Team:RHIT/KineticsModel
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Kinetics Model
Hover over the reactions on the left to see the equations that go with them! Click the "Kinetics Model" title to toggle our visual
These velocities are for systems of individual enzymes and with the assumption of unlimited amount of substrate. This is not accurate for a network system inside a cell, where there is limited resources and an enzyme pathway that uses the products. In our cell simulations, we used differential equations with the product’s creation and degradation velocity and a dilution term for the growth of the cell size. In addition, we added one more equation for the degradation of PET, so we could quantify the amount of PET used. For example, here are the simulation equations for PET and MHET:
Simulations:
Since PET, the system’s substrate, is a polymer solid and the monomer unit MHET is soluble, we made an assumption about the substrate concentration. PET is given in grams so we converted that to number of moles of the repeat units in that amount. Then the amount was put into a concentration given the 10 mL of water of the culture. That concentration of repeat units is what was then used in the differential equations in the kinetics model and the overall model. For this to be biologically relevant, we had to assume a single long chain of PET that had every repeat unit readily accessible. From our interview with Dr. Jared Tatum at Ampacet, we learned that the polymer chain is just lengthened and eventually begins to twist up on itself to form sheets instead of single long chain. This means that our assumption holds some validity. In addition, we assume for this portion that all of the enzymes produced by plasmid 1 in the genetics model are quickly exported out of the cell. Since we use pelB to export the enzymes, this has informed our model assumptions.
When isolated from the rest of the model, the kinetics portion can be simulated for a fixed enzyme concentration. Figure 1 shows a simulation that was run in 100 mL of water and at an enzyme concentration of 0.5 μM. It was also initiated with 20 mM of repeat units of PET. As expected, the PET concentration decreases to zero and the ethylene glycol concentration increases to about the same level, showing conservation of the carbon. The intermediate substrate MHET is also consumed as the MHETase generates the ethylene glycol from it. Since this system only involves three equations it is relatively simple. The limited amount of substrate and the assumed 1:1 ratio of PET repeat unit to ethylene glycol means the lines are linear.
Figure 1. Enzyme Kinetics of PETase and MHETase
References:
- [1] H.P. Austin, et al. “Characterization and engineering of a plastic-degrading aromatic polyesterase.” PNAS. March 18 2018. [Online]. http://www.pnas.org/content/pnas/early/2018/04/16/1718804115.full.pdf
- [2] L. Wang, Y. J. Zhou, D. Ji, and Z.K. Zhao, “An accurate method for estimation of the intracellular aqueous volume of Escherichia coli cells,” Journal of Microbiological Methods, 2013, p. 8. [Online]. http://bionumbers.hms.harvard.edu/bionumber.aspx?id=108813&ver=3&trm=e%20coli%20cell%20volume&org
- [3] “Information on EC 3.1.1.101,” brenda-enzymes.org. Jul 2018. [Online]. https://www.brenda-enzymes.org/enzyme.php?ecno=3.1.1.101&Suchword=&reference=&UniProtAcc=&organism%5B%5D=Ideonella+sakaiensis&organism%5B%5D=Ideonella
+sakaiensis+201-F6&show_tm=0 - [4] V. K. Singh and A. Kumar, “Production and purification of an extracellular cellulose from Bacillus VS-1.” Biochemistry and Molecular Biology International. July 1998, vol. 45, no. 3, pp. 443-452. [Online]. https://iubmb.onlinelibrary.wiley.com/doi/pdf/10.1080/15216549800202832
- [5] “Information on EC 3.1.1.102,” brenda-enzymes.org. Jul 2018. [Online]. https://www.brenda-enzymes.org/enzyme.php?ecno=3.1.1.102&Suchword=&reference=&UniProtAcc=&organism[]=Ideonella+sakaiensis&organism[]=Ideonella+sakaiensis+201-F6&show_tm=0