Mathematical models in biology like in every other field, is a description of a system using mathematical concepts and language. Models have become indispensable tools, aiding researchers express their scientific knowledge.

Contents 1 Overview 2 Diffusion Model 3 Bio-Chemical Model 4 Structural Model

Overview

We decided to use the modeling expertise of the team members to achieve three key objectives for this years project.

• Develop scientific understanding of the yeast pheromone response pathway.
• Test the effects of the changes to the system.
• Aid decision making in the laboratory.

To achieve the stated objectives, three different models were built encompassing the different aspects of the project.

Diffusion Model

Bio-Chemical Model

The bio-chemical model was developed based on a scheme favouring the temporal order of the processes, which involved the four fundamental modules,

• Receptor Activation
• G - Protein Cycle
• MAPK Cascade
• Gene Expression

The dynamics of the system are described using a set of differential equations governing the concentration changes of individual components and of complexes over time. On account of the gene expression module being noisy, a stochastic model of the gene expression module was implemented using stochastic differential equations. Sensitivity and stability analysis were permformed to determine the sensitivity coefficients which were used to study the parametric dependence of the biological models.

Structural Model