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Robust replication initiation from coupled homeostatic mechanisms

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Berger, Mareike, Wolde, Pieter Rein ten·2022·Nature Communications
DOI 10.1038/s41467-022-33886-6PMC PMC9640692

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Abstract

The bacterium Escherichia coli initiates replication once per cell cycle at a precise volume per origin and adds an on average constant volume between successive initiation events, independent of the initiation size. Yet, a molecular model that can explain these observations has been lacking. Experiments indicate that E. coli controls replication initiation via titration and activation of the initiator protein DnaA. Here, we study by mathematical modelling how these two mechanisms interact to generate robust replication-initiation cycles. We first show that a mechanism solely based on titration generates stable replication cycles at low growth rates, but inevitably causes premature reinitiation events at higher growth rates. In this regime, the DnaA activation switch becomes essential for stable replication initiation. Conversely, while the activation switch alone yields robust rhythms at high growth rates, titration can strongly enhance the stability of the switch at low growth rates. Our analysis thus predicts that both mechanisms together drive robust replication cycles at all growth rates. In addition, it reveals how an origin-density sensor yields adder correlations.

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Fig. 1 We present two distinct models to elucidate the molecular mechanism by which E. coli initiates replication at an on average constant volume per origin. a The volume V(t), the number of origins nori(t) and the origin density ρori(t) = nori(t)/V(t) as a function of time. Initiating replication at a constant origin density ρ* (dashed red line) or respectively a constant volume per origin v* = 1/ρ* (dashed green line) and division a constant time τcc later (blue arrows) ensures that the cell initiates replication once per division cycle and that it maintains cell size homeostasis at slow (light blue regime) and fast (dark blue regime) growth rates. b Schematic representation of an E. coli chromosome: Replication starts at the origin (oriC, yellow circle) and proceeds via two replication forks to the terminus (ter, gray bar). Replication is initiated by the ATP-bound form of the initiator protein DnaA. DnaA is activated via the acidic phospholipids in the cell membrane and via the two chromosomal sites DARS1 and DARS2, and deactivated via the chromosomal site datA and via regulatory inactivation of DnaA (RIDA), a process coupled to active DNA replication. DnaA also has a high affinity for titration sites (gray circles) located on the DNA. c Scheme of the AIT model: In E. coli, the initiator DnaA (red circles) is negatively autoregulated with the dissociation constant KD^p, and can bind both to the oriC and the titration sites with dissociation constants KD^ori and KD^s, respectively. d Scheme of the initiator switch models: In the LD model, ATP-DnaA is mainly activated via the acidic phospholipids and deactivated via the site datA. In the LDDR model, replication forks overlap and RIDA is the main deactivator in combination with the activators DARS1 and DARS2.
Fig. 1 We present two distinct models to elucidate the molecular mechanism by which E. coli initiates replication at an on average constant volume per origin. a The volume V(t), the number of origins nori(t) and the origin density ρori(t) = nori(t)/V(t) as a function of time. Initiating replication at a constant origin density ρ* (dashed red line) or respectively a constant volume per origin v* = 1/ρ* (dashed green line) and division a constant time τcc later (blue arrows) ensures that the cell initiates replication once per division cycle and that it maintains cell size homeostasis at slow (light blue regime) and fast (dark blue regime) growth rates. b Schematic representation of an E. coli chromosome: Replication starts at the origin (oriC, yellow circle) and proceeds via two replication forks to the terminus (ter, gray bar). Replication is initiated by the ATP-bound form of the initiator protein DnaA. DnaA is activated via the acidic phospholipids in the cell membrane and via the two chromosomal sites DARS1 and DARS2, and deactivated via the chromosomal site datA and via regulatory inactivation of DnaA (RIDA), a process coupled to active DNA replication. DnaA also has a high affinity for titration sites (gray circles) located on the DNA. c Scheme of the AIT model: In E. coli, the initiator DnaA (red circles) is negatively autoregulated with the dissociation constant KD^p, and can bind both to the oriC and the titration sites with dissociation constants KD^ori and KD^s, respectively. d Scheme of the initiator switch models: In the LD model, ATP-DnaA is mainly activated via the acidic phospholipids and deactivated via the site datA. In the LDDR model, replication forks overlap and RIDA is the main deactivator in combination with the activators DARS1 and DARS2.CC BY · PubMed Central
Fig. 2 A titration-based model can generate robust replication initiation cycles at low growth rates, but not at higher growth rates in the regime of overlapping replication forks. a–d The volume V(t), the number of initiator proteins Np(t) and titration sites Ns(t), the total concentration of initiator proteins [p]T(t), and the concentration of initiator proteins in the cytoplasm [p](t) as a function of time (in units of the doubling time of the cell τd) for τd = 2 h (a), τd = 35 min (b, c) and τd = 25 min (d), respectively. a When the number of initiator proteins per origin np(t) exceeds the number of titration sites per origin ns (yellow dashed line), the free concentration [p](t) rapidly rises to reach the threshold concentration KD^ori (blue dashed line), initiating a new round of replication. Due to the homogeneous distribution of titration sites on the chromosome of E. coli and the constant DNA replication rate, the number of titration sites then increases linearly in time. At low growth rates, new titration sites are synthesized faster than new initiator proteins and the free concentration [p](t) rapidly drops after initiation. After a fixed cycling time τcc (blue arrows) the cell divides. The initiation volume per origin v* (green dashed line) at low growth rates is constant in time. b However, in the regime of overlapping replication forks where the doubling time is smaller than the time to replicate the entire chromosome, τd < TC, new proteins are synthesized faster than new titration sites are formed. After a short period τb = 10 min (shaded red area) during which initiation at oriC is blocked via the protein SeqA, replication is reinitiated prematurely, dramatically raising the variation in the initiation volume (see Fig. 5c, green line). c, d Adding SeqA, which transiently blocks DnaA synthesis for a time τb = 10 min after replication initiation (shaded red area), prevents reinitiation events at high (d) but not at intermediate growth rates (c). (See Supplementary Table 1 for all parameters).
