Deterministic

Deterministic models are very powerful tools in systems biology. They analyse the behaviour of the bacteria on a culture level and use ordinary differential equations (ODEs) to relate each activation and repression. By constructing a cascade of differential equations you can build a very robust model of the average behaviour of the gene circuit.
The differential equation that applies to this first step in the system is:






Where did this equation come from?

Solving this ODE in Matlab (with zero basal rate) gives the response of the system to be:

While the analysis of this circuit isn’t critical to the successful outcome of this part of the project, it will provide us with a very good practice of both obtaining fluorescence time data and accurately fitting the data to the model. It will also help us develop our methods of predicting future system behaviour. This is because this system is already well documented in literature and so we should be able to test our methods and responses against well documented results from labs across the world.

As you can clearly see from the graph, the model predicts a large fluorescence increase as the input is added. This is the expected response from the real response and is the best approximation that is obtainable before we get data from the biochemists.

In the graph above, the model is set to have a basal rate of zero. This is why there is a zero fluorescence response before the input has been added. In biochemical terms, this is the same as the tetO promoter not being leaky at all. This basal rate will be calibrated alongside all of the other parameters in the model.