Team:Worldshaper-XSHS/Model
Model
In order to make the test results more scientific, we first drew the standard curve of RR concentration and absorbance. We prepared reactive red x (RR) into a solution of different concentrations and tested the absorbance at 530nm. We use matlab to process the data and get the following standard curve:
The relationship between absorbance (ABS) and concentration (c) is as follows:
，R2 is 0.9904.
After obtaining the standard curve, we formally tested the degradation ability of the two enzymes. We use matlab to model the degradation of two laccase (COTA and sclac).
We divided the experiment into two groups, one group was not induced by IPTG, the other group was induced by IPTG. When IPTG was not added, we found that the absorbance of dye decreased slowly with time, and no obvious change of cell color was observed.
Without IPTG
We made the following hypothesis: Although there was no IPTG induction and laccase was not expressed, the metabolism of the bacteria could cause the degradation of the dye.
We make the following model:
If the concentration of dye is c， and the inherent metabolic rate of bacteria is k
there are:
Transfer term and integral result on both sides
Among them, after modeling the data of cotA, the following curves are obtained:
among them,
R2＞0.9 and the fitting degree is high.
After modeling the data of scLac, the following curves are obtained:
among them,
R2＞0.9 and the fitting degree is high.
It can be seen from the above modeling that without IPTG induced expression, the bacteria itself can also cause dye degradation to a certain extent. For cotA and scLac, the K value is different, and the degradation ability of bacteria is slightly different.
With IPTG
In the second experiment, we added IPTG to induce expression. Whether the bacteria are transferred into cotA or scLac, we have obtained the following experimental results: the absorbance of the dye drops rapidly, the bacteria are dyed by the dye, and there is a visible discoloration.
Therefore, we speculated that under the induction of IPTG, laccase was expressed in large quantities, and the dye entered the cell in some way. Under the catalysis of laccase and the action of bacteria, the dye is gradually degraded.
In addition, we also assume that: in this process, the concentration of IPTG is constant, and the expression rate of laccase is constant; laccase starts to express immediately after IPTG is added; laccase has a certain degradation rate, and reaches the balance with expression in a short time, so that the enzyme amount remains constant; the concentration of dye is large enough, and the enzyme content is not saturated; dye is transported into cells in a certain way, and the transfer rate is only the same as that of solution. The concentration of middle dye is related.
Based on this, we establish the following models:
Dye transfer rate = external dye concentration × transfer coefficient
Dye degradation rate = dye concentration in solution × enzyme concentration
If the concentration of dye in the solution is c, the transfer coefficient of dye is k1 and the concentration of laccase is k2
there are：
Term transfer and integral on both sides:
Term transfer and make the exponentiation:
order 
，there
are：
After modeling the data of cotA, we get the following curves:
among them，
R2＞0.9 and the fitting degree is high.
After modeling the data of scLac, we get the following curves:
among them,
R2＞0.89 and the fitting degree is high.
Confidence Interval Residual Analysis
In order to determine the scientificity of the model, we also carry out the confidence interval residual analysis.
CotA without IPTG：
scLac without IPTG
CotA with IPTG
scLac with IPTG
It can be seen from the above images that when IPTG is not added, only one point of COTA and sclac is abnormal. After IPTG is added, there is no data abnormality in cotA, but only two data points in sclac are singular. So the model is reasonable.
A comparison of the two models
We also compare the two models.
For the analysis of cotA and scLac models without IPTG induction, it is not difficult to find:
It can be seen that the existence of the two genes will have different effects on the growth and metabolism of the bacteria, resulting in different degradation rates when the expression is not induced.
For the analysis of cotA and scLac models induced by IPTG, it is not difficult to find:
It can be seen that the degradation of dyes is not the same when the two enzymes are expressed. Compared with the degradation of bacteria, the degradation effect of laccase was stronger. For the two enzymes, the effect of scLac on the degradation of RR is better.
Conclusion
According to the model, we conclude as follows: When there was no IPTG induction, the metabolism of the bacteria still could cause the degradation of the dye. While with the induction of IPTG, laccase can be expressed in large quantities, and the dye entered the cell in some way. Under the catalysis of laccase and the action of bacteria, the dye is gradually degraded. Compared to CotA, the effect of scLac on the degradation of RR is better.