Introduction

Bacterial proliferation requires precise coordination between DNA replication and biomass growth to maintain cellular homeostasis. While biomass accumulates exponentially, DNA synthesis proceeds in a stepwise manner, creating temporal imbalances that demand continuous correction throughout the cell cycle (Fig. 1A-B). Failure to synchronize these processes risks catastrophic outcomes, such as growth defects, incomplete replication, unequal genetic segregation, and cell death (Boye et al., 1996; Khodursky et al., 2015; Lu et al., 1994; Mäkelä et al., 2024; Zaritsky & Pritchard, 1971). Central to this synchronization in Escherichia coli is the initiator protein DnaA, a DNA-binding protein that binds specifically to an asymmetric 9-bp DnaA-box, whose consensus sequence is TTWTNCACA (Hansen & Atlung, 2018; Speck et al., 1999). Although DnaA binding to the replication origin (oriC) triggers replication initiation (Dong et al., 2023; Kaguni, 2011; Ohbayashi et al., 2020; Ozaki & Katayama, 2012; Sekimizu et al., 1987), how DnaA activity is dynamically regulated to align replication initiation with cellular growth, particularly when DNA content and biomass diverge, remains a fundamental unresolved question in cell cycle biology.

Figure 1.

Two competing models have dominated the field. The titration model posits that DnaA activity is governed by the availability of free DnaA, which accumulates until it surpasses the buffering capacity of chromosomal DnaA-boxes (Christensen et al., 1999; Hansen et al., 1991). Here, replication initiation resets the system by increasing DNA content (and thus DnaA-boxes), titrating excess DnaA. In contrast, the switch model emphasizes the ATP/ADP-bound states of DnaA: DnaA-ATP, synthesized during biomass growth, triggers initiation, while hydrolysis to DnaA-ADP following replication resets the cycle(Berger & Wolde, 2022; Donachie & Blakely, 2003; Fu et al., 2023; Hansen & Atlung, 2018; Katayama et al., 2017). Crucially, the titration model depends on ongoing DnaA synthesis to reflect biomass accumulation, whereas the switch model relies on nucleotide-state transitions, independent of total DnaA levels. Despite these mechanistic differences, both models consider that replication initiation is regulated by oscillations in DnaA activity, driven by DnaA-chromosome interactions (Fig. 1C). However, direct evidence linking these oscillations to replication initiation remains lacking. Moreover, neither model fully explains recent experimental observations: replication initiation persists for multiple generations even when dnaA transcription is completely inhibited (Knöppel et al., 2023). This discrepancy suggests an uncharacterized mechanism that senses biomass-DNA imbalance and directly modulates DnaA activity.

Here, using a synthetic reporter coupled with single-cell mRNA fluorescence in situ hybridization (FISH), we demonstrate that DnaA activity peaks precisely at initiation across diverse growth conditions and genetic backgrounds, even when dnaA transcription is held constant. DnaA activity oscillations persist independently of transcriptional feedback, pointing to a post-translational regulatory mechanism. We propose an extrusion model in which nucleoid-associated proteins (NAPs) sense biomass-DNA imbalance and dynamically extrude DnaA from the chromosome, liberating it to activate oriC. This model not only explains the decoupling of replication timing from dnaA expression but also integrates disparate experimental findings. Perturbations of the NAP, H-NS for instance, modulate DnaA activity and replication timing, directly supporting the model’s predictions. By unifying regulatory principles across transcription, protein activity, and chromosome dynamics, our findings redefine the paradigm for bacterial replication control.

Results

Development of a DnaA activity reporter system

It has been known that changing DnaA expression levels affects DnaA activity, and further changes initiation mass (Berger & Wolde, 2022; Løbner-Olesen et al., 1989; Zheng et al., 2020). To investigate this further, we engineered a dnaA-titratable strain, where dnaA transcription is controlled by an inducible P_tet promoter (Lutz & Bujard, 1997) (Fig. 2A). This system enabled precise modulation of dnaA mRNA levels (0.25 to 6 times the wild-type level) via anhydrotetracycline (aTc) induction (0.75– 20 ng ml⁻¹) without altering growth rate or cell size (Fig. 2B–D). Strikingly, increasing DnaA expression doubled population-averaged oriC copy numbers and reduced initiation mass (the cell volume per oriC at replication initiation) by 50 % (Fig. 2E-F). The observed relationship between DnaA expression and initiation mass deviated significantly from both the titration and switch models (Fig. 2G), suggesting unaccounted regulatory mechanisms.

Figure 2.

To dissect DnaA activity dynamics, we constructed a library of synthetic promoters (n = 67) by replacing tetO operators in P_tet with DnaA-boxes (Fig. S1). To assess the degree of DnaA activity-mediated repression, we measured the fold change in GFP expression driven by each synthetic promoter under low and high levels of dnaA induction (Fig. 3A). Six synthetic promoters exhibited over 8-fold DnaA-mediated repression, whereas the promoter lacking DnaA-boxes (P_con) showed none, and the well-characterized native dnaA promoter (P_native)(Braun et al., 1985; Saggioro et al., 2013; Speck et al., 1999) displayed approximately two-fold repression (Fig. 3B; Fig. S1). P_syn66, which contains three strong and one weak DnaA-box, exhibited >8-fold repression under high DnaA induction (Fig. 3B). P_syn66’s design enables responsiveness to both free DnaA levels (via strong boxes) and the ATP/ADP ratio (via differential binding to the weak box)(Grimwade & Leonard, 2021; Katayama et al., 2017; Speck et al., 1999). Dose-response assays confirmed that P_syn66 was progressively repressed across a 40-fold range of dnaA expression (Fig. 3C), with no interference from SeqA-mediated sequestration (Fig. 3D-E). These results validated P_syn66 as a robust and specific reporter of DnaA activity.

