Team:Shanghai United/Model
Model
In order to determine the effective concentration range of the arsenic (C2H6AsNaO5), we tested the fluorescence intensity generated by an ARSD/amilGFP transformed E. coli reacting for 1 hour in C2H6AsNaO5 solutions.
The initial data is showing below and we also used the value of the fluorescence intensity when the arsenic concentration is zero as the baseline for the primary elimination.
Table 1. Fluorescence intensity of E. coli/ArsD_amilGFP in C2H6AsNaO5 solutions
Model I
According to the scatter plots, there seemed some ups and downs which would cause difficulties also less accuracy to build the model. We also thought to use the exponential equation or logarithmic equation to fit our data but the fitting degrees turn out quite low. Therefore, we chose to use the piecewise Hermite interpolation method to build the model and finally drew the fitting curve.
Coding we used is giving below:
“
clear;clc;
x0=[0 10 20 50 100 150];
y0=[0 48345.77778 45807.44444 390431.2222 258369.1111 245812.5556];
x=[0:0.5:150];
y=interp1(x0,y0,x,'pchip');
ymax=max(y);
i=find(y==max(y))
xmax=x(i)
plot(x,y,'LineWidth',2)
hold on
plot(xmax,max(y),'r*','LineWidth',2)
hold off
”
Figure 1. The fitting curve of E. coli/ArsD_amilGFP by piecewise Hermite interpolation
In figure 1, we noticed that the fluorescence intensity started to decline as the concentration of the arsenic increases after 50 ug/L. It is probably that the arsenic affects the growth of the engineered strain, the biosensor when the concentration exceeds 50ug/L. Therefore, we would indicate the effective detection range of our biosensor (E. coli/ArsD_amilGFP) to be 0~50 ug/L for the arsenic (C2H6AsNaO5).
Model II
As we have determined the effective detection range of our arsenic biosensor, we thought to further analyze the relationship between the fluorescence intensity and the concentration of the arsenic.
Therefore, we only picked the data when the concentration is not higher than 50 ug/L and adopted the following equation with the fitting degree, 1 by MATLAB:
Figure 2. Model result of
Figure 3. The fitting curve of
According to the model result of the cubic polynomial equation, it could establish the direct quantitative relationship between arsenic concentration and fluorescence intensity, which means we could read the fluorescence intensity to get the value of the arsenic amount. Hence, this model could be used for the numerical display screen set up in the future to facilitate the application and enhance the functionality.
