Introduction

Cells regulate the intracellular concentration of various proteins and macromolecules to modulate the rate of essential cellular processes, including growth. In bacteria, cell mass and volume typically double between division cycles. Proportionality between biosynthetic capacity and biomass accumulation results in exponential or near-exponential cell growth during the cell cycle (Campos et al., 2014; Schaechter et al., 1958; Siegal-Gaskins and Crosson, 2008; Taheri-Araghi et al., 2015; Wang et al., 2010). What drives exponential growth has been a longstanding question in the microbiology field (Belliveau et al., 2021; Churchward et al., 1982; Ecker and Schaechter, 1963; Zhurinsky et al., 2010). Quantitative studies on model bacteria such as Escherichia coli place the concentration of ribosomes and their kinetics as the principal rate-limiting factors (Belliveau et al., 2021; Bosdriesz et al., 2015; Koch, 1988; Scott et al., 2014, 2010). Most other cellular components essential for growth are estimated to be at least an order of magnitude above the level required for proper enzymatic reactions (Belliveau et al., 2021), indicating that they are well in excess in terms of metabolic concentrations. Thus, translation is generally seen as the rate-governing process for cellular growth. While the translocation rate of ribosomes poses an inherent limit on the growth rate of the cell, protein concentrations are predominantly set transcriptionally at the promoter level, with tight coordination between transcription and translation (Balakrishnan et al., 2022).

Whereas the importance of ribosome concentration in growth rate determination has been extensively studied, a potential role for genome concentration has received less attention. An early population study on an E. coli thymine auxotroph proposed that global transcription is not limited by the concentration of the genome but is instead constrained by the availability of RNA polymerases (RNAPs) (Churchward et al., 1982). However, the potential impact of DNA concentration on determining the growth rate of E. coli or other bacteria has, to our knowledge, not been formally tested. Interestingly, E. coli and Bacillus subtilis have been shown to display small but reproducible deviations from exponential growth during the division cycle (Kar et al., 2021; Nordholt et al., 2020), with the growth rate increasing after the initiation of DNA replication under some conditions. Furthermore, at the population level, these organisms initiate DNA replication at a fixed cell volume (mass) per chromosomal origin of replication (oriC) across a wide range of nutrient and genetic conditions (Donachie, 1968; Govers et al., 2024; Si et al., 2017; Zheng et al., 2016), suggesting that DNA concentration is an important physiological parameter for these bacteria. In eukaryotes where genome concentration is also tightly controlled (Ginzberg et al., 2015; Turner et al., 2012), a change in DNA-to-cell-volume ratio has recently been demonstrated to remodel the proteome and promote cellular senescence (Crozier et al., 2023; Foy et al., 2023; Lanz et al., 2023, 2022; Manohar et al., 2023; Neurohr et al., 2019; Wilson et al., 2023).

In this study, we combined single-cell and single-molecule microscopy experiments with tandem-mass-tag mass spectrometry and modeling to investigate the potential physiological role of genome concentration in cell growth and proteome composition in E. coli.

Results

Growth rate correlates with the genome copy number in E. coli

To examine the potential effect of DNA content on the growth rate of E. coli, we used two CRISPR interference (CRISPRi) strains with arabinose-inducible control of expression of dCas9 (Li et al., 2016; Si et al., 2017). One strain expressed a single guide RNA (sgRNA) against oriC where sequestration by dCas9 binding prevents the initiation of DNA replication, producing cells with a single copy of the chromosome (Figure 1A) (Si et al., 2017). These cells, referred to as “1N cells” below, grew into filaments as a block in DNA replication prevents cell division, but not cell growth, from occurring (Carl, 1970; Si et al., 2017; Withers and Bernander, 1998). The second CRISPRi strain, which served as a comparison, expressed a sgRNA against the cell division protein FtsZ. FtsZ depletion blocks cell division while allowing DNA replication to proceed (Figure 1A) (Addinall et al., 1996; Li et al., 2016). Ongoing growth resulted in filamenting cells with multiple replicating chromosomes, hereafter referred to as “multi-N cells”. For both strains, we used time-lapse microscopy to monitor growth at the single-cell level at 37°C in M9 minimal medium supplemented with glycerol, casamino acids, and thiamine (M9glyCAAT). Cell area (A) was automatically detected from phase-contrast images using a deep convolutional network (Wiktor et al., 2021), and the absolute growth rate was determined by calculating the difference in cell area between frames. The relative growth rate , which is constant for exponential growth, was calculated by dividing by the cell area. We chose to use cell area rather than cell volume for growth rate measurements because cell area is what we measured in our two-dimensional cell images, and the average cell width remained largely constant for 1N and multi-N cells following CRISPRi induction (Figure 1 – figure supplement 1A). Furthermore, we found that absolute and relative growth rates based on extracted cell volumes produced similar results (Figure 1 – figure supplement 1B-K) to those based on cell areas (Figure 1 and Figure 1 – figure supplement 2). Therefore, we will report growth rate measurements based on cell areas hereafter.

Figure 1.

For the CRISPRi oriC strain, we selected 1N cells that contained a single DNA object (nucleoid) labeled by a mCherry fusion to the nucleoid-binding protein HupA (referred to as HU below). To confirm this 1N chromosome designation, we used a CRISPRi oriC strain that expresses HU-CFP and carries an oriC-proximal parS site labeled with ParB-mCherry (Figure 1 – figure supplement 3A), used here to determine the number of nucleoids and chromosomal origins per cell. We found that 96 ± 1% (mean ± standard deviation, SD, n = 3378 cells, three biological replicates) of cells with a single HU-labeled nucleoid contained no more than one ParB-mCherry focus, indicative of a single oriC.

Using this methodology, we observed a significant difference in growth rate between 1N and multi-N cells as shown in representative single-cell growth trajectories (Figure 1B) and in aggregated absolute growth rate measurements (Figure 1C). In multi-N cells, the absolute growth rate rapidly increased with cell area. For these cells, the scaling between absolute growth rate and cell size might even be slightly greater than expected for exponential growth, as the relative growth rate was not perfectly constant and mildly increased with cell area (Figure 1E). This slight increase would be consistent with the super-exponential growth pattern previously described for wild-type (WT) cells (Cylke and Banerjee, 2023; Kar et al., 2021). Multi-N cells grew identically to WT within the same cell size range (Figure 1 – figure supplement 2). In contrast, 1N cells grew significantly slower than multi-N-cells and their absolute growth rate only moderately increased with cell area, approaching an apparent plateau at large cell sizes (Figure 1C-D). This sub-exponential growth resulted in a relative growth rate that decreased with cell area (Figure 1E). The striking divergence in growth between 1N and multi-N cells of the same size suggested that growth is dependent on DNA concentration. The difference in growth rate between 1N and multi-N cells was already apparent in the physiological range of cell sizes when compared to WT cells (Figure 1 – figure supplement 2), suggesting that growth rate reduction occurs soon after DNA replication fails to initiate.

We ruled out that the slower growth of 1N cells was due to an induction of the SOS response or to an increased level in the nucleotide alarmone (p)ppGpp, as inactivation of either stress pathway (through deletion of recA or spoT/relA, respectively) in 1N cells made little to no difference to their growth rate (Figure 1 – figure supplement 4). Furthermore, as an independent validation, we used an orthogonal system to block DNA replication using the temperature-sensitive mutant dnaC2, which encodes a deficient DNA helicase loader at the restrictive temperature of 37°C (Carl, 1970; Withers and Bernander, 1998). We observed that the relationship between absolute growth rate and cell area in dnaC2 cells with a single nucleoid was similar to that of 1N cells produced by the CRISPRi oriC system (Figure 1D and E).

We noticed that, even at the restrictive temperature, the dnaC2 strain produced a sizeable fraction of cells with more than one HU-mCherry-labelled nucleoid (Figure 1 – figure supplement 3B and C), indicating that the temperate-sensitive effect on DNA replication is not fully penetrant. We took advantage of this phenotypic “leakiness” to measure the growth rate of cells with different numbers of nucleoids (and thus chromosomes) within the dnaC2 population. We observed a notable difference in growth rate between cells of 1, 2, and >2 nucleoids in the population, with each additional nucleoid contributing to higher cellular growth at a given cell size (Figure 1F-G). This finding is consistent with DNA-limited growth in which cellular growth rate increases with genome concentration.