Figure 3.

Decoupling DnaA activity oscillations from dnaA transcription fluctuations

To investigate DnaA activity dynamics throughout the cell cycle, we linked P_syn66 activity to cell size, a surrogate for cell-cycle progression, using single-cell mRNA FISH(Skinner et al., 2013) to quantify lacZ mRNA levels in MG1655Δlac cells harboring the P_syn66-lacZ plasmid (Fig. 4A). A control strain harboring a promoter-less lacZ construct (P_neg) showed undetectable fluorescence signals (Fig. 4A), confirming the specificity of lacZ mRNA detection. Quantitative analysis revealed that P_syn66-driven mRNA levels fluctuated approximately 3-fold over the cell cycle, whereas the DnaA-unresponsive constitutive promoter (P_con) exhibited stable expression (Fig. 4B). However, fluctuations in mRNA concentration may not directly correspond to changes in DnaA activity due to global factors such as plasmid copy number and RNA polymerase concentration (Balakrishnan et al., 2022; Bintu et al., 2005a; Bintu et al., 2005b). To account for these variables, we used a P_con-lacZ plasmid to estimate global effects on mRNA concentration and calculated DnaA activity as inversely proportional to . In wild-type cells (MG1655Δlac) harboring the synthetic reporter system (Fig. 4C), fluctuations in DnaA activity, as denoted by , displayed approximately a 3-fold variation across the cell cycle (Fig. 4D), underscoring the substantial cell cycle-dependent oscillations in DnaA activity.

Figure 4.

We then examined whether the observed fluctuations in DnaA activity were linked to oscillations in dnaA transcription. Comparing the dynamics of dnaA mRNA and DnaA activity, we found that the peak in DnaA activity coincided with the trough in dnaA mRNA levels (Fig. 4D-E). To test whether dnaA transcription drives these oscillations, we eliminated transcriptional fluctuations using the dnaA-titratable strain. Despite constant dnaA mRNA levels (2 ng ml⁻¹ aTc induction), DnaA activity was retained robust oscillations (Fig. 4F–H), demonstrating the decoupling of DnaA activity oscillations from transcriptional fluctuations. These suggest that post-translational regulation, not transcriptional feedback, governs the DnaA activity.

DnaA activity oscillations are tightly coupled to replication timing

To explore the relationship between DnaA activity oscillations and DNA replication initiation, we examined cells grown under various nutrient conditions supporting different doubling times (30–66 min). Significant fluctuations in DnaA activity were observed across all conditions (Fig. 5A). We also estimated the cell volume at replication initiation (V_i) based on population-averaged cell volume and oriC number (Bremer et al., 1979; Si et al., 2017; Zheng et al., 2016) (Fig. S2 A–C), marking this on the DnaA activity profiles. In a representative birth-to-division cell cycle (Pountain et al., 2024) (Fig. S2D), DnaA activity peaks consistently coincided with V_i, indicating a close correlation between DnaA activity and replication initiation (Fig. 5A).

Figure 5.

Further genetic perturbations, such as titrating DnaA expression, shifted DnaA activity fluctuations, yet the relationship between V^∗ (the cell volume at maximal DnaA activity in a representative birth-to-division cell cycle) and V_i remained locked (Fig. 5B). To quantify this relationship, we compared V_i with V^∗, revealing a strictly proportional relationship through the origin (slope= 1.0, R² = 0.98), indicating equivalence between V^∗ and V_i (Fig. 5C). These results confirm that DnaA activity oscillations are tightly correlated with replication initiation, independent of transcriptional or nutrient perturbations.

An extrusion model reconciles paradoxical initiation events

Very recently, Knöppel et al. reported that multiple rounds of initiation occurred even after DnaA synthesis is shut down (Knöppel et al., 2023). In their experiment, DnaA was supplied in excess before expression ceased (Knöppel et al., 2023), potentially allowing continued replication initiation due to residual DnaA. To address this issue, we shut down DnaA expression from its native level using the deactivated miniature Un1Cas12f1 (dUn1Cas12f1) system, guided by sgRNA to repress dnaA transcription (Fig. 6A). This system effectively diminished dnaA transcription to an extremely low level, yet total oriC numbers increased fourfold within 90 min, consistent with two rounds of replication initiation (Fig. 6B). These findings demonstrate that halting DnaA synthesis does not immediately abolish replication initiation.

Figure 6.

Both the titration and switch models predict a close relationship between DnaA activity oscillations and replication initiation(Berger & Wolde, 2022). However, they fail to account for the multiple rounds of initiation observed after DnaA synthesis was shut down. According to the titration model, initiation should cease immediately once DnaA expression is shut down, as the reduction in DnaA concentration would prevent it from reaching the threshold required to trigger new rounds of replication. In contrast, the switch model predicts infinite initiations following the cessation of DnaA expression (Fig. 6C). This is because the cessation of DnaA synthesis only reduce the production rate of DnaA-ATP and had no effect on the conversion rates between DnaA-ATP and DnaA-ADP. As a result, the ratio of DnaA-ATP to DnaA-ADP would temporarily decrease, causing a brief lag before initiation resumes indefinitely (Fig. 6C).

