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 bind 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 affected 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

Characterising the DcmR - DCM - P_dcmA interaction

To find out whether the DcmR acts as a repressor or an activator on the promoter of the dcmA gene, we attempted to build the genetic circuit shown above on the right. Having dcmR under inducible TetR expression should allow us to have very good control of the amount of DcmR present. Additionally a translational fusion with DcmR and a mCherry fluorescence tag will act as another confirmation to the amount of DcmR present.

We then extensively modelled the circuit to discover how the response of the system would differ if it was either of the two circuit systems. Click the modelling bubbles (pink) to find out exactly how we achieved this.

Predicting the mCherry fluorescence

We simplified the first double repression by modelling it as an activation of dcmR by anhydrotetracycline (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.

Biochemical equations

The biochemical equations that describe the behaviour of the top half of the genetic circuit are:

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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 describes this first step of the system is:












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

This model works assuming that sufficient TetR is always present.

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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 Ptet promoter not being leaky. 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 GFP 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. Before we determined which reaction happened, we had to work out when the reaction happened. Using the random number r1 (taken from a uniform distribution between 0 and 1), we produced another random number τ, which determined the time until the next reaction.







Where α0 represents the probability that any reaction will happen, given by the following equation:






We modelled the probability of a molecule of GFP being created using the Michaelis-Menten model (α1), incorporating a basal transcription rate (b1). For the degradation, we assumed a simple proportional relationship: the more GFP you have, the more likely it is that a molecule degrades (δ1). The constant of proportionality will be a function of the intrinsic life time of the protein in the cell. We considered there to be no DCM originally, then a large step in DCM at time=0. This is similar to placing the detector in a DCM polluted source, to make the model more realistic the level of DCM would go down as it is degraded but we had no time to obtain data for this rate.

To decide if GFP was produced, we looked at the percentage of “reactions” which were productive, and then we compared this to a second random number r2 (again taken from a uniform distribution from 0 to 1). If the random number was lower, then GFP was created. If it was higher, then GFP was degraded. In this way we make a weighted random choice about whether GFP was created or degraded. We only stored the time and amount of GFP when there was a reaction, to save on computation time.







Stochastic modelling is useful because it can show us the stochastic effects which are often observed in individual bacteria. By calculating the variation of the mean of multiple GFP producing bacteria, we can also work out the standard deviation. Then, if we assume that the system varies with respect to the normal distribution, we can produce error bounds for the production of GFP, such that we can say that 90% of the time we can expect the production of GFP from a single bacterium to be within these two curves. This could be useful for seeing if results are unexpected, or, if there are multiple outliers, that our model is incorrect. If we average an increasing number bacteria, then the mean curve tends towards the deterministic response. This is to be expected, as we are now looking at the system as a whole and fluctuations in the production from individual bacteria are averaged out. In terms of their use, when looking at small amounts of bacterium the stochastic model would be better, because real random fluctuations can be seen. For larger bacterial populations, the deterministic response models the growth very well. The stochastic model can also model large groups but requires large number of realisations which causes simulations to take a lot longer to run.

When running the models, we picked arbitrary constants to view the general response. If we had more time we would have attempted to work out the basal rate, transcription rate and degradation rate of the GFP from DCM.

Predicting the sfGFP fluorescence

Introduction

To allow us to characterize the second half of the genetic circuit, we needed to be able to predict the difference in response. To do this, we constructed models by cascading the differential equations according to the respective circuit structures thereby producing two different potential system responses.

We then set up the differential equations necessary to solve this problem in Matlab. The method and results are as detailed below:

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Conclusion

The bottom graphs illustrate the predicted response of each system to a simultaneous step input of both DCM and ATC. As you can see, there is little difference in the predicted steady-state value of the fluorescence, however, providing the basal transcription rate of GFP is relatively low, there should be a clear difference in the level of fluorescence before either of these inputs are added. This very easily identifiable difference between the two systems will enable us to characterize the genetic circuit present in our particular system.

Calculating the parameters

Calculating the many parameters for this system will be undoubtedly challenging.

How are we calculating the parameters?

Go to the data section where we calculated parameters for this part of the circuit.