In the relatively nutrient-rich M9glyCAAT condition, WT cells at birth are expected to have higher DNA content than 1N cells on average due to overlapping DNA replication (Fossum et al., 2007). This difference in DNA concentration explains the lower absolute growth rate of 1N cells relative to WT even at the smallest cell sizes (Figure 1- figure supplement 2). To examine whether cells are also subject to DNA-limited growth when multi-fork DNA replication is rare or nonexistent, we measured growth of 1N cells in two different nutrient-poor media, M9 glycerol (M9gly) and M9 L-alanine (M9ala). In both conditions, the growth rate scaled slower with cell area in 1N cells relative to WT cells (Figure 1H-K). Here again, this difference in growth was apparent in the cell size range of WT cells, indicating that the difference in growth rate is not simply the result of a non-physiological regime. Altogether, our data suggest that in WT cells, the genome concentration is (or is close to be) limiting for growth and that growth rate scales with ploidy.

The concentration of ribosomal proteins remains relatively constant in DNA-diluted cells

Ribosome content is often proposed to explain the approximately exponential growth of biomass in bacteria, with growth rate being directly proportional to ribosome concentration (Bremer and Dennis, 1996; Ecker and Schaechter, 1963; Scott et al., 2014, 2010). Therefore, we first quantified the fluorescence concentration of a monomeric superfolder green fluorescent protein (msfGFP) fusion to the ribosomal protein RpsB (expressed from the native chromosomal locus) in 1N and multi-N cells in M9glyCAAT as a function of cell area. We found it to be almost identical between the two CRISPRi strains and relatively constant across cell areas, regardless of DNA content (Figure 2A).

Figure 2.

To exclude the possibility that the msfGFP tag altered the synthesis of RpsB or that this protein behaved differently from other ribosomal proteins, we adapted a tandem-mass-tag (TMT) mass spectrometry (MS) method recently developed to examine cell size-dependent proteome scaling in yeast and human cells (Lanz et al., 2022). Note that for the CRISPRi oriC strain, a minority (∼10-15%) of cells have more than one nucleoid. These cells were excluded from the analysis of our single-cell microscopy experiments. However, this could not be done for the TMT-MS experiments, which provide population-level measurements. Therefore, for this TMT-MS section, we will refer to the CRISPRi oriC cell population as “1N-rich” cells, instead of just “1N” cells. Using the TMT-MS approach, we found that the relative concentration of all (54) high-abundance ribosomal proteins (including untagged RpsB) remained approximately constant across all sizes of 1N-rich cells and was relatively similar between 1N-rich and multi-N cells (Figure 2B). Only the ribosomal protein L31B, a stationary phase paralog of the more prevalent exponential phase ribosomal protein L31A (Lilleorg et al., 2019), displayed significant dilution in 1N cells (Dataset 1). Ribosomal protein concentration also appeared to remain constant in 1N cells in nutrient-poor media based on RpsB-msfGFP fluorescence intensity measurements in single cells (Figure 2 – figure supplement 1). Thus, the concentration of ribosomal proteins does not explain the difference in growth rate between cells with different ploidy.

The fraction of active ribosomes is reduced in DNA-diluted cells

To more specifically probe the translational activity of ribosomes in 1N cells, we performed single-molecule tracking in live cells growing in M9glyCAAT. Ribosomes are expected to exhibit at least two different dynamic states: slow mobility when active (i.e., engaged in translation on the mRNA, often in polyribosome form), and faster mobility when inactive ribosomes (or ribosomal subunits) are diffusing in the cytoplasm (Mohapatra and Weisshaar, 2018; Sanamrad et al., 2014). To track ribosomes, we introduced a HaloTag fusion to RpsB at the endogenous locus and labeled the HaloTag using the membrane-permeable Janelia Fluor 549 (JF549) fluorescent dye (Grimm et al., 2015). We quantified the apparent diffusion coefficient (D_a) of single-molecule tracks in WT cells as well as in 1N and multi-N cells at multiple time points following CRISPRi induction (Figure 2C). We found that the distribution of D_a in multi-N cells of all sizes (∼2-10 µm²) was similar to that in WT cells despite the considerable differences in cell sizes. In contrast, 1N cells displayed distributions clearly distinct from WT and multi-N cells, gradually shifting toward faster mobilities (higher D_a) with increasing cell size. This shift suggests that ribosome activity is altered in 1N cells.

Gaussian fitting of the D_a logarithmic data in WT cells revealed two predominant dynamic states of ribosomes: a slow-diffusing and a fast-diffusing state, representing 77 ± 1% (mean ± standard error of the mean (SEM)) and 20 ± 1% of the ribosome population, respectively (Figure 2D). In addition, we observed a small fraction (3.2 ± 0.5%) of faster-moving molecules with D_a expected for freely-diffusing proteins (Banaz et al., 2019; Elowitz et al., 1999), likely indicative of a small pool of free RpsB-HaloTag proteins (i.e., not assembled into ribosomes). To confirm that the slow-diffusing fraction corresponded to translationally active ribosomes, we showed that this fraction nearly vanished (down to 1.10 ± 0.02%) when cells were depleted of mRNAs following 30 min treatment with the transcription inhibitor rifampicin (Figure 2 – figure supplement 2). The estimated fraction (∼77%) of active ribosomes in untreated cells was in good agreement with previous single-molecule and biochemical studies under these growth conditions (Blundell and Wild, 1971; Mohapatra and Weisshaar, 2018; Phillips et al., 1969; Sanamrad et al., 2014).

Upon fitting the D_a values of ribosomes in 1N cells of different sizes (Figure 2E), we observed a significant reduction in the slow-diffusing ribosome population (Figure 2 – figure supplement 3). Quantification of the active (slow-diffusing) ribosome fraction per cell revealed that 1N cells have overall lower ribosome activity than WT cells, and that ribosome activity decreases monotonically with increasing cell area (Figure 2F). In contrast, ribosome activity in multi-N cells remained the same as in WT across different cell sizes (Figure 2G). The reduction in fraction of active ribosomes was less pronounced in 1N cells growing in M9gly and M9ala (Figure 2 – figure supplement 4), consistent with the smaller deviation in growth rate between 1N and WT cells (Figure 1H-K).

To estimate the total number of active ribosomes per cell in M9glyCAAT, we multiplied the total amount of ribosomes by the fraction of active ribosomes and plotted the result as a function of cell area (Figure 2H). We found that the difference in the total number of active ribosomes between 1N and multi-N cells matches the observed difference in growth rate in M9glyCAAT (Figure 2H), indicating cell growth rate is directly proportional to the increase in total active ribosomes. We also estimated the total number of active ribosomes in WT and 1N cells in M9gly and M9ala, where, overall, we observed similar trends (Figure 2 – figure supplement 4G-H). Altogether, the results are consistent with the hypothesis that DNA limitation decreases ribosome activity, which in turn reduces the growth rate.

DNA dilution reduces the activity of RNA polymerases

We reasoned that the observed changes in ribosome activity in 1N cells may reflect the available mRNA pool in cells. If true, we would expect the total activity of RNAPs to be reduced in 1N cells. In cells, the total activity of RNAPs is determined by the concentration of RNAPs multiplied by the fraction of active RNAPs. Therefore, we first determined whether RNAP concentration was lower in 1N cells relative to multi-N cells in M9glyCAAT by quantifying the fluorescence intensity of a functional fusion of YFP to the RNAP β’ subunit (encoded by rpoC) expressed from its native chromosomal locus. As expected, RNAP concentration remained constant in multi-N cells (Figure 3A). In 1N cells, the RNAP concentration increased with cell size (Figure 3A), the opposite of what would be expected to explain the growth rate defect. We confirmed this increasing trend in concentration for other protein subunits of the core RNAP and the primary sigma factor σ⁷⁰ (encoded by rpoD) using TMT-MS (Figure 3B), clearly demonstrating that the abundance of RNAPs was not the limiting factor. RNAP concentration also increased, albeit to a lesser degree, in 1N cells in nutrient-poor media based on fluorescence intensity measurements (Figure 3 – figure supplement 1).

Figure 3.

To quantify RNAP activity in 1N and multi-N cells, we performed single-molecule tracking in live cells in M9glyCAAT using a functional fusion of HaloTag to the β’ protein subunit RpoC labeled with the JF549 dye. As expected, the D_a values of RpoC-HaloTag in multi-N cells were distributed similarly to those in WT cells (Figure 3C). In contrast, the distribution in 1N cells changed gradually toward higher D_a values (faster mobility) with increasing cell size (Figure 3C).

