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Team:Oxford/biosensor characterisation
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Revision as of 12:55, 29 September 2014
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Characterisation
Introduction: what are we characterising?
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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:
Solving this ODE in Matlab (with zero basal rate) gives the response of the system to be:
Oxford iGEM 2014
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.
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.
Stochastic Modelling
Stochastic modelling uses probability to calculate what happens next in a system. For our project we used it to model the expression of genes from bacteria.We started with the Gillespie Algorithm, which considers the expression of GFP to be binary; either a molecule of GFP was produced or it was degraded. We modelled the chance of a molecule of GFP being created using the Michaelis-Mentin equation and incorporating a basal rate. For the degradation, we assumed a simple proportional relationship, the reasoning being that if we have more GFP then we are more likely that a single GFP molecule will degrade. The constant of proportionality will be a function of the intrinsic life time of the protein in the cell. Now at every increment in time we will not have a GFP reaction occurring, so before we decided what reaction occurs we had to work out if I a reaction occurred. We did this by writing an equation involving the probability of any reaction occurring with a random number generator. To work out which reaction occurred we compared the relative probability of a production to degradation, and used a random number to make a weighted choice.
We later changed this code so that a reaction occurred every time increment, but included a null reaction where no GFP was degraded or created. Although this made the code a lot more data heavy, it allowed for much easier calculation of the mean response of multiple realisations.
Stochastic modelling is useful because it can show us the randomness which is often seen in real bacteria. Calculating the variation of the mean of multiple GFP producing bacteria we can also work out the standard deviation, and if we assume that the system varies with respect to the normal distribution, we can produce error bounds for the error growth. Such that we can say, 90% of the time we can expect the production of GFP from a single bacterium to be within these 2 curves. This could be useful for seeing if results are unexpected, or if there are multiple outliers, that our model is not correct. If we average more and more realisations of reactions then the mean curve tend towards the deterministic response. This is equivalent to looking at the mean of more and more bacteria until we are looking at the system as a whole and fluctuations in individual bacteria are averaged out.
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?
Oxford iGEM 2014
