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Modeling
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2. Reasons for the choice of modification 2.1 Modifiable parameters in the system 2.3 Prhl or Plux should be changed
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1. Abstract |
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Since our system should describe the economy, we have to make sure the culture grows well. To ensure the system’s robustness, we analyzed which components should be concerned. As the result, we found that the Prhl and Plux promoters should be strong and balanced. |
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2. Reason for the choice of modification |
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2.1. Modifiable parameters in the system |
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Since the system has fewest components to achieve the mutualism, what we can change is the values of parameters. In the parameters of the equations, modifiable parameters are listed in Table 4-2-2-1. |
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Table 4-2-2-1 Modifiable parameters |
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Leak is not listed above because Company and Customer will be independent if the leak increase. |
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2.2. Modifications |
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Since there was no time to modify two or more components in the system, we should be able to achieve the goal with just one modification of the components. In the following we will examine which one to be concerned one by one. |
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2.2.1. The growth of cells (corresponds to k in equation (1) and (2) (Fig. 4-2-2-2.)) What we can do about this parameter is just to make the value lower than the previous one because maximum growth rate of E. coli is estimated to be 0.02 /min. Since lowering down the value results lower population, this change of parameter is not suitable to make cells grow more. |
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2.2.2. C4HSL, 3OC12HSL production rate by RhlI, LasI (corresponds to k in (3) and (4)) Signaling molecule production rate by RhlI, LasI can be changed by modifying RhlI , LasI protein to make more signaling molecule. We set these values to be 0.1 originally. The following graph shows how the final populations of Company and Customer change depending on the value of signaling molecule production rate. In this simulation the value of k in equation (4) is varied. |
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Fig. 4-2-2-3. Final growth dependency of C4HSL production rate by RhlI |
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As shown in Fig. 4-2-2-1, if the value is over 0.1, then the final populations of Company and Customer get higher. Thus this value should be concerned when we want to make this system robust. |
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2.2.3. Degradation rate of C4HSL and 3OC12HSL Changing pH of the medium can change degradation rates of C4HSL and 3OC12HSL. Degradation rates d of equation (3) and (4) are varied simultaneously because the variation of pH affects not only d of one signaling molecule, but both of them. In the simulation shown in Fig. 4-2-2-4 , the degradation rates are varied from 10^-4 to 10^0. |
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Fig. 4-2-2-4. Final growth dependency of degradation rate of signaling molecules |
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The result implies both Company and Customer will grow well if the degradation rates of signaling molecules are low. Thus this value should be concerned when we want to make the system robust. |
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2.2.4 Maximum expression rate of proteins following Prhl and Plux promoters (corresponds to alpha in equation (5) and (6)) Mutating promoter can result improving the maximum production rate of the following proteins. Thus the dependency of the final populations of Company and Customer was examined by varying the value of maximum expression rate alpha. The result is shown in Fig. 4-2-2-5. |
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Fig. 4-2-2-5. Final growth dependency of strength levels of Plux and Prhl promoters |
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The parameter alpha was originally set to 10. From the graph, if the parameter value increase, the populations of Company and Customer also increase. This means improving promoter can result in increasing populations. Thus this value should be concerned. |
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2.2.5. Degradation rates of RhlI, LasI, chloramphenicol resistance (corresponds to d in equation (5), (6), (7), (8)) The final populations are simulated with varying the parameter values. First degradation rate of RhlI was changed. The original value was 0.01. The graph in Fig. 4-2-2-6 is the result of the simulation. |
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Fig. 4-2-2-6. Final growth dependency of RhlI degradation rate |
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The graph tells population of Company and Customer can be higher if the degradation rate of RhlI is made to be lower. But we have no way to make the degradation rate higher, we cannot make the system robust in this way. About degradation rate of chloramphenicol resistance, there’s no meaning in changing values. What we can do is only increase the degradation rate, but that results in reducing the internal chloramphenicol resistance concentration. This means the cells become easy to be killed. This is not an expected outcome. |
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2.3. Prhl or Plux promoter should be changed |
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From the examination above, components which should be concerned are C4HSL, 3OC12HSL production rate by RhlI, LasI and Maximum expression rate of proteins following Prhl and Plux promoters. Since it is difficult to change the protein’s properties, we decided to change thestrength levels of Prhl and Plux promoters. |
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3. Further analysis |
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Finally, since we can change both of the promoters in the system, we simulated many combinations of promoter strengths. The following shows the result of our examination. |
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Fig. 4-2-3-1. Relation of growth and intensity of Plux and Prhl promoters |
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The above diagram shows the intensity of the two promoters should be in the red region in the figure. The figure shows not only we have to make the intensity stronger, but also have to make the intensity equal. Thus we made Prhl_RL(BBa_K1529300) which has approximately same intensity to the Plux promoter. |
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