Introduction

All living organisms rely on multiple molecular mechanisms to repair their chromosomes in order to preserve genome integrity. DNA double-strand breaks (DSBs), simultaneous lesions on both strands of the chromosome, are one of the most detrimental types of DNA damage because they can lead to loss of genetic information. If not repaired or repaired incorrectly, DSBs can trigger cell death, deleterious mutations and genomic rearrangements [1]. In addition to various exogenous sources such as ionizing radiation, mechanical stresses and DNA-damaging agents, DSBs can occur during the normal cell cycle as a results of endogenous metabolic reactions and replication events [2]. For instance, replication fork breakage has been shown to result in spontaneous DSBs in 18% of wild-type Escherichia coli (E. coli) cells in each generation [3], underscoring the crucial need to repair these breaks to ensure faithful DNA replication.

In E. coli, DSBs are repaired by homologous recombination using an intact copy of the chromosome as a template. Initially, the multi-subunit nuclease/helicase enzyme RecBCD detects a double-strand DNA (dsDNA) end and degrades both strands. Upon recognition of a short DNA sequence, known as a chi (χ) site (5’-GCTGGTGG-3’), the RecBCD complex stops cleaving the 3’-ended strand and initiates loading of the RecA protein onto the 3’-single-strand (ssDNA) overhang [4, 5]. This leads to the formation of a RecA-ssDNA nucleoprotein filament [6], which catalyses homology search and strand exchange [7].

Recent in vitro and in vivo experiments have highlighted the extraordinary processive DNA degradation activity of RecBCD upon recognition of a dsDNA end [8, 9, 10]. Indeed, RecBCD has been shown to process the chromosome for up to ∼ 100 kb at ∼ 1.6 kb/s in live bacteria [5]. Such a potent DNA degradation activity is controlled by chi recognition [11]. However, because this recognition is probabilistic [12], RecBCD can degrade large chromosome fragments before DNA repair is initiated. As a result, overproduction of RecBCD has been shown to sensitize wild-type cells to ultraviolet and gamma irradiations [13]. This strongly suggests that an excess of RecBCD imposes a threat to cells upon DNA damage. In contrast, RecBCD expression is essential upon DSB induction [14, 15], hence too low levels might impair DNA repair. Thus, the observation that RecBCD can positively and negatively impact cell fitness upon DNA damage suggests that its activity needs to be tightly controlled.

Whilst the biochemical and in vivo activities of RecBCD have been extensively studied ([11, 16, 17, 18, 19], and [7, 20] for review), less is known about the regulation of its expression. RecBCD has been reported to be expressed at very low levels [21, 22] and is present in less than ten molecules per cell [23]. In E. coli, the RecBCD subunits are encoded in the same locus by two operons. One operon controls the expression of RecC whilst the other is polycistronic and encodes PtrA, RecB and RecD [24, 25] (Fig. 1A). PtrA is a periplasmic protease with no known function in DNA repair, and the positioning of its gene likely results from a horizontal gene transfer event that has interrupted the usual order recC-recB-recD [26]. As sometimes found in bacterial operons [27, 28], the ribosome binding site (RBS) of recB is located within the coding sequence of ptrA, suggesting a potential translational coupling mechanism between these genes. Previous attempts to explore RecBCD expression upon DNA-damage conditions did not reveal any transcriptional regulation [21, 29] and the recBCD genes were shown not to belong to the SOS-response regulon [30]. Thus, RecBCD transcription is considered to be constitutive.

Figure 1:

Given that RecBCD is essential for cell survival upon DSB formation and toxic when overproduced, it is likely that its expression needs to be tightly regulated to avoid fluctuations leading to cellular death or deleterious genomic rearrangements. However, its very low abundance, often leading to high stochastic fluctuations, could result in large cell-to-cell variability [31, 32, 33]. Although these fluctuations might not play a significant role during normal cell growth, they may become crucial and determine cell fate upon stress conditions [34, 35, 36]. Thus, the low abundance of RecBCD enzyme molecules raises the following questions: (i) to what extent do RecBCD numbers fluctuate, (ii) are these fluctuations controlled, (iii) if this is the case, at which level (transcription, translation, mRNA or protein degradation) is the control operating.

The lack of evidence of RecBCD transcriptional regulation does not preclude that other mechanisms may be involved in regulating its expression. For example, RNA-binding proteins (RBPs) have been shown to fine tune gene expression both co- and post-transcriptionally during stress responses and adaptation to environmental changes [37, 38]. One of the most studied RBPs in E. coli, a Sm-like hexameric ring-shaped protein called Hfq, has been shown to regulate RNA stability and degradation, transcription elongation and translation initiation through various mechanisms (for review [39, 40, 41, 42]). In the most prevalent case, Hfq facilitates base-paring between small non-coding RNAs (sRNAs) and target mRNAs which often results in mRNA translation and/or stability modulation [43]. There is also increasing evidence that Hfq can control mRNA translation directly [44, 45]. This mechanism is typically based on altering the accessibility of the RBS of a target mRNA by direct binding near this region [46, 47, 48].

Here, we show that the expression of RecB is regulated post-transcriptionally in an Hfq-dependent manner in E. coli. By quantifying RecB mRNAs and proteins at single-molecule resolution, we found that constitutive transcription leads to low levels of recB mRNAs and a noisy distribution. In contrast, fluctuations in RecB protein levels are significantly lower than expected, given the very low number of proteins present in cells. We show that Hfq negatively regulates RecB translation and demonstrate the specificity of this post-transcriptional control in vivo. Furthermore, we provide evidence of the role of Hfq in reducing RecB protein fluctuations and propose that this could constitute a fine-tuning mechanism to control RecBCD molecules within an optimal range.

Results

recB mRNAs are present at very low levels and are short-lived

To quantitatively measure RecB expression, we first precisely quantified recB mRNAs using single-molecule fluorescent in situ hybridization (smFISH) [49]. We confirmed that our hybridization conditions are highly specific as recB mRNA quantification in a ∆recB strain resulted in a negligible error (∼ 0.007 molecules per cell, Fig. 1B). In wild-type cells, we detected a very low average level of recB transcripts: ∼ 0.62 molecules per cell. Notably, ∼ 70% of cells did not have any recB mRNAs (Fig. 1C). To confirm that this result was not because of low sensitivity of the smFISH protocol, we over-expressed recB mRNAs from an arabinose-inducible low-copy plasmid and detected the expected gradual amplification of the fluorescence signal with increased arabinose concentration (Fig. S2).

