Model
We encountered a huge problem with the genetic circuit in the project's design phase: how to export lacc6 in vitro? Since E. coli has many ways to export proteins to outside, we needed to choose the most efficient way to enhance the practicality of our project. Through consult, we know that E. coli export protein mainly by anchoring, transport, and diffusion. The molecular mechanisms of each of these three methods are vastly different, which makes it difficult to directly choose the right one.
A valid mathematical model can simplify the experimental work and also provide an intuitive demonstration of the results, so we developed a model of protein export. This model can calculate the amount of protein exported by different ways of intracellular protein export. By consulting materials [1-4], we constructed four molecular dynamic models respectively. Based on the results of molecular dynamics simulation, we finally selected INP protein to output lacc6 by anchoring:
The intracellular protein content of E. coli:
The significance of this model is to provide the concentration of E.coli intracellular proteins as an input to the other three molecular dynamics models, so as to explore the efficiency of different export methods.
Figure:
The amount of intracellular protein transported out of the cell in E. coli:
The main transport mode in E.coli is Sec system, so we constructed a model based on the molecular mechanism of Sec system according to the theory proposed by Allen et al. E. coli intracellular proteins are transported out of the cell through multiple steps, and this complex process can be simplified into two steps: Multiple protein transport steps are integrated into a one-step transport process with rate Kstep. Protein transport failures are blocked in protein channels.
Figure:
The amount of intracellular protein diffused out of the cell in E. coli:
Although biological macromolecules are difficult to export the cell membrane by diffusion, according to data [4], protein diffusion exists in the cell membrane of E.oli. We used the diffusion coefficients of the data and calculated the diffusion rate per unit time according to Fick's first law and Fick's second law[2]. In addition, we assume that the concentration of protein in the cell is 0 with distance, thus simplifying the gradient operator.
Figure:
The amount of E. coli intracellular proteins anchor on cells:
Anchoring is the process of fusing the expression of the membrane anchor protein and the target protein to export the target protein out of the membrane. This process can also combine the rate of multiple steps into one.
Figure:
Conclusion:
After summarizing the results of protein content of the three export methods, it can be found that the three methods have obvious differences in the efficiency, among which the anchoring method export the most protein, which guides our project to use INP protein to export lacc6 by anchoring method.
Reference:
[1] Allen W J, Corey R A, Watkins D W, et al. Rate-limiting transport of positively charged arginine residues through the Sec-machinery is integral to the mechanism of protein secretion[J]. Elife, 2022, 11: e77586.
[2] Stewart P S. Theoretical aspects of antibiotic diffusion into microbial biofilms[J]. Antimicrobial agents and chemotherapy, 1996, 40(11): 2517-2522.
[3] 2015.igem.org/Team:HUST-China/Modeling_on_Ecosystem_Level
[4] Alon U. An introduction to systems biology: design principles of biological circuits[M]. Chapman and Hall/CRC, 2006.