The failure of both models prompts us to revisit the regulatory mechanisms of replication initiation. In the titration model, a substantial fraction of DnaA proteins binds to DnaA-boxes along the chromosome, raising the possibility that these bound proteins serve as a reservoir of free DnaA, sustaining replication initiation even after DnaA synthesis ceases. We thus considered the possibility of some extruder(s) alongside DnaA to sense biomass-DNA deviation, and flush DnaA proteins away from the DnaA-boxes, thus releasing free DnaA to dynamically restore DnaA activity, even in the absence of ongoing DnaA synthesis (Fig. 6D).

In this proposed “extrusion model”, the extruder is constitutively expressed, synthesized at a constant rate throughout the cell cycle, accumulating in proportion to biomass growth, enabling replication initiation when free DnaA concentrations exceed the critical threshold, as described in the titration model(Hansen & Atlung, 2018; Hansen et al., 1991) (Fig. 6D). This model guarantees the long-term coordination of biomass growth and oriC abundance, as well as stable oscillations in free DnaA and oriC concentrations (Fig. S3 A). Notably, the extrusion model accounts for the persistence of replication initiation and free DnaA oscillations over multiple cell cycles after DnaA synthesis is halted (Fig. 6C; Fig. S3 B). Moreover, since the extruder mitigates the impact of perturbations on DnaA synthesis, the model predicts a quantitative relationship between initiation mass and DnaA expression levels that aligns with experimental observations (Fig. 6E). Furthermore, a stochastic implementation of the extrusion model shows the lack of correlation between successive replication initiation events (Fig. S3 C), as observed in recent studies (Si et al., 2019; Witz et al., 2019).

Perturbation of H-NS validates the extrusion mechanism

The extrusion model could be validated by changing the expression level of the extruder, which modulates DnaA activity by releasing DnaA from DnaA-boxes. Given their DNA binding properties, NAPs(Dillon & Dorman, 2010) are likely candidates for this extruder role. Therefore, we selected H-NS(Dorman, 2004), a major NAP, which is capable of promoting the release of DnaA from bound DnaA-boxes in vitro (Fig. S4), to experimentally assess the validity of the extrusion model. To this end, we constructed a hns-titratable strain, incorporating a reporting plasmid to capture changes in DnaA activity across various H-NS expression levels (Fig. 7A). Under steady-state cultivation, increasing aTc concentrations from 0 to 50 ng·ml^-1 resulted in hns mRNA levels ranging from 0.25 to 5 times the wild-type levels, without affecting growth rate (Fig. S5 A-B). Within this range, DnaA activity increased by approximately 60 % (Fig. 7B), while the initiation mass decreased by 30 % (Fig. 7C; calculated with Fig. 5S C-D), in qualitative agreement with the predictions of the extrusion model (Fig. S5 E-F).

Figure 7.

Since H-NS is a global transcriptional regulator (Hommais et al., 2001), we wonder whether its effect on DnaA activity was mediated through dnaA transcription. To test this, we measured DnaA activity and dnaA mRNA levels during an H-NS shift-up. Upon addition of 50 ng·ml-1 aTc, hns levels increased more than 20-fold within a short period, followed by approximately 80 % increase in DnaA activity, with no significant change in dnaA mRNA levels (Fig. 7D). Additionally, cellular oriC content increased significantly within 30 minutes, while cell mass remained unchanged (Fig. 7E). These results suggest that the rapid increase in DnaA activity and accelerated replication initiation induced by H-NS upregulation is not driven by changes in dnaA transcription.

Leveraging the hns-titratable strain, we re-examined the tight correlation between DnaA activity oscillations and replication initiation. In two different growth media with varying hns levels, the peak of DnaA activity fluctuations (V^∗) shifted in concert with the independently measured volume at replication initiation (V_i) (Fig. 7F). Plotting V^∗ against V_i, revealed the same equivalency observed in wild-type and dnaA-titratable cells (Fig. 7G). Collectively, these results support the notion that DnaA activity oscillations, modulated by extrusion, coordinate DNA replication and biomass growth.

Discussion

In this study, we proposed chromosome-driven DnaA activity oscillations as a post-translational “rheostat” coordinating DNA replication with biomass growth in E. coli. By developing a SeqA-independent synthetic promoter reporter (P_syn66) on a plasmid, we circumvented confounding factors inherent to native systems (Pountain et al., 2024), thereby achieving the direct quantification of DnaA activity dynamics. Crucially, these oscillations persist when dnaA transcription is fixed, operate independently of SeqA-mediated repression, and peak precisely at replication initiation across all tested growth conditions. This reveals an essential paradigm: bacteria bypass transcriptional control to synchronize genome duplication with growth through spatial regulation of DnaA-chromosome interactions.

Very recently, Iuliani et al. also reported DnaA activity oscillations (Iuliani et al., 2024), which is a significant milestone, innovatively using a chromosomal promoter-reporter system and microfluidics for single-cell DnaA activity observations. They revealed key relationships between DnaA activity, cell size, and division. Our work, however, differs in multiple ways. Methodologically, we engineered a dnaA-titratable strain and synthetic promoters like P_syn66, enabling precise dnaA expression control and cleaner DnaA activity reporting. Our mRNA FISH approach uniquely compares DnaA activity and transcription at the single-cell level. By decoupling initiation volume measurement from DnaA monitoring, we resolve a 1:1 coupling between DnaA activity thresholds and replication initiation events. Regarding research questions, while Iuliani et al. focused on DnaA-cell size-division relationships, we addressed the decoupling of replication initiation from dnaA expression with our novel extrusion model.