We next measured the degradation rate of recB transcripts in a time-series experiment. Initiation of transcription was inhibited with rifampicin and recB mRNA expression levels were quantified by sm-FISH at subsequent time points. By fitting the mean mRNA value evolution over time to an exponential function, we estimated the recB degradation rate as γ_m = 0.62 min⁻¹ (CI_95% [0.48, 0.75]) (Fig. 1D). This corresponds to a recB mRNA lifetime of 1.6 min and is consistent with the genome-wide studies in E. coli where transcript lifetimes were shown to be on average ∼2.5 min across all mRNA species [50, 51].

recB transcription is constitutive and weak

As noted previously, quantitative analysis of transcription at the single-cell level needs to take into account the variation of gene copy number during the cell cycle [52, 53, 54]. Therefore, we analysed RNA molecule abundance using cell size as a proxy for the cell cycle. Specifically, we binned all bacteria in groups based on cell area and averaged mRNA numbers in each of those size-sorted groups (Fig. 1E). A two-fold increase in mRNA abundance was observed within a narrow cell-size interval (∼ 3.0-3.5 μm²), which is consistent with an expected doubling of the transcriptional output as a result of the replication of the recB gene. We further showed that recB transcription from sister chromosomes happens independently, in full agreement with the hypothesis of an unregulated gene (Fig. S3). Taken together, this evidence indicates that recB mRNA levels follow a gene-dosage trend, strongly suggesting that recB is constitutively expressed [52].

Next, to infer recB transcription rate, we used a simple stochastic model of transcription where mR-NAs are produced in bursts of an average size b at a constant rate k_m and degraded exponentially at a rate γ_m (Suppl. Info.: Section 1). The expected probability distribution for mRNA numbers at steady-state is given by a negative binomial [55, 56, 57]. We used maximum likelihood estimation to infer the parameters of the negative binomial distribution from the experimental data (Fig. 1F, Methods). For the inference, we restricted our analysis to newborn cells (Fig. 1E) as this model does not take into account cell growth. We then inferred the burst size for the recB gene, b ∼ 0.95 molec, and the rate of transcription, k_m = 0.21 min⁻¹ (Table 7, Methods). The latter is remarkably low and close to the lower-bound reported range of transcription rates in E. coli, 0.17-1.7 min⁻¹ [58, 59, 60]. Therefore, the low abundance of recB mRNAs can be explained by infrequent transcription combined with fast mRNA decay.

Variations in mRNA molecule numbers, as a result of their low abundance and short lifetimes, can significantly contribute to gene expression noise [31, 61, 62]. To evaluate fluctuations of recB transcription, we calculated a commonly-used measure of noise, the squared coefficient of variation , defined as the variance divided by the squared mean . The average in newborn cells was found to be times larger than the lower bound given by a Poisson process . This suggests that recB mRNA production is noisy and further supports the absence of a regulation mechanism at the level of mRNA synthesis.

RecB proteins are present in low numbers and are long-lived

To determine whether the mRNA fluctuations we observed are transmitted to the protein level, we quantified RecB protein abundance with single-molecule accuracy in fixed individual cells using the Halo self-labelling tag [23] (Fig. 2A&B). As we previously reported, the translational RecB-HaloTag fusion does not affect the activity of the RecBCD enzyme [23]. We obtained RecB protein distributions for cells of all sizes and confirmed its low abundance: 3.9 ± 0.6 molecules per cell (Fig. 2C).

Figure 2:

To test if RecB is actively degraded by proteases or mainly diluted as a result of cell growth and division, we estimated the RecB protein removal rate. This is usually obtained from either pulse-chase experiments using radio-labelled amino acids or detection of protein concentration decay after treatment with a translation inhibitor [63, 64, 65]. While the first approach is not amenable to single-cell assays, the latter may affect the measurements on long time scales because of the physiological impacts of stopping all protein production. Therefore, we used an alternative approach [66, 67] where we pulselabelled RecB molecules with the HaloTag ligand, then removed the excess of the dye by extensive washing and measured the abundance of the labelled molecules over time. Assuming protein removal can be described by a first-order reaction, we fitted the mean protein counts over time to an exponential function on a subset of time points (Fig. 2D, shaded area). The decay rate was extracted from the fit and resulted in γ_p = 0.015 min⁻¹ (CI_95% [0.011, 0.019]). Comparison to the population growth rate in these conditions (0.017 min⁻¹) suggests that RecB protein is stable and effectively removed only as a result of dilution and molecule partitioning between daughter cells.

RecB protein cell-to-cell fluctuations are lower than expected

We then extended the transcription model described above by considering protein synthesis and removal. This is known as the two-stage or mRNA-protein model of gene expression [57, 68, 69]. In this model, a protein is produced from an mRNA at a constant translation rate k_p while protein dilution is implicitly modelled by a first-order chemical reaction with rate γ_p (Suppl. Info.: Section 1). As discussed earlier, we focused on newborn cells and estimated the rate of translation as 0.15 min⁻¹ (CI_95% [0.12, 0.18], Table 7, Methods). This value fell below the lower bound of previously reported range of the translation rates in E. coli (0.25-1 min⁻¹) [58, 59]. Therefore, we concluded that recB mRNAs are translated at low levels compared to other proteins in the cell.

Next, we examined whether the two-stage model can reproduce the cell-to-cell variability in the protein levels observed in our experiments. To this end, we simulated single trajectories of protein abundance over time using the Stochastic Simulation Algorithm (SSA) [70] for the two-stage model with the estimated parameters (Table 7). Strikingly, the simulated distribution had larger fluctuations than the experimentally measured one (Fig. 2E). While both protein means were equal because of the first-moment-based parameter estimation we used (Methods), we found the standard deviations to be higher in simulation (2.2) than in experiments (1.5) (Fig. 2E). In other words, a two-stage protein production model predicts a higher level of fluctuations than what is observed experimentally.

This phenomenon can also be analysed using the squared coefficient of variation of the protein distribution , which is defined as . For the two-stage gene expression model with bursty transcription, it has been established that the following expression gives the coefficient of variation (Suppl. Info.: Section 1) [57, 68, 69, 71]:

where ⟨p⟩ and ⟨m⟩ are the mean protein and mRNA counts (per cell), b is the average (mRNA) burst size, γ_m and γ_p are the mRNA degradation and protein removal rates, respectively. We found that the experimental coefficient of variation is approximately half of the analytically predicted one (Fig. 2F). On the contrary and as expected, both the theoretically predicted and the one computed from the simulated data are in good agreement. This deviation from the theoretical prediction implies a potential regulatory mechanism of RecB expression that actively suppresses protein production variation to maintain protein levels within a certain range.

