Team:FAFU-CHINA/Modeling
In
FAFU’s project, it is difficult to measure the quantitative data and determine
the amount of dsRNAs which is fed to the larvae. So
in the modeling part, we devoted to establishing an accurate mathematical
model to simulate the dsRNA expression according to the mechanism of T7
promoter. After the model is built, we can determine the relationship between
the concentration of IPTG and the production of dsRNA .
Then we can control the amount of dsRNAs
which if fed to the larvae by controlling the concentration of IPTG easily.
We
know that T7 promoter is a kind of inducible promoter. Hill equation can be
used to simulate the effect of T7 promoter. In T7 strength model, the
independent variable is the concentration of IPTG, and the dependent variable
is the production of dsRNA.
1. The Model Simulating the Change of
dsRNA with Time in Different Concentration of IPTG
By
observing the pattern of the data, we figure out that the Logistic equation,
which is often used to simulate the growth of population, can model the trend
best. Thus, we adapt the formula
When
the concentration of IPTG=0.3mmol/L, the result of curve fitting is:
General
model:
Coefficients
(with 95% confidence bounds):
a = 0.3241 (0.299, 0.3492)
b = 35.95 (-79.99, 151.9)
c = 1.829 (0.3231, 3.334)
Goodness
of fit:
SSE: 0.00333
R-square: 0.9676
Adjusted R-square: 0.9567
RMSE: 0.02356
Figure 1.
The curve is matched by the formula mentioned above.
When
the concentration of IPTG=0. 4mmol/L, the result of curve fitting is:
General
model:
Coefficients
(with 95% confidence bounds):
a = 0.3474 (0.3261,
0.3686)
b = 46.66 (-63.55,
156.9)
c = 1.828 (0.7647,
2.892)
Goodness
of fit:
SSE: 0.00232
R-square: 0.9808
Adjusted R-square: 0.9744
RMSE: 0.01966
Figure 2.
The curve is matched by the formula mentioned above.
When
the concentration of IPTG=0. 5mmol/L, the result of curve fitting is:
General
model:
Coefficients
(with 95% confidence bounds):
a = 0.3465 (0.3206,
0.3723)
b = 49.63 (-79.79,
179)
c = 1.76 (0.6333,
2.886)
Goodness
of fit:
SSE: 0.003338
R-square: 0.9732
Adjusted R-square: 0.9642
RMSE: 0.02359
Figure
3 The curve is matched by the formula mentioned above.
2. The Hill Equation
By
the work of first part, it is found that the concentration of dsRNA will become
steady after around 4 hours, so we regard the concentration of dsRNA after 4
hours’ culture as that of steady state. Then the Hill equation is applied to
model the relationship between the concentration of IPTG and the production of
dsRNA, the result of curve fitting is: (where
General
model:
Coefficients
(with 95% confidence bounds):
XM
= 0.1265 (0.08411,
0.1689)
n = 2.239 (0.8187,
3.658)
Goodness
of fit:
SSE: 0.003107
R-square: 0.9062
Adjusted R-square: 0.8828
RMSE: 0.02787
Figure
4 The curve is matched by the formula mentioned above.
We
sorted out data and parameters and then beautified the graph.
|
Parameter |
value |
unit |
|
n |
2.239 |
|
|
XM |
0.1265 |
μg/μL |
Figure 5.
It shows the relationship between the concentration of IPTG and the production
of dsRNA
Figure
5 shows the relationship between the concentration of IPTG and the production
of dsRNA. According to this mathematical model, we can work out the accurate
production of dsRNA which is fed to the larvae with the concentration of IPTG
which is put into the bacterial system to induce T7 promoter.
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