Team:WITS-South Africa/Modelling


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The biological sciences have generally been qualitative fields of study. However, due to the "top up" approach of synthetic biology, the need for quantitative mathematical models naturally arises. These models allow the biological system to be simulated and are necessary if control of the system is desired. We attempt to model a genetically engineered system implemented in the bacterium lactobacilus gasserii that is capable of detecting the presence of a pathogen, expressing a reported and also signaling others cells of the presence of the pathogen.

Project Outline

The aim of our machine is to identify an infection of Human papillomavirus in vivo. From a modelling point of view the mechanism has a number of points of interest expounded on in the following sections.

Extracellular Activity: Varying concentrations and effects of the genetic machine on the habitat outside the cell

Intracellular Activity: Responses to inputs and outputs as well as feedback loops

Intercellular Activity: A medium for communication between cells


The benefits of modelling reach far beyond a theoretical understanding of a system. Models allow us to determine how we hope a system will behave. From this and experimental findings we can go on to determine where assumptions and simplifications made are critically important, whether it be positively or negatively.

Components of the Model

Extracellular Model

The extracellular model describes the change in substances outside of the cell. These fluctuations are modeled by a system of differential equations, which are likely to be non linear and of an order higher than one. This model will be used to try and describe each cell as a 'black box'. This will then be used to model the intercellular communication.

Intercellular Model (Cell Communication)

This portion of the model describes the behaviour of the cells as a network of communicating individuals. They communicate via a signalling process called quorum sensing.

Intracellular Model (Genetic Circuit)

The genetic circuit describes the biochemical reactions taking place inside the cell. The intracellular model describes the fluctuations in concentrations of each substance by modelling each chemical reaction by means of an appropriate kinetic law.

The intra cellular model is based on the block diagram shown in the figure below. The concentration of the proteins in the model can be expressed in terms of three ordinary differential equations.