RecB translational efficiency is increased upon DSB induction

Next, we addressed whether there was any further evidence of this potential regulation once bacterial cells are exposed to stress. We hypothesized that RecB mRNA and/or protein levels may exhibit a concentration change upon DNA damage to stimulate DNA repair. To test this, we treated bacterial cells with a sub-lethal concentration of ciprofloxacin (4 ng/ml), an antibiotic that leads to DNA DSB formation [72]. After two hours of exposure to ciprofloxacin, we quantified proteins by Halo-labelling and mRNAs by smFISH (Fig. 3A). This induction duration is sufficient to detect changes in mRNA and protein levels (see Suppl. Info.: Section 2 for the mathematical model supporting this choice). Because E. coli cells filament upon activation of the DNA damage response (Fig. 3B&C), we measured single-cell distributions of mRNA and protein concentrations (calculated as molecule numbers normalized by cell area) rather than absolute numbers. Cell area is a reasonable proxy for cell volume as rod-shaped E. coli cells maintain their diameter while elongating in length upon ciprofloxacin treatment. RecB protein concentration did not change upon DSB induction (Fig. 3E). In fact, the average cellular RecB concentration was surprisingly conserved: 2.28 mol/μm² (CI_95%: [2.21, 2.32]) in perturbed condition and 2.12 mol/μm² (CI_95%: [2.01, 2.32]) in intact cells. Additionally, we analysed RecB concentration in size-sorted groups of cells (Fig. S5b). Regardless of moderate fluctuations in protein concentration over a cell cycle, both samples significantly overlap along the whole range of cell sizes.

Figure 3:

In contrast, single-cell mRNA concentration quantification showed a sharp decrease in recB transcripts upon DNA damage (Fig. 3D). Specifically, mRNA concentrations upon DSB induction are ∼ 2.4-fold lower than in the unperturbed control (Fig. 3D: insert): 0.12 mol/μm² (CI_95%: [0.06, 0.17]) upon DNA damage versus 0.28 mol/μm² (CI_95%: [0.23, 0.32]) in the control. We further confirmed the decrease in all cell-size sorted groups (Fig. S5a). As previously reported, the recB gene is not part of the SOS regulon [30], hence its transcription is not necessarily expected to be upregulated upon DNA damage. However, downregulation of recB transcription is an unforeseen observation and may be a result of lower concentration of genomic DNA and/or shortage of resources (such as RNA polymerases) upon SOS response activation.

We then computed the average number of proteins produced per mRNA in both conditions. The ratio between the average protein and mRNA concentrations in damaged cells is 19.7 (CI_95%: [17.5, 24.2]) whereas it is 7.9 proteins/mRNA (CI_95%: [7.5, 8.3]) in intact cells (Fig. 3F). Thus, a ∼ 2.5 increase in translational efficiency was detected upon DSB induction (p-value < 0.001, two sample t-test). Taken together, our results show decoupling between mRNA and protein production upon DNA damage, suggesting the existence of a post-transcriptional regulatory mechanism that controls RecB protein level.

Hfq controls the translation of recB mRNA

To identify the post-transcriptional mechanism controlling recB expression, we focused on Hfq because (i) it has been shown to regulate a vast number of mRNAs [73, 74, 75] and (ii) its activity has been directly linked to the DNA damage and SOS responses [45, 76, 77].

To assess whether Hfq is involved in post-transcriptional regulation of RecBCD, we analysed the available transcriptome-wide dataset, wherein Hfq binding sites were identified in E. coli using CLASH (cross-linking and analysis of cDNA) [78]. In a CLASH experiment, Hfq-RNA complexes are cross-linked in vivo and purified under highly stringent conditions, ensuring specific recovery of Hfq RNA targets [78]. Analysis of the Hfq binding profile across recBCD transcripts showed the interaction of Hfq with the recBCD mRNAs (Fig. 4A). Hfq binding is mainly localized at two sites: one in close proximity to the RBS of the ptrA gene, and the second further downstream in the coding sequence of recB gene. Interestingly, multiple trinucleotide Hfq-binding motifs, A-R(A/G)-N(any nucleotide) [73, 79] were found ∼ 8 nucleotides upstream of the RBS of the ptrA sequence (Fig. S6), suggesting that Hfq may control translation initiation and/or decay of the operon mRNA.

Figure 4:

To test this hypothesis, we quantified RecB protein and mRNA levels in an E. coli strain lacking Hfq. ∆hfq mutant has been reported to have an increased average cell size and various growth defects [80, 81, 82]. Indeed, we confirmed the increased cell size of our ∆hfq mutant compared to wild-type cells (Fig. S7a&b). In our conditions, no difference between the growth rates of WT and the ∆hfq mutant was observed in the exponential phase of growth (Fig. S7d).

Using Halo-labelling technique, we performed RecB protein quantification in ∆hfq. Remarkably, we observed an increase of RecB protein concentration in the ∆hfq cells (Fig. 4B&C). The ∆hfq mutant showed more fluorescent foci relative to the wild-type strain (Fig. 4B). Even after normalization by cell area to take into account the larger cell size in ∆hfq cells, RecB concentration distribution was shifted towards higher values (Fig. 4C). Quantification across five replicated experiments showed a statistically significant 30% increase in RecB protein concentration in the ∆hfq strain (Fig. 4C: insert). The concentration was 2.67 mol/μm² (CI_95%: [2.54, 2.80]) in ∆hfq compared to 2.17 mol/μm² (CI_95%: [2.01, 2.32]) in the control.

We further quantified recB mRNA molecules in the ∆hfq strain using smFISH and analysed mRNA concentration distributions (Fig. 4D&E). Although the average recB mRNA concentration is slightly decreased in the ∆hfq: 0.21 mol/μm² (CI_95%: [0.08, 0.30]) versus 0.28 mol/μm² (CI_95%: [0.23, 0.32]) in the wild-type cells, this difference is insignificant (p-value = 0.11, two sample t-test). These results were confirmed by RT-qPCR measurements, which did not show any significant changes for recB mRNA steady-state levels (Fig. S7c). Thus, we conclude that Hfq binding to the recBCD mRNA does not sub-stantially alter the stability of the transcript.

The observed increase of RecB protein concentration without a significant change in recB mRNA steady-state levels is reflected in a rise in RecB translational efficiency (Fig. 4F). The average level of proteins produced per mRNA in the ∆hfq mutant is 14.0 (CI_95%: [13.0, 18.1]), which is two-fold higher than in the wild-type cells (p-value < 0.05, two-sample t-test). Altogether, this demonstrates that Hfq alters RecB translation in vivo.

