Narang Atul
Department of Chemical Engineering, University of Florida, Gainesville, FL 32611-6005, USA.
J Theor Biol. 2007 Aug 21;247(4):695-712. doi: 10.1016/j.jtbi.2007.03.030. Epub 2007 Mar 28.
The induction of the lac operon follows cooperative kinetics. The first mechanistic model of these kinetics is the de facto standard in the modeling literature [Yagil, G., Yagil, E., 1971. On the relation between effector concentration and the rate of induced enzyme synthesis. Biophys. J. 11, 11-17]. Yet, subsequent studies have shown that the model is based on incorrect assumptions. Specifically, the repressor is a tetramer with four (not two) inducer-binding sites, and the operon contains two auxiliary operators (in addition to the main operator). Furthermore, these structural features are crucial for the formation of DNA loops, the key determinants of lac repression and induction. Indeed, the repression is determined almost entirely (>95%) by the looped complexes [Oehler, S., Eismann, E.R., Krämer, H., Müller-Hill, B., 1990. The three operators of the lac operon cooperate in repression. EMBO J. 9(4), 973-979], and the pronounced cooperativity of the induction curve hinges upon the existence of the looped complexes [Oehler, S., Alberti, S., Müller-Hill, B., 2006. Induction of the lac promoter in the absence of DNA loops and the stoichiometry of induction. Nucleic Acids Res. 34(2), 606-612]. Here, we formulate a model of lac induction taking due account of the tetrameric structure of the repressor and the existence of looped complexes. We show that: (1) The kinetics are significantly more cooperative than those predicted by the Yagil and Yagil model. The cooperativity is higher because the formation of looped complexes is easily abolished by repressor-inducer binding. (2) The model provides good fits to the repression data for cells containing wild-type tetrameric or mutant dimeric repressor, as well as the induction curves for 6 different strains of Escherichia coli. It also implies that the ratios of certain looped and non-looped complexes are independent of inducer and repressor levels, a conclusion that can be rigorously tested by gel electrophoresis. (3) Repressor overexpression dramatically increases the cooperativity of the induction curve. This suggests that repressor overexpression can induce bistability in systems, such as growth of E. coli on lactose, that are otherwise monostable.
乳糖操纵子的诱导遵循协同动力学。这些动力学的第一个机制模型实际上是建模文献中的标准模型[Yagil, G., Yagil, E., 1971. 效应物浓度与诱导酶合成速率之间的关系。生物物理杂志。11, 11 - 17]。然而，随后的研究表明该模型基于错误的假设。具体而言，阻遏物是一个具有四个（而非两个）诱导物结合位点的四聚体，并且操纵子除了主要操纵基因外还包含两个辅助操纵基因。此外，这些结构特征对于DNA环的形成至关重要，而DNA环是乳糖抑制和诱导的关键决定因素。实际上，抑制几乎完全（>95%）由环状复合物决定[Oehler, S., Eismann, E.R., Krämer, H., Müller - Hill, B., 1990. 乳糖操纵子的三个操纵基因在抑制中协同作用。欧洲分子生物学组织杂志。9(4), 973 - 979]，并且诱导曲线明显的协同性取决于环状复合物的存在[Oehler, S., Alberti, S., Müller - Hill, B., 2006. 在没有DNA环的情况下乳糖启动子的诱导及诱导的化学计量。核酸研究。34(2), 606 - 612]。在此，我们构建了一个充分考虑阻遏物四聚体结构和环状复合物存在的乳糖诱导模型。我们表明：(1) 动力学的协同性比Yagil和Yagil模型预测的显著更高。协同性更高是因为阻遏物 - 诱导物结合很容易消除环状复合物的形成。(2) 该模型很好地拟合了含有野生型四聚体或突变二聚体阻遏物的细胞的抑制数据，以及6种不同大肠杆菌菌株的诱导曲线。它还意味着某些环状和非环状复合物的比例与诱导物和阻遏物水平无关，这一结论可通过凝胶电泳进行严格检验。(3) 阻遏物的过表达显著增加了诱导曲线的协同性。这表明阻遏物的过表达可以在原本是单稳态的系统中诱导双稳态，例如大肠杆菌在乳糖上的生长。
