Modeling

Introduction

In our project, we want to calculate the bacteria concentration in the testing devices.

However, our devices can only detect GFP intensity, so we can only utilize GFP intensity to calculate bacteria concentration.

What’s more, with the view to making sure our system works successfully, we need to make sure that GFP can be detected in our testing devices. Since the GFP in mosquitoes take some time to be synthesized, we can detect the green fluorescence only few hours after the mosquitoes take in the tester’s blood. To prevent from the misleading of our devices and system, we should calculate the very beginning time that the green fluorescence can be detected in the testing devices.

Guiding Questions

1. How many bacteria can be tested in our model ? (Model 1)

2. How long do our devices take to send out signal ? (Model 2)

Focus on Our Model

Since our devices can only detect the GFP intensity, we can only utilize GFP intensity to calculate E.coli concentration. After obtaining E.coli concentration, we will utilize it to calculate the very beginning time that GFP can be detected in the testing devices. Finally, the two parameters will be demonstrated on our devices for the testing devices to take as reference.

Model 1: Calculating E.coli Concentration by GFP Intensity

Method

To find the mathematical relationship between GFP and E.coli concentration, we measure the GFP intensities with different MOI value every two hours. Then, perform a series of calculations and finally obtain the mathematical relationship between GFP intensity and E.coli concentration.

Obtaining the Mathematical Relationship

Table 1.0 shows the corresponding Fluorescence intensity with different MOI values. First of all, we transformed the MOI to E. coli density.

Conversion of MOI to E.coli density

The equation of E.coli density is shown below:

Since the MOI value refers to the ratio of E.coli cells to mosquito cells, we can use the density of mosquito cells to calculate the E.coli density. Plus, the mosquito cells are seeded at the density of 1.8×〖10〗^5 cells/well, and the volume of each well is 100μL.

Thus, the equation become

Forming the mathematical expression

The GFP intensity has background level in the existence of E.coli. Thus, the background intensity of GFP should be eliminated for the relationship between E.coli concentration and GFP intensity, which means [GFP] should minus the [〖GFP〗_0] in the presence of E.coli before DNA transfection (Table 1.2). With that in mind, we form the Table 1.2

Now we can begin with our data analyzing.

Data Analyzing

Figure 2.0 shows the graphic expression between the [E.coli] and GFP intensity, the Exponential Function is shown below:

Next, we will bring in that [〖GFP〗_0 ]=813 to the Exponential Function and obtain the final graphic expression and function.

Combining the constants, we arrive at

Conclusion

Application

With the formula, we can calculate the [E.coli] based on GFP Intensity, and apply the formula to our prototype design.

Model 2: The GAM 1 Promoter in Response to Number of E. coli Cells Increase With Time

Method

To know when GAM 1 promoter could be induced by E. coli concentration, we measure the GFP intensity with different MOI value every two hours, and differentiate the curves to find the time that the instant GFP expression level reaches the maximum, which is the time all the E.coli cells activate GAM 1 promoter.

Relative fluorescence units of GFP intensity in different MOIs of E. coli

The RFU of GFP intensities of GAM 1 promoter activities induced by different E.coli concentrations were shown in Table 2.

The RFU curves in the function of time were illustrated by different MOIs of E. coli, as shown from Figure 3.0 to Figure 3.4

Also, the mathematical expressions of these cubic equations were shown as Table 3.0 and the graphic expressions were shown as Figure 4.0

Derivative of the GFP Intensity Curve

We conducted the derivative of the mathematical formula in Table 3.0 and form Table 3.1

The Responding Time to The Maximum of The Formula

To calculate the maximum of the derivative of the GFP intensity curve, we conducted the second derivative and found the maximum and responding time. The results were shown in Table 3.2

The graphic expression of the relationship between time and E.coli density was shown in Table 3.3 and Figure 5.0

We also arrive at the equation between time and E.coli concentration

Application

With the formula, we can use the [E.coli] to calculate the responding time. Then, the formula will also be applied to our calculator and prototype, too.

CALCULATOR

Conclusion

Our model not only help to build the mathematical system which applied to our devices, but also make us better understand our project. Because our devices can only detect the GFP intensity, our model is required to build a well-designed devices and system. In our model 1, we obtain the formula which allows us to calculate [E.coli] from GFP intensity. While in model 2, we obtain the formula which allows us to calculate how long the testing devices should wait to get the result of the test based on the [E.coli] calculated in mode 1. For [E.coli] and the time interval, they will be demonstrated on our devices to show them to the testing devices. To sum up, Our model act as a bridge between our testing devices and the testers, and quantifies the significant parameters in our project, which allow the masses to simply get the result of the test without complex calculations.