Avcu N, Alyürük H, Demir G K, Pekergin F, Cavas L, Güzeliş C
Department of Electrical and Electronics Engineering, Faculty of Engineering, Dokuz Eylül University, D1-041 Buca Izmir, 35390 Izmir, Turkey.
Institute of Marine Sciences and Technology, Dokuz Eylül University, 35340 Izmir, Turkey.
Comput Biol Med. 2015 Jun;61:75-91. doi: 10.1016/j.compbiomed.2015.03.009. Epub 2015 Mar 24.
This paper employs the root locus method to conduct a detailed investigation of the parameter regions that ensure bistability in a well-studied gene regulatory network namely, lac operon of Escherichia coli (E. coli). In contrast to previous works, the parametric bistability conditions observed in this study constitute a complete set of necessary and sufficient conditions. These conditions were derived by applying the root locus method to the polynomial equilibrium equation of the lac operon model to determine the parameter values yielding the multiple real roots necessary for bistability. The lac operon model used was defined as an ordinary differential equation system in a state equation form with a rational right hand side, and it was compatible with the Hill and Michaelis-Menten approaches of enzyme kinetics used to describe biochemical reactions that govern lactose metabolism. The developed root locus method can be used to study the steady-state behavior of any type of convergent biological system model based on mass action kinetics. This method provides a solution to the problem of analyzing gene regulatory networks under parameter uncertainties because the root locus method considers the model parameters as variable, rather than fixed. The obtained bistability ranges for the lac operon model parameters have the potential to elucidate the appearance of bistability for E. coli cells in in vivo experiments, and they could also be used to design robust hysteretic switches in synthetic biology.
本文采用根轨迹法，对一个经过充分研究的基因调控网络（即大肠杆菌的乳糖操纵子）中确保双稳态的参数区域进行了详细研究。与先前的研究不同，本研究中观察到的参数双稳态条件构成了一套完整的充要条件。这些条件是通过将根轨迹法应用于乳糖操纵子模型的多项式平衡方程来确定产生双稳态所需多个实根的参数值而得出的。所使用的乳糖操纵子模型被定义为一个具有有理右侧的状态方程形式的常微分方程系统，并且它与用于描述控制乳糖代谢的生化反应的酶动力学的希尔和米氏方法兼容。所开发的根轨迹法可用于研究基于质量作用动力学任何类型的收敛生物系统模型的稳态行为。该方法为分析参数不确定情况下的基因调控网络问题提供了解决方案，因为根轨迹法将模型参数视为可变而非固定的。所获得的乳糖操纵子模型参数的双稳态范围有可能在体内实验中阐明大肠杆菌细胞双稳态的出现情况，并且它们还可用于合成生物学中设计鲁棒的滞后开关。
