Team:SydneyUni Australia/Modelling Intro

From 2013.igem.org

Introduction

So why bother with modelling?

Generally, a model of a natural/physical system allows humans to probe the inner workings of that system. They are used to quantitatively and/or qualititatively understand the mechanisms by which the system exists. Mathematics is a language which connects the human brain to the world in which it exists in. A model is the screen which translates nature's languange into one which we can interprate and try to begin to understand. By designing a model based on truths, we try to learn what nature has to say. Modelling is story-telling. Mathematicians and poets both try to condeense experience into simple, beautiful truths.

As described in other sections of our wiki, our project aims to manufacture an E. coli cell which removes DCA from the cells environment by metabolising it to glycolate (potentially growing off of DCA). The 2 engineered metabolic pathways in mind are the monooxygenase pathway(which involves p450 instead of alcohol dehydrogenase) and non-monooxygenase pathway (which involves alcohol dehydrogenase instead of p450), of which involves 3 and 4 introduced enzymes respectively.

There were 2 motives in mind when concocting our model:

1. At what rate will our engineered cells (our DCA degraders) remove DCA from solution given the DCA and cell concentration.

2. At what intracellular concentration does the cytotoxic chloracetaldehyde (metabolic intermediate) reach?

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

So, a pharmacokinetic model was constructed 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 2 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 by classifying them simultaneously as a product and substrate (bar the initial substrate and final product), a system of ordinary differential equations (ODE) is born.

To properly address point 1 (the rate of DCA removal from solution), the model had to incorporate the rate at which the DCA passes across the E. coli’s 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 be used to describe any biochemical process accurate enough for quantitative reliability. The answers we required from it needed only for the model to be qualitative, so for undergraduate simplicity we made many assumptions, of which are listed at the end of the article.