In order to help analyze, construct and optimise the biochemical pathways in The Lung Ranger, we used a variety of mathematical tools to create algorithms and simulations. This allowed us to accelerate the development and testing of various project-driven hypotheses.

Methodology
Mathematical modelling has played a significant role in the development of synthetic biology. As an investigative tool, modelling is capable of abstracting complex systems, reducing them to their core components. Thus a quantitative understanding of the interaction between these core components can be generated allow for optimal system design and control.

In our project, we used a variety of mathematical tools with which to design and study our engineered signal transduction pathways. As illustrated below, each of the approaches; ordinary differential equations (ODEs), stochastic simulation algorithm (SSA) and NetLogo, provided a different, but complementary understanding of each system.

Each modelling technique allows for the investigation of processes at different levels of observation. ODE allows for prediction as the population level. SSA takes account of low molecule numbers (intrinsic noise) and allows for single cell comparison and a better understanding of sub-population behaviour. The NetLogo simulation tool affords single, intra-cellular resolution and provides the most visually accessible representation of the biochemistry under study.