Lac Operon Boolean Models: Dynamical Robustness and Alternative Improvements

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.

Chronological and Carbohydrate-Dependent Transformation of Fatty Acids in the Larvae of Black Soldier Fly Following Food Waste Treatment

“…This phenomenon is similar to the findings observed in the lactose operon of Escherichia coli . The shift of nutrients from glucose to lactose resulted in a fluctuation of the cell growth curve and the transcriptional regulation of lactose metabolism genes in Escherichia coli [ 42 ]. The alternation of nutrient substrates for BSFL could also initiate gene regulation of larval transcriptome, especially the lipid metabolism genes.…”

Set Stability and Set Stabilization of Boolean Control Networks Avoiding Undesirable Set

“…Example 2. Consider the BCN model presented in [36], which is a simplified model of the lac operon in the bacterium Escherichia coli:…”

“…Then, according to(36), we obtain thatW 2 =E 2 ∩ S 0 = {δ 4 8 , δ 8 8 }, W 1 =E 1 ∩ S 0 ∪ R(W 2 ) = {δ 6 8 , δ 7 8 },…”

Boolean Networks Models in Science and Engineering

“…In [6], Montalva-Medel et al study the dynamical robustness of two Boolean models for the lac operon in Escherichia coli under any deterministic update schedule. In addition, alternative improvements consisting in biologically supported modifications are proposed for these two models.…”