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Multi-scale genetic dynamic modelling II: application to synthetic biology

An algorithmic Markov chain based approach

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Abstract

We model in detail a simple synthetic genetic clock that was engineered in Atkinson et al. (Cell 113(5):597–607, 2003) using Escherichia coli as a host organism. Based on this engineered clock its theoretical description uses the modelling framework presented in Kirkilionis et al. (Theory Biosci. doi:10.1007/s12064-011-0125-0, 2011, this volume). The main goal of this accompanying article was to illustrate that parts of the modelling process can be algorithmically automatised once the model framework we called ‘average dynamics’ is accepted (Sbano and Kirkilionis, WMI Preprint 7/2007, 2008c; Kirkilionis and Sbano, Adv Complex Syst 13(3):293–326, 2010). The advantage of the ‘average dynamics’ framework is that system components (especially in genetics) can be easier represented in the model. In particular, if once discovered and characterised, specific molecular players together with their function can be incorporated. This means that, for example, the ‘gene’ concept becomes more clear, for example, in the way the genetic component would react under different regulatory conditions. Using the framework it has become a realistic aim to link mathematical modelling to novel tools of bioinformatics in the future, at least if the number of regulatory units can be estimated. This should hold in any case in synthetic environments due to the fact that the different synthetic genetic components are simply known (Elowitz and Leibler, Nature 403(6767):335–338, 2000; Gardner et al., Nature 403(6767):339–342, 2000; Hasty et al., Nature 420(6912):224–230, 2002). The paper illustrates therefore as a necessary first step how a detailed modelling of molecular interactions with known molecular components leads to a dynamic mathematical model that can be compared to experimental results on various levels or scales. The different genetic modules or components are represented in different detail by model variants. We explain how the framework can be used for investigating other more complex genetic systems in terms of regulation and feedback.

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Acknowledgements

We would like to thank Isabelle Carré (Biological Sciences, University of Warwick) for valuable experimental support and general guidance to the genetic literature. In addition we would like to thank the unknown referees for valuable comments. The work in this paper was partially supported by UniNet contract 12990 funded by the European Commission in the context of the VI Framework Programme.

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  1. Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK

    Markus Kirkilionis & Ulrich Janus

  2. I.T.I.S. “Von Neumann”, Rome, Italy

    Luca Sbano

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  1. Markus Kirkilionis
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  2. Ulrich Janus
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Correspondence to Markus Kirkilionis.

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Kirkilionis, M., Janus, U. & Sbano, L. Multi-scale genetic dynamic modelling II: application to synthetic biology. Theory Biosci. 130, 183–201 (2011). https://doi.org/10.1007/s12064-011-0126-z

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