Recently, an integrated “titration-switch” model has been proposed to improve replication cycle stability across different growth rates (Berger & Wolde, 2022; Fu et al., 2023). Although this integrated model predicts a relationship between initiation mass and dnaA mRNA levels that aligns closely with steady-state experimental data (Fig. S6 A), it fails to account for the additional replication initiation observed after dnaA shutdown (Fig. S6 B). By incorporating an extruder into this model, we successfully reproduced the additional replication initiation (Fig. S6 C), thus validating the extrusion concept and aligning with experimental observations. These findings highlight the critical role of extrusion in refining our mechanistic understanding of biomass-DNA coordination.

Mechanistically, we propose that NAPs sense biomass-DNA imbalances and extrude DnaA from chromosomal sites, converting physical displacement into biochemical activation, a spatial control strategy mirroring eukaryotic chromatin regulation. H-NS emerges as a prime extruder candidate given its DNA-condensing ability (Dame et al., 2000; Zimmerman, 2006) and replication-timing effects (Fig. 7). This functional multiplicity likely enhances robustness, allowing cells to maintain replication homeostasis despite fluctuating environments, an evolutionary advantage paralleling eukaryotic checkpoint system.

These findings redefine bacterial cell cycle control as a dynamic interplay between physical chromosome remodeling and metabolic sensing. By tethering DnaA activation to biomass accumulation through extrusion, cells achieve a critical feat: noise suppression via spatial filtering of transcriptional fluctuations. Such mechanistic parsimony, using chromosome structure to both store genetic information and regulate replication timing, may represent a fundamental principle of cellular organization. Indeed, parallels to eukaryotic systems are striking: DnaA extrusion resembles ORC licensing through chromatin accessibility (Fragkos et al., 2015), while biomass-DNA coupling evokes yeast size-control checkpoints (Xie et al., 2022).

Future studies could map the complete extruder interactome and elucidate how metabolic signals modulate their activity. Our synthetic reporter system provides a blueprint for dissecting the spatial regulation of DNA-binding proteins, with translational potential in antimicrobial development (targeting pathogen-specific extruders) and synthetic biology (engineering tunable replication circuits). More broadly, this work establishes physical chromosome remodeling as a central coordinator of cellular homeostasis, a concept bridging prokaryotic and eukaryotic cell cycle paradigms.

Materials and Methods

Plasmid and strain Construction

Strains used in this study were derived from E.coli MG1655. Information for all strains and plasmids are listed in Tables S1 and S2.

Plasmids for reporting DnaA activity

Plasmids expressing GFP, mCherry, or LacZ under synthetic promoters were constructed based on the pPT plasmid backbone (Zong et al., 2017). The lacZ amplified from the MG1655 genome and mcherry gene amplified from pMD19-hupA-mcherry plasmid, were assembled into the BspQI/BsrGI-digested pPT backbone via the One Step Cloning Kit (Vazyme, C112), to generate the pPT-lacZ and pPT-RFP plasmids, respectively. Synthetic promoters, generated by annealing the primer pairs listed in Table S3, were ligated directly into the BsaI-digested pPT, pPT-RFP or pPT-lacZ plasmid as required. The native dnaA promoter (P_native) amplified from the MG1655 genome was digested with BsaI, and ligated into the BsaI-digested pPT plasmid. The P_con-gfp cassette amplified from P_con-GFP plasmid was assembled into the SpeI-digested P_syn66-RFP plasmid to generate the P_sny66-P_con-FPs plasmid. Primer information for amplifying DNA fragments is detailed in Table S4.

Plasmids for strain construction

For constructing the plasmid pMD19-Rhns, pMD19-RseqA and pMD19-RdnaA, the hns, seqA and dnaA gene were amplified from MG1655 genome, digested, and ligated into the same enzyme-digested pMD19-tetR plasmid. For constructing the plasmid p15A-RdnaA, the T3-P_tet-tetR-dnaA cassette, kan^r gene and p15A-T1 fragment were amplified from plasmidpMD19-RdnaA, pEcCas and PZA31-P_tet-M2-GFP, respectively, and then assembled via MultiS One Step Cloning Kit (Vazyme, C113). The plasmid P_CRidnaA1 were obtained by ligating the annealed primer pairs to the BsaI-digested CPP00458 plasmid for the dnaA targeting. The chloramphenicol resistance gene Cm^r amplified from the PZA31-P_tet-M2-GFP plasmid replaced the kan^r gene in the pEcCas plasmid via λRed recombination method, resulting in the CmPcas plasmid. Primer information is detailed in Table S4.

Strain construction

The seqA-, and hns-titratable strains were constructed as previously described (Zheng et al., 2016). Briefly, after transforming pSIM5 plasmid into MG1655 cells, the P_tet-tetR-driven seqA or hns cassette was inserted at the attB site on the genome, and then the native gene was replaced with the kan^r gene amplified from plkml plasmid.

For the construction of dnaA-titratable strain, we first inserted the P_tet-tetR cassette into the intS site via CRISPR/Cas9-λRed genome editing system (Jiang et al., 2015) by targeting 20-nucleotide sequence (tcttcctgcagaccagatcc). Then applying the λRed recombination systems in the CmPcas plasmid, the bla:P_tet-dnaA cassette amplified from the pMD19-RdnaA plasmid via overlap PCR, was inserted between the yidA and yidX genes, and the negative P_native-dnaA was replaced with the T₃-Kan-T₁ cassette amplified from the p15A-RdnaA plasmid.

In order to delete the native lacZ gene in the genome of the RdnaA1, Rhns1 and MG1655 cells, the homologous recombination fragment amplified from the genome of CL1 strain, was used to knock out the native lac operon via CRISPR/Cas9-λRed editing system (Jiang et al., 2015) by targeting 20-nucleotide sequence (cttccggctcgtatgttgtg).