As with ribosomes, RNAPs primarily exhibited two major states of diffusivity (Figure 3D): a slower-diffusing fraction (49 ± 4%; mean ± SEM) and a faster-diffusing fraction (49 ± 4%), likely representing transcriptionally active RNAPs and inactive, diffusing RNAPs, respectively. A small fraction of RpoC-HaloTag (2 ± 0.1%) diffused very fast, with D_a values expected for free proteins, suggesting that it reflects the few β’ proteins not assembled into the RNAP core complex. Using rifampicin treatment, we confirmed that the slowest state corresponded to RNAPs actively engaged in transcription (Figure 3 – figure supplement 2). In these rifampicin-treated cells, the slow-diffusing fraction was reduced to 13 ± 4%. Rifampicin does not prevent promoter binding or open complex formation and instead blocks transcription elongation following the synthesis of 3-nucleotide-long RNAs (Campbell et al., 2001). Thus, the observation that slow-moving RNAPs did not completely disappear after rifampicin treatment is consistent with the mechanism of action of the drug, leaving a fraction of RNAPs bound at promoter sites.

Unlike in WT and multi-N cells, the fraction of active RNAPs in 1N cells decreased monotonically with increasing cell area in all tested media (Figure 3F-G and Figure 3 – figure supplements 3 and 4). However, because the RNAP concentration simultaneously increased in 1N cells, it was possible that the total amount of active RNAP, which is the relevant metric of transcription activity, remained equal to that of multi-N cells. By calculating the total amount of active RNAPs, we showed that the decrease in active fraction in 1N cells was not the mere result of the increase in RNAP concentration. Indeed, in M9glyCAAT, the total amount of active RNAPs hardly increased with cell size in 1N cells whereas it increased proportionally with cell size in both multi-N and WT cells (Figure 3H). This was also true in M9gly and M9ala (Figure 3 – figure supplement 4G-H). The reduction in the total amount of active RNAPs was also readily apparent in 1N cells within the range of WT cell sizes (Figure 3H and Figure 3 – figure supplement 4G-H).

A recent study has shown that the intracellular concentration of Rsd, the anti-sigma factor of σ⁷⁰, increases in WT cells under slower growth conditions, causing a reduction in global mRNA synthesis (Balakrishnan et al., 2022). Therefore, we verified that the concentration of Rsd remains approximately constant in both 1N-rich and multi-N cells based on our TMT-MS data (Figure 3 – figure supplement 5), eliminating Rsd as possible source of reduced RNAP activity in 1N cells. Instead, our data supports the notion that substrate (DNA) limitation leads to a reduced transcription rate, which would reduce the pool of mRNAs available for ribosomes.

DNA dilution can result in sub-exponential growth through mRNA limitation

In a previous theoretical study, Lin and Amir (2018) considered distinct scenarios for gene expression. Their model predicted that if DNA and mRNAs are in excess, cells display exponential growth, whereas if DNA and mRNAs are limiting, cells will adopt linear growth. Our experiments showed that 1N cells converge toward linear growth (toward slope = 0 in Figure 1C, H, and J), though the complete transition to linear growth required a large decrease in DNA concentration. To quantitatively examine this transition from exponential to linear growth through DNA dilution, we developed two deterministic ordinary differential equation (ODE) models of the flow of genetic information that include parameters for the fractions of active RNAPs and ribosomes. In these models, the dynamics of mRNA (X) and protein (Y) numbers in the cell are described by

Where r₁ is the bulk transcription rate normalized by the total protein number, r₂ is the bulk translation rate normalized by the total protein number, α_RNAP(X, Y) is the fraction of active RNAPs, δ, is the mRNA degradation rate, α_ribo(X, Y) is the fraction of active ribosomes, and corresponds to the absolute growth rate. For simplicity, we assumed that the protein degradation is negligible and that the cell volume and the number of rRNAs grow proportional to protein Y (Balakrishnan et al., 2022; Lin and Amir, 2018). For detailed description and estimation of the model parameters, see Table 1 and Appendix 1.

Table 1:

Based on the function form of α_RNA(X, Y), we consider two ODE model variants. Model A examined the effect of DNA limitation with minimal mathematical complexity by assuming that the proteome does not change (see Materials and Methods). Model B considered RNAP kinetics (with three different RNAP states: free, promoter-bound, and transcribing) and took into consideration the experimentally observed increase in RNAP concentration in 1N cells (Figure 3A-B, see Materials and Methods and Appendix 2). For both models, α_RNAP depended on DNA concentration. In 1N cells, the DNA amount was fixed to 1 genome while it scaled with cell volume in multi-N cells. We then used both models to perform simulations and compared the results to our measurements, starting with parameter values extracted or estimated from the E. coli literature (Table 2). The parameters were then optimized to fit six experimental datasets simultaneously: cell growth rate, the fraction of active RNAPs, and the fraction of active ribosomes in both 1N and multi-N cells in M9glyCAAT (see Materials and Methods and Appendix 3).

Table 2:

As shown in Figure 4A-D (model A) and Figure 4 – figure supplement 1 (model B), both models performed similarly after parameter optimization. While the model curves (solid lines) did not exactly match the average behavior of our experimental results (open squares), they displayed similar trends and fell within the variance of the single-cell data (dots). The models showed that multi-N cells (blue) display balanced exponential growth while the 1N cells (yellow) exhibit sub-exponential growth (Figure 4A and Figure 4 – figure supplement 1A), consistent with experiments. At the same time, both models recapitulated the observed experimental trends in active fractions of both ribosomes and RNAPs, which remained constant in multi-N cells while decaying gradually with DNA concentration in 1N cells (Figure 4B-D and Figure 4 – figure supplement 1B-D).

Figure 4.

In the absence of published values for the RNAP kinetic constants in nutrient-poor media, we only used the simpler model A for the M9gly and M9ala conditions. Here again, the model reproduced the trends for the experimental measurements of WT cells (gray) and 1N cells (yellow) (Figure 4 – figure supplement 2), with one notable deviation. At cell birth, the curves of fractions of active RNAPs and ribosomes for 1N cells started slightly higher than the ones for WT cells due to a limitation of our ODE model, which uses the average concentration of genome and does not include DNA replication dynamics.

The simulation results of 1N cells suggest the following cascade of events when DNA is limiting. Lower DNA concentration results in fewer substrates for RNAPs, which reduces the transcription rate. This results in a decrease in mRNA concentration (Figure 4E). As mRNAs become limiting, the fraction of ribosomes engaged in translation decreases. This, in turn, decreases the rate in bulk protein synthesis, which decreases the relative growth rate. The greater the DNA dilution (through cell growth), the more severe the downstream effects become, explaining the decay in relative growth rate in 1N cells (Figure 4E).

Since the models predicted a reduced mRNA pool in 1N cells, we performed live-cell staining with SYTO RNASelect (Wu et al., 2020), a fluorogenic RNA-specific dye that primarily (∼70% of the signal) binds mRNAs in E. coli based on rifampicin treatment (Bakshi et al., 2014). In our RNASelect staining experiments, we mixed 1N cells with multi-N cells of similar size ranges prior to incubation with the dye to mitigate variability in staining. We next imaged the mixed populations and distinguished 1N cells from multi-N cells by examining the difference in nucleoid number (one vs. multiple) per cell (Figure 4F). Single cells were then sampled to ensure that the cell area distributions of the two populations perfectly matched (Figure 4 – figure supplement 3). Comparison between the two sampled populations from five independent experiments revealed a reduced concentration of RNASelect signal (by ∼50%) in 1N cells relative to multi-N cells for a cell size range of 4 to 10 µm² (Figure 4G-H). We also found that the RNASelect concentration ratio between 1N and multi-N cells decreased exponentially with increasing cell area and thus DNA dilution (Figure 4I), in line with the model prediction (Figure 4E). Furthermore, both the model (Figure 4E) and our experimental findings (Figure 4I) suggest that the effects of DNA limitation on the mRNA concentration already appear at physiological cell area ranges (between 2 and 3 μm²).

To verify that the decrease in RNASelect signal in 1N cells was not caused by a global change in membrane permeability to small molecules, we performed similar staining experiments with the HaloTag dye JF549 in CRISPRi strains expressing RpoC-HaloTag (Figure 4 – figure supplement 4A-B). Because RpoC concentration increases with cell size in 1N cells relative to multi-N cells (Figure 3A-B), we expected a similar increase in the ratio of JF549 signal between these two cell types if the membrane permeability to small molecules remained unchanged. This is indeed what we observed (Figure 4 – figure supplement 4C-E). Hence the RNASelect results are consistent with a reduced mRNA concentration in 1N cells caused by DNA dilution and reduced global transcription activity.

