Fig. 5: Combining the DnaA activation switch with titration and SeqA generates robust replication-initiation cycles over a wide range of growth rates.

a, b The concentration of free ATP-DnaA [D]_ATP,f(t) as a function of time (in units of the doubling time τ_d) for λ = 0.35 h⁻¹ as indicated in panel c. The dashed red line is the critical free ATP-DnaA concentration \({[D]}_{{{{{{{{\rm{ATP,f}}}}}}}}}^{*}\) at which replication is initiated. While in the LDDR model the free ATP-DnaA fraction is high during a large fraction of the cell cycle (a, see also Supplementary Note 3C2), combining it with titration sites and SeqA gives rise to a much sharper increase of the free ATP-DnaA concentration at low growth rates (b). c The coefficient of variation CV = σ/μ with the standard deviation σ and the average initiation volume μ = 〈v^*〉 as a function of the growth rate for different models in the presence of noise in the lipid concentration. Even in the absence of biochemical noise in DnaA synthesis, the titration model gives rise to a very high CV at high growth rates, due to premature reinitiation (Fig. 2b). Adding SeqA to the titration model can reduce the CV at high, but not at intermediate growth rates (Fig. 2c). The large coefficient of variation in the LDDR model at low growth rates is reduced significantly by the titration sites. Conversely, the LDDR model prevents the reinitiation events that inevitably occur at intermediate growth rates in the AIT+SeqA model. Combining DnaA activation with titration thus enhances the robustness of replication initiation at all growth rates, also in the presence of noise in DnaA synthesis (Supplementary Fig. 14). All models include an eclipse period of about 10 min following replication initiation to prevent immediate reinitiation^54,55,56. (See Supplementary Table 2 for all parameters).