Team:Shanghai City United/Model
MODEL
In order to determine the optimal duration of our engineered Lactobacillus reuteri
to express the most enzyme activities, we used the SppIP to induce the expression of L. reuteri by several
hours and the enzyme activity was measured by DNS assay.
Below is the data of the units of enzyme activity of our engineered L. reuteri:
Table 1.
According to the scatter plots, we notice that the data when the induction time is
24 hours and 48 hours quite deviate from the trend. In order to find the optimal induction time of our
engineered L. reuteri, we attempted several methods to build the model and wish to contribute to predicting
the optimal condition for our product, L. reuteri/pSIP403-PUS-xyn AM to work.
MODEL I_Hermite interpolation
In order to obtain a curve of units of enzyme activity against induction time
without kicking out any data, we introduced Hermite interpolation by MATLAB and the coding is given below:
“
clear;clc;
t0=[0 3 8 12 16 24 48];
y1=[38.60214035 52.4481485 149.8437352 139.0661995 98.70252865 80.32957666 81.82593049];
y2=[61.23685955 93.09593712 158.2536225 134.1414907 127.1521924 72.90463112 81.31451842];
y0=(y1+y2)/2
t=[0:0.5:48];
y=interp1(t0,y0,t,'pchip');
ymax=max(y)
i=find(y==max(y));
tmax=t(i)
plot(t,y,'LineWidth',2)
hold on
plot(tmax,ymax,'r*','LineWidth',2)
hold off
”
clear;clc;
t0=[0 3 8 12 16 24 48];
y1=[38.60214035 52.4481485 149.8437352 139.0661995 98.70252865 80.32957666 81.82593049];
y2=[61.23685955 93.09593712 158.2536225 134.1414907 127.1521924 72.90463112 81.31451842];
y0=(y1+y2)/2
t=[0:0.5:48];
y=interp1(t0,y0,t,'pchip');
ymax=max(y)
i=find(y==max(y));
tmax=t(i)
plot(t,y,'LineWidth',2)
hold on
plot(tmax,ymax,'r*','LineWidth',2)
hold off
”
Figure 1. The fitting curve of the model by Hermite interpolation
In figure 1, we could easily predict that the optimal induction time would be 8
hours for the engineered L. reuteri and it would tend to decline to the least value (around 80 U/mL) after
that.
MODEL II_Fourier Function
After deleting the data in 48 hours as it seriously deviated from the
trend, the model built by the Fourier function fits the data very well and the model result is given below
with a high fitting degree, 1.
The second-order Fourier Function:
f(x) = a0 + a1cos(wx) + b1sin(wx) + a2cos(2wx) + b2sin(2wx)
Figure 2. The model result by Fourier function
Figure 3. The fitting curve of the model built by Fourier function
According to the fitting curve we built based on Fourier function, there are
several ups and downs but the top point lies down to (9, 157). Therefore, it would be recommended that the
optimal induction time is 9 hours. But this model has its limit that it only fits the trend before 24 hours.
MODEL III_Quartic Polynomial
After deleting the data in 24 and 48 hours, we chose to use the quartic polynomial
function to adapt to our data.
The quartic polynomial function:
Figure 4. The model result by quartic polynomial function
Figure 5. The fitting curve of the model built by quartic polynomial function
According to the fitting curve built by the quartic polynomial function which only
works before 16 hours, we will recommend the induction time of our engineered L. reuteri is 9 hours.
Conclusion
Based on the models above, 8~9 hours would be the most recommended induction time
for our engineered L. reuteri to express the enzyme and work best. In addition, above models would also
contribute to the application of our product - "drink" for poultry in the future as the reference to analyze
the expiry time, stability, store conditions .