Model

Modelling help us to choose which kind of switch to be the best one ,and tell us which part should be improved after a experimental data-correction. Then, we use modelling to simulate the long-term co-culture in suspension system and tell us the relatively exact ratio of bacteria and algae number would be, which is also helpful in biofilm system to control its growth.

I.Optical switch modeling simulation and experimental correction

1. Optical switch modeling simulation

At the beginning of the design, we did not decide whether to use chemical signal or light signal to control two kinds of proteins ‘ expression. We used simbiology software to built a theoretical model for the whole pathway, which respectively simulated the control system of optical signal and chemical signals.

There are two types of proteins, one for absorption and one for release. Our idea is to use one control switch to control the expression of one type of protein, add a Not Gate to control another type.

As shown, there are several possibilities for switches that switch between state 1 and 0: chemical control, light control, and natural oscillation. Natural oscillation is very difficult to control protein expression time, so we used modeling to simulate both chemical control and light control.

(1).Chemical switch:

I represents the concentration of the chemical, A and B represent PPK and PPX-PPN respectively (because PPX and PPN are simultaneously expressed and closed, thus can be regarded as one protein),Gx refers to promoter and X refers to tet(Not Gate). We take appropriate time period, the rest of the parameters are set according to the default value, the concentration of the chemical is ideally a “jump” change, so each time we restart, we make the chemical concentration become a fixed value, the simulation results are as follows :

Figure1 shows the simulation of ideal chemical control pathway

From the modeling results, it can be concluded that after proper adjustment, the two proteins can be cyclically alternated in concentration. However, the actual situation becomes more complicated if a given chemical signal is used as a switch. We add a high concentration of a chemical in one of the different places (phosphor-absorbing turbines and recycling pool). During each transfer of the conveyor, chemicals accumulate in the bacteria, and the accumulation rate can be simply abstracted into a linear increase in the early stage. That is, the absolute value of the chemical concentration will increase at the end of each cycle. Simulations of various kinds of increases have been made, and the results are the same - as long as there is a accumulation of chemical signals, the entire system will eventually collapse.

We give an example of 25 percent increments:

Figure2 shows the simulation in chemical control pathway if accumulation happens

It can be seen that the kind of protein directly controlled by the chemical signal will eventually dominate. The non-gate can no longer reverse the expression of the pathway, and the system will continue to absorb or continue to release, and the circulatory system collapses. Therefore, the control switch of the chemical signal seems not so reliable in applications.

(2).Optical switch:

In this pathway, there is no accumulation of signal, and the concentration of photo-sensed protein(Ccas) can be considered to be relatively constant. A and B represent the two types of functional proteins. We simulate it, giving the parameters with default values, and select appropriate time period, the simulation results obtained are as follows.

Figure3 shows the simulation of light control pathway

It can be seen that the results of the simulation is as expected. The two proteins are expressed in alternating cycles for a long time. Combined with our conveyor, the position of the engineered bacteria is periodically changed, the phosphorus is continuously absorbed in the environment, and released in the ark. That allows our system to continuously collect phosphorus in the environment. Through modeling simulation, we finally determined the optical signal as a switch.

2.Experimental corrections and improvements:

The actual experimental situation is not as ideal as the modeling simulation. Since the time period can be freely chosen, most of the parameters after experimental fitting have no significant influence on the pathway compared with the default value, such as the degradation rate of the protein. However, we have identified several key factors that may cause the system to be quite different from the simulation:

(1). Incompleteness of Not Gate:

In the simulated case, the Not Gate is the immediate switching state of expression, but in biological systems, this is not the case - We used the classic tetR-PtetR Not Gate system, which makes the expression of the Not Gate appears to be delayed and incomplete. We have conducted optical signals simultaneously on the path of the regular pathway and the Not Gate-contained pathway in the experiment. We reverse the light condition (red-green, green-red) and compared the reversal amplitude of the regular one with the Not Gate-contained one, the incompleteness of the non-gate is obtained. In the model, the k-forward simulation of the Not gate changed from 1 to 0.63, and the experimental correction of the modeling was performed. Got the following results.

Figure4 shows the simulation after the correction of experiments(Not Gate)

Surprisingly, the incompleteness of the Not Gate does not have a significant impact on the overall cyclical trend, because time is free to choose to adjust, thus the delay has no effect. Modeling simulation corrections suggest that the choice of Not Gate may not be as important as we thought at first.

(2).Leakage of light control switch:

Considering the actual situation and the symbiosis of our bacteria and algae, we chose a relatively common light control switch - Ccas/Ccar-PcpcG switch, which is a green light-on, red light-inhibited system. However, this pathway have some leaking expressions. Leaking expressions will make the pathways not completely controlled by light, and we thought it may also influence the system's work. We calculated the leakage amount for the data that was induced for 5 hours. In the modeling, we found that the deviation from the original curve was huge. We then lowered the leakage amount. Although we have adjusted the leakage to 10%, the result is still very terrible.

Figure5 shows the simulation after the correction of experiments(leakage expression)

Figure 6 shows the simulation after correction of experimental (adjust leakage to 0.1)

Taking the situation in the figure as an example, the time at which B is controlled to be expressed can hardly exceed A. Since the pathway component is determined, and other conditions cannot be changed to make the situation back to our original simulation. situation. That is to say, once the leakage exceeds the critical value, the system will also experience continuous absorption or continuous release, causing the circulation system to collapse. This suggests that in the subsequent improvement of this system, the very and only(almost) important factor to be considered is the leakage expression of the light control switch. Before the modeling analysis, we thought that the first thing in the subsequent improvement is to choose a better Not Gate. Now it seems that there is a new choice in the direction of improvement.

II.Long-term growth curve fitting of suspension co-culture of bacteria and algae

You can’t verify enough for the best symbiotic system experiments. A multi-organism system involves debugging and co-living of two kinds of creatures.

Although we have explored the optimal ratio of bacteria and algae in the co-culture, the model simulation of optimal ratio still remains meaningful. Not only can tell us about the best condition to co-culture both of the bacteria and algae ,but also has great significance for the debugging of the symbiotic system and the growth control of the symbiotic biofilm. We measured NPOC, total nitrogen, total phosphorus to ensure the culture system to be stable. And we measured the bacterial and algae number and used dynamic fitting to simulate long-term co-culture. Finally we draw a growth curve of four different groups that are different in the initial ratio of bacteria to algae.

Figure 7 these four figures uses growth curve to simulate a long term co-culture situation

Finally, we selected four experimental groups with stable culture environment. The prediction results of long-term culture provide us with a more detailed range to make the system to be stable，and that ratio is close to 1:1(number).

Team:WHU-China/Model