Browning Samuel T, Castellanos Mariajosé, Shuler Michael L
Bank of America, New York, New York, USA.
Biotechnol Bioeng. 2004 Dec 5;88(5):575-84. doi: 10.1002/bit.20223.
A genomically and chemically detailed mathematical model of a "minimal cell" would be useful to understand better the "design logic" of cellular regulation. A "minimal cell" will be a prokaryote with the minimum number of genes necessary for growth and replication in an ideal environment (i.e., preformed precursors, constant temperature, etc.). The Cornell single-cell model of Escherichia coli serves as the basic framework upon which a minimal cell model can be constructed. A critical issue for any cell model is to describe a mechanism for control of initiation of chromosome replication. There is strong evidence that the essence of chromosome replication control is highly conserved in eubacteria and even extends to the archae. A generalized mechanism is possible based on binding of the protein DnaA-ATP to the origin of replication (oriC) as a primary control. Other features, such as regulatory inactivation of DnaA (RIDA) by conversion of DnaA-ATP to DnaA-ADP and titration of DnaA by binding to other DnaA boxes on the chromosome, have emerged as critical elements in obtaining a functional system to control initiation of chromosome synthesis. We describe a biologically realistic model of chromosome replication initiation control embedded in a complete whole-cell model that explicitly links the external environment to the mechanism of replication control. The base model is deterministic and then modified to include stochastic variation in the components for replication control. The stochastic model allows evaluation of the model's robustness, employing a low standard deviation of interinitiation time as a measure of robustness. Four factors were examined: DnaA synthesis rate; DnaA-ATP binding sites at oriC; the binding rate of DnaA-ATP to the nonfunctional DnaA boxes; and the effect of changing the number of nonfunctional binding sites. The observed DnaA synthesis rate (2000 molecules/cell) and the number of DnaA binding sites per origin (30) are close to the values predicted by the model to provide good control (low variance of interinitiation time), with a reasonable expenditure of cell resources. At relatively high binding rates for DnaA-ATP to the DnaA boxes (10(16) M(-1) s(-1)), increasing the number of DnaA binding sites to about 300, improved control (but little further improvement was seen by extension to 1000 boxes); however, at a low binding rate (10(10) M(-1) s(-1)), an increase in DnaA boxes had an adverse effect on control. The combination of all four factors is probably necessary to obtain a robust control system. Although this mechanism of replication initiation control is highly conserved, it is not clear if simpler control in a minimal cell might exist based on experimental observations with Mycoplasma. This issue is discussed in this investigation.
一个在基因组和化学方面细节丰富的“最小细胞”数学模型，将有助于更好地理解细胞调控的“设计逻辑”。“最小细胞”将是一种原核生物，在理想环境（即预制前体、恒温等）中生长和复制所需的基因数量最少。大肠杆菌的康奈尔单细胞模型可作为构建最小细胞模型的基本框架。任何细胞模型的一个关键问题是描述染色体复制起始控制的机制。有强有力的证据表明，染色体复制控制的本质在真细菌中高度保守，甚至延伸到古细菌。基于蛋白质DnaA - ATP与复制起点（oriC）的结合作为主要控制，可能存在一种通用机制。其他特征，如通过将DnaA - ATP转化为DnaA - ADP使DnaA发生调控失活（RIDA）以及通过与染色体上其他DnaA框结合来滴定DnaA，已成为获得控制染色体合成起始功能系统的关键要素。我们描述了一个嵌入完整全细胞模型中的染色体复制起始控制的生物学现实模型，该模型明确将外部环境与复制控制机制联系起来。基础模型是确定性的，然后进行修改以纳入复制控制组件中的随机变化。随机模型允许评估模型的稳健性，采用起始间隔时间的低标准差作为稳健性的度量。研究了四个因素：DnaA合成速率；oriC处的DnaA - ATP结合位点；DnaA - ATP与无功能DnaA框的结合速率；以及改变无功能结合位点数量的影响。观察到的DnaA合成速率（2000个分子/细胞）和每个起点的DnaA结合位点数量（30个）接近模型预测的值，以提供良好的控制（起始间隔时间的低方差），同时合理消耗细胞资源。在DnaA - ATP与DnaA框的结合速率相对较高时（10¹⁶ M⁻¹ s⁻¹），将DnaA结合位点数量增加到约300个可改善控制（但扩展到1000个框时进一步改善不大）；然而，在低结合速率（10¹⁰ M⁻¹ s⁻¹）下，增加DnaA框对控制有不利影响。可能需要所有四个因素的组合才能获得一个稳健的控制系统。尽管这种复制起始控制机制高度保守，但基于对支原体的实验观察，尚不清楚在最小细胞中是否可能存在更简单的控制。本研究将讨论这个问题。
