Santillán M, Mackey M C, Zeron E S
Unidad Monterrey, Centro de Investigación y Estudios Avanzados del Instituto Politécnico Nacional, Monterrey, México.
Biophys J. 2007 Jun 1;92(11):3830-42. doi: 10.1529/biophysj.106.101717. Epub 2007 Mar 9.
Multistability is an emergent dynamic property that has been invoked to explain multiple coexisting biological states. In this work, we investigate the origin of bistability in the lac operon. To do this, we develop a mathematical model for the regulatory pathway in this system and compare the model predictions with other experimental results in which a nonmetabolizable inducer was employed. We investigate the effect of lactose metabolism using this model, and show that it greatly modifies the bistable region in the external lactose (Le) versus external glucose (Ge) parameter space. The model also predicts that lactose metabolism can cause bistability to disappear for very low Ge. We have also carried out stochastic numerical simulations of the model for several values of Ge and Le. Our results indicate that bistability can help guarantee that Escherichia coli consumes glucose and lactose in the most efficient possible way. Namely, the lac operon is induced only when there is almost no glucose in the growing medium, but if Le is high, the operon induction level increases abruptly when the levels of glucose in the environment decrease to very low values. We demonstrate that this behavior could not be obtained without bistability if the stability of the induced and uninduced states is to be preserved. Finally, we point out that the present methods and results may be useful to study the emergence of multistability in biological systems other than the lac operon.
多稳态是一种新兴的动态特性，已被用于解释多种共存的生物状态。在这项工作中，我们研究了乳糖操纵子中双稳态的起源。为此，我们为该系统中的调控途径建立了一个数学模型，并将模型预测结果与使用不可代谢诱导剂的其他实验结果进行比较。我们使用该模型研究乳糖代谢的影响，并表明它极大地改变了外部乳糖（Le）与外部葡萄糖（Ge）参数空间中的双稳态区域。该模型还预测，对于非常低的Ge，乳糖代谢会导致双稳态消失。我们还对几种Ge和Le值进行了模型的随机数值模拟。我们的结果表明，双稳态有助于确保大肠杆菌以最有效的方式消耗葡萄糖和乳糖。也就是说，只有当生长培养基中几乎没有葡萄糖时，乳糖操纵子才会被诱导，但如果Le很高，当环境中的葡萄糖水平降至非常低的值时，操纵子的诱导水平会突然增加。我们证明，如果要保持诱导态和未诱导态的稳定性，没有双稳态就无法获得这种行为。最后，我们指出，目前的方法和结果可能有助于研究除乳糖操纵子之外的生物系统中多稳态的出现。
