# Team:Nanjing-China/model

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Figure 6, the simulation of circuit 3.

Figure 6, the simulation of circuit 3.

- Let's see the characteristics of each circuit respectively first. Bacteria with circuit 1 move randomly all the time, so the result of their aggregation exhibit uncertain scene. The results of bacteria with circuit 2, meeting our expectation, demonstrate the dull response of the complex circuit. As to circuit 3, this kind of bacteria gets together in the region of much atrazine gradually. Circuit 1 is the classical design, which is proved by so many researchers to have a good result of attracting bacteria.
+ Let's see the characteristics of each circuit respectively first. Bacteria with circuit 1 move randomly all the time, so the result of their aggregation exhibit uncertain scene. The results of bacteria with circuit 2, meeting our expectation, demonstrate the dull response of the complex circuit. As to circuit 3, this kind of bacteria gets together in the region of much atrazine gradually. Circuit 1 is the classical design, which is proved by so many researchers to have a good result of attracting bacteria.

- Compared to circuit 1, circuit 2 may have a more stable result. However, circuit 2 just need too much time to respond to the signal of cell density.
+ Compared to circuit 1, circuit 2 may have a more stable result. However, circuit 2 just need too much time to respond to the signal of cell density.

Circuit 3 has speed up the respond time of circuit 2. Besides, circuit 3 can attract the bacteria around the atrazine step by step, which can prevent the situation of too many bacteria aggregate at one point as circuit 1. In another word, circuit 3 works more stably and make it possible to have a mean distribution of bacteria to each atrazine region.
Circuit 3 has speed up the respond time of circuit 2. Besides, circuit 3 can attract the bacteria around the atrazine step by step, which can prevent the situation of too many bacteria aggregate at one point as circuit 1. In another word, circuit 3 works more stably and make it possible to have a mean distribution of bacteria to each atrazine region.

## Revision as of 19:30, 27 September 2013

Introduction
As you can see in the previous parts, the shining point of our design is that we have introduced the quorum sensing device into our circuit. In order to see what the characteristics of our design are during the process of attracting E. coli to atrazine, we have built three models respectively and compared their possible behaviors.

The first circuit, we called circuit one, is the most simple one, which has been constructed by Joy sinha et al in 2010. In this circuit, bacteria will stop walking in the region with high concentration of atrazine, in which way bacteria will finally get together to this region. However, bacteria can't tell each other the information about the destination like ants, which will tell their companies the location of food.

Figure 1, Circuit 1. Atrazine will promote the translation of the CI protein. However, the CheZ protein, which represent the motility, will be repressed when the concentration of CI protein is high. So, the consequence will be more and more bacteria stopping in the region with high Atrazine.

The second circuit is our original blueprint with a complex structure and you can see the quorum sensing device here. It is a little complex and has a cascade, which is believed to prolong the respond time of our system. In short, the behavior of bacteria will be affected by the concentration of AHL, which represents the density of bacteria. In this way, the bacteria around the atrazine region are expected to move faster than the bacteria far away from this region.

Figure 2, circuit2. The movement of the bacteria with this circuit will affected by the presence of AHL. In our initiate consideration, the cascade, AHL&LuxR→Plux-tetr---Ptet-CI---Pci-CheZ, will lead to the promotion of the production of CheZ protein.

The third circuit is the ultimate one that we have designed and optimized.We have replaced the cascade mentioned above with a hybridize promoter, which can be repressed by CI protein and activated by AHL-LuxR compound. As thus, we are able to short the respond time of bacteria, which in turn can make our circuit more efficient.

Figure 3, circuit 3. The greatest difference between circuit 2 and circuit 3, as you can see, is that the cascade in circuit 2 have been replaced by the hybridize promoter, Plux/CI. Then, we got a new organism that will respond quickly to the presence of AHL.

The most important is that we want to have a preview of the behavior of the three circuits mentioned above. Thus, we can compare them and prove that our final design can attract bacteria efficiently and send out the information of atrazine to bacteria around these regions to make them have a stable movement.
Results
These three models were all coded in MATLAB. As mentioned above, we have just changed several statements in the second model to construct the first and the third. Finally, we have got how the distribution of bacteria changed with time, which can make us catch the major difference among three circuits more directly.

