Fig. 4. Fluctuations in the switch components can give rise to the experimentally observed adder correlations in the initiation volume per origin v^*, illustrated using the LD model with lipid concentration fluctuations (Eq. (4)).

a The added volume per origin between successive initiation events, $\mathrm{\Delta }{v}_{\mathrm{n}}^{*}=2v_{\mathrm{n+1}}^{*}-v_{\mathrm{n}}^{*}$, is independent of the initiation volume $v_{\mathrm{n}}^{*}$ per origin and on average equal to the average initiation volume, 〈Δv^*〉 = 〈v^*〉, as expected for an initiation volume adder. The cartoon below illustrates the volume Δv^* n_ori that is added between successive initiation events (here, the number of origins before initiation is n_ori = 1). b Lipid-concentration fluctuations l(t) ≡ [l](t) regress to the mean on a timescale ${\tau }_{\mathrm{d}}=ln\left(2\right)/\lambda$ set by the growth rate λ, such that an initial perturbation l₀ − 〈l〉 is halved every subsequent cell cycle. The thin gray lines are time traces from N = 100 simulations starting at an initial lipid concentration perturbation δl₀, while the solid line is the analytical prediction for the mean obtained by solving Eq. (4) subject to the same initial condition. The colored dots indicate the average lipid concentration perturbation δl^* at the moment of initiation in generation n and the horizontal dashed line shows the average lipid concentration at steady state. c The mapping between the initiation volume v^* and the normalized lipid concentration l/〈l〉 (blue line), obtained by solving Eq. (3) in steady state in the limit of high (de)activation rates (Supplementary Note 3B1 and Supplementary Fig. 11). As in a, the colored dots show the average initiation volume v^* as a function of l/〈l〉 at the successive initiation events. d The average initiation volume (colored dots) relaxes on the same timescale τ_d as the lipid concentration, such that a perturbation $v_0^{*}-⟨v^{*}⟩$ is halved every cell cycle, giving rise to adder correlations. In a the dark blue line shows the mean of the binned data and the error bars represent the standard error of the mean (SEM) per bin. The number of data points N and the Pearson correlation coefficient R are indicated. The model includes an eclipse period of about 10 min following replication initiation to prevent immediate reinitiation. (See Supplementary Table 2 for all parameters).