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	When there is no lactose operon, different concentrations of lactic acid are added. Although the engineered bacteria will still react according to different concentrations of lactic acid, the curve of the function is obviously irregular with different reaction times.		When there is no lactose operon, different concentrations of lactic acid are added. Although the engineered bacteria will still react according to different concentrations of lactic acid, the curve of the function is obviously irregular with different reaction times.

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Revision as of 04:32, 17 October 2018

Modeling Part Structure

Overview

In the following article, we describe the process of building our model. During the construction, we aim to build a model by combining the data fitting principle in mathematical modeling with the help of MATLAB through multiple experiments, and obtain a relatively successful fitting formula after multiple optimization, so as to reflect the data trend reasonably.

During the experiment, we first controlled the consistency of the concentration of the bacterial liquid so that it would not affect the experimental results. There are 3 groups of experimental statistic, they record 3 kinds of mutant statistic——The independent variable—concentration of lactic acid(lactate)，time of reaction(t), the dependent variable—intensity of fluorescence(Fluorescence). On the basis of reasonable hypothesis and correlation coefficient test, according to the fitting of known data, we get the function and function curve that can reflect data trend reasonably. This curve illustrates the functional relationship between the fluorescence intensity of the dependent variable and the independent variable.

How do we derive this model?

1: According to some reasonable assumptions given in professional knowledge, we believe that the linear function may be a non-linear function between the dependent variable and the independent variable, since the addition of lactic acid and IPTG will tend to influence the growth rate of the organism, and the lactic acid into the cell and the ai-2 generated by the Luxs catalysis also need to be of a certain and unequal time, so that the whole reaction process does not constitute a linear function requirement. So it's a logarithmic function or a polynomial function.
2: Under each reasonable hypothesis, MATLAB is used to perform corresponding fitting. According to the correlation coefficient R to test the fitting effect, the fitting function formula that can reasonably reflect the data trend can be obtained after continuous optimization.
T7- lldPRD operon promoter-GFP：
[IPTG]=1 mM：
t=0 min Relative Fluorescence= 1.496 t 3 -8.148 t 2 + 10.31 t + 8.919 R2= 0.1473
t=5 min Relative Fluorescence= 9.304 t 3 -49.68 t 2 + 63.56 t + 22.25 R2= 0.9464
t=10 min Relative Fluorescence= 1.286 t 3 -12.36 t 2 + 19.78 t + 29.03 R2= 0.9986
t=20 min Relative Fluorescence= 17.26 t 3 -83.37 t 2 + 96.5 t + 19.91 R2= 0.9957
t=30 min Relative Fluorescence= 9.669 t 3 - 48.15 t 2 + 58.23 t + 39.34 R2= 0.8645
t=60 min Relative Fluorescence= 20.96 t 3 - 106.2 t 2 + 134.9 t + 42.16 R2= 0.9482

Lldr- T7-lldPRD operon promoter-GFP：

[IPTG]=1 mM：
t=0 min Relative Fluorescence= 6.123 t 3-32.29 t 2+41.51 t+ 34.97 R2=0.4449
t=5 min Relative Fluorescence= 6.669 t 3 -38.13 t 2 + 55.27 t + 13.89 R2= 0.9808
t=10 min Relative Fluorescence= -3.422 t 3 +7.808 t 2 + 8.072 t + 11.18 R2=0.9946
t=20 min Relative Fluorescence= 10.74 t 3-48.53 t 2+57.9 t+ 9.947 R2= 0.9621
t=30 min Relative Fluorescence= 7.02 t 3 - 37.92 t 2 + 55.03 t + 9.921 R2= 0.9998
t=60 min Relative Fluorescence= 9.403 t 3 - 55.39 t 2 + 80.41 t + 8.451 R2= 0.9787

lldPRD operon promoter-GFP：

[IPTG]=0 mM：
t=0 min Relative Fluorescence= 2.27 t 3 - 12.95 t 2 +23.4 t+ 8.107 R2= 0.9883
t=5 min Relative Fluorescence= -2.332 t 3 +8.402 t 2 + 2.239 t + 20.74 R2= 0.9834
t=10 min Relative Fluorescence= 0.4742 t 3 -1.957 t 2 + 5.059 t +26.94 R2= 0.9544
t=20 min Relative Fluorescence= -3.069 t 3+17.46 t 2-25.51 t+ 21.98 R2= 0.9398
t=30 min Relative Fluorescence= -7.451 t 3 +36.49 t 2 -44.01 t + 39.25 R2= 0.9645
t=60 min Relative Fluorescence= -0.7971 t 3 +4.694 t 2 -13.22 t + 39.88 R2= 0.9761

lldPRD operon promoter-Luxs-Lldr × LsrA promoter-GFP：

t=0 min Relative Fluorescence= -9.425 t 3+43.48 t 2-48.63 t+ 44.85 R2= 0.9985
t=5 min Relative Fluorescence= 9.999 t 3 -56.32 t 2 +79.92 t + 12.47 R2= 0.9696
t=10 min Relative Fluorescence= 12.03 t^3 -62.83 * t^2 +86.66 * t+10.36 R2= 0.7222
t=20 min Relative Fluorescence= 4.578 t 3-32.79 t 2+59.31 t+9.459 R2= 0.898
t=30 min Relative Fluorescence= 6.297 t 3 -35.63 t 2 + 53.2 t + 9.274 R2= 0.8867
t=60 min Relative Fluorescence= 9.122 * t 3 - 51.26 * t 2 + 73.33 * t + 5.924 R2= 0.9866

lldPRD operon promoter-Luxs × LsrA promoter-GFP

t=0 min Relative Fluorescence= -11.78 t 3+46.85 t 2-28.71 t+ 10.35 R2= 0.9764
t=5 min Relative Fluorescence= -12.48 t 3 +45.65 t 2 -26.91 t + 18.86 R2= 0.9762
t=10 min Relative Fluorescence= -1.135 t 3 +5.337 t 2 -3.825 t + 23.12 R2= 0.511
t=20 min Relative Fluorescence= -10.64 t 3+35.98 t 2-12.38 t+ 9.098 R2= 0.9716
t=30 min Relative Fluorescence= 3.63 t 3 - 25.57 t 2 + 40.87 t + 14.54 R2= 0.893
t=60 min Relative Fluorescence= 9.562 t 3 - 53.63 t 2 + 74.38 t + 9.515 R2= 0.9907

