Zhang Qing, Zhang Zhichao, Shi Hualin
CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China.
CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, China.
Biophys J. 2020 Dec 15;119(12):2537-2557. doi: 10.1016/j.bpj.2020.10.034. Epub 2020 Nov 13.
Sixty years ago, bacterial cell size was found to be an exponential function of growth rate. Fifty years ago, a more general relationship was proposed, in which cell mass was equal to the initiation mass multiplied by 2 to the power of the ratio of the total time of C and D periods to the doubling time. This relationship has recently been experimentally confirmed by perturbing doubling time, C period, D period, or initiation mass. However, the underlying molecular mechanism remains unclear. Here, we developed a theoretical model for initiator protein DnaA mediating DNA replication initiation in Escherichia coli. We introduced an initiation probability function for competitive binding of DnaA-ATP and DnaA-ADP at oriC. We established a kinetic description of regulatory processes (e.g., expression regulation, titration, inactivation, and reactivation) of DnaA. Cell size as a spatial constraint also participates in the regulation of DnaA. By simulating DnaA kinetics, we obtained a regular DnaA oscillation coordinated with cell cycle and a converged cell size that matches replication initiation frequency to the growth rate. The relationship between the simulated cell size and growth rate, C period, D period, or initiation mass reproduces experimental results. The model also predicts how DnaA number and initiation mass vary with perturbation parameters, comparable with experimental data. The results suggest that 1) when growth rate, C period, or D period changes, the regulation of DnaA determines the invariance of initiation mass; 2) ppGpp inhibition of replication initiation may be important for the growth rate independence of initiation mass because three possible mechanisms therein produce different DnaA dynamics, which is experimentally verifiable; and 3) perturbation of some DnaA regulatory process causes a changing initiation mass or even an abnormal cell cycle. This study may provide clues for concerted control of cell size and cell cycle in synthetic biology.
六十年前，人们发现细菌细胞大小是生长速率的指数函数。五十年前，有人提出了一种更普遍的关系，即细胞质量等于起始质量乘以2的（C期和D期总时间与倍增时间之比）次方。最近，通过扰动倍增时间、C期、D期或起始质量，这一关系已得到实验证实。然而，其潜在的分子机制仍不清楚。在此，我们构建了一个理论模型，用于描述大肠杆菌中起始蛋白DnaA介导的DNA复制起始过程。我们引入了一个起始概率函数，用于描述DnaA-ATP和DnaA-ADP在oriC处的竞争性结合。我们建立了DnaA调控过程（如表达调控、滴定、失活和再激活）的动力学描述。细胞大小作为一种空间限制因素也参与了对DnaA的调控。通过模拟DnaA动力学，我们获得了与细胞周期协调的规则DnaA振荡以及与复制起始频率和生长速率相匹配的收敛细胞大小。模拟的细胞大小与生长速率、C期、D期或起始质量之间的关系重现了实验结果。该模型还预测了DnaA数量和起始质量如何随扰动参数变化，与实验数据具有可比性。结果表明：1）当生长速率、C期或D期发生变化时，DnaA的调控决定了起始质量的不变性；2）ppGpp对复制起始的抑制作用对于起始质量不依赖于生长速率可能很重要，因为其中三种可能的机制会产生不同的DnaA动态变化，这是可以通过实验验证的；3）对某些DnaA调控过程的扰动会导致起始质量变化甚至细胞周期异常。这项研究可能为合成生物学中细胞大小和细胞周期的协同控制提供线索。
