Our team designed three separate models to monitor behaviors of the genetics system, enzyme kinetics, and metabolism. Then they were fused into one mechanism predicting P.E.B.B.L.E’s growth.

Kinetics Model

The enzyme kinetics model describes the biochemical pathway that our bacteria have to degrade and assimilate PET plastic. Kinetics models in general use differential equations to describe the interactions between the enzymes in the metabolites, chemicals used in metabolism, and they describe the rate of change in the concentration of these metabolites. Click on the biochemical pathway in the picture to see the equations and assumptions used to describe the main metabolites in the PET degradation pathway.

Example of the Kinetics

Metabolism Model

The last modeled portion of the project used the Flux Balance Analysis tool to predict the growth rate of the E. coli cells on the sole carbon source of PET. The original matrix and parameters where downloaded from the CoBRA toolbox iJO1366 model [ ]. The model was then expanded to include this new pathway and genes and then the system was optimized for biomass growth and 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:

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 homogenous assumption that the rates of the metabolites changing are zero. The dimensions of the matrix is MxN, where M is number of metabolites and N is number of reactions in the metabolism. The maximized flux, vg, is the flux for the biomass growth equation.

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 amounts 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. Click on the plasmid and genetics section to read about our description.

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:

Modeling

Mathematical models and computer simulations provide a great way to describe the function and operation of BioBrick Parts and Devices. Synthetic Biology is an engineering discipline, and part of engineering is simulation and modeling to determine the behavior of your design before you build it. Designing and simulating can be iterated many times in a computer before moving to the lab. This award is for teams who build a model of their system and use it to inform system design or simulate expected behavior in conjunction with experiments in the wetlab.

Gold Medal Criterion #3

Convince the judges that your project's design and/or implementation is based on insight you have gained from modeling. This could be either a new model you develop or the implementation of a model from a previous team. You must thoroughly document your model's contribution to your project on your team's wiki, including assumptions, relevant data, model results, and a clear explanation of your model that anyone can understand.

The model should impact your project design in a meaningful way. Modeling may include, but is not limited to, deterministic, exploratory, molecular dynamic, and stochastic models. Teams may also explore the physical modeling of a single component within a system or utilize mathematical modeling for predicting function of a more complex device.

Please see the 2018 Medals Page for more information.