Veliz-Cuba Alan, Stigler Brandilyn
Department of Mathematics, University of Nebraska-Lincoln, Lincoln, Nebraska, USA.
J Comput Biol. 2011 Jun;18(6):783-94. doi: 10.1089/cmb.2011.0031. Epub 2011 May 12.
The lac operon in Escherichia coli has been studied extensively and is one of the earliest gene systems found to undergo both positive and negative control. The lac operon is known to exhibit bistability, in the sense that the operon is either induced or uninduced. Many dynamical models have been proposed to capture this phenomenon. While most are based on complex mathematical formulations, it has been suggested that for other gene systems network topology is sufficient to produce the desired dynamical behavior. We present a Boolean network as a discrete model for the lac operon. Our model includes the two main glucose control mechanisms of catabolite repression and inducer exclusion. We show that this Boolean model is capable of predicting the ON and OFF steady states and bistability. Further, we present a reduced model which shows that lac mRNA and lactose form the core of the lac operon, and that this reduced model exhibits the same dynamics. This work suggests that the key to model qualitative dynamics of gene systems is the topology of the network and Boolean models are well suited for this purpose.
大肠杆菌中的乳糖操纵子已得到广泛研究，是最早发现同时受到正调控和负调控的基因系统之一。已知乳糖操纵子具有双稳态，即该操纵子要么被诱导，要么未被诱导。已经提出了许多动力学模型来捕捉这一现象。虽然大多数模型基于复杂的数学公式，但有人认为对于其他基因系统，网络拓扑结构足以产生所需的动力学行为。我们提出一个布尔网络作为乳糖操纵子的离散模型。我们的模型包括分解代谢物阻遏和诱导物排除这两种主要的葡萄糖控制机制。我们表明，这个布尔模型能够预测开启和关闭稳态以及双稳态。此外，我们提出了一个简化模型，该模型表明乳糖信使核糖核酸（lac mRNA）和乳糖构成了乳糖操纵子的核心，并且这个简化模型表现出相同的动力学。这项工作表明，对基因系统定性动力学进行建模的关键在于网络拓扑结构，而布尔模型非常适合这一目的。
