Team:FAFU-CHINA/Modeling

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 formulain the following fitting, where a is the concentration of dsRNA in the steady state.

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 is the maximal data we can get from the data)

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.

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.