Team:Nanjing-China/model

From 2013.igem.org

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.

Fig. 4-1 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. It means that the bacteria can communicate with each other.

Fig. 4-2 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.

Fig. 4-3 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 The greatest difference between circuit 2 and circuit 3, as you can see, is that the cascade in circuit 2 have been replaced by the hybridize promoter, Plux/CI.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 their movement more valuable rather than walking aimless.

Results

These three models were all coded in MATLAB (all can be download here). 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.

Then, we have made census of the number of bacteria within the atrazine region in different circuits respectively. Finally, we have considered the randomness of their movement. We have introduced the Markov chain into the model. We have also counted out the effective aggregation rate, which will dem-onstrate the value of the movement.

Fig. 4-4 The simulation of circuit 1.

Fig. 4-5 The simulation of circuit 2.

Fig. 4-6 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 thay can aggregate much faster than other two. 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 need too much time to respond.

Circuit 3 has speed up the respond time of circuit 2. Besides, circuit 3 can attract the bacteria around the atrazine step by step as circuit 2.

Fig. 4-7 The number of cells in the atrazine region of circuit1.

Fig. 4-8 The number of cells in the atrazine region of circuit2.

Fig. 4-9 The number of cells in the atrazine region of circuit3.

The Fig. 4-7~9 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. Here, it is clear that, the bacteria with circuit 3 aggregate in specified gradually, which shows a nearly straight-line slope in the fig. 4-9 as the behavior of circuit 2. At last, fig. 4-8, which present circuit 2, exhibits little change about the number of cells in specified region at the beginning. Shortly，the census has further proved the result obtained from figure 4-4~6.

We have mentioned that we have introduced the QS systems into our design as circuit 2 and circuit 3. However, we can't find out its advantages in figure 4-4~9 and our result is got from limited times of simulations. In order to solve these questions, we have got the figure 4-10~12, which can illustrate this question clearly.

Fig. 4-10 The aggregation/ the number of moving bacteria ratio of circuit 1.

Fig. 4-11 The aggregation/ the number of moving bacteria ratio of circuit 2.

Fig. 4-12 The aggregation/ the number of moving bacteria ratio of circuit 3.

The figure 4-10~12 have showed the effective aggregation, which is described by the number of cells in regions to the number of moving cells ratio. In this way, we have considered the number of moving bacteria rather than all the bacteria. Because only the moving bacteria are trying to move toward atrazine region.

As we can see from figure 4-10~12, the value of effective aggregation of circuit 1 is always below 1, which means even though their can aggregate so fast at the beginning, their movement is aimless. The circuit 2 respond too slowly and the value of their effective aggregation is low as well. So it has neither fast aggregation nor effective aggregation. Circuit 3 have a peak in the figure, which reached 3 at the beginning. It proved that their movement is goal-directed and our design is more intelligent than circuit 1.

Besides, we have introduced the Markov chain into our model in order to takerandomness of movement of bacteria into consideration. As you can see in the figure 4-10~12, they have 3 curves related to the 3 omega values (=1, 3, 5) and these curve are similar, which suggested that the result of our simulation has little variance. It means that our data in figure 4-4~9 are credible and our designed system is robust and their behaviors are stable.

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.

Markov Chain:

The markov chain is used to evaluate the reliability of limited times of simulations and the robustness of our circuit.

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).