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Coordination between E. coli Cell Size and Cell Cycle Mediated by DnaA

Sixty years ago, bacterial cell size was found as an exponential function of growth rate. Fifty years ago, a more general relationship was proposed, in which the cell mass was equal to the initiation mass multiplied by the ratio of the total time of the C and D periods to the doubling time. This relationship has recently been experimentally confirmed by perturbing doubling time, C period, D period or the initiation mass. However, the underlying molecular mechanism remains unclear. Here, we developed a mechanistic and kinetic model to describe how the initiator protein DnaA mediates the initiation of DNA replication in E. coli. In the model, we introduced an initiation probability function involving competitive binding of DnaA-ATP (active) and DnaA-ADP (inactive) at replication origin to determine the initiation of replication. In addition, we considered RNAP availability, ppGpp inhibition, DnaA autorepression, DnaA titration by chromosomal sites, hydrolysis of DnaA-ATP along with DNA replication, reactivation of DnaA-ADP and established a kinetic description of these DnaA regulatory processes. We simulated DnaA kinetics and obtained a self-consistent cell size and a regular DnaA oscillation coordinated with the cell cycle at steady state. The relationship between the cell size obtained by the simulation and the growth rate, C period, D period or initiation mass reproduces the results of the experiment. This model also predicts how the number of DnaA and the initiation mass vary with the perturbation parameters (including those reflecting the mutation or interference of DnaA regulatory processes), which is comparable to experimental data. The results suggest that the regulatory mechanisms of DnaA level and activity are associated with the invariance of initiation mass and the cell size general relationship for matching frequencies of replication initiation and cell division. This study may provide clues for concerted control of cell size and cell cycle in synthetic biology.