We discuss here the values of the model parameters used in the plots and how they were fixed. The cyan lines in Fig. 2C represent theoretical predictions and have a negative slope corresponding to Eq. 8 with pH = 0.48, 0.3, and 0.75 for an adder between initiations (see below), respectively, for the Wallden et al. slow growth, Adiciptaningrum et al., and Wallden et al. intermediate growth datasets (6, 12). These values were fixed from Fig. 2A and Eq. 8. The same values of pH are used in all other plots. In Fig. 2D, the orange lines are the best fit for the case where replication is limiting [corresponding to the model of (7)]. The average duration of the C + D period is set from the empirical averages to 160, 102, and 75 min for the Wallden et al. slow growth, Adiciptaningrum et al., and Wallden et al. intermediate growth datasets, respectively. Cyan curves follow Eq. 9 with pH fixed as above, and Embedded Image was fixed from Eq. 11 to the following values: 49 min (Wallden et al. slow growth), 52 min (Adiciptaningrum et al.), and 41 min (Wallden et al. intermediate growth).

Figure 3 (B and D) shows the result of numerical simulations, where the parameters were constrained from the data. The plots in Fig. 2 fix the values of pH and Embedded Image for the three datasets in Fig. 3B, while Fig. 3D corresponds to a wide range of growth conditions and required more general choices. Specifically, the numerical simulations use the following input parameters, directly fixed from the data: (i and ii) The average growth rate 〈α〉 and its variance Embedded Image. In Fig. 3D, the average growth rates range from 0.002 to 0.04 min−1 to match the experimental values. The variance of the growth rate was chosen by keeping a constant coefficient of variation (CV) of 0.15. The growth rate was a normal or log-normal random variable (the two choices do not affect the results, see below), extracted independently for every cell cycle. (iii and iv) The average added volume per origin between consecutive initiations 〈νI〉 and its variance Embedded Image. The average added volume per origin was fixed to 0.45 μm3 as measured in (6), and the variance was fixed to a constant CV of 0.15. The added volume between consecutive initiations was assumed to be log-normally distributed (and extracted independently for every cell cycle). (v and vi) The average time needed for replication and segregation (the C + D′ period) Embedded Image and its variance Embedded Image. In Fig. 3D, the average duration of the C + D′ period was set to 45 min independently from the average growth rate, and its CV was maintained constant and equal to 0.2 for the simulations corresponding to replication always limiting (orange lines) and concurrent processes (cyan lines). The average duration of the C + D′ period was set to 0 for the simulations where replication is never limiting (purple lines). Embedded Image was assumed to be a normal random variable (extracted independently for every cell cycle). Note that the average added volume per origin between consecutive initiations, the average growth rate, and the average C + D′ duration set the characteristic division size of the interinitiation process, Embedded Image. (vii and viii) The average interdivision added volume 〈ΔH〉 and its variance Embedded Image. Note that 〈ΔH〉 sets the characteristic size of the interdivision process Embedded Image. In Fig. 3B, 〈ΔH〉 was fixed to achieve the same values of pH as in Fig. 2 (B and D). In Fig. 3D, the interdivision added volume was fixed so that for the case of concurrent cycles, the replication-related process and the interdivision process would compete to set division in the same way across all conditions. Specifically, we chose 〈ΔH〉 = 〈νI〉 exp(45 min ⋅ 〈α〉) for the case of concurrent processes (Fig. 3D, cyan line). The case where replication is never limiting (purple line) was simulated by assuming the same 〈ΔH〉 but setting Embedded Image to zero. Last, we set 〈ΔH〉 = 0 to simulate the case of replication always limiting (orange line). With these choices, pH ≈ 0 for the replication always limiting case (Fig. 3D, orange line), pH ≈ 0.6 for concurrent cycles (cyan line), and pH ≈ 1 for the replication never limiting models (purple line). The variance Embedded Image was set to a constant CV of 0.15 over the different growth conditions. The interdivision volume was assumed to be a log-normally distributed random variable as above.

We chose to present the data with Embedded Image (adder) simulations, but we explored other values of these parameters, and in particular Embedded Image and Embedded Image, initiation triggered at fixed size per origin, finding very robust results. In addition, while Fig. 3 follows a specific set of parameters, we explored systematically in simulations different characteristic sizes and noise levels for the two processes. For instance, as mentioned above, the simulations for Gaussian-distributed growth rate, interdivision volume, and added volume per origin between consecutive initiations show no substantial differences in the trends shown in Fig. 3 (data not shown).

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