Lac Operon Boolean Models: Dynamical Robustness and Alternative Improvements
In Veliz-Cuba and Stigler 2011, Boolean models were proposed for the <i>lac</i> operon in <i>Escherichia coli</i> 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 ra...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-03-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/9/6/600 |
| _version_ | 1797541757301293056 |
|---|---|
| author | Marco Montalva-Medel Thomas Ledger Gonzalo A. Ruz Eric Goles |
| author_facet | Marco Montalva-Medel Thomas Ledger Gonzalo A. Ruz Eric Goles |
| author_sort | Marco Montalva-Medel |
| collection | DOAJ |
| description | In Veliz-Cuba and Stigler 2011, Boolean models were proposed for the <i>lac</i> operon in <i>Escherichia coli</i> 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. |
| first_indexed | 2024-03-10T13:20:18Z |
| format | Article |
| id | doaj.art-65f09de53fd54cef96a7875f6c14f7d9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T13:20:18Z |
| publishDate | 2021-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-65f09de53fd54cef96a7875f6c14f7d92023-11-21T10:03:11ZengMDPI AGMathematics2227-73902021-03-019660010.3390/math9060600Lac Operon Boolean Models: Dynamical Robustness and Alternative ImprovementsMarco Montalva-Medel0Thomas Ledger1Gonzalo A. Ruz2Eric Goles3Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Diagonal Las Torres 2700, Peñalolén, Santiago 7941169, ChileFacultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Diagonal Las Torres 2700, Peñalolén, Santiago 7941169, ChileFacultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Diagonal Las Torres 2700, Peñalolén, Santiago 7941169, ChileFacultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Diagonal Las Torres 2700, Peñalolén, Santiago 7941169, ChileIn Veliz-Cuba and Stigler 2011, Boolean models were proposed for the <i>lac</i> operon in <i>Escherichia coli</i> 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.https://www.mdpi.com/2227-7390/9/6/600lac operoncatabolite repressionbistabilityBoolean networkdynamicattractor |
| spellingShingle | Marco Montalva-Medel Thomas Ledger Gonzalo A. Ruz Eric Goles Lac Operon Boolean Models: Dynamical Robustness and Alternative Improvements Mathematics lac operon catabolite repression bistability Boolean network dynamic attractor |
| title | Lac Operon Boolean Models: Dynamical Robustness and Alternative Improvements |
| title_full | Lac Operon Boolean Models: Dynamical Robustness and Alternative Improvements |
| title_fullStr | Lac Operon Boolean Models: Dynamical Robustness and Alternative Improvements |
| title_full_unstemmed | Lac Operon Boolean Models: Dynamical Robustness and Alternative Improvements |
| title_short | Lac Operon Boolean Models: Dynamical Robustness and Alternative Improvements |
| title_sort | lac operon boolean models dynamical robustness and alternative improvements |
| topic | lac operon catabolite repression bistability Boolean network dynamic attractor |
| url | https://www.mdpi.com/2227-7390/9/6/600 |
| work_keys_str_mv | AT marcomontalvamedel lacoperonbooleanmodelsdynamicalrobustnessandalternativeimprovements AT thomasledger lacoperonbooleanmodelsdynamicalrobustnessandalternativeimprovements AT gonzaloaruz lacoperonbooleanmodelsdynamicalrobustnessandalternativeimprovements AT ericgoles lacoperonbooleanmodelsdynamicalrobustnessandalternativeimprovements |