Modeling
In our project, we release four enzymes produced by our engineering bacteria to degrade the serotonin and guaiacol based on the synchronized lysis circuit (SLC). In order to predict the effectiveness of final design of our project, we did the modeling for the prediction.
Figure 1: Gene circuit of SLC in the Nature article: the system contains activator plasmid to express LuxR and LuxI, and lytic plasmid to initiate cell lysis. When the number of bacterial populations reaches the threshold, bacteria will show fluorescence, and then lysis [1].
In our project, we referred the M. Omar Din et al., Nature, 2016, which provided a marvelous idea for us to release enzymes into environment. In their work, they made the ordinary differential equations to illustrate how the SLC works. Following modeling shows how the population of bacteria is changed based on the SLC.
Equations 1: The dynamics equations of SLC：the ordinary differential equations show the changing rate N (the population of bacteria), H (the concentration of AHL molecules), L (the concentration of lysis protein), I (the concentration of luxI protein) [1].
Table1: The Parameters Table of SLC
The changing rate of N (the population of bacteria) is determined by the normal growth of bacteria and L (the concentration of lysis protein). Furthermore, L is changed because of the changeable Plux (Promoter strength). At the same time, H (the concentration of AHL molecules) determines the value of Plux. Also the H are transformed from I (the concentration of Lux I). As the result, the population of bacteria is oscillated in a certain interval over time. Following graph demonstrates that N changes over time.
Figure 2: The trend of bacterial growth with time. The population of bacteria exhibits a oscillation over time.
We modified the original model, which is fitted to the locust intestinal canal condition, by adding some parameters, which considers Intestinal peristalsis of locusts. Also, we added a new equation which shows the rate of releasing enzymes from E. coli cells and the degradation of pheromones over time. We assume that the copy number of activator plasmid and the lysis plasmid is same. Figures below are the modified ordinary differential equations and the results.
Equation 2: the modified equations of SLC. Variables：I: LuxI, H:AHL, L: Lysis protein, N：population, P: enzymes, Pt：pheromones.
Table2：The Parameters Table of Modified SLC
Figure 3: The result of modified SLC and the changing of concentration of pheromone. The population of bacteria is oscillated concentration of protein increases and maintains in a high concentration, which is effective to reduce the concentration of pheromones.
Furthermore, in order to optimize our system, we changed the value of the copy number of two plasmids. We tried the 0.1,1,10 as the copy number of plasmids. Figures below are the results of that.
A
B
C
Figure 4: The SLC With Different Copy Number; A: Copy number = 0.1; B: Copy number = 1; C: Copy number = 0.1
When the copy number equals to 0.1 or 1, the perfect oscillation of bacteria number and absolutely decreases the pheromones. However, when the plasmid copy number is higher, the population of bacteria decreases rapidly because of high copy number of plasmids.
According to the graphs above, we predicted that when copy number is 0.1, it shows the best oscillation of bacteria population. However, it is the invalid value of copy number. Then, when the copy number is 1, the population of bacteria also oscillates in an interval, and it is effective to reduce the concentration of pheromones. For the copy number 10, the population of bacteria and the concentration of enzymes decreases rapidly, which can’t lower the concentration of pheromones. Obviously, the low copy number vector is the best option for our system.
To certify the effectiveness of our system, we compared the quantity of pheromones in locusts with our bacteria to without our bacteria by our calculations. The outcome shows below.
Figure 5: The comparison of the concentration of Pheromone among with SLC and without it;the graph above the concentration of pheromones in locust without our system and the graph below is with our system.
In summary, according to the results showed above, we speculated that the concentration of enzymes can keep in an interval steadily, which is really effective for the degradation of serotonin and guaiacol.
References
[1] Din, M. O., Danino, T., Prindle, A., Skalak, M., Selimkhanov, J., Allen, K., ... & Hasty, J. (2016). Synchronized cycles of bacterial lysis for in vivo delivery. Nature, 536(7614), 81-85.