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Efficient Reduction of Kappa Models by Static Inspection of the Rule-Set

Part of the Lecture Notes in Computer Science book series (LNBI,volume 9271)

Abstract

When designing genetic circuits, the typical primitives used in major existing modelling formalisms are gene interaction graphs, where edges between genes denote either an activation or inhibition relation. However, when designing experiments, it is important to be precise about the low-level mechanistic details as to how each such relation is implemented. The rule-based modelling language Kappa allows to unambiguously specify mechanistic details such as DNA binding sites, dimerisation of transcription factors, or co-operative interactions. Such a detailed description comes with complexity and computationally costly executions. We propose a general method for automatically transforming a rule-based program, by eliminating intermediate species and adjusting the rate constants accordingly. To the best of our knowledge, we show the first automated reduction of rule-based models based on equilibrium approximations.

Our algorithm is an adaptation of an existing algorithm, which was designed for reducing reaction-based programs; our version of the algorithm scans the rule-based Kappa model in search for those interaction patterns known to be amenable to equilibrium approximations (e.g. Michaelis-Menten scheme). Additional checks are then performed in order to verify if the reduction is meaningful in the context of the full model. The reduced model is efficiently obtained by static inspection over the rule-set. The tool is tested on a detailed rule-based model of a \(\lambda \)-phage switch, which lists 92 rules and 13 agents. The reduced model has 11 rules and 5 agents, and provides a dramatic reduction in simulation time of several orders of magnitude.

Keywords

  • Operator Site
  • Linear Temporal Logic
  • Enzymatic Reduction
  • Genetic Circuit
  • Equilibrium Approximation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This research was supported by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no. 291734, and the SNSF Early Postdoc.Mobility Fellowship, the grant number P2EZP2_148797.

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Notes

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    for explicit algorithms, please consult the Appendix of the online paper version [27].

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Acknowledgements

The authors would like to thank to Jérôme Feret, for the inspiring discussions and useful suggestions.

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Correspondence to Tatjana Petrov .

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Beica, A., Guet, C.C., Petrov, T. (2015). Efficient Reduction of Kappa Models by Static Inspection of the Rule-Set. In: Abate, A., Šafránek, D. (eds) Hybrid Systems Biology. HSB 2015. Lecture Notes in Computer Science(), vol 9271. Springer, Cham. https://doi.org/10.1007/978-3-319-26916-0_10

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