Jenkins Andy, Macauley Matthew
Department of Mathematics, University of Georgia, Athens, GA, USA.
Department of Mathematical Sciences, Clemson University, Clemson, SC, USA.
Bull Math Biol. 2017 Aug;79(8):1778-1795. doi: 10.1007/s11538-017-0306-1. Epub 2017 Jun 21.
The lactose operon in Escherichia coli was the first known gene regulatory network, and it is frequently used as a prototype for new modeling paradigms. Historically, many of these modeling frameworks use differential equations. More recently, Stigler and Veliz-Cuba proposed a Boolean model that captures the bistability of the system and all of the biological steady states. In this paper, we model the well-known arabinose operon in E. coli with a Boolean network. This has several complex features not found in the lac operon, such as a protein that is both an activator and repressor, a DNA looping mechanism for gene repression, and the lack of inducer exclusion by glucose. For 11 out of 12 choices of initial conditions, we use computational algebra and Sage to verify that the state space contains a single fixed point that correctly matches the biology. The final initial condition, medium levels of arabinose and no glucose, successfully predicts the system's bistability. Finally, we compare the state space under synchronous and asynchronous update and see that the former has several artificial cycles that go away under a general asynchronous update.
大肠杆菌中的乳糖操纵子是首个被发现的基因调控网络，常被用作新型建模范式的原型。从历史角度来看，许多此类建模框架都使用微分方程。最近，施蒂格勒和维利兹 - 古巴提出了一个布尔模型，该模型能够捕捉系统的双稳态以及所有生物稳态。在本文中，我们用布尔网络对大肠杆菌中著名的阿拉伯糖操纵子进行建模。它具有一些乳糖操纵子中未发现的复杂特征，比如一种兼具激活剂和阻遏物功能的蛋白质、一种用于基因抑制的DNA环化机制，以及不存在葡萄糖介导的诱导物排除现象。对于12种初始条件选择中的11种，我们使用计算代数和Sage来验证状态空间包含一个与生物学现象正确匹配的单一不动点。最后一种初始条件，即中等水平的阿拉伯糖且无葡萄糖的情况，成功预测了系统的双稳态。最后，我们比较了同步更新和异步更新下的状态空间，发现前者存在一些在一般异步更新下会消失的人为循环。
