Team:UESTC-China/Model2
Overview
In order to find the optimal degradation conditions for engineered E.coli, we found the main factors affecting the degradation rate from the related paper[1]. Firstly, we used the Plackett-Burman design to screen factors. In the future we can get the important factors by experimental data. Secondly, the Box-Behnken design was used in the experimental design to reflect objective reality with fewer experiments. According to the experimental results, the response surface equation can be obtained, and optimal degradation conditions can be found. Finally, after obtaining the extreme value of the equation (optimal degradation conditions), it can be verified by experiments in the future.
Goals
1. Screen all factors to obtain important factors affecting the degradation rate of CrpP enzyme
2. Find the optimal working conditions for engineered E.coli
3. To achieve the optimal CIP degradation rate with as little experimental cost as possible.
2. Find the optimal working conditions for engineered E.coli
3. To achieve the optimal CIP degradation rate with as little experimental cost as possible.
Factor screening
In the process of degrading ciprofloxacin, we found several factors affecting the degradation rate of CrpP enzyme (y) such as PH (x1), temperature (x2), ATP concentration (x3), Mg2+ concentration (x4), CIP concentration (x5)[1]. We chose the Plackett-Burman design to screen the main factors that have significant effects on the degradation rate of the enzyme, and then we will use the important factors to find the optimal combination of degradation rate.
Based on the range of variables provided by the related paper and our experimental conditions, we have determined the range of the five independent variables. The variation range and normalized value of x1、x2、x3、x4、x5 are as follows:
| Name | Variable | Low level(-1) | Zero level(0) | High level(1) |
|---|---|---|---|---|
| x1 | Initial pH | 6 | 7 | 8 |
| x2 | Temperature(℃) | 31 | 34 | 37 |
| x3 | ATP concentration(mmol/L) | 1.7 | 2 | 2.3 |
| x4 | Mg2+concentration(mmol/L) | 8 | 10 | 12 |
| x5 | CIP concentration(μg/ml) | 0.5 | 1 | 1.5 |
The Plackett-Burman design with N=12 is shown in Table 2 and the experimental data are not shown in Table 2. Due to the limited and urgent time, we do not have enough experimental data at present. But we will continue to improve this model later.
| Test number | x1 | x2 | x3 | x4 | x5 |
|---|---|---|---|---|---|
| 1 | -1 | 1 | -1 | 1 | 1 |
| 2 | -1 | -1 | -1 | 1 | -1 |
| 3 | -1 | 1 | 1 | -1 | 1 |
| 4 | 1 | -1 | 1 | 1 | 1 |
| 5 | 1 | 1 | -1 | -1 | -1 |
| 6 | 1 | 1 | 1 | -1 | -1 |
| 7 | 1 | -1 | -1 | -1 | 1 |
| 8 | -1 | 1 | 1 | 1 | -1 |
| 9 | -1 | -1 | 1 | -1 | 1 |
| 10 | 1 | 1 | -1 | 1 | 1 |
| 11 | -1 | -1 | -1 | -1 | -1 |
| 12 | 1 | -1 | 1 | 1 | -1 |
We can analyze five variables by ANOVA and observe their p-values to determine their degree of effect on the experimental index y. If the p value of a variable is greater than 0.05, the effect of this variable on y is not significant. Based on this way, we can screen out the important factors, and then carry out the Box-Behnken design on the selected factors to find the optimal external factors.
Plackett-Burman design and analysis is to judge the importance of factors by analyzing the experimental data of the design.
Experiment design
Since we have not implemented all the experiments yet, we have not been able to screen all the factors for the time being. Here we assume that three factors are selected: pH, temperature and ATP concentration, then we perform the following process.
In order to find the optimal external conditions in the degradation process and reduce the number of experiments to save costs, we used Box-Behnken design to arrange experiments.
Firstly, we need to find quantitative relationship between Ciprofloxacin degradation rate(y) and initial pH (x1), temperature (x2) and ATP concentration (x3). Quantitative relationships can be expressed as:
\[
y=f(x_{1},x_{2},x_{3})
\]
\( y=f(x_{1},x_{2},x_{3})\) is unknown, so we need several experiments to estimate \( y=f(x_{1},x_{2},x_{3})\),using the data from the finite experiment. The test point arrangement is shown in Fig. 1[2].
Fig. 1. (a)test points for Box-Behnken design (b)test points projection on z1, z2 plane
The maximum and minimum values of x1, x2, x3 are called upper levels and lower levels and the average of upper levels and lower levels is zero levels. Taking into account the limitations of actual factors, the variation range is as follows.
| Name | Variable | Low level(-1) | Zero level(0) | High level(1) |
|---|---|---|---|---|
| x1 | Initial pH | 6 | 7 | 8 |
| x2 | Temperature(℃) | 31 | 34 | 37 |
| x3 | ATP concentration(mmol/L) | 1.7 | 2 | 2.3 |
The test points of the Box-Behnken design is shown in the following table:
| Test number | x1 | x2 | x3 |
|---|---|---|---|
| 1 | 0 | 1 | -1 |
| 2 | -1 | 1 | 0 |
| 3 | 0 | -1 | 1 |
| 4 | -1 | 0 | 1 |
| 5 | 1 | 1 | 0 |
| 6 | 1 | 0 | 1 |
| 7 | 1 | -1 | 0 |
| 8 | 0 | 0 | 0 |
| 9 | 0 | 1 | 1 |
| 10 | 1 | 0 | -1 |
| 11 | -1 | 0 | -1 |
| 12 | 0 | 0 | 0 |
| 13 | -1 | -1 | 0 |
| 14 | 0 | 0 | 0 |
| 15 | 0 | 0 | 0 |
| 16 | 0 | 0 | 0 |
| 17 | 0 | -1 | -1 |
After we get the experimental data, we can analyze the experimental data to get the best external degradation conditions. Finally, we can find the optimal conditions with low experimental cost.
Optimal solution
Based on the experimental data, we can obtain the regression equation analysis table and get response surface equation using Design Expert 10. Then We will get the partial derivative of the equation and make the derivative zero. By solving the equations, the optimal degradation conditions can be obtained. In order to verify the effectiveness of the optimization results, we should conduct experiments again under the optimal conditions. If the results are consistent with our expectation, we find the best external conditions within the experimental range.
References
[1] Chávez-Jacobo, V. M., Hernández-Ramírez, K. C., et.al. (2018). CrpP is a novel ciprofloxacin-modifying enzyme encoded by the Pseudomonas aeruginosa pUM505 plasmid.
[2] Xu X. H. & He M. Z. (2010). Test design, Design-Expert and SPSS application. Beijing: Science Press.
Antimicrobial agents and chemotherapy, 62
(6), e02629-17.[2] Xu X. H. & He M. Z. (2010). Test design, Design-Expert and SPSS application. Beijing: Science Press.