Team:St Andrews/project/modelling/models

Our Models

Components

Each of our models is made up of several key elements which have common elements between the models but also show variation in other respects. These can be categorised as:

• Ordinary differential equations (ODEs)
• Differential solver (RK4)
• Rate constants
• Initial values

Further details on each of these aspects can be found by clicking on the links. Each of our models shared the same Runge-Kutta solver and largely the same differential equations, with the exception being our equation describing the change in HSL. Our rate constants remained relatively unchanged throughout but some alterations were made, details of which are explained in each individual model's section. Initial values also remain the same throughout.

The Models

Over the course of the project, our model has evolved through various stages of operability and complexity. These can be split into four key stages of development, the culmination of which being our finalised model of the LuxR quorum sensing network. Each model has its own set of assumptions and theoretical foundation which was either reaffirmed or dispelled as our understanding of the biology behind the system became more complete. However we present our methodology and our results for all of our models in order to allow the interested party to better understand the reasoning behind our work and follow the logic that brought us to our final conclusions.

The four models are labelled:

Model 1: Single Cell No Loop

Model 2: Single Cell With Loop

Model 3: Psuedo Multi Cell One Dimension

Model 4: Psuedo Multi Cell Two Dimensions

We also created a framework for modelling the v.Cholerae quorum sensing network:

v.Cholerae quorum sensing network