Cell Size Is Coordinated with Cell Cycle by Regulating Initiator Protein DnaA in E. coli

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.