To test if Hfq regulation contributes to the noise suppression detected in the wild-type cells (Fig. 2F), we looked at the level of fluctuations of RecB copy numbers in ∆hfq. To this end, we computed the difference between the analytically predicted noise and the noise observed experimentally . Since in the ∆hfq mutant recB transcription is not affected, the theoretical noise was calculated using Eq. (1) assuming the same mRNA contribution (the second term of the equation). As seen in Fig. 4G, the wild-type strain shows effective noise suppression as the theoretically predicted noise is larger than the one detected experimentally. Interestingly, this suppression is less effective in the ∆hfq mutant. In other words, in the absence of Hfq, the mismatch between the model and the experimental data is decreased in comparison to the native conditions of the wild-type cells (p-value = 0.0088, two sample t-test). This provides evidence that, in addition to the average RecB abundance, Hfq affects RecB protein fluctuations.

RecB protein number distribution is recovered by Hfq complementation

To further confirm that Hfq regulates RecB expression, we complemented the ∆hfq mutant with a multi-copy plasmid that expresses Hfq, pQE-Hfq [83]. After complementation, the RecB protein concentration distribution was shifted towards lower values (Fig. 5B) whilst no change of RecB protein level was detected in the ∆hfq cells carrying the backbone plasmid, pQE80L (Fig. S8a). Although in our experimental conditions, Hfq is expressed at lower levels than in wild-type cells (transcription is ∼ a third of the wild-type level, Fig. S8b), RecB protein concentration was nearly fully recovered to the wild-type conditions: 2.57 mol/μm² (CI_95%: [2.50, 2.65]). We avoided full induction of Hfq from the plasmid as it can interfere with its self-regulation and lead to cell filamentation. We did not detect significant changes in the recB mRNA levels when expressing Hfq from the plasmid (Fig. S8c), confirming that Hfq complementation impacts recB mRNA translation but not its stability.

Figure 5:

Sequestering Hfq leads to an increase in RecB production

To further ascertain the role of Hfq in controlling RecB expression, we characterized RecB expression while sequestering Hfq proteins away from its recB mRNA targets. Hfq is known to bind ∼ 100 sRNAs [73, 75], some of which can reach high expression levels and/or have a higher affinity for Hfq and, thus, compete for Hfq binding [84, 85]. We reasoned that because recB mRNA is present in very low abundance, it could be outcompeted for Hfq binding by over-expression of a small RNA that efficiently binds Hfq, such as ChiX [85, 86]. We constructed a multi-copy plasmid pZA21-ChiX to over-express ChiX and obtained a ∼ 30-fold increase in ChiX expression relative to its native expression in wild-type cells (Fig. S9). Given its already high abundance in wild-type cells, ChiX overproduction has been demonstrated to effectively sequester a large number of Hfq molecules [46, 48, 87].

Wild-type cells carrying the pZA21-ChiX plasmid (or the backbone plasmid) were grown to mid-exponential phase, and RecB mRNA and protein levels were quantified with RT-qPCR and Halo-labelling, respectively. No significant changes were detected at the recB transcript levels when ChiX was overproduced (Fig. S9). In contrast, a significant increase in RecB protein production was detected upon ChiX over-expression (Fig. 5C). Indeed, RecB concentration in the cells where ChiX was over-expressed almost fully overlapped with the distributions in the ∆hfq mutant. This suggests that when fewer Hfq molecules are available for RecB regulation because ChiX is overproduced, RecB is translated at a higher rate. A similar experiment with a plasmid that carried a different sRNA, CyaR which is not expected to titrate Hfq, did not change RecB protein concentration. This indicates that ChiX over-expression specifically impairs RecB post-transcriptional regulation (Fig. S9).

To exclude the possibility of a direct ChiX involvement in RecB regulation, we characterized RecB expression in ∆chiX. No significant change relative to wild-type cells was detected in RecB mRNA or protein levels (Fig. S10). Thus, we concluded that ChiX does not affect RecB translation. Instead, titration of Hfq proteins from a shared pool by ChiX sRNAs leads to the increased availability of ptrA-recB RBS for ribosomes and, thus, results in more efficient RecB translation.

Deletion of an Hfq-binding site results in increased RecB translational efficiency

To further investigate the mechanism of RecB translation, we tested the specificity of Hfq interaction with the mRNA of recB without affecting other functions of Hfq. Based on the localization of the Hfq-binding uncovered in the CLASH data (Fig. 4A), we deleted a 36 nucleotide region (5’-TTAACGTGTTGAATCTGGACAGAAAATTAAGTTGAT-3’) located in 5’UTR of the operon, in front of ptrA gene. This region showed the highest enrichment of Hfq binding (Fig. S6). It is closely located to the RBS site and 76 nucleotides downstream of the promoter sequence of ptrA-recB. To get a complete picture of RecB expression in the mutant strain carrying this deletion (which we further refer to as the recB-5’UTR* mutant), we performed single-cell quantification of both mRNA and protein levels of RecB and quantified its translational efficiency.

Firstly, we quantified recB mRNAs molecules in the recB-5’UTR* strain using smFISH (Fig. 5D). We detected a significant decrease in the concentration of mRNAs in the strain with the modified sequence: 0.14 mol/μm² (CI_95%: [0.07, 0.17]) compared to 0.28 mol/μm² (CI_95%: [0.23, 0.32]) in the wild type. This is not an unexpected outcome as the 5’-untranslated region of a transcript can control its degradation and stability [88, 89]. Despite the mRNA steady-state level decreasing two-fold in the modified recB-5’UTR* strain, only a slight decrease in RecB protein concentration was detected in comparison with the wild type (Fig. 5E): 1.96 mol/μm² (CI_95%: [1.56, 2.36]) in recB-5’UTR* and 2.17 mol/μm² (CI_95%: [2.01, 2.32]) in the wild type.

We calculated the translational efficiency of recB transcripts based on our single-cell mRNA and protein quantification. The resulting translational efficiency in the recB-5’UTR* strain was found to be significantly higher than in the wild-type cells: 16.3 (CI_95%: [14.3, 19.7]) in recB-5’UTR*, whereas it is 7.9 (CI_95%: [7.5, 8.3]) proteins/mRNA in the wild type (Fig. 5F). Remarkably, the RecB translational efficiency in the recB-5’UTR* strain is comparable with the values observed in the ∆hfq mutant (a two-sample t-test confirmed that the difference is not significant). Thus, when the main Hfq binding site was deleted, the lower abundance of the mRNA was compensated by more efficient translation. This demonstrates that the translation of recB mRNA is limited by a specific interaction with Hfq.

