Bleecken S
Central Institute of Microbiology and Experimental Therapy, Academy of Science of the GDR, Jena.
J Theor Biol. 1989 Dec 7;141(3):325-62. doi: 10.1016/s0022-5193(89)80118-3.
A mathematical model is developed that describes substrate limited bacterial growth in a continuous culture and that is based upon the conceptual framework elaborated in a previous paper for describing the feedback control system of cell growth [S. Bleecken, (1988). J. theor. Biol. 133, 37.] Central to the theory are the ideas that the limiting substrate is converted into low molecular weight building blocks of macromolecular synthesis which again are converted into biomass (RNA and protein) and that the rates of RNA and protein synthesis are controlled by the intracellular concentration of building blocks. It is shown that a continuous culture can be simulated by two interconnected feedback control systems the actuating signals of which are limiting substrate concentration and the intracellular concentration of building blocks, respectively. Three types of steady-states are found to appear in a continuous culture, besides the well-known stable steady-state of the whole culture there exist two batchlike steady-states of the biotic part of the culture which are metastable. The model is used to analyse the steady-states and their stability properties as well as the dynamic responses of biomass, RNA, protein, building block and substrate concentrations to changes in environmental conditions. Especially the inoculation of a continuous culture and the effects of step changes in dilution rate, inlet substrate concentration and growth temperature are studied in detail. Relations between the growth behaviour of a single cell and that of a continuous culture are derived. The RNA to protein ratio is introduced as a rough measure of the physiological state of cells and it is shown that a cell reacts to environmental changes with a simple pattern of basic responses in growth rate and physiological state. There are reasons to assume that the model presented is the minimal version of a structured model of bacterial growth and represents an optimum compromise between biological relevance and mathematical practicability.
建立了一个数学模型，该模型描述了连续培养中底物限制的细菌生长，并且基于先前一篇论文中阐述的用于描述细胞生长反馈控制系统的概念框架[S. Bleecken, (1988). J. theor. Biol. 133, 37.]。该理论的核心思想是，限制性底物被转化为大分子合成的低分子量构建块，这些构建块又被转化为生物量（RNA和蛋白质），并且RNA和蛋白质合成的速率由构建块的细胞内浓度控制。结果表明，连续培养可以由两个相互连接的反馈控制系统模拟，其驱动信号分别是限制性底物浓度和构建块的细胞内浓度。除了整个培养物众所周知的稳定稳态之外，在连续培养中还发现出现三种类型的稳态，培养物生物部分存在两种类似分批培养的稳态，它们是亚稳态。该模型用于分析稳态及其稳定性特性，以及生物量、RNA、蛋白质、构建块和底物浓度对环境条件变化的动态响应。特别详细研究了连续培养的接种以及稀释率、入口底物浓度和生长温度的阶跃变化的影响。推导了单细胞生长行为与连续培养生长行为之间的关系。引入RNA与蛋白质的比率作为细胞生理状态的粗略度量，结果表明细胞以生长速率和生理状态的基本响应的简单模式对环境变化做出反应。有理由假设所提出的模型是细菌生长结构化模型的最小版本，并且代表了生物学相关性和数学实用性之间的最佳折衷。
