Narang Atul
Department of Chemical Engineering, University of Florida, Gainesville, FL 32611-6005, USA.
J Theor Biol. 2006 Sep 21;242(2):489-501. doi: 10.1016/j.jtbi.2006.03.017. Epub 2006 Mar 29.
Mixed-substrate microbial growth is of fundamental interest in microbiology and bioengineering. Several mathematical models have been developed to account for the genetic regulation of such systems, especially those resulting in diauxic growth. In this work, we compare the dynamics of three such models (Narang, 1998a. The dynamical analogy between microbial growth on mixtures of substrates and population growth of competing species. Biotechnol. Bioeng. 59, 116-121; Thattai and Shraiman, 2003. Metabolic switching in the sugar phosphotransferase system of Escherichia coli. Biophys. J. 85(2), 744-754; Brandt et al., 2004. Modelling microbial adaptation to changing availability of substrates. Water Res. 38, 1004-1013). We show that these models are dynamically similar--the initial motion of the inducible enzymes in all the models is described by the Lotka-Volterra equations for competing species. In particular, the prediction of diauxic growth corresponds to "extinction" of one of the enzymes during the first few hours of growth. The dynamic similarity occurs because in all the models, the inducible enzymes possess properties characteristic of competing species: they are required for their own synthesis, and they inhibit each other. Despite this dynamic similarity, the models vary with respect to the range of dynamics captured. The Brandt et al. model always predicts the diauxic growth pattern, whereas the remaining two models exhibit both diauxic and non-diauxic growth patterns. The models also differ with respect to the mechanisms that generate the mutual inhibition between the enzymes. In the Narang model, mutual inhibition occurs because the enzymes for each substrate enhance the dilution of the enzymes for the other substrate. The Brandt et al. model superimposes upon this dilution effect an additional mechanism of mutual inhibition. In the Thattai and Shraiman model, the mutual inhibition is entirely due to competition for the phosphoryl groups. For quantitative agreement with the data, all models must be modified to account for specific mechanisms of mutual inhibition, such as inducer exclusion.
混合底物微生物生长是微生物学和生物工程学中具有根本重要性的研究内容。已经开发了几种数学模型来解释此类系统的遗传调控，特别是那些导致二次生长的系统。在这项工作中，我们比较了三个这样的模型的动力学（纳朗，1998a。底物混合物上微生物生长与竞争物种种群生长之间的动力学类比。生物技术与生物工程。59，116 - 121；塔泰伊和施拉伊曼，2003。大肠杆菌糖磷酸转移酶系统中的代谢转换。生物物理学杂志。85(2)，744 - 754；布兰特等人，2004。模拟微生物对底物可用性变化的适应性。水研究。38，1004 - 1013）。我们表明这些模型在动力学上是相似的——所有模型中诱导酶的初始运动都由竞争物种的洛特卡 - 沃尔泰拉方程描述。特别是，二次生长的预测对应于生长最初几小时内一种酶的“灭绝”。动态相似性的出现是因为在所有模型中，诱导酶具有竞争物种的特征性质：它们自身的合成需要它们，并且它们相互抑制。尽管存在这种动态相似性，但这些模型在捕获的动力学范围方面有所不同。布兰特等人的模型总是预测二次生长模式，而其余两个模型既表现出二次生长模式也表现出非二次生长模式。这些模型在产生酶之间相互抑制的机制方面也有所不同。在纳朗模型中，相互抑制的发生是因为每种底物的酶会增强另一种底物的酶的稀释。布兰特等人的模型在这种稀释效应之上叠加了一种额外的相互抑制机制。在塔泰伊和施拉伊曼模型中，相互抑制完全是由于对磷酸基团的竞争。为了与数据达成定量一致，所有模型都必须进行修改以考虑相互抑制的具体机制，例如诱导物排除。