Discussion

Despite its essential role in DSB repair, over-expression of RecBCD decreases cell viability upon DNA damage induction [13]. Such a dual impact on cell fitness suggests the existence of an underlying regulation that controls RecBCD expression within an optimal range. Using state-of-the-art single-molecule mRNA and protein quantification, we (i) characterize RecB expression at transcriptional and translational levels in normal and DNA-damaging conditions and (ii) describe a novel post-transcriptional mechanism of RecB expression mediated by the global regulator Hfq in vivo. Utilizing stochastic modelling, we provide evidence that Hfq contributes to suppressing fluctuations of RecB molecules. To our knowledge, this is the first experimental evidence of an RNA-binding protein involved in noise suppression in bacterial cells under native conditions.

While our observations are consistent with recent studies demonstrating direct gene regulation by Hfq in a sRNA-independent manner [45, 46, 47, 48, 90], we cannot entirely exclude a small RNA being involved. Using the available Hfq CLASH and RIL-seq datasets [78, 91], CyaR and ChiX sRNAs were identified as potentially interacting with the ptrA-recB-recD mRNA. However, we did not find any significant changes in RecB expression when CyaR was overexpressed (Fig. S9) and we showed that ChiX was involved indirectly by sequestering Hfq (Fig. 5 & Fig. S10). Strictly speaking, we cannot totally rule out the possibility of another small RNA candidate, but the very low abundance of the recB transcripts is likely to make it particularly difficult to detect RNA-RNA interactions in bulk experiments, making it necessary to develop a specific approach with single-molecule resolution.

Hfq-mediated control of RecB expression may be just a hint of a larger bacterial post-transcriptional stress-response programme to DNA damage. Indeed, post-transcriptional regulation has already been shown to impact DNA repair and genome maintenance pathways [76, 77, 92, 93]. For instance, the DNA mismatch repair protein, MutS, was shown to be regulated by a sRNA-independent Hfq binding mechanism and its translation repression was linked to increased mutagenesis in stationary phase [45]. In addition, a modest decrease (∼ 30%) in Hfq protein abundance has been seen in a proteomic study in E. coli upon DSB induction with ciprofloxacin [94]. It is conceivable that even modest changes in Hfq availability could result in significant changes in gene expression, and this could explain the increased translational efficiency of RecB upon DBS induction (Fig. 3F). Therefore, Hfq-mediated regulation might play a larger role in DNA repair pathways than previously considered. As many metabolic pathways are regulated through Hfq [95, 96, 97], the control of RecB (and other DNA repair proteins) expression may even provide a way of coordinating DNA repair pathways with other cellular response processes upon stress.

Mechanisms similar to the one described in our study might underlay the expression networks of other DNA repair proteins, many of which are known to be present in small quantities. In this regard, it is worth emphasizing the valuable methodological insights which can be taken from our study. By utilizing single-molecule mRNA and protein quantification techniques, we show the importance of detailed investigation of both mRNA and protein levels when establishing novel regulation mechanisms of gene expression. Indeed, measuring the protein level only would not be sufficient to draw the correct interpretation, for example, in the case of recB-5’UTR* mutants (Fig. 5). Moreover, single-molecule measurements combined with stochastic modelling allow access to cell-to-cell variability, which can be a powerful and, possibly, the only approach to investigate the regulation mechanisms of gene expression for low abundant molecules.

In agreement with a previous report [13], we confirm that RecBCD overproduction led to less efficient repair when DSBs were induced using ciprofloxacin (Fig. S11). We note that another study did not detect any toxicity of RecBCD overproduction upon DNA damage [98]. However, this is likely because the level of UV irradiation was too low to detect a significant reduction in cell viability. We only observed the effect at a relatively high level of ciprofloxacin exposure (>10 ng/ml with the minimum inhibitory concentration at 16 ng/ml in our conditions).

In addition to the regulation of the average number of proteins per cell, fluctuation control might be crucial for a quasi-essential enzyme with very low abundance, such as RecBCD. Our analysis of RecB fluctuations suggests that Hfq is playing a role in protein copy number noise reduction (Fig. 4G). Post-transcriptional regulation has been proposed theoretically as an effective strategy for reducing protein noise [62, 99, 100, 101, 102]. Conceptually, this is achieved via buffering stochastic fluctuations of mRNA transcription and enabling more rapid response. Based on these principles, suppression of protein fluctuations via post-transcriptional control has been demonstrated in synthetically engineered systems in bacteria, yeast and mammalian cells [103, 104, 105]. However, do cells employ these strategies under native conditions? Suppressed fluctuations of protein expression were experimentally detected for hundreds of microRNA-regulated genes in mammalian cells [106]. Remarkably, those genes were expressed at a very low level. This is precisely the case for the regulation of recB translation by Hfq, where a very abundant post-transcriptional regulator can effectively buffer the fluctuations of the low-abundant RecB enzyme. Taken together, these previous observations and our results could hint at a universal functional ‘niche’ for post-transcriptional regulators across a wide range of organisms.

Methods

Strains and plasmids

All strains and plasmids, used in the study, are listed in Table 1 and Table 2, respectively. The E. coli MG1655 and its derivatives were used for all conducted experiments except the one with arabinose-inducible expression where we used E. coli BW27783 background strain. The strains with RecB-HaloTag fusion were used in Halo-labelling experiments while the corresponding parental strains were used in smFISH experiments.

Table 1:

Table 2:

MEK1329 and MEK1938 were built using the plasmid-mediated gene replacement method [107] with pTOF24 derivative plasmids, pTOF∆recB [108] and pTOFrecB-5’UTR (this work), respectively. The deletion of recB gene and a 36 bp region (5’-TTAACGTGTTGAATCTGGACAGAAAATTAAGTTGAT-3’) were verified with Sanger sequencing.

MEK1902 and MEK1457 were constructed with lambda red cloning technique using hfq_H1_P1 and hfq_H2_P2 primers (Table 3). MEK1888 and MEK1449 were constructed with lambda red using ChiX_H1_P1 and ChiX_H2_P2 primers (Table 3). hfq and chiX deletions were verified by PCR.

Table 3:

pIK02 was constructed to induce recB expression. The backbone was amplified with the primers oIK03/oIK04 from pBAD33 vector while the recB gene was amplified from E. coli chromosome using oIK10/oIK11 oligos (Table 3). The PCR products were ligated using Gibson. Plasmid construction was verified by PCR and sequencing.

pZA21-ChiX plasmid was constructed to allow overproduction of a small RNA ChiX. The plasmid, derived from the pZA21MCS (Expressys), was generated according to the protocol described here [78] using chiX_ZA21 and pZA21MCS_5P_rev primers (Table 3).

To construct pTOFrecB-5’UTR, the pTOF24 plasmid was digested with XhoI and SalI and ligated using Gibson assembly with the gBlock recB-5’UTR (Table 4). The deletion of a 36 bp region was confirmed by sequencing.

