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 and reducing them to their core components. Thus a quantitative understanding of the interaction between these core components can be generated leading to 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 the 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.

We applied the same methodology to the study of each of the systems: PQS, BDSF and DSF. Our approach was to first build models for the core components within the engineered system. In this way, we could generate predictions regarding the expected outcome - qualitative and quantitative promoter expression behaviour in response to varying signal input levels. Having built this theoretical framework, we could then more easily address questions and technical problems generate by the wet science. Most importantly, we were able to use out modelling framework to suggest improvements and solutions to the technical issues the arose, that were subsequently implemented.