# Team:SydneyUni Australia/Modelling Intro

## Introduction

#### Why bother modelling?

Mathematicians and poets both try to condense experience into simple, beautiful truths. A model is a screen that simplifies nature, but also translates nature's language into one which we can interpret and try to begin to understand. Generally, models of natural systems allow humans to probe the inner workings of those systems. They are used to quantitatively and/or qualitatively understand the mechanisms by which the system exists.

As described in other sections of our wiki, our project aims to create an E. coli cell which removes DCA from the environment by metabolising it to glycolate (potentially allowing it to grow on DCA). The two engineered metabolic pathways in mind are the monooxygenase pathway (which involves p450) and non-monooxygenase pathway (which involves a dehalogenase and an alcohol dehydrogenase instead of p450).

#### The three questions behind our model:

1. At what rate will our engineered DCA degraders remove DCA from solution?

2. What is the maximum intracellular concentration that the cytotoxic chloroacetaldehyde (metabolic intermediate) reaches?

3. Of our 2 possible pathways (monooxygenase and non-monooxygenase), which has the highest rate of DCA removal? Which keeps chloroacetaldehyde at the lowest possible concentration?

We constructed a pharmacokinetic model in order to gauge how the intracellular concentrations of each of our metabolites change over time. The rate at which our metabolite concentration changes was modelled by two additive Michaelis-Menton equations: one describing the rate at which the metabolite is formed (acting as a product) and the other described the rate at which the metabolite is removed/used (acting as a substrate). By linking all metabolites together and classifying them simultaneously as a product and substrate (bar the initial substrate and final product), a system of ordinary differential equations (ODEs) is born.

To properly answer question 1. (the rate of DCA removal), the model had to incorporate the rate at which the DCA passes across the E. coli cellular membrane (the flux rate). This was modelled with a combination of physical chemistry equations.

We had no illusions of this model being quantitative, nor would we need it (we are of the strong opinion that any mathematic model of simple ODEs could not be used to describe any biochemical process accurately enough for quantitative reliability). The answers we required from it needed only for the model to be qualitative, so for simplicity we made many assumptions, which are detailed in the next section.