The value of OD600 is proportional to the number of bacteria in a certain interval, so it was used to present the number of bacteria.

Parameters can be obtained by least square method to fitting the curve into the experiment data.

We considered the growth of bacteria carrying different plasmid, which corresponding to two of our outputs. It can be seen that different plasmids bring different metabolism burden to bacterium. The total expression of outputs can toughly be considered to be proportional to the number of bacteria. The model of free growth is important to predict the total expression, and is also basic for other models.

Part 2 Light’s influence to the growth of bacteria

We developed a model to assess the influence of illuminance to the growth of bacteria.

Questions to answer:

1. How does the illuminance change with distance?

2. What is influence of illuminance to the growth of bacteria?

3. In which illuminance the change rate of growth is lowest?

We measure the illuminance in different distance and get an experience formula describing how illuminance change with distance. Let I(lux) be the illuminance, let x(cm) be the distance, we get:

Let h(cm) be the vertical distance from the plate to the light, and d(cm) be the horizontal distance from the light. We get:

x²=d²+h²

And by measuring d, h, OD600, we get the curve.

It can be seen from the figure 3 that the light has a negative effect to the growth of bacteria. And larger the illuminance is, slower the bacteria grow. Figure 4 is obtained by the curve from Figure 3, which describes the absolute value of change rate of OD600. And the decrease rate is lowest when the illuminance is around 2200lux, in which condition the growth of bacteria is even。

Part 3 How expression of fluorescent changes with time.

We created a kinetic model to simulate the dynamics of the fluorescent expression system we sued.

Questions to answer:

1. What are the reactions happened in this process?

2. How does the concentrate of outputs change with time?

The following reactions were modelled:

The process of expression of RFP and GFP are similar, the process of GFP are different.

We consider the expression of RFP first.

[X] refers to the concentration of X in equations appearing behind.

The sensor sense light and influence the product of OmpR1.

k1 refers to generation rate of OmpR1, and is related to the type of light. For a certain light, k1 is a const.

k32 refers to the decay rate of OmpR1, and is related to the concentration of OmpR1.

The transcription of protein CI is regulated by OmpR1.

We get

By the assumption that the decay rate of mRNA is large, the concentration change of mRNA is nearly zero.

k4 is a function of [OmpR1] and [RNAP]. The concentration of RNAP can be considered as a const. The regulation of OmpR1 can be expressed as a form of Hill equation [2]. We get:

The translation of CI:

The expression σKIF is regulated by CI:

We get

k10 is a function of [OmpR1] and [RNAP]. The concentration of RNAP can be considered as a const. The repression of CI can be expressed as a form of a transformative Hill equation [2].

Then σKIF combine with the core, forming Core:mRNAKIF, a complete RNAP. We consider the concentration of Core:mRNAKIF is in direct proportion to the concentration of mRNAKIF[3].The combination is then involved in the transcription of RFP:

We get

k15 is a function of [Core:mRNAKIF], and according to Michaelis-Menten equation[4], the function is in form of:

And then is the translation of RFP:

We get the last equation:

This is a summation of mentioned equations:

Similarly, we can get the equations BFP’s expression:

The progress of GFP’s expression is different, the equations are:

We take expression of fluorescent in red light as example.

The data and the curve obtained by equations have similar value and trend, which proves that the simulation is reliable.

We can acquire a better understanding of the light sensor and RNAP system[4] through the model. The relationship between concentration of three flourescence and time are shown in figure5 and figure6.

Figure 7 shows the change of BFP and GFP concentration when the concentration of mRNAKIF is twice, five, and ten times than the concentration in figure 6.

The relationship between concentration of three flourescence and time are simulized, which can help us get assumed flourescence concentration by altering the time.

Part 2 Light’s influence to the growth of bacteria

Part 4 The light’s influence to the expression of fluorescent.

We established models to assess how illuminance and wavelength effect the expression of fluorescent.

Questions to answer:

1. How does illuminance effect the expression of fluorescent?

2. How does wavelength effect the expression of fluorescent?

3. What is the color difference among difference color acquired in different light of wavelength?

We consider the influence of intensity first.

Bacteria are put in different illuminance of light, and it is shown that the illuminance of light has a negative effect to the expression of fluorescent. The expression of RFP gradually increases at beginning several hours, and reaches a plateau.

The expression of fluorescent decreases when the illuminance increases though the light can motivate the light sensor, indicating that at a certain illuminance, the switch is open and will not change even the illuminance is larger. As the increase of illuminance, the growth and expression of fluorescent are slower, causing the decrease of fluorescent.

Except illustrating the influence between wavelength and fluorescent, we choose another way to show the influence of wavelength more directly. We project 11 kinds of different monochromatic light to plate with our bacteria in a certain intensity, and motivate three kinds of fluorescent separately, take the photo in a same condition, and compound the three pictures. As expected, the compound pictures are nearly in one color. We get the color’s RGB value, and get a fitting curve.

• 2016 Manchester
• 2016 TU Delft
• 2014 ETH Zurich
• 2014 Waterloo