For the construction of DnaA shut-down strain (CRidnaA1), the P_J23119-sgRNA_dnaA:P_J23100-tetR:P_tet-dUn1Cas12f1 cassette was amplified from the P_CRidnaA1 plasmid and flanked with homologous sequences to the asnA and viaA gene. This cassette was then inserted into the MG1655 genome using

CRISPR/Cas9-λRed editing system, targeting the 19-nucleotide sequence (aagccgcctgctcagacgc). The CPP00458 plasmid, kindly provided by the Xiongfei Fu lab, contains the Un1Cas12f1 variant, which carries mutations D143R, T147R, D326A, and K330R that abolish its DNA-cleaving activity. However, it retains the ability to bind DNA in a sgRNA-guided manner, thereby inhibiting the expression of the target gene.

All primers for the construction of DNA fragments are detailed in Table S4.

Growth conditions

Cells for strain construction were grown in in Luria-Bertani (LB) medium with appropriate antibiotics: ampicillin (100 μg·ml^-1), kanamycin (50 μg·ml^-1), spectinomycin (50 μg·ml^-1), chloramphenicol (25 μg·ml^-1), based on plasmid presents. For titratable strains, 10 ng·ml⁻¹ anhydrotetracycline (aTc) was added during strain construction and seed culture preparation. Seed cultures were initiated by inoculating 3–6 individual colonies from an LB agar plate into 14 ml round-bottom test tubes containing 2 ml of the desired medium for overnight growth.

For physiological phenotypic characterization, all cells were cultivated at 37°C with shaking at 150 rpm in a water bath shaker. The dnaA-, seqA- and hns-titratable cells were characterized under varying aTc concentrations in rich defined medium supplemented with glycerol (M6). hns-titratable cells were also characterized in rich defined medium supplemented with glucose (M1). When strains contained reporter plasmid, 25 μg·ml⁻¹ chloramphenicol was added. The autoregulated-dnaA strain (MGCL1) with a reporter plasmid, was tested in seven different media: M1 (MOPS + EZ + AUCG + Glucose), M2 (MOPS + EZ + Glucose), M3 (MOPS + EZ + AUCG + Gluconate), M6 (MOPS + EZ + AUCG + Glycerol),

M12 (MOPS + EZ + Glycerol), M13 (MOPS + CAA + Glycerol), and M18 (MOPS + Glucose). Detailed medium compositions were provided previously (Zheng et al., 2020). Steady-state growth was established as previously described(Zheng et al., 2020) by culturing cells for ∼10 generations in exponential growth phase with ∼15-fold dilution at OD₆₀₀ ∼0.2, using the same medium supplemented with antibiotic or aTc as required. OD₆₀₀ measurements were taken at consecutive time points using a spectrometer (Genesys 10s, Thermo Fisher Scientific), and the growth rate (or doubling time) was calculated by fitting the data to an exponential growth curve. Samples for determination of population-averaged cell mass and cellular origin number , quantification of mRNA levels, and mRNA fluorescence in situ hybridization (FISH) were collected when OD₆₀₀ reached ∼0.2.

Measurements of population-averaged cellular mass , cellular oriC number , and initiation mass (m_i)

The population-averaged cell mass , cellular oriC number , and initiation mass (m_i) were calculated as described previously(Zheng et al., 2020). Briefly, was determined by dividing the OD₆₀₀ by the cell concentration (OD₆₀₀ ml per 10⁹ cells). For cell counting, samples were collected in precooled cell count buffer (0.9% NaCl with 0.12% formaldehyde, filtered with a 0.22 μm filter) and stained with 1 μg·ml⁻¹ DAPI in the same buffer. Cell number concentration was measured by counting the DAPI-stained particles using flow cytometry equipped with 405 nm laser (CytoFLEX, Beckman Coulter Life Sciences). The was calculated based on the classical run-out experiments(Zheng et al., 2020). In brief, cell suspensions were treated with 500 μg·ml⁻¹ rifampicin and 30 μg·ml⁻¹ cephalexin to inhibit new initiation and cell division, respectively, and maintained for 2-3 mass doublings to complete ongoing replication. Cells were fixed with 70% precooled absolute ethanol, and treated with stain buffer (20mM Tris-HCl, pH 8.0, 130 mM NaCl, 10 ng·ml⁻¹ DAPI). Using the same flow cytometry, we measured the cellular origin distribution based on DAPI signaling, from which was calculated. m_i was calculated based on the equation: (Bremer et al., 1979; Si et al., 2017; Zheng et al., 2016).

Screening of the synthetic promoter library

After transforming the reporter plasmid into dnaA-titratable cells, the seed culture was cultivated in M6 medium with 10 ng·ml^-1 aTc, then diluted 1:180 in fresh medium containing either 0.5 or 50 ng·ml^-1 aTc and cultivated at 37 °C and 800 r.p.m. in a digital thermo-shaker (AOSHENG) using flat-bottom 96-well plates (Corning). Following approximately 4 hours of pre-cultivation, the cultures were diluted 1:180 in fresh medium with the same aTc concentration. The OD₆₀₀ and GFP fluorescence intensity were continuously monitored during cell growth using a Synergy H1 microplate reader (BioTek). The non-fluorescent strain (MG1655) cultured in 180ul of M6 medium for each experiment was used to subtract the background fluorescence. For OD₆₀₀ between 0.1 and 0.2, the repression fold change was calculated by dividing the mean fluorescence intensity per OD₆₀₀ of the cells grown with 0.5 ng·ml^-1 aTc induction by the corresponding intensity for cells grown with 50 ng·ml^-1 aTc induction.