Fig. 2 A titration-based model can generate robust replication initiation cycles at low growth rates, but not at higher growth rates in the regime of overlapping replication forks. a–d The volume V(t), the number of initiator proteins Np(t) and titration sites Ns(t), the total concentration of initiator proteins [p]T(t), and the concentration of initiator proteins in the cytoplasm [p](t) as a function of time (in units of the doubling time of the cell τd) for τd = 2 h (a), τd = 35 min (b, c) and τd = 25 min (d), respectively. a When the number of initiator proteins per origin np(t) exceeds the number of titration sites per origin ns (yellow dashed line), the free concentration [p](t) rapidly rises to reach the threshold concentration KD^ori (blue dashed line), initiating a new round of replication. Due to the homogeneous distribution of titration sites on the chromosome of E. coli and the constant DNA replication rate, the number of titration sites then increases linearly in time. At low growth rates, new titration sites are synthesized faster than new initiator proteins and the free concentration [p](t) rapidly drops after initiation. After a fixed cycling time τcc (blue arrows) the cell divides. The initiation volume per origin v* (green dashed line) at low growth rates is constant in time. b However, in the regime of overlapping replication forks where the doubling time is smaller than the time to replicate the entire chromosome, τd < TC, new proteins are synthesized faster than new titration sites are formed. After a short period τb = 10 min (shaded red area) during which initiation at oriC is blocked via the protein SeqA, replication is reinitiated prematurely, dramatically raising the variation in the initiation volume (see Fig. 5c, green line). c, d Adding SeqA, which transiently blocks DnaA synthesis for a time τb = 10 min after replication initiation (shaded red area), prevents reinitiation events at high (d) but not at intermediate growth rates (c). (See Supplementary Table 1 for all parameters).CC BY · PubMed Central
Fig. 3 An ultra-sensitive switch between ATP-DnaA and ADP-DnaA gives rise to stable cell cycles. a LD model: The constant activation rate (red curve) and the origin density-dependent deactivation rate (blue curve) as a function of the active fraction of the initiator protein f at different moments of the cell cycle. The steady-state active fractions are given by the intersection of the activation and deactivation rates (colored dots) and when f equals the critical initiator fraction f*, replication is initiated. A doubling of the number of origins leads to a decrease of the active fraction f. b LD model: The volume of the cell V(t), the number of origins nori(t) and the fraction of ATP-DnaA f(t) from Eq. (3) as a function of time (in units of the doubling time τd = 2 h). The average active fraction over one cell cycle 〈f〉 is indicated in red in the third panel. Replication is initiated at a critical initiator fraction f* (red dashed line) and the system gives rise to a constant initiation volume per origin v* over time (green dashed line). c The amplitude Δf of the oscillations in the active fraction f as a function of the growth rate for different magnitudes of the (de)activation rates (αl = 4.6 × βdatA). The amplitude of the oscillations Δf becomes small for biologically realistic values of the (de)activation rates in the LD model (red solid curve), but not in the LDDR model (red dashed curve). (See Supplementary Table 2 for all parameters and Supplementary Fig. 9 for time traces of LDDR model).
Fig. 3 An ultra-sensitive switch between ATP-DnaA and ADP-DnaA gives rise to stable cell cycles. a LD model: The constant activation rate (red curve) and the origin density-dependent deactivation rate (blue curve) as a function of the active fraction of the initiator protein f at different moments of the cell cycle. The steady-state active fractions are given by the intersection of the activation and deactivation rates (colored dots) and when f equals the critical initiator fraction f*, replication is initiated. A doubling of the number of origins leads to a decrease of the active fraction f. b LD model: The volume of the cell V(t), the number of origins nori(t) and the fraction of ATP-DnaA f(t) from Eq. (3) as a function of time (in units of the doubling time τd = 2 h). The average active fraction over one cell cycle 〈f〉 is indicated in red in the third panel. Replication is initiated at a critical initiator fraction f* (red dashed line) and the system gives rise to a constant initiation volume per origin v* over time (green dashed line). c The amplitude Δf of the oscillations in the active fraction f as a function of the growth rate for different magnitudes of the (de)activation rates (αl = 4.6 × βdatA). The amplitude of the oscillations Δf becomes small for biologically realistic values of the (de)activation rates in the LD model (red solid curve), but not in the LDDR model (red dashed curve). (See Supplementary Table 2 for all parameters and Supplementary Fig. 9 for time traces of LDDR model).CC BY · PubMed Central
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, Δvn^(*)=2vn+1^(*)−vn^(*), is independent of the initiation volume vn^(*) 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* nori that is added between successive initiation events (here, the number of origins before initiation is nori = 1). b Lipid-concentration fluctuations l(t) ≡ [l](t) regress to the mean on a timescale τd=ln(2)/λ 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 τd as the lipid concentration, such that a perturbation v0^(*)−⟨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).
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, Δvn^(*)=2vn+1^(*)−vn^(*), is independent of the initiation volume vn^(*) 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* nori that is added between successive initiation events (here, the number of origins before initiation is nori = 1). b Lipid-concentration fluctuations l(t) ≡ [l](t) regress to the mean on a timescale τd=ln(2)/λ 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 τd as the lipid concentration, such that a perturbation v0^(*)−⟨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).CC BY · PubMed Central
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 τd) for λ = 0.35 h−1 as indicated in panel c. The dashed red line is the critical free ATP-DnaA concentration ([D])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 reinitiation54–56. (See Supplementary Table 2 for all parameters).
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 τd) for λ = 0.35 h−1 as indicated in panel c. The dashed red line is the critical free ATP-DnaA concentration ([D])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 reinitiation54–56. (See Supplementary Table 2 for all parameters).CC BY · PubMed Central