Genome dilution incrementally changes the composition of the proteome

The fact that the relative concentrations of ribosomal proteins and RNAP subunits scaled differently with cell area in 1N cells (Figures 2A-B and 3A-B) indicated that all genes are not equally impacted by DNA dilution. In yeast and mammalian cells, a decrease in the DNA-per-volume ratio has recently been demonstrated to alter the composition of the proteome, with some proteins increasing in relative concentration while others become comparatively more diluted (Lanz et al., 2023, 2022). To examine whether this effect may be conserved across domains of life, we used our proteomic TMT-MS data on the CRISPRi strains to quantify the relative concentration of each detected protein across cell areas following DNA replication or cell division arrest. For each protein, we calculated the relative change in concentration against the relative change in cell size through regression fitting, yielding a slope value. A slope of zero indicates that the relative concentration of a protein remains constant whereas a slope of -1 (or 1) means that the relative concentration is decreasing (or increasing) by two-fold with each cell size doubling (Figure 5A).

Figure 5.

We found that the slope distribution was highly reproducible between biological replicates (Figure 5 – figure supplement 1A-B) but drastically different between 1N-rich cells and multi-N cells (Figure 5B, Dataset 1). In the control multi-N cells where the genome concentration does not change with cell growth, the concentration of ∼94% of the detected proteins (2217/2360) remained roughly constant, with their concentrations decreasing or increasing by less than 20% per cell size doubling (i.e., slopes > -0.2 or < 0.2; Figure 5B and Dataset 1). This indicates that protein amounts largely scale with cell size, as generally assumed. However, in 1N-rich cells where the genome dilutes with cell growth, the proportion of detected proteins that maintained similarly constant concentrations across cell areas (i.e., slopes > -0.2 or < 0.2) dropped to ∼37% (859/2360) (Figure 5B and Dataset 1). A principal component analysis on the relative protein concentration during cell growth confirmed that the relative proteome composition changes proportionally with genome dilution (1N-rich cells), whereas it remains constant when the DNA-to-cell volume is maintained (multi-N cells) (Figure 5C).

Interestingly, for 1N-rich cells, we also observed a slight yet significant positive correlation (Spearman ρ = 0.23, p-value < 10^-10, for genes within 1.35 Mb from oriC) between protein slope and the gene distance from oriC (Figure 5D). In other words, genes closer to oriC were more likely to encode proteins that dilute during DNA-limited growth (protein slope < 0) compared to distal genes (Figure 5D). This was irrespective of their total protein abundance based on summed ion intensities normalized by protein sequence lengths (Figure 5E). This may suggest the existence of a mechanism that compensates for the gene dosage associated with DNA replication.

To examine whether the proteome scaling behavior stems from changes in mRNA levels, we performed transcriptomic (RNA-seq) analysis on two biological replicates of 1N-rich cells at different time points after induction of DNA replication arrest. The two replicates were strongly correlated at the transcript level (Spearman ρ = 0.91, Figure 5 – figure supplement 1C). We also found a strong correlation in scaling behavior with cell area between mRNAs and proteins across the genome (Spearman ρ = 0.76, Figure 5F and Dataset 2), indicating that most of the changes in protein levels observed upon genome dilution take place at the mRNA level.

Discussion

In this study, we show that genome concentration acts as a rate-limiting factor for exponential cellular growth and a modulator of proteome composition in E. coli. These roles for genome concentration help explain why the timing of DNA replication is so robustly linked to cell volume across environmental and genetic conditions that affect cell size (Donachie, 1968; Govers et al., 2024; Si et al., 2017; Zheng et al., 2016).

Our data suggest that DNA limitation in 1N cells affects cell growth rate through modulation of downstream transcription and translation activities (Figures 2-4 and associated figure supplements). As a result of growth-induced dilution, the genome becomes increasingly limiting as a template, decreasing the fraction of active RNAPs (Figure 3). This indicates a sub-linear scaling of global transcription relative to the cell size. We propose that this reduced transcription activity in comparison to cells undergoing DNA replication results in a gradual decrease in total mRNA concentration (Figure 4E-G). Reduced mRNA availability would cause a decrease in the fraction of ribosomes engaged in translation (Figure 2F and Figure 2 – supplement 4), which would, in turn, lead to sub-linear scaling of global protein synthesis and absolute growth rate with cell size (Figure 2H and Figure 2 – supplement 4). It is also possible that the cumulative effect of small changes in proteome composition in 1N cells contributes to their growth rate defect.

The growth rate dependency on genome concentration is unlikely to be a particularity of E. coli, as we also observed a divergence in absolute and relative growth rates with increasing cell area between 1N and multi-N cells of Caulobacter crescentus (Figure 1 – supplement 6A and B). In this organism, filamenting 1N and multi-N cells were generated by depleting the DNA replication initiation factor DnaA (Gorbatyuk and Marczynski, 2001) and the cell division protein FtsZ (Wang et al., 2001), respectively. The 1N versus multi-N designation was confirmed by visualizing the number of chromosomal origins of replication (one versus multiple) per cell using the parS/ParB-eCFP labeling system (Figure 1 –supplement 6C). The fact that DNA limitation for cellular growth was also observed in C. crescentus is significant not only because this bacterium is distantly related to E. coli, but also because it has a different pattern of cell wall growth and distinct control mechanisms of DNA replication (Aaron et al., 2007; Banerjee et al., 2017; Frandi and Collier, 2019; Lasker et al., 2016; Terrana and Newton, 1975). This suggests that DNA concentration may be a prevalent growth constraint across bacterial species.

We found that even a relatively small dilution in DNA concentration—as expected in DNA replication-arrested cells that are still within or close to physiological sizes—results in growth rate reduction in E. coli and C. crescentus (Figure 1 and Figure 1 – supplements 2 and 6). Thus, under our standard growth conditions, cells appear to live at the cusp of DNA limitation for cellular growth. This suggests that cells make enough—but not too much—DNA, presumably because DNA replication is a costly process that represents a significant fraction (∼6% in minimal media) of the cellular energy budget (Neidhardt et al., 1990). What may be the implications of living at the cusp of DNA limitation in bacteria? While E. coli carefully controls its DNA concentration across various conditions and growth rates at the population level (Donachie, 1968; Govers et al., 2024; Si et al., 2017; Zheng et al., 2016), there remains some variability in DNA concentration at the single-cell level, with some cells initiating DNA replication at smaller or larger cell volumes than others (Si et al., 2019; Witz et al., 2019). It will be interesting to explore in future studies whether this variability contributes to the known growth rate heterogeneity across isogenic cells (Lin and Jacobs-Wagner, 2022; Wang et al., 2010). It is also tempting to speculate that changes in DNA concentration may, at least in part, contribute to the deviations from exponential growth that have been reported during the division cycle of B. subtilis, E. coli, and stalked C. crescentus progeny (Banerjee et al., 2017; Kar et al., 2021; Nordholt et al., 2020; Reshes et al., 2008). More substantial forms of DNA dilution may occur under other circumstances as well. C. crescentus cells in freshwater lakes often form long filaments during algal blooms in the summer months (Heinrich et al., 2019). These filament cells are thought to be the result of a DNA replication arrest in response to the combination of an alkaline pH, a depletion in phosphate, and an excess in ammonium (Heinrich et al., 2019). Another example is illustrated by the Lyme disease agent Borrelia burgdorferi. This pathogen, which forms long polyploid cells during exponential growth, experiences a progressive decrease in genome concentration (up to eightfold) in stationary phase cultures through the gradual loss of genome copies (Takacs et al., 2022).

Comparison with studies on eukaryotic cells suggests conservation of gene expression principles across domains of life. For instance, in yeast, it has been shown that the global transcription rate in G1-arrested cells is higher in diploids than haploids of similar sizes (Swaffer et al., 2023), consistent with DNA concentration being a limiting factor for transcription. Furthermore, in both yeast and mammalian cells, small G1-arrested cells display higher growth rate (or global RNA or protein synthesis rate) per cell volume than large ones that have exceeded a certain volume (Cadart et al., 2018; Liu et al., 2022; Neurohr et al., 2019; Zatulovskiy et al., 2022). This is likely due to a change in genome concentration rather than a change in cell volume, as the relative growth rate is unaffected in very large cells as long as they undergo a proportional increase in ploidy (Mu et al., 2020).