Quantitative real-time PCR

Quantitative real-time PCR was performed using a protocol similar to previously described(Zheng et al., 2016). Briefly, RNA was stabilized using Bacteria Protect Reagent (Qiagen) and extracted using RNeasy mini kit (Qiagen). 500 ng RNA was reverse transcribed (TAKARA), and the resulting cDNA samples were diluted 1:25 with PCR-grade water. Quantitative real-time PCR was carried out on a qTower3 (Analytikjena) or CFX Connect system (Bio-Rad), using the following program: 30 s at 95 °C, followed by 40 cycles of denaturation (5 s at 95 °C), annealing, and elongation (30 s at 58 °C). Primer sequences were listed in Table S4. The rpoA gene was used as the reference gene.

lacZ and dnaA mRNA fluorescence in situ hybridization (FISH)

FISH for lacZ or dnaA mRNA was preformed using a method similar to previously described(Skinner et al., 2013). Briefly, antisense DNA oligo probes were designed against lacZ or dnaA, and synthesized with TAMRA labeling at the 3’ end. The sequences of probes targeting lacZ or dnaA are either as previously described(Skinner et al., 2013) or listed in Table S5. 27 ml steady-state growth culture (OD₆₀₀∼0.2) was fixed by direct adding 3 ml of 37 % (vol/vol) formaldehyde, following by incubation for 30 min at room temperature with gentle mixing using a nutator. The fixed cells were collected by centrifugation at 600 g for 8 minutes, and washed twice with 1 ml RNase-free PBS. The cell pellet was resuspended in 300 μl DEPC water, and 700 μl precooled absolute ethanol was added to permeabilize the cells for 1 hour at room temperature in the nutator. After permeabilization, the cells were divided into two equal parts for characterization of lacZ or dnaA mRNA as needed. Hybridization was performed as described previously(Skinner et al., 2013), with the stringency of the hybridization and wash solutions adjusted by changing the concentration of formamide, 30 % for dnaA probes and 40 % for lacZ probes. After hybridization, the cells were washed with the appropriate wash solution and prepared for imaging.

Cell imaging and cell size parameters measurement

For imaging, 3 μl of cell suspension was pipetted onto the center of a 24×60-mm coverslip. A thin 1.5 % agarose pad (prepared with 1xPBS) was then placed on top of the cell suspension droplet. Fluorescent and phase images were acquired using an inverted microscope (IX-83, Olympus) equipped with a 100x oil objective (Olympus), an automated xy-stage (ASI, MS2000), and a sCMOS camera (Prime BSI, photometrics). Fluorescence excitation was performed as previously described (Xia et al., 2022). Solid-state lasers (Coherent OBIS: 405–100 LX, 561–100 LS) and Semrock emission bandpass filters (445/40 nm for DAPI and 598/25 nm for RFP) were used for excitation and collecting fluorescent signals.

Images were aligned with phase contrast channel by selecting at least six pairs of common control points and applying a geometric transformation using the MATLAB imwarp function. This allowed for adjustment of the cell masks in the RFP or DAPI channel. A customized ImageJ -based image-processing package, MicrobeJ (v5.13l₁) plugin for Fiji (Ducret et al., 2016), was used to contour cells and calculate cell size parameters and fluorescence intensity, including the mean cell width, cell length, and cell area from phase-contrast images. The cell volume was calculated using a cylinder-plus-two-hemispheres geometry. The total RFP intensity, corrected for background subtraction per cell volume, was then used to estimate the concentration of the related mRNA level.

Characterization of cell cycle-dependent fluctuations in DnaA activity

Data filtering was first performed based on the intensity of the DAPI fluorescence signal. To eliminate non-cell regions resulting from incorrect segmentation of the phase contrast images, only DAPI-positive cells were included in the analysis. To further minimize the potential impact of variability in fixation, permeabilization, and wash efficiencies, which could affect the TAMRA fluorescence signal (representing the mRNA FISH signal), only cells with mean DAPI signals within the 95% confidence intervals were included in the subsequent analysis.

The concentration of the lacZ mRNA ([mZ]) can be expressed as [mZ] = J/δ_Z, where δ_Z is the degradation rate and J is the mRNA synthesis flux. J is in turn given by the promoter on-rate (k), the RNAP concentration ([RNAP]), and the concentration of the lacZ gene ([G_Z]). Assuming that the factors δ_Z, [RNAP], and [G_Z] are the same between the two strains with P_syn66 and P_con driving lacZ, then the ratio of the mRNA concentration obtained at each point of the cell cycle gives the ratio of the promoter on-rates, k_Psyn66 and k_Pcon. Since a constitutive promoter is non-responsive to DnaA activity, k_con is independent of cell cycle and we can obtain DnaA activity regulated promoter activity as , then the DnaA activity is denoted as .

The concentration of the lacZ mRNA were binned based on cell volume, with a bin size of 0.1 μm³, was used to determine [mZ] (P_syn66) and [mZ] (P_con). The relation between [mZ] (P_con) and cell volume was smoothed using the MATLAB smooth function, and from this, k_syn66 was deduced. Based on the DnaA activity oscillations, the cell volume where DnaA activity reaches maximum (V^∗) was calculated during a representative birth-to-division cell cycle. The cell volume distribution was used to calculate the number of cells in each volume-doubling range. The range containing the highest cells was considered the representative birth-to-division cell cycle and was shaded in gray (Fig. S2 D). From this, V^∗ was obtained.