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Metadata

Authors
Berger, M., & Wolde, P. R. T.
Affiliations
Institute for Atomic and Molecular Physics (NL)
ORCID
Venue
Nature Communications
Publisher
Springer Science and Business Media LLC
Published
2022-11-07
Volume
13
Issue
1
Pages
6556-6556
ISSN
2041-1723 (ISSN-L)
DOI
10.1038/s41467-022-33886-6
PMC
PMC9640692
OpenAlex
W4287123557
Cited by
41
References
6
Citations by year
2026: 8 · 2025: 7 · 2024: 6 · 2023: 19 · 2022: 1
FWCI
2.69
Type
journal article
Language
en
Open access
Licence
Locations
  • Nature Communications (publishedVersion, cc-by)
  • bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • AMOLF Institutional Repository (AMOLF) (submittedVersion, cc-by)
  • RePEc: Research Papers in Economics (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • arXiv (Cornell University) (cc-by)
Funders
Nederlandse Organisatie voor Wetenschappelijk Onderzoek (024.003.019)
Topics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Bacterial Genetics and Biotechnology
  • Physical Sciences › Mathematics › Modeling and Simulation › Mathematical Biology Tumor Growth
Keywords
DNA replication initiation, Escherichia coli, DnaA, cell cycle, growth rate dependence, robustness, mathematical modeling, homeostatic mechanisms, reinitiation
MeSH terms
Bacterial Proteins, Chromosomes, Bacterial, DNA Replication, DNA-Binding Proteins, Escherichia coli, Replication Origin, Escherichia coli Proteins

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