Insert intro here
Insert biochem here
Modelling genetic circuits
Predicting the mCherry fluorescence
To model the first double repression, we took the fact that we won’t need to know the amount of tetR in the system and used the assumption that ATC is effectively activating the expression of dcmR, albeit parameterised by different constants. This assumption should be justified by the fact that we will be able to precisely control the addition of ATC and we will be able to measure the fluorescence of the mCherry.
We modelled this first step using both deterministic and stochastic models.
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.
Insert biochem here
How can we tell the systems apart?
Predicting the sfGFP fluorescence
Introduction
To allow us to be able to identify which system was in the second half of the circuit, it was important to be able to predict the difference in response. To do this, we constructed models that involved cascading the differential equations in different formats to model the response.
To be able to do this, we had to construct simplified equivalent circuits that were made out of direct activations and repressions.
It is important to understand that these simplified equivalent circuits will not give the correct mCherry response but they will give the correct GFP response after correct parameterisation.
We then set up the differential equations necessary to solve this problem in Matlab. The method and results are as detailed below:
Conclusion
The bottom graphs show how each hypothesised system would respond to a step input of both ATC and DCM at the same time. As you can see, there isn’t much difference in the predicted steady state value of the fluorescence. However, providing the basal rate of GFP is low enough, there should be a clear difference in the level of fluorescence before either of these inputs are added. Eventually, we plan to test which gene circuit is present in this system by using this method of differentiating between them.
Calculating the many parameters for this system will be tricky. How are we calculating the parameters?
Having made the models and understanding the assumptions that we’ve made, it is very important to understand where the limits of the predictions are and what range of inputs the model will give reliable information for. After all, no model is perfect. <-- BACK THIS UP?
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