Team:ECNUAS/Model
MODEL
When we conducted the function tests of our biosensor, we noticed that basically
there is an increasing trend of the fluorescence intensity of bacteria C as the induction hour increases.
Therefore, we decided to analyze the quantitative relationship between the fluorescence intensity and the
detection time by building a model and determine the most appropriate hour for our biosensor to confirm the
result.
Below is the initial data:
Table 1. The Fluorescence intensity of the bacteria C solution under different concentrations of
cyanuric acid (CYA) by time
As each group was conducted with three duplicates in order to minimize the error,
we used the average to draw scatter plots by MATLAB to further find the fitting function. After several
attempts, we chose the cubic polynomial equation to adapt to our data and the results are given below where
all fitting degrees are higher than 0.99, even reaching 1.
The Cubic Polynomial Equation: y = p1x3 +
p2x2 + p3x +
p4
Figure 1. The model result when CYA concentration was given 10 uM/L
Figure 2. The fitting curve of the model when CYA concentration was given 10 uM/L
Figure 3. The model result when CYA concentration was given 30 uM/L
Figure 4. The fitting curve of the model when CYA concentration was given 30 uM/L
Figure 5. The model result when CYA concentration was given 50 uM/L
Figure 6. The fitting curve of the model when CYA concentration was given 50 uM/L
Comparison
The coding we used to combine all fitting curves in one graph is given below:
“
clear;clc;
t0=[0 1 2 4 6];
c10=[549.883333 945.896667 1768.9 4414.20667 6189.83];
c30=[490.156667 895.046667 1993.16 4270.30333 5789.22333];
c50=[674.69 1177.77 1953.85667 3809.30667 5341.35333];
pc10=polyfit(t0,c10,3);
pc30=polyfit(t0,c30,3);
pc50=polyfit(t0,c50,3);
t=[0:0.1:6];
yc10=polyval(pc10,t);
yc30=polyval(pc30,t);
yc50=polyval(pc50,t);
plot(t,yc10,'r',t,yc30,'b',t,yc50,'g','LineWidth',1)
x1=0.5;y1=647.6;x2=2.1;y2=2037;x3=2.5;y3=2396;x4=3.3;y4=3472;
hold on
plot(x1,y1,'k*');
plot(x2,y2,'k*');
plot(x3,y3,'k*');
plot(x4,y4,'k*');
hold off
”
clear;clc;
t0=[0 1 2 4 6];
c10=[549.883333 945.896667 1768.9 4414.20667 6189.83];
c30=[490.156667 895.046667 1993.16 4270.30333 5789.22333];
c50=[674.69 1177.77 1953.85667 3809.30667 5341.35333];
pc10=polyfit(t0,c10,3);
pc30=polyfit(t0,c30,3);
pc50=polyfit(t0,c50,3);
t=[0:0.1:6];
yc10=polyval(pc10,t);
yc30=polyval(pc30,t);
yc50=polyval(pc50,t);
plot(t,yc10,'r',t,yc30,'b',t,yc50,'g','LineWidth',1)
x1=0.5;y1=647.6;x2=2.1;y2=2037;x3=2.5;y3=2396;x4=3.3;y4=3472;
hold on
plot(x1,y1,'k*');
plot(x2,y2,'k*');
plot(x3,y3,'k*');
plot(x4,y4,'k*');
hold off
”
Figure 7. Comparison among three fitting curves
Conclusion
Based on the model results (Fig. 1, 3, 5), the constants (p1) of the cubic are picked and listed
below:
p1 in the model (CYA=10 uM): -44.03
p1 in the model (CYA=30 uM): -37.33
p1 in the model (CYA=50 uM): -19.03
p1 in the model (CYA=10 uM): -44.03
p1 in the model (CYA=30 uM): -37.33
p1 in the model (CYA=50 uM): -19.03
Hence, we could infer that the less the concentration of CYA is given, the higher
the changing rate of the curve presents. Especially when the detection hour is given more than 3.3 hours,
the changing rate of the fitting curve (CYA=10 uM) is obviously higher than the other two, namely, our live
bacteria biosensor is more sensitive to the lower concentration of CYA solution.
In this case, our biosensor with the live bacteria carrier would be more
recommended for the low concentration detection of CYA and the detection time is recommended to wait for
more than 3.3 hours in order to amplify the differences.
In addition, it also indicates that Cell-Free Expression Biosensor is necessary
which is expected to cover the detection on the higher concentration of CYA.