Table 4:

Table 5:

Growth media and conditions

In microscopy and population experiments, cell cultures were grown in M9-based medium supplemented with 0.2% glucose, 2 mM MgSO₄, 0.1 mM CaCl₂ and either 10% Luria Broth (Figs 1&2) or MEM amino acids (from Gibco) (Figs 3–5). In the recB induction smFISH experiments, 0.2% glucose was replaced with 0.2% glycerol, and arabinose ranging from 10⁻⁵% to 1% was added to the medium. For mRNA lifetime measurements with smFISH, rifampicin (Sigma-Aldrich) was added to cell cultures to a final concentration of 500 μg/ml. In the DSB induction experiments, a sub-lethal concentration of ciprofloxacin 4 ng/ml was used. Ampicillin (50 μg/ml), kanamycin (50 μg/ml) or chloramphenicol (30 μg/ml) were added to cultures where appropriate.

Cell cultures were grown in medium overnight (14–16 hours) at 37°C. The overnight cultures were diluted (1:300) and grown at 37°C until the mid-exponential phase (optical density OD₆₀₀ = 0.2–0.3). Unless otherwise stated, cells were further treated according to the smFISH or Halo-labelling procedures described below.

In the recB induction smFISH experiments, arabinose was added after one hour of overday growth, the cultures were grown for one more hour, and then samples were collected. For the smFISH experiments with rifampicin, the antibiotic was added once the cultures had reached OD₆₀₀ = 0.2. Cells were harvested at 1 min intervals and fixed in 16% formaldehyde. The following steps of smFISH procedure were followed as described below.

In the DSB induction experiments, ciprofloxacin was added at OD₆₀₀ ∼ 0.1 and cell cultures continued growing for one hour. For mRNA quantification with smFISH, the cultures were grown for one more hour before being harvested and fixed in the final concentration of 3.2% formaldehyde. For protein quantification, the Halo-labelling protocol was followed as described below with ciprofloxacin being kept in the medium during labelling and washing steps.

Single-molecule RNA FISH (smFISH)

Single-molecule fluorescent in situ hybridization (smFISH) experiments were carried out according to the established protocol [49]. Bacterial cells were grown as described above, fixed in formaldehyde solution, permeabilised in ethanol and hybridized with a recB specific set of TAMRA-labelled RNA FISH probes (LGC Biosearch Technologies). Probe sequences are listed in Table 6. Unbound RNA FISH probes were removed with multiple washes, and then samples were visualized as described below.

Table 6:

Table 7:

Halo-labelling

For single-molecule RecB protein quantification, we followed the Halo-labelling protocol described previously [23]. E. coli strains with RecB-HaloTag fusion, grown as described above, were labelled with JaneliaFluor549 dye (purchased from Promega) for one hour, washed with aspiration pump (4-5 times), fixed in 2.5% formaldehyde and mounted onto agar pads before imaging. In each experiment, a parental strain which does not have the HaloTag fusion (‘no HaloTag’) was subjected to the protocol in parallel with the primary samples as a control.

Microscopy set-up and conditions

Image acquisition was performed using an inverted fluorescence microscope (Nikon Ti-E) equipped with an EMCCD Camera (iXion Ultra 897, Andor), a Spectra X Line engine (Lumencor), dichronic mirror T590LPXR, 100X oil-immersion Plan Apo objective (NA 1.45, Nikon) and 1.5X magnification lens (Nikon). A TRITC (ET545/30nm, Nikon) filter was used for imaging Halo-labelling experiments while smFISH data were acquired with an mCherry (ET572/35nm, Nikon) filter.

Once a protocol (smFISH or Halo-labelling) had been carried out, fixed cells were resuspended in 1X PBS and mounted onto a 2% agarose pad. The snapshots were acquired in bright-field and fluorescence channels. In all experiments, an electron-multiplying (EM) gain of 4 and an exposure time of 30 ms were used for bright-field imaging. In the fluorescence channel, smFISH data were acquired with a 2 s exposure time and a gain of 4, while RecB proteins were visualized with the same exposure time but EM gain 200. For each XY position on an agarose pad, a Z-stack of 6 images centred around the focal plane (total range of 1 μm with a step of 0.2 μm) was obtained in both channels. A set of multiple XY positions were acquired for each slide to visualize ∼1000 cells per sample.

Cell segmentation

Microscopy bright-field images were used to identify positions of bacterial cells with an automated MATLAB-based pipeline [109]. Briefly, the segmentation algorithm is based on detection of cell edges by passing an image through a low-pass filter. In comparison to the original version, we applied this analysis to defocused bright-field images (instead of fluorescence signal from a constitutive reporter [109]) and tuned segmentation parameters for our conditions. The segmentation outputs were manually corrected by discarding misidentified cells in the accompanied graphical interface. The corrected segmentation results were saved as MATLAB matrices (cell masks) containing mapping information between pixels and cell ID numbers. The cell masks were used as an input for the spot-finding software described below.

Spot detection

The Spätzcell package (MATLAB) was utilized to detect foci in fluorescent smFISH images [49]. Principally, the analysis consists of the following steps: (i) identification of local maxima above a chosen intensity threshold, (ii) matching the maxima across frames in a Z-stack, (iii) performing 2D-Gaussian fitting of the detected maxima. Based on the peak height and spot intensity, computed from the fitting output, the specific signal was separated from false positive spots (Fig. S1a). The integrated spot intensity histograms were fitted to the sum of two Gaussian distributions, which correspond to one and two mRNA molecules per focus. An intensity equivalent corresponding to the integrated intensity of FISH probes in average bound to one mRNA was computed as a result of multiple-Gaussian fitting procedure (Fig. S1b), and all identified spots were normalized by the one-mRNA equivalent.

To detect fluorescent single-molecule foci in the Halo-labelling experiments, the first step of Spätzcell analysis was modified (similar to the modification for fluorescent protein detection implemented here [52]). For the Halo-labelling single-molecule data, we tested two modifications: (i) removing a Gaussian filter (that was used to smooth raw signal in the original version) or (ii) calculating the Laplacian of a Gaussian-filtered image. Both versions gave similar and consistent quantification results. Peak height intensity profiles allowed the separation of specific signal from false positive spots (Fig. S4). As a result of low-abundance of the protein of interest and single-molecule labelling, the analysis of integrated intensity was skipped for Halo-labelling images. All other steps of the Spätzcell software remained unchanged.

Total (mRNA or protein) molecule numbers per cell were obtained by matching spot positions to cell segmentation masks and quantifying the number of (mRNA or protein) spots within each cell. Molecule concentration was calculated for each cell as total number of (mRNA or protein) molecules (per cell) divided by the area of the cell (1/μm²).

