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Revision as of 16:49, 2 August 2018
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Background
Our team designed three separate models to monitor behaviors of the genetics system, enzyme kinetics, and metabolism. They were fused into one mechanism to predict P.E.B.B.L.E.’s growth.
Kinetics Model
The enzyme kinetics model describes the biochemical pathway that our bacteria follow to degrade and assimilate PET plastic. In general, kinetics models use differential equations to describe the interactions between the enzymes in the metabolites and the chemicals used in metabolism. They also describe the rate of change in the concentration of these metabolites. Below is a simplified example of how a kinetics model is made. If you would like to see the kinetics model that describes our system's behavior go to the Kinetics Model page by clicking on the biochemical pathway or by going to the model sub-menu.
Example of the Kinetics
Metabolism Model
The final portion of the model used the Flux Balance Analysis (FBA) tool to predict the growth rate of the E. coli cells on the sole carbon source of PET. The original matrix and parameters were downloaded from the CoBRA toolbox iJO1366 model [ ]. The model was then expanded to include the new pathway and genes, and then the system was optimized for biomass growth. The objective value was proportional to the growth rate of the bacteria. FBA uses a stochastic matrix of the all the metabolisms’ chemical reactions and optimizes these various equations to produce a unit of biomass, which is inferred as another metabolite of the system. The general form of the model is shown below. If you want to find out more information about our FBA model go to the Metabolism Model link in the model sub-menu or click on the metabolism portion of the picture above.
The variable column V are fluxes, which are bounded by the upper and lower bounds of U and L. The S matrix is a matrix of stoichiometric coefficients for the metabolites in the reactions. A flux is best described as the number of times the reaction must run forwards or backwards for the entire system to meet the homogeneous assumption that the rates of the metabolites changing are zero. The dimensions of the matrix are MxN, where M is the number of metabolites and N is the number of reactions in the metabolism. The maximized flux, vg, is the flux for the biomass growth equation.
For the fake chemical reaction: 2 [A] ↔ [B] + 3 [C]
The reaction is input into the matrix so that metabolite A loses 2 units, while metabolites B and C gain 1 and 3 units, respectively.
The dotted column shows the biomass growth reaction producing 1 unit of biomass. All the reactions have some bounds on the flux values so that the system will return a real number.
Genetics Model
The genetics system used in our experiments has the degradation of PET and the assimilation of PET carbons in the cell on two separate plasmids. The relevant numbers of copies of the 6 enzyme genes and their rates of change were described in differential equations. The different promoter interactions of each plasmid were also taken into account and the secretion of mechanisms for PETase and/or MHETase were also included to help us predict the amount of enzymes breaking down the PET. Below is a simplified example of how a genetics model is made. If you would like to see the genetics model that describes our system's behavior go to the Genetics Model page by clicking on the plasmid or by going to the model sub-menu.
Example of the Genetics Model
This set of reactions models what is happening in the pictures. The first reaction shows the production of the B protein. The second shows that when B binds to O, it creates an inhibited complex that does not allow the polymerase to bind. The polymerase not being able to bind means that the protein cannot be synthesized. The third reaction describes when the polymerase is able to bind to the operator. When the polymerase does bind, the mRNA is able to be synthesized. The fourth shows the mRNA creating the protein.
Once assumptions that the rate of creating C_I is at equilibrium and that k_2 and k_3 are grouped into one k ̂_2 are made, a simplified equation can be written to describe what is happening. This equation will be written in the form of:
k ̂_2, Υ , and ρ would be known. The amount of free operator could be determined by the following steps:
