Team:Bilkent-UNAMBG/Model
Modelling is the one of the essential part of the synthetic biology. The understanding and standardizing of how a genetic circuit works are crucial to use this circuit for future applications. In this model, we are trying to optimize our system to choose its components such as plasmid origin, promoter strength. Moreover, this model gives us the time scale if we would like to use this system as a probiotic treatment. When should be the probiotic and inducer taken? When does the system come expected working concentration? In order to answer these questions, our model contains four different part.
1) Escherichia coli (E. coli) growth model 2) Single chain insulin (SCI) production and transportation model 3) TEV enzyme production and transportation model 4) Stochastic model of single chain insulin release via TEV enzyme activity
In order to calculate total SCI amount in a culture, we should know how fast bacteria are grown. After finding the SCI production level per bacterium, we can easily gather these two equation together to see SCI amount at a population level. According to our literature search, we have found an article about population growth for bacteria (Koseki et al). In the article, recommended differential equation for population growth is
The results for 6 different bacterial culture and their prediction with modelling are in the figure.
After getting the true equation for growth, we can generate our second model. We have got experimental data for fluorescent/OD600 for 12 hours of incubation.
Since our model can be used for protein amount per bacterium, we should convert these graphs to that unit. In order to make this, unit conversions and fluorescence - mass relationship were used from TU_Delft 2015 iGEM team.
According to their fluorescence-mass relationship,
After conversion of fluorescence/OD600 to protein/cell, the graph becomes,
Now, we can start to write our model according to Michaelis-Menten kinetics.
After equations were solved via dsolve function in MatLab, graphs seemed like below. Predictions were done to create correlation between limitedly available experimental data.
These graphs show us protein amount for single bacterium. If we gather these model with growth model and 1 OD600 = 8*10^8
bacteria conversion, we can get the total protein amount per ml.
Same equations in the model 2 are still valid for TEV enzyme production and transportation model. Only differences are promoter strength (11) and the constants which depend on protein length . Also, the occupancy can be still 0.85 to prevent confusion (Normally, we assume 60% occupancy with bacteria’s own proteins, 15% for other protein in model 2 and 15% for the protein in this model.
For the last model, we create a Gillespie algorithm to make stochastic release model. Since all inductions for TEV production were done after single chain insulin amount became steady state, we can make the model dependent on TEV amount at a random time. Also released single chain insulin will be degraded and it should be faster than the degradation rate inside the cell. Thus, our model takes the degradation rate outside of the cell as 5.4*10^-3 (10-fold faster). The activity rate is taken from (12).
The maximal amount of released protein per ml is 3.8331*10^14. This means 0.6 nM of concentration. This is maximal concentration at a time. In a human body, this can be produced in every single second after it reaches the steady state since it will be not degraded, it will be used!
(No Title). (n.d.-a). Retrieved December 14, 2019, from https://bionumbers.hms.harvard.edu/files/Protein half-lives in E. coli.pdf
Modeling
1) Escherichia coli (E. coli) Growth Model
After equation was solved via dsolve in MatLab, experimental observastion was used to optimize constants such as q0 , μmax and ODmax. Optimized constants are
#
Constants
Value
Unit
1
q0
1.5
-
2
μmax
0.5
h-1
3
ODmax
0.9
-
2) Single chain insulin (SCI) production and transportation model
and unit conversions are
For pZA plasmid containing cultures, number of plasmid was chosen as 40. For pZS, this number became 13(10).
3) TEV enzyme production and transportation model
For this construct, we have 3 different plasmid type: pZE, pZA, pZS. Their copy number are chosen from literature as 85, 40, 13 respectively.
These graphs show that the TEV amount per ml at the steady state is 6.637*10^13.
4) Stochastic model of single chain insulin release via TEV enzyme activity
After simulating our algorithm on MatLab, the graphs are
To sum up, after a probiotic treatment and induction at least 5 days (bacteria with pZA Single chain insulin and pZE TEV) at most 17 days (bacteria with pZS Single chain insulin and pZS TEV) were needed to observe a meaningful response. This gives us a chance to make individual treatment for every situation. This range is important for creating organ-like response to glucose since it will be tunable with different bacterial combinations.
References
(No Title). (n.d.-b). Retrieved December 14, 2019, from https://www.iitm.ac.in/bioinfo/fold-rate/
Ahan, R. E., Kırpat, B. M., Saltepe, B., & Şeker, U. Ö. Ş. (2019). A Self-Actuated Cellular Protein Delivery Machine. ACS Synthetic Biology, 8(4), 686–696. https://doi.org/10.1021/acssynbio.9b00062
Davis, J. H., Rubin, A. J., & Sauer, R. T. (2011). Design, construction and characterization of a set of insulated bacterial promoters. Nucleic Acids Research, 39(3), 1131–1141. https://doi.org/10.1093/nar/gkq810
EXPRESSYS - pZ Vectors. (n.d.). Retrieved December 14, 2019, from http://www.expressys.com/main_vectors.html
Hink, M. A., Griep, R. A., Borst, J. W., Van Hoek, A., Eppink, M. H. M., Schots, A., & Visser, A. J. W. G. (2000). Structural dynamics of green fluorescent protein alone and fused with a single chain Fv protein. Journal of Biological Chemistry, 275(23), 17556–17560. https://doi.org/10.1074/jbc.M001348200
Kelly, J. R., Rubin, A. J., Davis, J. H., Ajo-Franklin, C. M., Cumbers, J., Czar, M. J., … Endy, D. (2009). Measuring the activity of BioBrick promoters using an in vivo reference standard. Journal of Biological Engineering, 3(1), 4. https://doi.org/10.1186/1754-1611-3-4
Koseki, S., & Nonaka, J. (2012). Alternative approach to modeling bacterial lag time, using logistic regression as a function of time, temperature, pH, and sodium chloride concentration. Applied and Environmental Microbiology, 78(17), 6103–6112. https://doi.org/10.1128/AEM.01245-12
Kudva, R., Denks, K., Kuhn, P., Vogt, A., Müller, M., & Koch, H. G. (2013). Protein translocation across the inner membrane of Gram-negative bacteria: The Sec and Tat dependent protein transport pathways. Research in Microbiology, 164(6), 505–534. https://doi.org/10.1016/j.resmic.2013.03.016
Length, diameter, volume and surface area of - Bacteria Escherichia coli - BNID 106614. (n.d.). Retrieved December 14, 2019, from https://bionumbers.hms.harvard.edu/bionumber.aspx?id=106614
Team:Bilkent-UNAMBG/Project/modeling - 2018.igem.org. (n.d.). Retrieved December 14, 2019, from https://2018.igem.org/Team:Bilkent-UNAMBG/Project/modeling
Team:Sydney Australia/Model - 2017.igem.org. (n.d.). Retrieved December 13, 2019, from https://2017.igem.org/Team:Sydney_Australia/Model
Team:TU Delft/Modeling - 2015.igem.org. (n.d.). Retrieved December 14, 2019, from https://2015.igem.org/Team:TU_Delft/Modeling#gene