Team:Worldshaper-XSHS/Model

Modeling

Nicotine Detection System

To better detect the existence of nicotine, we made a first and a second generation detection system. Built on the pSB1C3 backbone, the first generation system contains a nicA2 promoter and a GFP gene, while the second one adds a T7 RNA polymerase gene and a T7 promoter in the middle of the first generation design 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 to both generations of systems for testing, and used the results to build the following math models using MATLAB (R2018b).

Ⅰ. Correlation Modals of Nicotine Concentration and Detection with the First Generation Detection System

A. Model Assumptions:

1. The growth of the E. coli strain is regarded as exponential within 4 hours. 2. The concentration of nicotine in the environment is constant. 3. The nicotine concentration is above the lower detection limit of the promoter. 4. The fluorescent protein shows no significant signs of degradation.

B. Used Modal:

where t stands for time; k is the assumed coefficient of the bacteria growth, which is related to the concentration of nicotine; k_c is the coefficient of fluorescence expression.

C. Time-Varying Fluorescence Intensity Under Different Concentrations Of Nicotine

(1) When the concentration of nicotine is equal to 0.001 g/L, the fluorescence can be detected by the plate reader. As time goes by, the fluorescence expression appears to be increasing, which becomes significant at the point of 4h. The function is fitted as following:

where, the growth coefficient is positive, meaning that the bacteria are still able to grow.

(2) When the concentration of nicotine is equal to 0.01 g/L, the plate reader can still detect fluorescence. But compared with when the concentration is 0.001 g/L, the fluorescence intensity is no longer increasing with time. The fitted function is

where the bacteria growth coefficient is 1.205, which is close to that of 0.001 g/L. Based on the models, we conjecture that under these two concentrations of nicotine, the growth of the bacteria is not affected.

(3) When the concentration of nicotine is equal to 0. 1 g/L, the fluorescence intensities detected at several time points are substantially lower than those of the blank control, and are shown as negative numerically. We conjecture that at the concentration of 0.1 g/L, nicotine has significant toxicity to the strain, which may have caused a large number of damage to the bacteria or even death, resulting in a decrease in the fluorescence value. A peak of fluorescence expression appears at 4h, probably because the strongest induction effect of nicotine is shown at that time, offsetting some of the variation in fluorescence intensity caused by bacterial damage. The fitted function is:

where the growth coefficient is -3.65, indicating that this concentration of nicotine has seriously affected bacterial growth and thus lowered the expression of fluorescence.

(4) When the concentration of nicotine is equal to 1 g/L, the fluorescence intensity is basically negative at all times. We suppose that this is due to the great damage caused by nicotine at this concentration to the bacteria. The fitted function is:

where the growth coefficient is -71.06, indicating that the bacterial growth is significantly affected.

(5) We analyzed the correlation between k (bacterial growth coefficient) and the concentration of nicotine, the results of which showed that k and pC (-lg c) had a significant positive correlation. The higher the concentration of nicotine, the smaller k will result in, that is, the stronger the inhibition of growth. The fitted function is as follows:

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 changes to 〖10〗^(-1) g/L (0.1 g/L), the bacteria growth is inhibited to a certain degree, where k is calculated to be -3.62038186 based on the formula. When the concentration increases to 〖10〗^(-0.5) g/L (around 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 the one hand, it can activate the promoter and induce the expression of fluorescence; on the other, nicotine has a toxic effect on the bacteria. Under the combined effect of these two properties, our detection system detected a great variety of fluorescence intensities. Based on the above models, we analyzed that the inhibition effect is not significant when the concentration of nicotine is less than 0.03g/L, and the fluorescence intensity increases with time. When the concentration is greater than 0.3 g/L, the inhibition effect is significant. And if the concentration is too high, the inhibitory effect of nicotine on bacteria will be overwhelming, resulting in a significant decrease in fluorescence expression.

Ⅱ. The Growth Curves under Different Nicotine Concentrations by the First Generation Detection System

To better explore the relationship between nicotine concentrations and bacterial growth, we prepared 10 different concentrations of nicotine solutions for testing, i.e. 0.02 g/L, 0.04 g/L, 0.08 g/L, 0.16 g/L, 0.32 g/L, 0.64 g/L, 1.28 g/L, 2.56 g/L, 5.12 g/L and 10.24g/ L. During the data analysis, we performed the following substitution of the concentration:

in order to better discover its relationship with OD600. For the X-axis, 1, 2, 3 until 10 respectively represent the 10 different concentrations of nicotine, i.e. 0.02 g/L, 0.04 g/L, 0.08 g/L, 0.16 g/L, 0.32 g/L, 0.64 g/L, 1.28 g/L, 2.56 g/L, 5.12 g/L and 10.24g/L. We can see that the OD values at 0h in different groups are all 0.05, which means that all the groups share the same starting point. At 2h, the OD values detected at various concentration groups are basically the same, and have not increased much since 0h. At 4h, the OD values of the low concentration groups increased significantly. And for the groups larger than 5 (that is, 0.32 g/L), there is a downward trend, that is, the toxicity of nicotine has begun to manifest. The critical value, the concentration of 0.32 g/L, is basically consistent with our conjecture based on the models in the first part. As time goes on, the toxicity of nicotine becomes more and more significant. At 12h, when the concentrations are greater than 0.32 g/L, the number of bacteria decreases significantly. And as the concentration increases, the inhibiting effect also increases. Based on this model, we speculate that the effect of nicotine on bacterial growth is related to time and nicotine concentration. When the exposure time is less than 4 hours and the concentration is lower than 0.32 g/L, the inhibition is not significant. While with the increase of time and nicotine concentration, its inhibitory effect gradually increases.

Ⅲ. Sensitivities of the First and the Second Generation Detection Systems

Based on the structure of plasmids, we predict that the sensitivity of the second generation detection system should be higher than that of the first generation. In order to better test their sensitivities, we have chosen a very low nicotine concentration that can still induce fluorescence to do the experiment. The concentration is 0.0001 g/L. By analyzing the experiment data, we get the following models:

We can see that the detected fluorescence of the second generation detection system is higher than the first generation detection system. The difference is most significant at 3h. However, the fluorescence intensity detected by the second-generation system was significantly decreased at 4h. We conjecture that this may be related to the toxic effect of nicotine on the bacteria. Although the first generation of detection system can detect fluorescence, it is not as sensitive as the second generation system.

In conclusion, we should choose the second generation detection system to detect the nicotine concentration and the best detection time is at 3h. However, if the first generation system is selected, the detection is better done after 4 hours, with the optimal detection concentration of less than 0.32 g/L.