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Lac Operon Boolean Models: Dynamical Robustness and Alternative Improvements

Author

Listed:
  • Marco Montalva-Medel

    (Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Diagonal Las Torres 2700, Peñalolén, Santiago 7941169, Chile)

  • Thomas Ledger

    (Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Diagonal Las Torres 2700, Peñalolén, Santiago 7941169, Chile
    Center of Applied Ecology and Sustainability (CAPES), Santiago 8331150, Chile)

  • Gonzalo A. Ruz

    (Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Diagonal Las Torres 2700, Peñalolén, Santiago 7941169, Chile
    Center of Applied Ecology and Sustainability (CAPES), Santiago 8331150, Chile)

  • Eric Goles

    (Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Diagonal Las Torres 2700, Peñalolén, Santiago 7941169, Chile)

Abstract

In Veliz-Cuba and Stigler 2011, Boolean models were proposed for the lac operon in Escherichia coli capable of reproducing the operon being OFF, ON and bistable for three (low, medium and high) and two (low and high) parameters, representing the concentration ranges of lactose and glucose, respectively. Of these 6 possible combinations of parameters, 5 produce results that match with the biological experiments of Ozbudak et al., 2004. In the remaining one, the models predict the operon being OFF while biological experiments show a bistable behavior. In this paper, we first explore the robustness of two such models in the sense of how much its attractors change against any deterministic update schedule. We prove mathematically that, in cases where there is no bistability, all the dynamics in both models lack limit cycles while, when bistability appears, one model presents 30% of its dynamics with limit cycles while the other only 23%. Secondly, we propose two alternative improvements consisting of biologically supported modifications; one in which both models match with Ozbudak et al., 2004 in all 6 combinations of parameters and, the other one, where we increase the number of parameters to 9, matching in all these cases with the biological experiments of Ozbudak et al., 2004.

Suggested Citation

  • Marco Montalva-Medel & Thomas Ledger & Gonzalo A. Ruz & Eric Goles, 2021. "Lac Operon Boolean Models: Dynamical Robustness and Alternative Improvements," Mathematics, MDPI, vol. 9(6), pages 1-19, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:600-:d:514923
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    References listed on IDEAS

    as
    1. Ruivo, Eurico L.P. & Montalva-Medel, Marco & P.B. de Oliveira, Pedro & Perrot, Kévin, 2018. "Characterisation of the elementary cellular automata in terms of their maximum sensitivity to all possible asynchronous updates," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 209-220.
    2. Ertugrul M. Ozbudak & Mukund Thattai & Han N. Lim & Boris I. Shraiman & Alexander van Oudenaarden, 2004. "Multistability in the lactose utilization network of Escherichia coli," Nature, Nature, vol. 427(6976), pages 737-740, February.
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