0 1,000 2,000 3,000 4,000 5,000 6,000 0
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T ime
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mRN A LacI
Figure 6.6: 1 simulation of the model of the negative feedback device.
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mRN A LacI
Figure 6.7: 10 simulations of the model of the negative feedback device.
6.4 Example: Oscillator
Here we show how a genetic device can be modelled differently than shown up until now. This example goes through the oscillator device used to construct the negative feedback device studied in this chapter. The oscillator has already been modelled by Elowitz and Leibler (2000), a description of the model has
0 1,000 2,000 3,000 4,000 5,000 6,000 0
20 40
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mRN A LacI
Figure 6.8: 1 simulation of the model of the negative feedback device with stronger promoter binding.
been submitted to the BioModels Database4 which we will be studying here.
Here it is interesting how relatively simple the model is: promoters and binding of proteins to promoters are not modelled by transitions and places but simply by rate functions on the transitionsts_LacI,ts_cI, etc. E.g. the rate function (transitionts_LacI) for transcription ofLacI is described by:
a0tr+ atr·KMn
KMn+cIn (6.7)
This rate function is explained in detail in Appendix A, but it should be ob-vious that transcription is decreasing when the concentration of cI increases.
The more simpler modifier arcs are used instead of e.g. read arcs, because the behaviour of the model is primarily described by the rate functions (and not the design of the SPN).
6.5 Discussion
In this chapter we have seen how we can go from a set of biochemical reactions with rates to a complete SPN describing a desired behaviour. The mapping from biochemical reactions to SPNs is unproblematic as SPNs are an extension of PNs which originally were invented for chemical reactions. The challenge is to define a satisfiable set of biochemical reactions defining the behaviour we want.
4http://www.ebi.ac.uk/biomodels-main/BIOMD0000000012, the SBML format will be fur-ther described in the next chapter about the implementation.
6.5 Discussion 61
Figure 6.9: The SPN model of the oscillator.
Initially the goal was to standardise how the different parts can be modelled, but we soon realised that to do this we always need to be certain that specific parameters can be obtained for specific reactions. There is a great challenge in finding these parameters: often it is not possible to find the parameters that fit in the specific reaction and the model needs to be modified to reflect the available parameters.
Another issue arose in our review of different literature: there is no de facto standard of describing the internal mechanics of parts in synthetic engineered devices. Hence different literature describe these details of the parts and the processes of gene expression on very different levels.
The purpose of modelling synthetic devices is to be able to predict the behaviour of a device before the device is constructed in wet-labs and by that hopefully save both money and time. This scenario is greatly desirable but the reality is that this is still one of the main challenges in synthetic biology: to get the level of understanding of biological systems to be able to construct a model with all important interactions and parameters, see the email from professor Chris
J. Myers, author of Engineering Genetic Circuits, in AppendixB. Currently it is still very hard to find literature with experiments and models with complete justification of all parameters that simulate the behaviour of the experiment (Lodhi and Muggleton,2010, Ch. 2).
The consequence of this is that detailed, e.g. time-series with protein levels, comparisons of simulations of these models with wet-lab experiments is not always meaningful, on the other hand the overall behaviour of these models can still be compared with the desired behaviour of the wet-lab devices.
The case study of the negative feedback device shows that a SPN model with appropriate parameters exhibit the desired behaviour, which is why we in the remainder of this thesis assume the modelling techniques proposed here are usable for modeling of genetic devices.
Chapter 7
A framework: DTU-SB
In this chapter we present a framework: DTU-SB1. The purpose of this frame-work is to model synthetic engineered genetic devices and make simulations of these models. In this chapter we will list the requirements for the framework, sketch the overall architecture of it, go into details with some interesting parts of the implementation and finally we will list how the framework can be used in different use cases.
7.1 Requirements
The framework should be able to simulate arbitrary complex models of real genetic devices. This means the theory from the previous chapters on SPNs, modelling and simulation should be used to construct the framework.
The simplest form of the framework should be able to take some specification of a model as input, internally this specification should be transformed to a SPN, which in turn should be simulated using Gillespie’s direct method SSA explained earlier. At last the result of the simulation should be presented in some pre-defined format.
1Short for DTU Synthetic Biology.
To allow comparisons with other tools, a very important requirement is that input parsers and output formatters should be modularised. Specifically the framework should allow the following modules:
• It should be possible to define custom parsers for arbitrary input speci-fication languages. This allows support for an endless amount of model specification languages.
• It should be possible to define a custom algorithm or easily modify or extend existing algorithms for the simulator. This allows optimisations of existing algorithms and experimenting with new algorithms.
• It should be possible to define custom output formatters.
• It should be possible to add intermediate compilers of the SPN models produced by the input parsers. These compilers could be used to e.g. hook up a database with additional information or by making optimisations on SPN models.
One might notice that the framework sketched here differ from the proposed tool-chain in Fig. 3.2 on page 22 in that the output here focuses on simu-lation results rather than complete DNA sequences describing some synthetic engineered biological function.
In addition to the requirements of the behaviour and features of the framework described above, there is also some requirements to how the framework should be implemented to achieve these features. As the framework is not only in-tended as proof-of-concept but should form the basis for a long living modelling framework for synthetic biology, the following requirements capture how this can be achieved:
Maintainable It should be easy to modify, update and fix the current be-haviour.
Flexible It should be possible to add functionality purely by adding new mod-ules, not by modifying existing modules.
Testable It should be possible to verify the internal logic of the framework components through test cases.
Wide OS Support The user’s operating system should not be an obstacle to the availability of this framework.