Bacterial RNA extraction and RT-qPCR

Bacterial cells were grown as described earlier, harvested in the equivalent of volume × OD₆₀₀ = 2.5 ml and flash-frozen in liquid nitrogen. In the Halo-labelling experiments, samples for RNA extraction were grown at 37°C and collected before the fixation step. Total RNA extraction was performed with the guanidium thiocyanate phenol protocol [110].

Primers for real-time qPCR experiments are listed in Table 5. RT-qPCR quantification was carried out on 20 ng of RNA with the Luna One-Step RT-qPCR Kit (NEB). All qPCRs were performed in technical triplicates. The qPCR reactions were carried out on a LightCycler^®96 (Roche). The rrfD gene (5S rRNA) was used as a reference gene to compute a fold-change relative to a control sample with the 2^−∆∆Ct method. Outlier samples with the standard deviation std(Ct) > 0.3 across technical replicates were removed from the analysis.

Population growth and viability assays

Bacterial cells, seeded by inoculating from fresh colonies, were grown in an appropriate medium at 37°C overnight. The cultures were diluted (1:1000) and grown in a shaking incubator at 37°C. Optical density measurements were taken overday at OD₆₀₀ with the interval of 15 min. The exponential phase of growth, OD₆₀₀ = [0.08, 0.4], was used for the fitting procedure. The fitting was performed with a linear regression model in MATLAB.

In the viability assays, cells were grown overnight in Luria Broth at 37°C in a shaking incubator. The optical density of the overnight cultures was normalized to OD₆₀₀ = 1.0. 10-fold serial dilutions were then performed in 96-well plates for the range of OD₆₀₀ from 1.0 to 10⁻⁷. 100 μl of cells of a specific dilution were plated onto LB agar plates containing ciprofloxacin and ampicillin at a concentration of 0–16 ng/ml and 100 μg/ml, respectively. For each condition, two dilutions were optimally chosen to have 30-300 colonies per plate. After 24 hours of incubation at 37°C, the colonies on each plate were counted and colony forming units (CFU) per ml were calculated using the following formula:

The survival factor (SF) was calculated by normalizing against the CFU/ml in the absence of ciprofloxacin.

Data analysis of CRAC data

The CLASH data (NCBI Gene Expression Omnibus (GEO), accession number GSE123050) were analysed in the study [78] with the entire pipeline available here [111, 112]. The SGR file, generated with CRAC_pipeline_PE.py, was used to plot the genome browser track in Fig. 4A.

Fitting and parameter estimation

The smFISH data from Fig. 1C was conditioned on cell size (cell area < 3.0 μm², newborns) and the updated distribution was fitted by a negative binomial distribution. In mathematical terms, a negative binomial NB(r, p) is defined by two parameters: r, the number of successful outcomes, and p, the probability of success. Mean and variance of X ∼ NB(r, p) are given as:

The probability density function of the fitted distribution was found with the maximum likelihood estimation method in MATLAB. The fitted parameters, r and p, are given as r = 0.335 and p = 0.513.

The average mRNA burst size b and transcription rate k_m were calculated using the fitted parameters, r and p, and the recB mRNA degradation rate (γ_m = 0.615 min⁻¹, measured in an independent time-course experiment: Fig. 1D) according to the following analytical expressions (Eq. (A4), Eq. (A5) & Eq. (3)):

The RecB protein distribution from Fig. 2C was conditioned on cell size (cell area < 3.0 μm², newborns). Then, the average protein count number in newborns (∼3.2 molecules per cell) was matched to the theoretical expression for the protein mean Eq. (A4). The rate of translation k_p was calculated as follows (using protein removal rate, γ_p = 0.015 min⁻¹, and mean mRNA number in newborns, ⟨m⟩ = 0.323):

All parameters of the model are listed in Table 7.

Statistical analysis

Unless otherwise stated, histograms and RT-qPCR results represent the average across at least three replicated experiments and error bars reflect the maximum difference between the repeats.

The Kullback–Leibler divergence (D_KL) between simulated and experimental distributions was calculated with the MATLAB function [113]. Comparison between the average protein or mRNA concentrations among different conditions were performed with a two-sample t-test and P values were calculated in the MATLAB built-in function ttest2.

Average translational efficiency was calculated as the ratio between the mean protein concentration c_p and the mean mRNA concentration c_m (Fig. 3F & Fig. 4F). The error bars are standard deviations across replicated experiments.

Stochastic simulations

Single trajectories of mRNA and protein abundance over time were generated for the reaction scheme Eq. (A1) with the Gillespie’s algorithm, executed in MATLAB environment [114]. Parameters, used in simulations, are listed in Table 7. 10,000 simulations were performed for a given condition and probabilistic steady-state distributions were recovered for population snapshot data.

Data and code availability

All data that support this study including microscopy data, RT-qPCRs, growth rates, viability assays, and source codes for image analysis are available on Zenodo (10.5281/zenodo.8431113).The modified versions of the image analysis used for spot detection in Halo-labelling experiments and bright-field segmentation pipeline are also available on GitLab https://gitlab.com/ikalita/spotdetection_spatzcells and https://gitlab.com/ikalita/cellsegmentation_mek, respectively. The CRAC/CLASH dataset (NCBI Gene Expression Omnibus ID GSE123050) [78], used in this study, is available from GSE123050. The pipeline for the analysis of the CRAC/CLASH data is available from https://git.ecdf.ed.ac.uk/sgrannem and https://pypi.org/user/g_ronimo/.

Article and author information

Author contributions

Irina Kalita: Conceptualization, Methodology, Software, Investigation (experiments), Formal analysis (computational analysis & modelling), Writing – Original Draft Preparation, Writing – Review & Editing, Visualization;

Ira Alexandra Iosub: Conceptualization, Methodology, Software, Investigation (experiments), Formal analysis (computational analysis), Writing – Review & Editing, Visualization;

Lorna McLaren: Investigation (experiments), Writing – Review & Editing; Louise Goossens: Investigation (experiments), Writing – Review & Editing;

Sander Granneman: Conceptualization, Methodology, Software, Formal analysis (computational analysis), Writing – Review & Editing, Supervision, Funding Acquisition;

Meriem El Karoui: Conceptualization, Methodology, Formal analysis (modelling), Writing – Original Draft Preparation, Writing – Review & Editing, Supervision, Funding Acquisition.

