03g/L, the inhibition of growth is not significant, and the fluorescence intensity increases with the passage of time, and a peak of expression appears at 4-hour timepoint. When the concentration is too high, the inhibitory effect of nicotine on bacteria is overwhelming, resulting in a significant decrease in fluorescence expression.
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