Team:Imperial College/PHB Recycling/Modelling


Ordinary differential equations (ODEs)

To model the genetic expression of these enzymes, transcription and translation need to be taken into account. At this stage, we have taken constitutive gene expression by mass action as the basis for our model and used ODEs to describe it:

Michaelis-Menten kinetics

Enzyme kinetics can be described by 4 ODEs. However, it is impossible to measure [ES] experimentally and that means the ODEs have to be simplified for modelling. Michaelis-Menten kinetics assumes quasi-stationary approximation to solve this problem.

Matlab Simbiology

Simbiology is an extension of Matlab that we used to build and simulate our models. It allows modelling in graphical and programmable environments and uses in-built ODE solvers to simulate the time profile of species levels involved in the model.

1. P(3HB) synthesis

In terms of synthesis, our engineered E. coli will be able to take in extracellular feedstock monomer into themselves. Such action is mediated by permease activity in their membranes. Once inside the cell, a cascade of reactions involving 4 different enzymes will take place. To generate these enzymes inside the cell they need to be genetically expressed in the first place. Therefore, it is necessary to model these expressions and how they could affect the corresponding enzymes produced within a certain amount of time.

1.1 Building the model

1.2 Results


1.3 Experimental validation

Vmax and Km values were obtained from different sources of literature. They are not accurate for our model because we may have different growth conditions and experimental procedures. Therefore,a reaction rate vs. substrate concentration plot needs to be generated for each enzyme in order to determine the parameters. A double-reciprocal plot, or a Lineweave-Burk plot will then need to be derived from the reaction rate plot, such that we can obtain -1/Km from the x-intercept, 1/vmax from the Y-intercept and Km/Vmax from its gradient.


2. P(3HB) degradation

2.1 Building the model

2.2 Results


2.3 Experimental validation