Acknowledgements

We thank David Leach, Gerald Smith, Teppei Morita, and Hiroji Aiba for providing strains. We also thank Léna Le Quellec, Sebastian Jaramillo-Riveri, Alessia Lepore, Benura Azeroglu, James Hole-house, and Rachel Jackson for their technical support and assistance with cloning, image analysis, and modelling. We thank Livia Scorza from the the Biological Research Data Management team for expert data curation. We are grateful to Ramon Grima, Rosalind Allen, David Leach, Peter Swain, and Johan Paulsson for fruitful discussions and generous advice. This work was supported by a Wellcome Trust Investigator Award 205008/Z/16/Z (to M.E.K.), a grant from the Wellcome Trust 102334 (to I.A.I.), the Wellcome Trust Centre for Cell Biology core grant 092076, a Medical Research Council non Clinical Senior Research Fellowship MR/R008205/1 (to S.G.) and a Darwin Trust of Edinburgh postgraduate studentship (to I.K.).

Competing interests

The authors have no competing interests.

Supplementary Information

1 A stochastic two-stage model of RecB expression

To model RecB expression, we applied a well-established stochastic mRNA-protein model of gene expression and inferred its parameters by fitting to the experimental data. Here, we briefly introduce the model, discuss its underlying assumptions and provide the analytical expressions used in the fitting procedure.

Model description

A stochastic two-stage model of gene expression has been widely utilized to study fluctuations underlying protein production in prokaryotic and eukaryotic cells [57, 68, 69, 115, 116, 117]. Generally, the model is based on four biological processes: transcription of a gene by an RNA polymerase, translation of an mRNA by a ribosome, mRNA degradation and protein decay. As elsewhere, we assume a cell to be a well-stirred system of biochemical molecules, the interaction between which can be described with a common approach of chemical reactions [118]. We focus on two species, mRNAs and proteins, and denote molecule numbers in a cell as m and p, respectively.

Considering gene expression in bacterial cells allows several further assumptions to be made. First, transcription of bacterial genes was demonstrated to occur in bursts [119, 120] and quite a few transcriptional models describing gene bursting have been proposed in the literature [69, 121, 122, 123]. Thus, mRNA production is described as a zeroth-order chemical reaction where a gene is transcribed in mRNA bursts with a constant rate k_m and the number of mRNAs per each burst n is sampled from a geometric distribution with a mean size b [55, 56, 61]. Secondly, based on a broadly accepted view of the exponential RNA degradation in bacteria [124, 125, 126], mRNA decay is modelled as a first order reaction with a constant rate γ_m. Furthermore, proteins in bacteria were shown to be diluted exclusively because of cell growth and division [127, 128]. This process can be implicitly modelled by a first-order chemical reaction with a constant rate equal to growth rate γ_p. Finally, we assume that a protein is produced from an mRNA with a constant rate k_p. Thus, the entire reaction network for the two-stage model with burst transcription is summarized in the following schematic:

The dynamics of the mRNA and protein average levels (denoted as ⟨m⟩ and⟨ p⟩) is described by a set of the following rate equations:

Steady-state mRNA and protein mean and variance

The stationary solutions for mean mRNA and protein numbers can be found by imposing the steady-state conditions (d ⟨m⟩ /dt = 0 and d ⟨p⟩ /dt = 0) to the rate equations (Eq. (A2) & Eq. (A3)):

As a result of the linearity of the system, the mRNA and protein variances can be found exactly by van Kampen’s Ω-expansion (also known as the Linear Noise Approximation and the Fluctuation-Dissipation Theorem) [31, 118, 129].

Finally, the mRNA and protein coefficients of variation (squared), defined as variance over squared mean, are given as follows [57, 68, 69, 71]:

The analytical probability distribution of protein numbers under assumption of a long-lived protein relative to short-lived mRNA was derived here [57].

2 Deterministic model of RecB expression upon DSB induction

In this section, we analytically describe the dynamics of RecB mRNA and protein levels after a per-turbation made by DSB induction with a sub-lethal dose of ciprofloxacin. Taking into account different time-scales of the response in mRNA and protein levels, we address the following question: how long does the DSB induction need to be applied for to see changes (if any) in both species? We focus on the average mRNA and protein concentrations instead of molecule numbers (because of cell elongation upon ciprofloxacin treatment (Fig. 3B&C) and modify a two-stage model of RecB expression by including deterministic time-dependency of cell volume, V(t).

As discussed above, we consider the same set of reactions for two species of the system: mRNAs and proteins. While the processes of translation, active mRNA and protein degradation are described by first-order reactions with constant rates: k_p, γ_m and , respectively, mRNA transcription is given by a zeroth-order reaction. According to the law of mass action, we shall scale a zeroth-order reaction rate by the volume of the system, as k_mV(t) [118, 130]. We define the number of mRNA and protein molecules at time t in a cell of volume V(t) as m(t) and p(t), respectively. Then, the evolution of the average numbers of mRNA and protein molecules in time is described by the following rate equations:

We further define recB mRNA and RecB protein concentration as c_m(t) = m(t)/V(t) and c_p(t) = p(t)/V(t) and differentiate with respect to t:

In order to obtain time-dependent solutions for mRNA and protein concentrations, we divide the rate equations (Eq. (A8) & Eq. (A9)) by cell volume V(t) and replace dm(t)/dt and dp(t)/dt with the expressions from the equations (Eq. (A10) & Eq. (A11)). Based on the experimental evidence [131, 132], we assume the exponential dependence of cell volume from time, V(t) = V₀e^γt, where γ is a growth rate. Thus, we obtain the following ordinary differential equations for mRNA and protein concentrations:

By equating the left-hand sides of the equations to zero, we find the steady-state mRNA and protein concentrations, and :

Next, by assuming the initial conditions for mRNA and protein concentration to be c_{m (t=0)} and c_p(t=0), we obtain the time-dependent solutions for mRNA and protein concentrations:

The last expression can be simplified by taking into account that the RecB protein does not have an active degradation mechanism (Fig. 2D). Thus, after imposing the condition of , we obtain a time-dependent solution for RecB protein concentration as follows:

Now we can estimate the mRNA and protein response times from the expressions Eq. (A15) & Eq. (A17), respectively. It is worth noting that although cells are elongated upon ciprofloxacin treatment, they do not slow down the growth (Fig. S5). Thus, the analysis of the obtained equations shows that mRNA solution has one mode, , and hence a characteristic response time-scale can be estimated as 1/(γ_m + γ) ∼ 1.6 min (the results of growth rate measurements, γ = γ_cipro+ = 0.0165 min⁻¹, are shown in Fig. S5c). In contrast, the expression for protein concentration is given by two time-scales: e^−γt and , where the slowest one defines the response time as 1/γ ∼ 61 min. This means that a perturbation needs to be applied for at least ∼ 1 hour in order to be able to detect changes in protein concentrations. In our experiments, DSBs were induced for two hours to guarantee fulfillment of the time-scale requirement (Fig. 3).

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