Narang Atul, Pilyugin Sergei S
Department of Chemical Engineering, University of Florida, Gainesville, FL 32611-6005, USA.
J Theor Biol. 2007 Jan 21;244(2):326-48. doi: 10.1016/j.jtbi.2006.08.007. Epub 2006 Aug 12.
When bacteria are grown in a batch culture containing a mixture of two growth-limiting substrates, they exhibit a rich spectrum of substrate consumption patterns including diauxic growth, simultaneous consumption, and bistable growth. In previous work, we showed that a minimal model accounting only for enzyme induction and dilution captures all the substrate consumption patterns [Narang, A., 1998a. The dynamical analogy between microbial growth on mixtures of substrates and population growth of competing species. Biotechnol. Bioeng. 59, 116-121, Narang, A., 2006. Comparitive analysis of some models of gene regulation in mixed-substrate microbial growth, J. Theor. Biol. 242, 489-501]. In this work, we construct the bifurcation diagram of the minimal model, which shows the substrate consumption pattern at any given set of parameter values. The bifurcation diagram explains several general properties of mixed-substrate growth. (1) In almost all the cases of diauxic growth, the "preferred" substrate is the one that, by itself, supports a higher specific growth rate. In the literature, this property is often attributed to the optimality of regulatory mechanisms. Here, we show that the minimal model, which accounts for induction and growth only, displays the property under fairly general conditions. This suggests that the higher growth rate of the preferred substrate is an intrinsic property of the induction and dilution kinetics. It can be explained mechanistically without appealing to optimality principles. (2) The model explains the phenotypes of various mutants containing lesions in the regions encoding for the operator, repressor, and peripheral enzymes. A particularly striking phenotype is the "reversal of the diauxie" in which the wild-type and mutant strains consume the very same two substrates in opposite order. This phenotype is difficult to explain in terms of molecular mechanisms, such as inducer exclusion or CAP activation, but it turns out to be a natural consequence of the model. We show furthermore that the model is robust. The key property of the model, namely, the competitive dynamics of the enzymes, is preserved even if the model is modified to account for various regulatory mechanisms. Finally, the model has important implications for the problem of size regulation in development. It suggests that protein dilution may be the mechanism coupling patterning and growth.
当细菌在含有两种生长限制底物混合物的分批培养物中生长时，它们会呈现出丰富的底物消耗模式，包括双相生长、同时消耗和双稳态生长。在之前的工作中，我们表明一个仅考虑酶诱导和稀释的最小模型能够捕捉所有的底物消耗模式 [纳朗，A.，1998a。微生物在底物混合物上生长与竞争物种种群增长之间的动力学类比。生物技术与生物工程。59，116 - 121，纳朗，A.，2006。混合底物微生物生长中一些基因调控模型的比较分析，理论生物学杂志。242，489 - 501]。在这项工作中，我们构建了最小模型的分岔图，该图展示了在任何给定参数值集下的底物消耗模式。分岔图解释了混合底物生长的几个一般特性。(1) 在几乎所有双相生长的情况下，“首选”底物是其自身能支持更高比生长速率的底物。在文献中，这一特性通常归因于调控机制的最优性。在此，我们表明仅考虑诱导和生长的最小模型在相当一般的条件下呈现出这一特性。这表明首选底物的较高生长速率是诱导和稀释动力学的固有特性。无需诉诸最优性原理就可以从机制上对其进行解释。(2) 该模型解释了在编码操纵子、阻遏物和外周酶的区域含有损伤的各种突变体的表型。一种特别显著的表型是“双相生长的逆转”，即野生型和突变体菌株以相反的顺序消耗完全相同的两种底物。就分子机制而言，如诱导物排斥或CAP激活，这种表型很难解释，但结果表明它是该模型的自然结果。我们进一步表明该模型具有鲁棒性。即使对模型进行修改以考虑各种调控机制，模型的关键特性，即酶的竞争动力学，仍得以保留。最后，该模型对发育中的大小调控问题具有重要意义。它表明蛋白质稀释可能是将模式形成与生长相耦合的机制。