Calculation of cell volume at the time of replication initiation (V_i)

Cell volume at the time of replication initiation (V_init) was calculated based on population-averaged cell volume , and the population-averaged cellular oriC number . The equation used for this calculation is as follows:

where v_i is the initiation volume by definition, i.e. cell volume per oriC at the time of replication initiation(Bremer et al., 1979; Si et al., 2017; Zheng et al., 2016). was obtained by analyzing the phase contrast images, was obtained by run-out experiments(Zheng et al., 2020). . is the cellular oriC number at the time of replication initiation. denotes the floor function of log₂ .

DnaA shut-down experiment

To shut-down DnaA expression, steady-state growth of the CRidnaA1 cells was first established after ∼10 generations of exponential growth in M1 medium. At OD₆₀₀ between 0.15 and 0.2, 24 mL of cell culture was transferred to 12 mL of pre-warmed M1 medium containing 150 ng·mL⁻¹ aTc to induce dUn1Cas12f1 expression at time 0. Under the guidance of sgRNA_dnaA, the transcription of dnaA gene was inhibited. Samples were collected at various time points to determine population-averaged cellular mass , cellular oriC number , and to quantify mRNA levels. When the OD₆₀₀ reached around 0.2, the cultures were diluted about 2-fold with pre-warmed M1 medium containing 50 ng·mL⁻¹ aTc to maintain adequate nutrition. The steady-state growing MG1655 cells in M1 medium were also collected for quantification of wild-type dnaA mRNA levels. Three independent experiments were conducted.

H-NS shift-up experiment

The DnaA activity reporter plasmid P_syn66-P_con-FPs was transformed into the hns-titratable strain (Rhns2), and cells were cultivated overnight in M6 medium containing 10 ng·mL⁻¹ aTc and 25 μg·mL⁻¹ chloramphenicol for seed culture. Seed cultures were washed and grown in the same medium without aTc for ∼10 generations of exponential growth. At an OD₆₀₀ of ∼0.2, 40 mL of cell culture was transferred to 20 mL of pre-warmed same medium containing 150 ng·mL⁻¹ aTc to induce H-NS expression at time 0. Samples were collected at time points -2, 1, 3, 5, 7, 10, 15, 20, 25, and 30 minutes for the determination of population-averaged cellular mass , cellular oriC number , and quantification of mRNA levels. Steady-state growing MG1655 in M6 medium were also collected for hns mRNA quantification. Three independent experiments were conducted.

Electrophoretic mobility shift assay (EMSA)

The genes encoding dnaA and hns from the MG1655 genome were individually amplified and cloned into the expression vector pET-28a using primers listed in Table S4. E. coli BL21 (DE3) carrying pET-28a-DnaA or pET-28a-H-NS was used for overproduction of His₆-DnaA or His₆-H-NS. For each protein purification, a 1 L culture was induced by the addition of 1 mM IPTG at OD₆₀₀ = 0.4. After 1.5 hours of incubation, cells were harvested by centrifugation (5,000 rpm for 20 min at 4 °C). The pellet was resuspended in 50 ml of buffer A (50 mM Tris-HCl, pH 7.0, 500 mM NaCl, 0.5 mM PMSF, 5 % glycerol). Cell resuspension was lysed on ice for 30 minutes (3 seconds on, 7 seconds off) using a sonicator at 4 °C, and cell debris was removed by centrifugation (14,000 rpm for 60 min at 4 °C). Subsequently, the protein was purified from the soluble supernatant by Ni²⁺-affinity chromatography (HisTrap™ HP Columns; GE Healthcares) with a ÄKTA Pure Protein Purification System. Proteins were collected using gradient elution with buffer B [20 mM Tris-HCl, pH 7.5, 500 mM NaCl, 400 mM imidazole, 5 % glycerol]. Eluted proteins were further purified and concentrated by ultrafiltration using Amicon Ultra 10K (for H-NS) and 30K (for DnaA) filters (Millipore). Finally, after overnight dialysis (0.025 μm Membrane Filter; MF-Millipore) at 4 °C, the protein was stored in buffer C [45 mM Hepes-KOH, pH 7.6, 600 mM potassium glutamate, 1 mM DTT, 10 mM magnesium acetate, 0.5 mM EDTA, 20 % glycerol]. Judgement by SDS/PAGE with Coomassie Brilliant blue staining, the purity of each protein was >90 %. For the experiments where H-NS acts on the datA bound by DnaA, the purified DnaA, datA and ATP were first incubated in buffer D (20 mM Tris-HCl, pH 7.5, 150 mM potassium glutamate, 10 mM magnesium acetate, 8 mM DTT) at 20 °C for 10 min. Then the H-NS was added to buffer D (15 μl) which contained DnaA-datA complexes and incubated for additional 10 min at 20 °C. The final complexes were separated by electrophoresis in 2 % (wt/vol) agarose gel at 80 V for 70 min in Tris-Borate buffer, followed by staining with SYBR Safe (Invitrogen).

Titration model

In the titration model, we posit that the cell mass grows exponentially according to the differential equation , where V represents the volume of the cell and λ = 1.54 hr⁻¹(corresponding to doubling time of 27 min) is the growth rate. Concurrently, DnaA protein synthesis occurs at a rate proportional to the cell’s mass, described by , with denoting the synthesis rate per unit volume. The chromosome’s structure is abstracted as a vector representing the copy numbers of uniformly distributed sites along its length. Specifically, DnaA-boxes, which are binding sites for DnaA proteins, are quantified by summing the copy numbers at their respective locations. In this model, 300 DnaA-boxes (A_b) are evenly distributed on the chromosome while an additional 100 DnaA-boxes are located near the origin of replication. This arrangement approximates a head-weighted distribution of DnaA-boxes and helps prevent over-initiation(Hansen et al., 1991). Binding of DnaA proteins to these DnaA-boxes allows us to calculate the concentration of free DnaA as [A_f] = (A − A_b)/V, under condition of (A − A_b) ≥ 0. DNA replication commences once the concentration of free DnaA exceeds a critical threshold . 10 min sequestration time was set after replication initiation to mimic the sequestration time(Campbell & Kleckner, 1990).