Besides, we have made census of the number of bacteria within the atrazine region in different circuits respectively. Then, we compared the outcome to find out the efficiency of different circuit.

Figure 4, the simulation of circuit 1.

Figure 5, the simulation of circuit 2.

Figure 6, the simulation of circuit 3.

Let's see the characteristics of each circuit respectively first. Bacteria with circuit 1 move randomly all the time, so the result of their aggregation exhibit uncertain scene. The results of bacteria with circuit 2, meeting our expectation, demonstrate the dull response of the complex circuit. As to circuit 3, this kind of bacteria gets together in the region of much atrazine gradually. Circuit 1 is the classical design, which is proved by so many researchers to have a good result of attracting bacteria.

Compared to circuit 1, circuit 2 may have a more stable result. However, circuit 2 just need too much time to respond to the signal of cell density.

Circuit 3 has speed up the respond time of circuit 2. Besides, circuit 3 can attract the bacteria around the atrazine step by step, which can prevent the situation of too many bacteria aggregate at one point as circuit 1. In another word, circuit 3 works more stably and make it possible to have a mean distribution of bacteria to each atrazine region.

Figure 7, the number of cells in the atrazine region of circuit1.

Figure 8, the number of cells in the atrazine region of circuit2.

Figure 9, the number of cells in the atrazine region of circuit3.

The Figure 7~9 exhibits some quantitative results of the three circuits. It is easy for us to find that the number of the cells in different circuits changed in different ways. The number of cells with circuit 1 in itself in specified region may have different rate in different situation due to randomness. However, the bacteria with circuit 3 aggregate in specified gradually, which shows a nearly straight-line slope in the figure 9. At last, figure 8, which present circuit 2, exhibits little change about the number of cells in specified region.
Equations
After drawing a profile of our project, we should make the process of every event more clearly. So, we have constructed the models of our three circuits by the principles of biochemistry.
First, we have constructed a model related to the circuit 2, the most complex one, with the help of Tsinghua-A. Then, in order to compare them, we have also constructed the other two based on the model of circuit 2. In our model, we use ODE to describe the process of chemical reaction in organisms.
In general, we have divided the chemical events in our bacteria into three parts, the transcription of DNA, the translation of RNA, the production of micromolecule-compounds. The rate of each event can be described by ODE listed below.
Circuit1:

Circuit2:

Circuit3:

m_CI1,m_CI2, m_CheZ, m_TetR, m_TrzN, m_LuxI represent mRNA of different protein.
CI1,CI2, CheZ, TetR, TrzN, LuxI represent proteins.
p_AHL represent the AHL produced in each cell.
We have used matrix to describe the state of AHL and the location of every bacteria. By the way, we have also made the density of bacteria related to the distance of bacteria. At last, we have considerate the degradation of atrazine as well, though which proved to have little influence on atrazine latter. And a space lattice of "culture dish" is demonstrated below.
Space relation:
e_AHL represent the AHL in the environment.
PXn, Pyn represent the location of bacteria.
Cdn represent the density of bacteria in a lattice.
Atz represent the atrazine.

Parameter

Reference
[1] The wiki of iGEM11 TsinghuaA, https://2011.igem.org/Team:Tsinghua-A/Modeling.
[2] The wiki of iGEM11 USTC, https://2011.igem.org/Team:USTC-China/Drylab/modeling.
[3] Basu, S., Gerchman, Y., Collins, C. H., Arnold, F. H. & Weiss, R. A synthetic multicellular system for programmed pattern formation. Nature434, 1130-1134 (2005).
[4] Goryachev, A., Toh, D. & Lee, T. Systems analysis of a quorum sensing network: design constraints imposed by the functional requirements, network topology and kinetic constants. Biosystems83, 178-187 (2006).
[5] Hooshangi, S. & Bentley, W. E. LsrR Quorum Sensing "Switch" Is Revealed by a Bottom-Up Approach. PLoS computational biology7, e1002172 (2011).