In yeast cells, an increase in RNAP II gene occupancy combined with a decrease in mRNA turnover helps mitigate DNA dilution on global transcription activities up to a certain cell volume beyond which the compensation breaks down (Swaffer et al., 2023; Zhurinsky et al., 2010). Such buffering activities, which are consistent with model predictions (Figure 4 – figure supplement 5) (Swaffer et al., 2023), may also be at play in bacteria, potentially in a growth medium-dependent manner. For example, in our E. coli experiments, we noted that the global transcriptional activity (total amount of active RNAPs) strongly deviated from proportional scaling with cell size in 1N cells compared to WT and multi-N cells in all tested medium conditions (Figure 3H and Figure 3 – supplement 4G-H). This indicates that the genome content limits transcription. However, the global translation activity (total amount of active ribosomes) only strongly deviated from proportional scaling with cell sizes in 1N cells growing in the relatively rich medium (M9glyCAAT) condition (Figure 2H). In poor media (M9gly and M9ala), the deviation was far less pronounced (Figure 2H and Figure 2 – supplement 4G-H), suggesting that a decrease in mRNA turnover and/or an increase in ribosome occupancy per transcript partially buffer(s) DNA limitation on transcription in poor media.

Another remarkable similarity between bacteria and eukaryotes is the effect of genome concentration on proteome composition. While protein abundance is typically assumed to scale with cell size in bacteria, we found that this is true at the proteome level only when ploidy also scales (Figure 5). This requirement was also recently shown in yeast and mammalian cells (Lanz et al., 2023, 2022). This conservation in scaling principle further highlights the importance of genome concentration in controlling protein expression.

At the GO term level, we did not identify any specific trends in proteome changes (Dataset 1). In eukaryotic cells, histones are known to scale in proportion with DNA rather than cell size (Claude et al., 2021; Swaffer et al., 2021; Wiśniewski et al., 2014). As a result, their concentration proportionally decreases (i.e., slope = -1) with growth in G1 phase. In E. coli, the relative abundance of some nucleoid-associated proteins (H-NS, HU and Dps) decreased with genome dilution, while others (IHF and Fis) displayed superscaling behavior (Figure 5 – supplement 2). What determines the scaling behavior of proteins is not clear. We found that, in E. coli, the alteration in proteome composition largely occurs at the mRNA level (Figure 5F) and partially involves chromosomal positioning (Figure 5D).

Finally, given the prevalent use of E. coli in the biotechnological world, we hope that our findings will be helpful to future bioengineering studies and growth rate optimization efforts. We show that protein content and cellular growth depend on the ploidy-to-cell volume ratio (Figures 1 and 5). As such, models of protein expression that take into consideration the DNA concentration and the active number of RNAPs and ribosomes could provide a starting point to identify the parameter space that leads to growth rate improvement.

Materials and methods

Bacterial strains and growth conditions

Bacterial strains and their construction can be found in Table 3. Oligomers used for polymerase chain reaction (PCR) are listed in Table 4. Transductions and Gibson assemblies were performed as described previously (Ely, 1991; Thomason et al., 2007).

Table 3.

Table 4.

E. coli strains were grown at 37°C in M9 minimal media with different supplements: 0.2% glycerol, 0.1% casamino acids and 1 µg/ml thiamine (M9glyCAAT); 0.2% glycerol (M9gly); or 0.2% L-alanine (M9ala). For microscopy, cells were grown in culture tubes to stationary phase, diluted 10,000-fold, and grown until they reached an optical density (OD₆₀₀) between 0.05 and 0.2. For imaging, cells were then spotted onto a 1% agarose pad on a glass slide prepared with the appropriate M9 medium and covered by a #1.5 thickness coverslip.

For time-lapse microscopy experiments with the CRISPRi strains (Li et al., 2016), the cells were induced by adding L-arabinose (0.2%) to liquid cultures after which a sample (∼1 µl) was immediately collected and spotted on an agarose pad containing the appropriate growth medium supplemented with 0.2% L-arabinose. This was promptly followed by imaging of individual cells. To determine the 1N status of CRISPRi oriC cells, we monitored the last division and number of nucleoids based on HU-mCherry fluorescence. In Figure 1B, the time point “0 min” refers to the time when cells have reached the 1N status.

For population microscopy experiments with the CRISPRi strains, the cells were induced with 0.2% L-arabinose and allowed to grow in normal conditions until a specific time point (depending on the growth medium and strain) was reached, after which the cells were spotted on an agarose pad containing the appropriate growth medium and 0.2% L-arabinose, and imaged (see information for each experiment in the corresponding Figure). Note that the CRISPRi strains do not metabolize arabinose due to the araBAD deletion.

For the TMT-MS experiments, CRISPRi oriC (SJ_XTL676) cells were supplemented with 0.2% L-arabinose and allowed to grow in liquid M9glyCAAT cultures at 37°C for 0, 120, 180, 240 and 300 min before harvesting, while CRISPRi ftsZ (SJ_XTL229) cells were collected after 0, 60, and 120 min after arabinose addition. For RNAseq experiments, CRISPRi oriC (SJ_XTL676) cells were supplemented with 0.2% L-arabinose and allowed to grow liquid M9glyCAAT cultures 37°C for 60, 120 200, and 240 min before harvesting.

Strains carrying the dnaC2 mutation were grown at a permissive temperature of 30°C and then shifted to 37°C to block replication initiation. Transcription inhibition and mRNA depletion were achieved by exposing cells to 200 µg/ml rifampicin for 30 min before spotting cells onto a 1% agarose pad containing the appropriate M9 medium and rifampicin concentration. The HaloTag was labeled with Janelia Fluor 549 (JF549) ligand (Grimm et al., 2015) as described previously (Banaz et al., 2019). Briefly, cells were incubated with 2.5 μM of the JF549 ligand for 30 min while shaking, washed 5 times with growth medium, and allowed to recover for several generations (while remaining in exponential phase) prior to imaging.

C. crescentus strains were grown at 22°C in PYE (2 g/L bacto-peptone, 1 g/L yeast extract, 1 mM MgSO₄, 0.5 mM CaCl₂) supplemented with 0.03% xylose to induce production of the essential protein FtsZ (Wang et al., 2001) or DnaA (Gorbatyuk and Marczynski, 2001). For microscopy, cells were grown in overnight cultures, then diluted at least 1:10,000 in fresh medium and grown to exponential phase (OD₆₆₀ nm < 0.3). To induce cell filamentation by depleting FtsZ or DnaA, xylose was removed from the medium by pelleting cells, washing twice with PYE, and resuspending in fresh PYE. Cultures were then allowed to grow for an additional 30 min to allow ongoing cell division cycles to complete before spotting on 1% agarose pads containing PYE but lacking xylose to deplete FtsZ or DnaA. To estimate the concentration of fluorescently-labeled ribosomes and RNAPs by fluorescence microscopy, cultures were sampled at 0, 4, 8, and sometimes 12 h following xylose depletion with 30 min outgrowth to allow late predivisional cells time to divide before spotting. For timelapse microscopy, new pads were spotted with cells from the original culture at 0, 4, 8, and sometimes 12 h following xylose removal with 30 min outgrowth in a liquid PYE medium.

Epifluorescence microscopy

For E. coli, phase contrast and fluorescence imaging (except for the RpoC-HaloTag-JF549 epifluorescence experiment), were performed on a Nikon Ti2 microscope equipped with a Perfect Focus System, a 100x Plan Apo λ 1.45 NA oil immersion objective, a motorized stage, a Prime BSI sCMOS camera (Photometrics), and a temperature chamber (Okolabs). Fluorescence emission was collected during a 100 or 200 ms exposure time provided by a Spectra III Light Engine LED excitation source (Lumencor): mCherry – 594 nm excitation, DAPI/FITC/TxRed filter cube (polychroic FF-409/493/596-Di02, triple-pass emitter FF-1-432/523/702-25); GFP and SYTO RNASelect – 488 nm excitation, DAPI/FITC/TxRed polychroic filter cube, and an ET525/50M emission filter; YFP – 514 nm excitation, CFP/YFP/mCherry filter cube (polychroic FF-459/526/596-Di01, triple-pass emitter FF-1-475/543/702-25), and a FF02-525/40-25 emission filter. The microscope was controlled using NIS-Elements AR. For time-lapse imaging, phase images were collected every 5 min.

Epifluorescence snapshots of RpoC-HaloTag-JF549 were taken using a Nikon Ti microscope, equipped with a Perfect Focus System, a 100x Plan Apo λ 1.45 NA oil immersion objective, a motorized stage, an ORCA Flash 4.0 camera (Hamamatsu) and a temperature chamber (Okolabs). Fluorescence emission was collected during a 200 ms exposure time provided by a Sola solid state white light source (Lumencor) and a Cy3 filter cube (excitation AT545/25x, dicrhoic T565lpxr, emission ET605/70m). The microscope was controlled using NIS-Elements AR.

