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Majority Rules with Random Tie-Breaking in Boolean Gene Regulatory Networks

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  • Claudine Chaouiya
  • Ouerdia Ourrad
  • Ricardo Lima

Abstract

We consider threshold Boolean gene regulatory networks, where the update function of each gene is described as a majority rule evaluated among the regulators of that gene: it is turned ON when the sum of its regulator contributions is positive (activators contribute positively whereas repressors contribute negatively) and turned OFF when this sum is negative. In case of a tie (when contributions cancel each other out), it is often assumed that the gene keeps it current state. This framework has been successfully used to model cell cycle control in yeast. Moreover, several studies consider stochastic extensions to assess the robustness of such a model.Here, we introduce a novel, natural stochastic extension of the majority rule. It consists in randomly choosing the next value of a gene only in case of a tie. Hence, the resulting model includes deterministic and probabilistic updates. We present variants of the majority rule, including alternate treatments of the tie situation. Impact of these variants on the corresponding dynamical behaviours is discussed. After a thorough study of a class of two-node networks, we illustrate the interest of our stochastic extension using a published cell cycle model. In particular, we demonstrate that steady state analysis can be rigorously performed and can lead to effective predictions; these relate for example to the identification of interactions whose addition would ensure that a specific state is absorbing.

Suggested Citation

  • Claudine Chaouiya & Ouerdia Ourrad & Ricardo Lima, 2013. "Majority Rules with Random Tie-Breaking in Boolean Gene Regulatory Networks," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-14, July.
  • Handle: RePEc:plo:pone00:0069626
    DOI: 10.1371/journal.pone.0069626
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    Cited by:

    1. Pedro J. Rivera Torres & Eileen I. Serrano Mercado & Orestes Llanes Santiago & Luis Anido Rifón, 2018. "Modeling preventive maintenance of manufacturing processes with probabilistic Boolean networks with interventions," Journal of Intelligent Manufacturing, Springer, vol. 29(8), pages 1941-1952, December.
    2. Pedro J. Rivera Torres & E. I. Serrano Mercado & Luis Anido Rifón, 2018. "Probabilistic Boolean network modeling of an industrial machine," Journal of Intelligent Manufacturing, Springer, vol. 29(4), pages 875-890, April.
    3. Floriani, Elena & Lima, Ricardo & Ourrad, Ouerdia & Spinelli, Lionel, 2016. "Flux through a Markov chain," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 136-146.

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