Difference between revisions of "Team:UESTC-China/Model2"

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The population mean of the peak areas of the experimental group and the control group is μ<sub>1</sub> and μ<sub>2</sub> respectively.<br>
 
The population mean of the peak areas of the experimental group and the control group is μ<sub>1</sub> and μ<sub>2</sub> respectively.<br>
 
The sample mean of the peak areas of the experimental group and the control group is x<sub>1</sub> and x<sub>2</sub> respectively.
 
The sample mean of the peak areas of the experimental group and the control group is x<sub>1</sub> and x<sub>2</sub> respectively.
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Null hypothesis H<sub>0</sub>：μ<sub>1</sub>-μ<sub>2</sub>=0<br>
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Alternative hypothesis H<sub>A</sub>：μ<sub>1</sub>-μ<sub>2</sub>≠0
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When we accept the hypothesis, the value of t is calculated by:When we accept the hypothesis, the value of t is calculated by:
 
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Revision as of 08:18, 18 October 2019

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Overview

Due to minor difference between the data of the experimental group and the control group in the experiments, we performed a significance test to verify the function of CrpP. Then considering the low degradation rate, we are going to optimize the external degradation conditions of the engineered bacteria.
In order to find the optimal degradation conditions for engineered E. coli, we found the main factors affecting the degradation rate from the paper. 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. Finally, after obtaining the extreme value of the equation (optimal degradation conditions), it can be verified by experiments.

Goals

1. verify the function of CrpP
2. Screen all factors to obtain important factors affecting the degradation rate of CrpP enzyme
3. Find the optimal working conditions for engineered E.coli
4. Try to save experimental cost and get optimal conditions with fewer experiments

Verification of CrpP function

Kolmogorov–Smirnov test
Firstly, we used the K-S test combined with SPSS software to test the normality of the data. The P values of the experimental group and the control group are greater than 0.05, so we can think that the experimental data of both groups are in accordance with normal distribution. The results are as follows:
Table 1 One-Sample Kolmogorov-Smirnov Test
VAR00001 VAR00002
1.00 N 30
Normal Parameters Mean 402223.7667
Std. Deviation 3219.62263
Most Extreme Differences Absolut 0.145
Positive 0.145
Negative -0.078
Kolmogorov-Smirnov Z 0.796
Asymp. Sig. (2-tailed) 0.55
2.00 N 6
Normal Parameters Mean 405566.6667
Std. Deviation 4449.85585
Most Extreme Differences Absolut 0.178
Positive 0.178
Negative -0.157
Kolmogorov-Smirnov Z 0.436
Asymp. Sig. (2-tailed) 0.991
The peak areas of the liquid chromatography solutions of the experimental group (1) (CIP solution of CrpP addition after 30 minutes) and the control group (2) (CIP solution of no CrpP after 30 minutes) are shown in the following table:
Table 2 Peak area of experimental group and control group after 30 minutes
Test number Group Peak area of liquid chromatography solution
1 1 408173
2 1 405072
3 1 406560
4 1 406027
5 1 401541
6 1 401222
7 1 401478
8 1 402695
9 1 405444
10 1 404834
11 1 401366
12 1 398795
13 1 395506
14 1 399605
15 1 407798
16 1 407647
17 1 401679
18 1 402321
19 1 399728
20 1 403798
21 1 400934
22 1 396259
23 1 400199
24 1 403449
25 1 397587
26 1 397587
27 1 401769
28 1 399936
29 1 401857
30 1 401740
31 2 409694
32 2 411826
33 2 401026
34 2 401052
35 2 405574
36 2 404228
After proving the two groups of data in accordance with the normal distribution, we can use the t test to analyze.
Homogeneity of variance test
σ12 and σ22 is the population variance of the peak areas of the experimental group and the control group respectively.
s12 and s22 is the sample variance of the peak areas of the experimental group and the control group respectively.
Null hypothesis H0：σ12=σ22
Alternative hypothesis HA：σ12≠σ22
The value of F is calculated by:

Student's t test

The population mean of the peak areas of the experimental group and the control group is μ1 and μ2 respectively.
The sample mean of the peak areas of the experimental group and the control group is x1 and x2 respectively.
Null hypothesis H0：μ1-μ2=0
Alternative hypothesis HA：μ1-μ2≠0
When we accept the hypothesis, the value of t is calculated by:When we accept the hypothesis, the value of t is calculated by:

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 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:
Table 1 Levels of the variables of Plackett-Burman design
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 tight experimental time, we do not have experimental data now. But we will continue to improve this model later.
Table 2 The Plackett-Burman experimental design with five independent variables
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 verified the experiment, we can't get the selected factors temporarily. 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 Figure 1.
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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.
Table 3 Levels of the variables of Box–Behnken design
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:
Table 4 The Box–Behnken experimental design with three independent variables
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. Undoubtedly, We can reduce the cost of the experiments and find the optimal conditions.

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 degradtion 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 as we expected, undoubtedly we find the best external conditions within the experimental range.

References

[1] Chávez-Jacobo, V. M., Hernández-Ramírez, K. C., Romo-Rodríguez, P., Pérez-Gallardo, R. V., Campos-García, J., Gutiérrez-Corona, J. F., ... & Ramírez-Díaz, M. I. (2018). CrpP is a novel ciprofloxacin-modifying enzyme encoded by the Pseudomonas aeruginosa pUM505 plasmid.

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.
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