For C. crescentus, phase contrast and fluorescence imaging were performed on a Nikon Ti-E microscope equipped with a Perfect Focus System, a 100x Plan Apo λ 1.45 NA oil immersion objective, a motorized stage, an Orca-Flash4.0 V2 142 CMOS camera (Hamamatsu) at room temperature. Chroma filter sets were used to acquire fluorescence images: CFP (excitation ET436/20x, dichroic T455lp, emission ET480/40m) and mCherry (excitation ET560/40x, dichroic T585lpxr, emission ET630/75m). The microscope was controlled using NIS-Elements AR. For time-lapse imaging, phase images were collected every 2.5 min.

Photoactivated localization microscopy

For single-molecule photoactivated localization (PALM) microscopy, coverslips were plasma-cleaned of background fluorescent particles using a plasma cleaner (PDC-32G, Harrick Plasma). Live cell PALM microscopy was performed on a Nikon N-STORM microscope equipped with a Perfect Focus System and a motorized stage. JF549 fluorescence was measured using an iXon3 DU 897 EMCCD camera (Andor) and excited from a 50 mW 561 nm laser (MLC400B laser unit, Agilent) with 50% transmission. The laser was focused through a 100x Apo TIRF 1.49 NA oil immersion objective (Nikon) onto the sample using an angle for highly inclined thin illumination to reduce background fluorescence (Tokunaga et al., 2008). Fluorescence emission was filtered by a C-N Storm 405/488/561/647 laser quad set. Transmission illumination was used to gather brightfield images. PALM movies of 20,000 frames were acquired with continuous laser illumination and a camera frame rate of 10.7 ms.

SYTO RNASelect staining experiments

In order to compare the mRNA concentration between 1N and multi-N cells, exponentially growing CJW7576 (CRISPRi ftsZ) and CJW7457 (CRISPRi oriC) cells were stained with the fluorogenic SYTO RNASelect dye (Invitrogen^TM, S7576) after CRISPRi induction with 0.2% L-arabinose. To ensure overlapping cell area distributions in the absence of cell division, considering the measured growth rate differences between the 1N and multi-N cells, CRISPRi oriC was was induced for 3.5 h whereas CRISPRi ftsZ was induced for 1.5 h. Then, the two populations were mixed at equal optical densities (OD₆₀₀) and stained with 0.5 μM SYTO RNASelect for 15 min at 37°C with shaking. For each staining, a fresh 5μM SYTO RNASelect stock was prepared in L-arabinose-containing medium. Stained cells (∼0.5 μL) were spotted on a 1% agarose pad prepared with the same growth medium with L-arabinose for imaging. Five biological replicates were performed.

RpoC-HaloTag-JF549 staining experiments for epifluorescence snapshots

For Figure 4 – supplement 5, CRISPRi oriC in CJW7520 cells was induced for 3.5 h whereas CRISPRi ftsZ (CJW7527) was induced for 1.5 h with 0.2% L-arabinose to obtain a similar range of cell sizes for imaging. Then the two populations were mixed at equal optical densities (OD₆₀₀) and stained with 2.5 μM JF549 at 37°C for 30 min with shaking. The mixed cells were then washed three times with L-arabinose-containing (0.2%) medium. All washes were performed at 4°C, using ice-cold medium to block cell growth and avoid the dilution of the dye. Then, the cells (∼0.5 μL) were spotted on a 1% agarose pad prepared with the same L-arabinose-containing growth medium for imaging. Two biological replicates were performed.

Image processing and data analysis

Data analysis was done in MATLAB (Mathworks) (MAIN_pop_analysis.m script for epifluorescence snapshots, MAIN_timelapse.m script for timelapse movies and MAIN_mol_tracking.m script for single-molecule tracking experiments), except for segmentation of phase contrast images, which was done in Python (segmentationRun.py) using a convolutional neural network, the Nested-Unet (Wiktor et al., 2021; Zhou et al., 2020), and the analysis of the SYTO RNASelect and RpoC-HaloTag-JF549 epifluorescence (snapshots_analysis_UNET_version_ND2.py class) that was also performed in Python 3.9 (DNA_limitation_python_environment.yml). The Nested-Unet network was trained for our microscopy setup using PyTorch 1.7.0 and NumPY 1.19.2 (trainerWrapper.py) (Harris et al., 2020; Paszke et al., 2019).

Cell area masks from segmentation were linked between time-lapse frames based on maximum overlap (trackCells.m). Two masks linked to the same cell area were considered a cell division event. To estimate the absolute growth rate, the cell area over time was smoothed by a sliding-average window of five data points (time interval 5 min) and the difference in the cell area between consecutive frames was calculated. The relative growth rate was calculated by dividing the absolute growth rate by the cell area. Cell areas were converted into volumes using Oufti’s scripts (Paintdakhi et al., 2016). To avoid bias from cells reaching sizes too large to support growth, the time-lapse data for filamenting cells was truncated based on their maximum absolute growth rate. We confirmed that the relative reduction in the growth rate of 1N in comparison to multi-N cells was not due to longer time-lapse duration as we observed no differences when acquiring shorter 2 h time-lapse sequences (Figure 1 – figure supplement 5A). Finally, we confirmed that cells were under stable growth conditions prior to starting imaging by showing that relative growth remained constant from the beginning of acquisition (Figure 1 – figure supplement 5B).

Fluorescent ParB-mCherry spots were detected by fitting a 2D Gaussian function to raw image data (detectSpots.m). First, the fluorescent image was filtered using a bandpass filter to identify the local maxima. Next, the local maxima were fitted by a Gaussian function and a spot quality score was calculated based on spot intensity and quality of a Gaussian fit (Intensity * quality_fit / σ_fit). The spot score threshold was determined by visual inspection of the training data and was set to remove poor-quality spots from analysis.

The number of HU-mCherry-labeled nucleoid areas were detected using Otsu’s thresholding (multithresh.m) (Otsu, 1979). Minimum and maximum area thresholds for an individual nucleoid were determined by measuring the number of fluorescent spots of ParB protein fusion in HU-labeled nucleoid areas of a strain (CJW7517) carrying a parS site from plasmid pMT1 at ori1 (Figure 1 – supplement 3A). Only cells containing a single nucleoid were considered 1N cells. To measure the total fluorescence intensity of a cell, the median intensity of the area outside the cell areas was subtracted from the fluorescent intensity of each pixel of a cell, and the intensity of all pixels was summed together.

For the SYTO RNASelect and RpoC-HaloTag-JF549 epi-fluorescence snapshot experiments (Figure 4F-I, Figure 4 – supplement 4 and Figure 4 – supplement 5), the nucleoid objects were segmented using the segment_nucleoids function in the snapshots_analysis_UNET_version_ND2.py class. This function combines a Laplacian of Gaussian (LoG) filter, an adaptive filter, and a hard threshold to detect the nucleoid boundaries and distinguish between 1N and multi-N cells in the mixed populations. The image filters were applied using the scikit-image (Van Der Walt et al., 2014) and NumPy (Harris et al., 2020) Python libraries. For the SYTO RNASelect-stained cells, the HU-mCherry fluorescence was used to segment the nucleoid objects. For the RpoC-HaloTag-JF549-stained cells, the fluorescence of RpoC-HaloTag-JF549 bound to nucleoids was used to segment the nucleoid objects.

The SYTO RNASelect concentration corresponds to the total fluorescence of the fluorogenic dye within the cell boundaries of the cell mask, divided by the area of the cell mask. Similarly, the RpoC-HaloTag-JF549 concentration was calculated in arbitrary units.

To ensure that the SYTO RNASelect or the RpoC-HaloTag-JF549 fluorescence was compared for the same distributions of cell areas between the 1N and multi-N cells in the mixed populations, random sampling was performed in each cell area bin using a sample size equal to the smaller cell number between the 1N and multi-N cells (Figure 4 – supplements 4 and 5B). For example, if in each cell area bin, there were 200 1N cells and 100 multi-N cells, 100 cells were randomly sampled from the 1N population to match the sample size of the multi-N population. Bins with less than 50 cells per population across biological replicates were removed from the analysis. This sampling was performed one time to compare the distributions of the SYTO RNASelect (Figure 4G) and RpoC-HaloTag-JF549 (Figure 4 – supplement 5C) concentrations between the 1N and multi-N cells. However, to estimate the average 1N/multi-N SYTO RNASelect or RpoC-HaloTag-JF549 ratio during cell growth (Figure 4I and Figure 4 – supplement 5E) multiple samplings (with substitution) were performed for each biological replicate and cell area bin. This allowed us to use all the data while still comparing equal numbers of 1N and multi-N cells per biological replicate and cell area bin. Cell area bins with less than 10 cells per biological replicate were removed from the analysis. Also here, the sample size was set by the smallest population size (1N or multi-N population) and the number of iterations was equal to the difference between the populations multiplied by 10.

