## 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 draw the infected 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 1.1 shows the relative fluorescence units (RFU) of GFP with different MOI values of E. coli. 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 cells transfected with DNA has basal levels of GFP before responding to the E. coli. Thus, the background intensity of GFP should be eliminated for the actual RFU to obtain the relationship between E. coli concentration and GFP intensity, which means [GFP] (i.e, RFU of GFP) should minus the [GFP_{0}] of cells before the addition of E. coli (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 [GFP], 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 GAM1 Promoter in Response to Number of E. coli Cells Increase With Time

### Method

To know how GAM1 promoter could be induced by E. coli concentration, we measure the GFP intensity with different MOI values every two hours. Then, we differentiate the curves, as are illustrated in Figure 3.0 - 3.4, to find the time that the instant GFP expression level reaches the maximum, which means the time E. coli cells begin to activate GAM1 promoter.

### Relative fluorescence units (RFU) of GFP intensity in different MOIs of E. coli

The RFU of GFP intensities of GAM1 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

### E. coli Concentration Calculator

Type in the value:The calculator can calculate E. coli density based on the GFP intensity.

Calculation Result

Variable | Value | Source |
---|---|---|

GFP Intensity | RFU | |

E. coli Concentration | Number of Cells Per uL | Model 1 |

### Responding Time Calculator

Enter value:The calculator can calculate responding time based on the E. coli concentration.

Calculation Result

Variable | Value | Source |
---|---|---|

E. coli Density | Number of Cells Per uL | |

Responding Time | Hr | Model 2 |

## Conclusion

Our model not only builds the mathematical system which could be applied to our devices, but also makes us better understand our project. Because our device can only detect the GFP intensity, our model is required for a well-established 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 device should take to get the result of the testing in response to a known concentration of bacteria. To sum up, our model obtain the significant parameters for our prototype design and provides information of the device limitation.

Introduction

Model 1

Model 2

Conclusion