To explore the dynamics of the oriC number following the cessation of dnaA expression, we can set the synthesis rate to be zero α_A = 0. To simulate the dependence of initiation mass on dnaA expression, α_A varies from 1hr⁻¹ml⁻¹ to 64hr⁻¹ml⁻¹.

Extrusion model

The extrusion model was formulated following the titration model, with an additional extruder introduced as a protein with constant concentration H = α_HV with α_H = 100 ml⁻¹. The additional extruder competes the DnaA-boxes with DnaA proteins, with higher affinity to DnaA-boxes. So that it can displace DnaA from the DnaA-boxes, leading to a revised calculation for free DnaA concentration as [A_f] = (A − (A_b − H))/V, under condition of (A_b − H) ≥ 0 and (A − (A_b − H)) ≥ 0.

To get the DnaA repression simulation at the population level, we introduced cell division by the assumption of Cooper and Helmstetter that a cell divides at a constant time (T_cyc = 60 mins) after DNA replication initiation. Meanwhile, we introduced noises on cell mass growth rate and the DnaA synthesis rate at each cell division: λ = λ₀ + ηλ₀, α_A = α₀ + ηα₀ where λ₀ = 0.66 hr⁻¹, α₀ = 5 hr⁻¹ml⁻¹ and η = 0.1 representing white noise. Symmetric cell division is used in the simulation for simplicity. This titration extrusion model is robust under various range of parameters.

DnaA-ATP/DnaA-ADP switch model

The switch model was simulated following the LDDR model in Berger et al. (Berger & Wolde, 2022). The same formulations of the DnaA-ATP fraction dynamics df/dt (equation 5) and the same parameters were used (Berger & Wolde, 2022). The cell division was determined when f reaches a threshold as defined previously (Berger & Wolde, 2022). To simulate the dnaA shut-down, we simply deleted the term of dnaA synthesis (λ(1 − f)).

Titration-switch model and titration-switch-extrusion model

In the integrated model combining titration and switch mechanisms, replication initiation is triggered when the concentration of free DnaA-ATP exceeds a threshold . The concentration of free DnaA-ATP is titrated by the DnaA-boxes on the chromosome as in the titration model, with , under condition of (A_ATP − A_b) ≥ 0. The parameters related to the titration dynamics remain consistent with those described in earlier sections of titration model.

The dynamics of total DnaA-ATP (A_ATP) is governed by both expression and conversion processes as described in Berger et al. (Berger & Wolde, 2022). According to this framework, the lipid and DARS systems facilitate the conversion of DnaA-ADP to DnaA-ATP at constant rates, while the datA site and RIDA systems also play a role in converting DnaA-ATP to DnaA-ADP, again at fixed rates. Additionally, the synthesis of new DnaA proteins provides another source of DnaA-ATP. For the parameters governing DnaA-ATP dynamics, we adhere to those specified by Berger et al., ensuring consistency with established research. To get a best fit of the initiation mass-dnaA expression relation, high threshold of free DnaA-ATP concentration was applied, .

To simulate the titration-switch-extrusion model, we incorporated the extruder as described in the extrusion model, where its amount was given by H = α_HV. The concentration of free DnaA-ATP was then calculated as , under condition of (Abox − H) ≥ 0 and (A_ATP − (A_b − H)) ≥ 0. To explore the best fit of continuous DNA replication rounds following dnaA shut-down, α_H = 400 ml⁻¹ is used.

Data availability

All data supporting the findings of this work are available from the corresponding author upon request. Source data are provided with this paper.

Acknowledgements

We thank numerous colleagues for discussions. We sincerely thank Dr. Aiguo Xia for his help with microscopy, and Dr. Sheng Yang for providing valuable suggestions on CRISPR-Cas9 system. Special thanks to Drs. Pan Chu and Yeqing Zong for kindly gifting us the CPP00458 and pPT plasmids. This research was financially supported by the National Natural Science Foundation of China (32025022, 32230062), Strategic Priority Research Program of the Chinese Academy of Sciences (XDB0480000), Joint NSFC-ISF Research Grant (32061143021) to C.L., National Natural Science Foundation of China (32170042), National Key R&D Program of China (2024YFA0916403), Youth Innovation Promotion Association CAS (number 2022369) to H.Z., National Key R&D Program of China (2021YFA0910703) to Y.B.

Additional information

Code availability

Simulation data can be generated using the custom-made code and the parameter sets provided. The code is publicly available at https://github.com/BaiYangBqdq/dynamics_of_biomass_DNA_coordination.

Author contributions

C.L. and T.H. initiated and directed the research. D.L. and T.W. designed and evaluated the synthetic promoter library and performed mRNA FISH experiments with contributions from C.L. and H.Z. D.L., H.Z. and H.C. characterized the phenotype related to H-NS protein; D.L. and X.H. performed the DnaA shut down experiments; Y.B., H.Z., Z.Z. and T.H. conceptualized the extrusion model and performed the numerical simulations. All the authors analyzed the results and wrote the manuscript.

Additional files

Supplementary information

Source data for figures