Single-molecule tracking analysis

Single-molecule tracking data was analyzed as previously described (Mäkelä and Sherratt, 2020). Candidate fluorescent spots were detected using band-pass filtering and an intensity threshold for each frame of the time-lapse sequence. These initial localizations were used as starting positions in phasor spot detection for high-precision localization (Martens et al., 2018). Individual molecules were then tracked in each cell area by linking positions to a trajectory if they appeared in consecutive frames within a distance of 0.8 µm. Cell areas were detected from bright-field images using MicrobeTracker (Sliusarenko et al., 2011). In the case of multiple localizations within the tracking radius, these localizations were omitted from the analysis. Tracking allowed for a single frame disappearance of the molecule within a trajectory due to blinking or missed localization. The mobility of each molecule was determined by calculating an apparent diffusion coefficient, D_a, from the stepwise mean-squared displacement (MSD) of the trajectory using:

where x(t) and y(t) indicate the coordinates of the molecule at time t, Δt is the frame rate of the camera, and n is the total number of the steps in the trajectory. Trajectories with less than 9 displacements were omitted due to the higher uncertainty in D_a.

The calculated D_a are expected to reflect different dynamic states of molecules. To determine the fraction of molecules in each state, log₁₀ transformed D_a data (Figure 2D) was fitted to a Gaussian mixture model (GMM) using the expectation-maximization algorithm (Bishop, Christopher, 2006). A mixture of 3 Gaussian distributions with free parameters for mean, SD, and weight of each state were fitted for different conditions (Figure 2D). Additionally, for 1N cells, single-molecule tracking data were binned and fitted as a function of cell area (Figure 2D – supplement 3). To determine the active RNAP or ribosome fraction of a single cell, the GMM was used to determine the state of each molecule from the measured D_a, and the fraction of molecules in the slowest (“active”) state was calculated. Only cells with at least 50 trajectories were considered in the analysis for more accurate quantification. The total quantity of active molecules was estimated by multiplying the measured total fluorescence intensity with the measured active fraction as a function of the cell area.

Sample preparation for liquid chromatography coupled to tandem mass spectrometry (LC-MS/MS)

CRISPRi oriC (SJ_XTL676) cells were collected 0, 120, 180, 240 and 300 min after addition of 0.2% arabinose, while CRISPRi ftsZ (SJ_XTL229) cells were collected after 0, 60, and 120 min of induction, and pelleted. Cell pellets were lysed in 1% SDS at 95°C for 10 min (with vigorous intermittent vortexing and in the presence of 5 mM β-mercaptoethanol as a reducing agent). Cell lysates were cleared by centrifugation at 15000 x g for 30 min at 4°C. The lysates were alkylated with 10 mM iodoacetamide for 15 min at room temperature, and then precipitated with three volumes of a solution containing 50% acetone and 50% ethanol. Precipitated proteins were re-solubilized in 2 M urea, 50 mM Tris-HCl, pH 8.0, and 150 mM NaCl, and then digested with TPCK-treated trypsin (50:1) overnight at 37°C. Trifluoroacetic acid was added to the digested peptides at a final concentration of 0.2%. Peptides were desalted with a Sep-Pak 50 mg C18 column (Waters). The C18 column was conditioned with five column volumes of 80% acetonitrile and 0.1% acetic acid, and then washed with five column volumes of 0.1% trifluoroacetic acid. After samples were loaded, the column was washed with five column volumes of 0.1% acetic acid followed by elution with four column volumes of 80% acetonitrile and 0.1% acetic acid. The elution was dried in a Concentrator at 45°C. Peptides (20 µg) resuspended in a 100-mM triethylammonium bicarbonate solution were labeled using 100 µg of Thermo TMT10plex™ in a reaction volume of 25 µl for 1 h. The labeling reaction was quenched with 8 µL of 5% hydroxylamine for 15 min. Labeled peptides were pooled, acidified to a pH of ∼2 using drops of 10% trifluoroacetic acid, and desalted again with a Sep-Pak 50 mg C18 column as described above. TMT-labeled peptides were pre-fractionated using a Pierce™ High pH Reversed-Phase Peptide Fractionation Kit. Pre-fractionated peptides were dried using a concentrator and re-suspended in 0.1% formic acid.

LC-MS/MS data acquisition

Pre-fractionated TMT-labeled peptides were analyzed on a Fusion Lumos mass spectrometer (Thermo Fisher Scientific) equipped with a Thermo EASY-nLC 1200 LC system (Thermo Fisher Scientific). Peptides were separated by capillary reverse phase chromatography on a 25 cm column (75 µm inner diameter, packed with 1.6 µm C18 resin, AUR2-25075C18A, Ionopticks). Electrospray Ionization voltage was set to 1550 V. Peptides were introduced into the Fusion Lumos mass spectrometer using a 180 min stepped linear gradient at a flow rate of 300 nL/min. The steps of the gradient were as follows: 6–33% buffer B (0.1% (v/v) formic acid in 80% acetonitrile) for 145 min, 33-45% buffer B for 15 min, 40-95% buffer B for 5 min, and 90% buffer B for 5 min. Column temperature was maintained at 50°C throughout the procedure. Xcalibur software (Thermo Fisher Scientific) was used for the data acquisition and the instrument was operated in data-dependent mode. Advanced peak detection was disabled. Survey scans were acquired in the Orbitrap mass analyzer (centroid mode) over the range of 380 to 1400 m/z with a mass resolution of 120,000 (at m/z 200). For MS1 (the survey scan), the normalized AGC target (%) was set at 250 and the maximum injection time was set to 100 ms. Selected ions were fragmented by the Collision Induced Dissociation (CID) method with normalized collision energies of 34 and the tandem mass spectra were acquired in the ion trap mass analyzer with the scan rate set to “Rapid”. The isolation window was set to 0.7 m/z. For MS2 (the peptide fragmentation scan), the normalized AGC target (%) and the maximum injection time were set to “standard” and 35 ms, respectively. Repeated sequencing of peptides was kept to a minimum by dynamic exclusion of the sequenced peptides for 30 s. The maximum duty cycle length was set to 3 s. Relative changes in peptide concentration were determined at the level of the MS3 (reporter ion fragmentation scan) by isolating and fragmenting the five most dominant MS2 ion peaks.

Spectral searches

All raw files were searched using the Andromeda engine (Thomason, Costantino, and Court 2007) embedded in MaxQuant (v2.3.1.0) (Cox and Mann, 2008). A Reporter ion MS3 search was conducted using 10plex TMT isobaric labels. Variable modifications included oxidation (M) and protein N-terminal acetylation. Carbamidomethylation of cysteines was a fixed modification. The number of modifications per peptide was capped at five. Digestion was set to tryptic (proline-blocked). Database search was conducted using the UniProt proteome Ecoli_UP000000625_83333. The minimum peptide length was seven amino acids. The false discovery rate was determined using a reverse decoy proteome (Elias and Gygi, 2007).

Proteomics data analysis

Normalization and protein slope calculations were performed as described previously (Lanz et al., 2022). In brief, the relative signal difference between the TMT channels for each peptide was plotted against the normalized cell area for each of the bins of E. coli cells. For protein detection, we used a minimum of three unique peptide measurements per protein as a threshold. To derive the protein slope values shown in Figure 5, individual peptide measurements were consolidated into a protein level measurement using Python’s groupby.median. Peptides with the same amino acid sequence that were identified as different charge states or in different fractions were considered independent measurements. We summarized the size scaling behavior of individual proteins as a slope value derived from a regression. Each protein slope value was based on the behavior of all detected peptides.

For a given protein, we calculated the cell size-dependent slope as follows:

y_i = relative signal in the i^th TMT channel (median of all corresponding peptides in this channel)

x_i = normalized cell size in the i^th TMT channel (cell area for a given timepoint / mean cell area for the experiment)

The protein slope value was determined from a linear fit to the log-transformed data using the equation:

Variables were log-transformed so that a slope of 1 corresponds to an increase in protein concentration that is proportional to the increase in cell volume, and a slope of -1 corresponds to 1/volume dilution. Pearson correlation coefficients and p values were calculated using SciPy’s pearsonr module in Python (Virtanen et al., 2020). The results were reproducible across the two replicates (Figure 5 – figure supplement 1).