Practical significance of model results

Figures

T7- lldPRD operon promoter-GFP：

[IPTG]=1 mM

When [IPTG]=1 mM , The concentration of fluorescence at each point of time shows a similar trend towards the change in the rate of lactate, which is increased by the increase in lactate concentration, and then the fluorescence starts to go up and then down, and then there's a tendency to increase the intensity of the fluorescence, at the end of the level of the lactic acid, which is at the peak of the lactic acid, which is at the level of 0.5 to the one, and the fluorescence is at a peak. According to actual production, the concentration of yogurt in fermentation cannot exceed 1mM[1]. Therefore, the engineered bacteria can monitor the lactic acid concentration of yogurt during fermentation. In terms of time, when IPTG was added with 1mm, the fluorescence value of 5-60 min was all higher than that of 0 min, indicating that the reaction of engineering bacteria to lactic acid was effective during this period. Therefore, 5 min was selected as the appropriate reaction time. Because the fluorescence intensity of fiber detection can be stable within 200 milliseconds, the actual production can be obtained, and the time for testing the lactic acid concentration by using this engineering bacteria is 5 min.

Lldr- T7-lldPRD operon promoter-GFP：

[IPTG]=1 mM

When [IPTG]=1 mM, with the increase of time, the intensity of fluorescence expressed by engineered bacteria all lower than the intensity at 0 min. This may be due to the fact that at 0 min, the expression of lldR has not yet started or the expression quantity is too low, so the opening of lldPRD operon promoter caused by the introduction of engineering bacteria is not prevented. However, as the reaction time increases, lldR gradually produces, and the GFP background expression decreases due to the opening of lldPRD operon promoter. From the perspective of time, when the reaction time was 5 min, the change trend of fluorescence intensity with the concentration of lactic acid was consistent with the initial reaction time, so the good reaction time of engineering bacteria could be achieved within 5 min.

lldPRD operon promoter-GFP：

[IPTG]=0 mM

When there is no lactose operon, different concentrations of lactic acid are added. Although the engineered bacteria will still react according to different concentrations of lactic acid, the curve of the function is obviously irregular with different reaction times.

lldPRD operon promoter-GFP & T7- lldPRD operon promoter-GFP& Lldr- T7-lldPRD operon promoter-GFP:
We fitted the change of fluorescence intensity expression of the three engineered bacteria at the reaction time of 5 min, hoping to obtain the difference of the three engineered bacteria.

In the process of production of yogurt, the lactic acid content should not exceed 1 mM. So when the lactic acid content was lower than 1 mM, the lactose operon or lldR is added to the engineered bacteria and the lactic acid concentration is lower than 1 mM, indicating that the two engineered bacteria can achieve high sensitivity. Besides, when lactic acid content was lower than 1 mM, the lactose operon or lldR is added to the engineered bacteria is higher than those which only have lldPRD operon, indicating that both the lactose operon and lldR have an improved effect on the initial engineered bacteria.(BBa_K822000 ). Compared with the improvement of BBa_K822000 by lldR, it is obvious that the addition of lactose operon makes engineering bacteria more sensitive.

lldPRD operon promoter-Luxs-Lldr × LsrA promoter-GFP

×

Except for the beginning of the reaction, The rest of the functional curves showed similar trends, especially when the reaction time was 5 min and 10 min, and the peak value was reached before the concentration of lactic acid was 1 mM. It proved that the engineering bacteria was best used to detect the lactic acid concentration in yogurt at the reaction time of 5 min and 10 min. In order to reduce the reaction time of engineered bacteria, the reaction time of 5 min was selected.

lldPRD operon promoter-Luxs × LsrA promoter-GFP

×

According to the result of fitting, after 30 min of reaction, the engineered bacteria were highly sensitive to different concentrations of lactic acid. However, the reacting time was to long, the increase of fluorescence value may be caused by the death of bacteria, which has no reference value.

lldPRD operon promoter-Luxs-Lldr × LsrA promoter-GFP & lldPRD operon promoter-Luxs × LsrA promoter-GFP& Lldr- T7-lldPRD operon promoter-GFP

We fitted the change of fluorescence intensity expression of the three engineered bacteria at the reaction time of 5 min, hoping to obtain the difference of the three engineering bacteria.

Apparently, when the lactic acid concentration is less than 1 mM, included lldPRD operon promoter - Luxs - Lldr x LsrA promoter - the GFP and Lldr - T7 has - lldPRD operon promoter - GFP, two kinds of engineering bacteria in the peak, and the sensitivity of the former than the latter. This indicates that when the lactic acid concentration of yogurt is not over the limit, these two types of engineered bacteria can produce higher sensitivity, and the addition of the swarm sensing system can improve the sensitivity of engineered bacteria to the lactic acid concentration. The engineering bacteria contains lldPRD operon promoter - Luxs x LsrA promoter - GFP in lactic acid concentration is lower than 2.5 mM, to produce higher sensitivity.

All in all, from what has been discussed above, we can learn that contains lldPRD operon promoter - Luxs - Lldr x LsrA promoter - GFP engineering bacteria is applied to we have the best equipment engineering bacteria.