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Article

Lac Operon Boolean Models: Dynamical Robustness and Alternative Improvements

1
Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Diagonal Las Torres 2700, Peñalolén, Santiago 7941169, Chile
2
Center of Applied Ecology and Sustainability (CAPES), Santiago 8331150, Chile
*
Author to whom correspondence should be addressed.
Academic Editors: Jose C. Valverde, Juan A. Aledo and Silvia Martínez
Mathematics 2021, 9(6), 600; https://doi.org/10.3390/math9060600
Received: 31 January 2021 / Revised: 27 February 2021 / Accepted: 9 March 2021 / Published: 11 March 2021
(This article belongs to the Special Issue Boolean Networks Models in Science and Engineering)
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. View Full-Text
Keywords: lac operon; catabolite repression; bistability; Boolean network; dynamic; attractor; steady state; limit cycle; update schedule lac operon; catabolite repression; bistability; Boolean network; dynamic; attractor; steady state; limit cycle; update schedule
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MDPI and ACS Style

Montalva-Medel, M.; Ledger, T.; Ruz, G.A.; Goles, E. Lac Operon Boolean Models: Dynamical Robustness and Alternative Improvements. Mathematics 2021, 9, 600. https://doi.org/10.3390/math9060600

AMA Style

Montalva-Medel M, Ledger T, Ruz GA, Goles E. Lac Operon Boolean Models: Dynamical Robustness and Alternative Improvements. Mathematics. 2021; 9(6):600. https://doi.org/10.3390/math9060600

Chicago/Turabian Style

Montalva-Medel, Marco, Thomas Ledger, Gonzalo A. Ruz, and Eric Goles. 2021. "Lac Operon Boolean Models: Dynamical Robustness and Alternative Improvements" Mathematics 9, no. 6: 600. https://doi.org/10.3390/math9060600

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