This year modeling plays a great role on our project because we used it to predict the precise time in which our systems start functioning. We showed two essential part modeling below, one is E. coli DH5α and the other one is B. subtilis B. subtilis strain 168(ATCC ® 23857). The showing data will demonstrate our project working result.
Part description pBAD
pBAD is the promoter regulated by both arabinose and the araC gene product. Since that araC gene protein regulates expression is also activated by arabinose, pBAD promoter is enormously effected by arabinose. We modeling the relationship between pBAD activity and arabinose concentration for finding out how to let pBAD reach it maximal activity.
We assumed that our system reacts as the following chemical system:
Assume that AraC is always in large concentration, the binding reaction between AraC and arabinose is very fast. Thus, we don’t have to consider the concentration of arabinose and AraC. We only need to focus on concentration of Arabinose AraC.
To describe the transcription of mRNA, we used Michaelis- Mentin kinetics and get the follow differential equation.
||15ntds−1/length of sequence
||Combineddegradation and dilution rate,of mRNA
||Combineddegradation and,dilution rate of GFP
||Maximal transcription rate
||50ntd,S-1/length of sequence
The above data is all from 2015 Oxford iGEM modeling
Using Polymath, we can get the different signal of GFP in different concentration of Arabinose-AraC.
Figure 1 The respond of GFP in different concentration of Arabinose-AraC. Range 0.13 μM~10μM
We can see that different concentration of Arabinose-AraC will affect the maximum amount of GFP production. We also can see that they reach maximum signal at the same time at approximate 60 minute.
Figure 2 The respond of GFP in different concentration of Arabinose-AraC. Range 6000 μM~130000μM
In high concentration of arabinose, we can see that all the line will overlap. The signal of GFP isn’t changing.
Assume that we want to make a difference in our system, the amount of arabinose shouldn’t be too large, and the interval should be too large either. Because pBAD system is very sensitive to arabinose, a trivial change can result in drastic impact. And we found out that the system would reach equilibrium at approximately 60 mins. So we learned that the kill switch would be activated after 1 hour. So the sampling point interval can be roughly 1 hour.
1. Ben-Samoun, K., Leblon, G., & Reyes, O. (1999). Positively regulated expression of the Escherichia coli araBAD promoter in Corynebacterium glutamicum. FEMS microbiology letters, 174(1), 125-130.
2. Guzman, L.-M., Belin, D., Carson, M. J., & Beckwith, J. (1995). Tight regulation, modulation, and high-level expression by vectors containing the arabinose PBAD promoter. Journal of bacteriology, 177(14), 4121-4130.