DcmR and regulation of dcmA expression

Mutants with dcmA and the intergenic region but without complete dcmR express DcmA constitutively. Re-integration of dcmR restores regulation of dcmA expression at the transcriptional level [1]. In addition, it has been shown that the region including dcmR, the intergenic region and dcmA is sufficient to confer a DCM dependent response in genetically engineered Methylobacterium extorquens DM4 [2].

DcmR and DNA-binding

DcmR is thought to be a DNA binding protein as structure predicting software indicates that there is a helix-turn-helix domain at the N-terminal of the protein. Since the region between the two promoters for dcmR and dcmA can be deleted without any effect on regulation it has been suggested that DcmR does not to a secondary regulatory site in between the genes but most likely acts directly on the dcmA promoter itself [1]. In addition, regulated expression of dcmA is not effected when the dcmR and dcmA transcriptional units are placed on separate replicons thereby suggesting that their topology is independent of the regulatory network. It is therefore suggested that DcmR binds the DNA in the intergenic region with the simplest model of its mode of action being as a trans-acting DNA-binding repressor; however this remains to be fully validated [1].

We have therefore proceeded on the assumption that DcmR is directly influenced by the presence or absence of DCM and furthermore that we can use dcmR, the intergenic region and dcmA alone to characterise the regulatory network.

[1] La Roche, S. D., and T. Leisinger. "Identification of dcmR, the regulatory gene governing expression of dichloromethane dehalogenase in Methylobacterium sp. strain DM4." Journal of bacteriology 173.21 (1991): 6714-6721.
[2] Lopes, N., et al “Detection of dichloromethane with a bioluminescent (lux) bacterial bioreporter” J Ind Microbiol Biotechnol (2012) 39:45–53

Predicting the mCherry fluorescence

We simplified the first double repression by modelling it as an activation of dcmR by ATC, albeit parameterised by different constants. This assumption is justified by the fact that we are able to precisely control the addition of ATC and measure the fluorescence of the mCherry.

We modelled this first step using both deterministic and stochastic models.

Deterministic

Deterministic models are very powerful tools for synthetic biology. They describe the behaviour of the bacteria at the population level and use Ordinary Differential Equations (ODEs) to relate each activation and repression. By constructing a cascade of differential equations one can build a realistic model of the average behaviour of the system.
The differential equation that descibes this first step of the system is:












Solving this ODE in Matlab (with zero basal transcription rate) predicts the following the response of the system:

Oxford iGEM 2014

While the analysis of this circuit is not critical to the successful outcome of this part of the project, it will provide us with very good practice of both obtaining fluorescence time series 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 the 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 what we expect from the actual system and is the best approximation that is obtainable before we get experimental data.

In the graph above, the model is set to have a basal transcription rate of zero. This is why there is a zero fluorescence response before the input has been added - this corresponds to 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 theory to predict the behaviour of 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; a molecule of GFP is either produced or degraded. We modelled the probability of a molecule of GFP being created using the Michaelis-Menten model, incorporating a basal transcription rate. For the degradation, we assumed a simple proportional relationship; the more you have the more likely it is that a molecule degrades. 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.

What is stochastic modelling?

How is it useful? Ads/Dis

Tending to deterministic

Modelling activator repressor

Parameter characterisation/Data matching

Matlab graphs

Wetlab data showing response in level of mCHERRY expressed with different concs of ATC

data analysis

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?

Wetlab data showing whether it is a repressor or activator

data and analysis