Estimation of protein abundance using summed ion intensity

MS1-level peptide ion intensities from experiment #1 were used to estimate the relative protein abundance. For each protein, all peptide intensities were summed together using the “Intensity” column of MaxQuant’s evidence.txt file. To adjust for the fact that larger proteins produce more tryptic peptides, the summed ion intensity for each protein was divided by its amino acid sequence length.

Calculation of distance from oriC

Gene coordinates were downloaded from EcoCyc database. The midpoint of each coding sequence was used to determine the circular distance (in base pairs) from oriC (base pair 3,925,859 of the total length of 4,641,652). A script was written to make three distance calculations. First, the direct distance (the midpoint of each gene minus 3,925,859 bp (oriC)) was determined. Next, the midpoint coordinate of each gene was subtracted by the total genome length (4,641,652 bp) and then subtracted again by the coordinate of oriC (3,925,859 bp). Finally, the midpoint coordinate of each gene was added to the total genome length (4,641,652 bp) and then subtracted by the coordinate of oriC (3,925,859 bp). The absolute values of these three calculations were then taken and the minimal values represent the circular distances between oriC and each gene.

Sample preparation for RNA-seq experiments

CRISPRi oriC strain (SJ_XTL676) was grown in M9glyCAAT at 37°C and cells were collected 60, 120, 200, and 240 min after addition of 0.2% L-arabinose. Images of cells were acquired at each timepoint to determine cell area, as described above. For each timepoint, the aliquot was spun down, the supernatant was removed, and the pellet was flash-frozen. E. coli pellets were resuspended in ice cold phosphate buffer saline solution (PBS) and mixed with C. crescentus cells in approximately a 1-to-1 ratio based on OD₆₀₀. C. crescentus cells were originally included with the intent of using them as a spike-in reference. However, the fraction of final reads obtained from C. crescentus transcripts was inconsistent with the initial mixing ratios. In addition, without knowing the exact DNA concentration in each 1N-rich cell sample, this spike-in became purposeless and thus was ignored for analysis. Cells (50 µL) in PBS were mixed with 250 µl TRI Reagent (Zymo Research) and lysed by bead beating on a Fastprep 24 (MPbio). Cell debris were pelleted (14k rpm, 2 min) and the supernatant was recovered. RNA was then extracted using the direct-zol RNA microprep kit (Zymo Research). Ribosomal RNA (rRNA) was then depleted using the NEBNext rRNA Depletion Kit for Bacteria (NEB, #E7850) and NEBNext Ultra II Directional RNA Library Prep Kit for Illumina (NEB, #E7760) was then used to prepare libraries for paired-end (2x150bp) Illumina sequencing (Novogene).

RNA-seq data analysis

A combined genome file of E. coli K-12 MG1655 and C. crescentus NA1000 with gene annotations was generated using a previously described approach (Swaffer et al., 2023). Read mapping statistics and genome browser tracks were generated using custom Python scripts. For quantification purposes, reads were aligned as 2x50mers in transcriptome space against an index generated from the combined gene annotation model using Bowtie (version 1.0.1 ; settings: -e 200 -a -X 1000) (Langmead et al., 2009). Alignments were then quantified using eXpress (version 1.5.1) (Roberts and Pachter, 2013) as TPM (Transcripts Per Million). TPM values were then recalculated after filtering for only E. coli genes. E. coli genes with TPM values below 1 were then removed from analysis.

The RNA slope (i.e., relative transcript concentration vs. cell area) was calculated for each gene as follows. TPM values were normalized to the mean of all values for that gene and then log2 transformed. The same normalization was applied to the cell area measurements for each condition. A linear model was fitted to the normalized log2 data and the slope of the linear regression was taken as the RNA slope.

Mathematical model and simulations

Phenomenological model: We developed a phenomenological model to illustrate cell growth dynamics. In our models, the number of mRNA (X) and the number of protein (Y) in the cell are described by the differential equations:

where , , α_RNAP(X, Y) is the fraction of active RNA polymerases, α_ribo(X, Y) is the fraction of active ribosomes, and, is the mRNA degradation rate. We assumed that the protein degradation is negligible because most bacterial proteins are stable (Balakrishnan et al., 2022; Lin and Amir, 2018). For the fraction of active RNAPs, we considered two different models (models A and B). In model A, the fraction of active RNAPs was modeled by . In model B, where we included different states of RNAP and promoter, the expression of α_RNAP is more complicated and is described in Appendix 2. For both models, the ribosomes were modeled by . We used [Z] and [X] to represent the genome and mRNA concentrations, respectively. We assumed that the cell volume (V) and cell area (A) are proportional to the protein number Y, which is a good approximation (Basan et al., 2015; Kubitschek et al., 1984). While this assumption has not been verified in 1N cells, the concentration of ribosomes, which constitute most of the protein mass, were found to remain constant in these cells (Figure 2A). Namely, in our model, V = cY and A = c′Y with constants c, c′. Under balanced growth conditions, [Z] was assumed to be constant. For the DNA-limited growth condition (as in 1N cells), we assumed that the genome does not duplicate and is kept at a single copy per cell ((t) = 1) while the cell volume continue to increase. The details for parameters used in this model are described in Table 1.

Numerical simulations: To simulate the model for balanced and DNA-limited growths, we first fixed a parameter set based on the literature (see Tables 1 and 2) and simulated Eq. 1 and Eq. 2 to reach the regime of balanced growth. Under balanced growth, we obtained the balanced growth vector (X^∗, Y^∗) where Y^∗ matches the initial protein number reported in the literature (see Table 2). Then, using the balanced growth vector as the initial condition, we simulated the balanced growth and DNA-limited growth using different assumptions of genome content (t) (described in the previous paragraph). The simulation was performed using the MATLAB built-in function ode23 with relative and absolute errors of the numerical values to be 10^-4 and 10^-5, respectively. For each growth condition, we obtained growth trajectories >(t), Y(t)), and from Y(t), we calculated the cell volume V(t) and area A(t) as described above. For model A, the fraction of active RNAPs was calculated by , while for model B, it is calculated using a more complicated formula that take into account RNAP kinetics (see Appendix 2). For both models, the fraction of active ribosomes was calculated as .

Parameter fitting: For either model A or B, we fitted our simulation results to all the experimental data including growth curves, the fraction of active RNAPs, and the fraction of active ribosomes for 1N and WT or multi-N cells (six datasets in total); see Appendix 1 for the initial parameter estimation and Appendix 3 for the optimization procedure details. The optimized parameter sets (see Table 2) were used for the numerical simulations shown in Figure 4. Note that the optimized parameter set remained within the realistic range for cellular physiology (see Appendix 3 - figure 1 for comparison between original and optimized parameters).

Data availability

Microscopy image analysis code is available on the Jacobs-Wagner lab github repository (https://github.com/JacobsWagnerLab/published/tree/master/Makela_2023). The TMT-MS and RNA-seq data analysis and processing code is available at https://github.com/mikechucklanz/Proteome_size_scaling_Ecoli and https://github.com/georgimarinov/GeorgiScripts.

For this study, the following TMT-MS and RNA-seq data were generated. Dataset 1 includes the calculated protein slopes from 1N-rich and multi-N cells, the normalized protein proportions, the summed ion intensities for each protein as well as the distance of its gene from the origin of replication (oriC) and the GO-term analysis. Dataset 2 includes the calculated mRNA slopes, in comparison with the average protein slopes from 1N-rich cells. All sequencing data associated with this study were submitted to the GEO repository on 2/10/2024 (GEO: GSEXXXX—will be updated when available). The mass spectrometry proteomics data have been deposited to the ProteomeXchange Consortium via the PRIDE partner repository with the dataset identifier PXD050093.

Acknowledgements

We thank Drs. Brun, Jun, Marczynski, Shapiro and Weisshaar for sharing published strains. We are grateful to Dr. Lavis for the gift of JF549 and Dr. Badrinarayanan for valuable discussion. We would also like to thank the Jacobs-Wagner laboratory for support, discussion, and critical reading of the manuscript. C.J.-W. is an investigator of the Howard Hughes Medical Institute. JM and AP contributed equally to this work.

Note

This reviewed preprint has been updated to add an equal contribution statement to the acknowledgements.

Supplementary figure legends

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Figure 5 – figure supplement 2.