High Osmolarity Modulates Bacterial Cell Size through Reducing Initiation Volume in Escherichia coli

Bacterial cell size depends on growth rate, cell cycle progression, and the cell volume per origin upon initiating chromosome replication (initiation volume). Here, we perform the first systematic and quantitative study of the effect of hyperosmotic stress on the E. coli cell size and cell cycle. We find that hyperosmotic stress significantly reduces the initiation volume. The reduced initiation volume is attributed to the increased DnaA concentration caused by water loss at high osmolarity, indicating a fundamental role of water content in cell size and cell cycle regulation.

A quantitative understanding of the cell size regulation remains a fundamental challenge in biology. Bacteria manage to coordinate biomass growth with cell cycle progression to achieve size homeostasis (1)(2)(3)(4)(5). The C period (the period required for chromosome replication) and the D period (the period between the completion of chromosome replication and cell division) are two key stages of bacterial cell cycles (6,7). The bacterial cell size is linked to growth rate and cell cycle progression by the following empirical equation: where V is the average cell size (volume) at division; V i is the average cell size per chromosome origin upon initiation of chromosome replication (referred to as "initiation volume" or unit cell), reflecting the timing of chromosome replication initiation; CϩD is the sum of the C period and D period (the time between replication initiation and the completion of cell division); and is the mass doubling time (8)(9)(10)(11). With the constancy of initiation volume and CϩD period, Equation 1 quantitatively explains the intriguing positive exponential correlation between cell size and growth rate under different nutrient conditions (2,3,8,9). Furthermore, recent phenomenological studies have confirmed that the cells initiate chromosome replication at a constant volume per origin under various growth perturbations and at the single-cell level (9)(10)(11). Those findings indicate the high robustness of Escherichia coli cells in controlling the timing of chromosome replication. With the constancy of initiation volume, bacterial cell size can be predicted given the information of growth rate and cell cycle parameters regardless of the actual growth conditions.
In previous studies, growth conditions used for studying cell size focused on extensive perturbations on biosynthetic pathways, including nutrient limitation, DNA replication limitation, transcription inhibition, translation inhibition, and perturbation of fatty acid synthesis and cell wall synthesis (5,9,12,13). In their natural habitat, bacterial cells frequently confront abruptly changing solute concentrations, which result in nonoptimal osmolarity (14). For example, E. coli encounters hyperosmotic stress when infecting the urinary tract due to the high osmolarity of the bladder and urine (15)(16)(17). The high salt contained in a Western diet has also been found to significantly affect the physiology of the gut microbiome, further accelerating the emergence of various human disorders (18). The effect of hyperosmotic stress is highly attractive since it profoundly affects the cellular water content, which is the basis of life (19)(20)(21). Water content accounts for the majority of the bacterial cellular mass and is the predominant factor that sets the total cellular volume of bacterial cells (19,20). Under hyperosmotic stress, the rapid loss of both water and turgor pressure severely inhibits bacterial biomass growth (20). To cope with this severe physiological challenge, bacterial cells must initiate related stress response programs to accumulate osmolytes, such as potassium, glutamate, and trehalose, to reestablish the balance of external and internal osmolarity (22). However, this process only partially restores the water content and growth of bacteria (19,23).
Though hyperosmotic stress profoundly affects bacteria physiology through reducing the cellular water content, it remains unclear how it affects the cell size and cell cycle of bacteria. In this study, we quantitatively characterized the cell size and cell cycle progression of E. coli growing under hyperosmotic stress. We found that initiation volume strongly decreased under hyperosmotic stress, implying an important role of water in cell size regulation.

RESULTS
Cell size and cell cycle parameters under hyperosmotic stress. We focused on the wild-type E. coli K-12 MG1655 strain exponentially growing under hyperosmotic stress created by large amounts of sodium chloride (NaCl) (19). The growth rate of E. coli in LB medium decreased 70% from 0 M extra NaCl to 0.8 M extra NaCl (Fig. 1A). The cell size of E. coli in various osmolarities was then measured using phase-contrast microscopy and the ImageJ software (Fig. 1B). The cell size of E. coli steadily decreases at high osmolarity (Fig. 1C). A similar result was also obtained for cells growing in glucose medium (see Fig. S1A and B in the supplemental material).
We next characterized related cell cycle parameters of E. coli growing under hyperosmotic stress. The C period was measured by the ori-ter method using quantitative PCR (qPCR). Strikingly, the C period of E. coli growing in LB medium increases by almost 4-fold (from 34 min to 128 min) from 0 M extra NaCl to 0.8 M extra NaCl, indicating that the movement of replication forks greatly slowed down under hyperosmotic stress ( Fig. 2A). This result for the C period was further confirmed by the DNA increment method (Fig. S2). Hyperosmotic stress also causes a 4-fold increase in the D period (Fig. 2B). The increase in both the C and D periods was also found for cells growing in glucose medium (Fig. S1C to E). Overall, the time from chromosome replication initiation to the completion of cell division (CϩD period) was severely prolonged by hyperosmotic stress (Fig. 2C). The increased CϩD period further led to an increase in both the cellular DNA content per cell and chromosome origins per cell [equal to 2 (CϩD)/ ] ( Fig. 2D and E).
Decreased initiation volume under hyperosmotic stress. Based on the prediction of Equation 1, the increased 2 (CϩD)/ should in principle cause a remarkable increase of cell size under hyperosmotic stress if the initiation volume remains unchanged. However, cell size actually decreases under hyperosmotic stress (Fig. 1C). This result suggests that hyperosmotic stress causes a significant reduction in initiation volume. As shown in Fig. 3A, the initiation volume of cells decreases 50% from 0 M extra NaCl to 0.6 M extra NaCl, further reaching a lower bound at even higher NaCl concentrations. The decrease of initiation volume at high osmolarity has also been observed for cells growing in glucose medium (Fig. S1F). The decrease in initiation volume could be clearly judged from the correlation between cell size and2 (CϩD)/ . In normal osmolarity, the correlation between cell size and 2 (CϩD)/ is linear, indicating a constant initiation volume (black and gray symbols in Fig. 3B) (9,11,13). However, this linear correlation  was remarkably broken under hyperosmotic stress (red symbols in Fig. 3B). We further plotted the initiation volume versus cell size as another way to see the constancy of initiation volume at normal osmolarity, as well as its decrease at high osmolarity ( Fig. 3C and S3).
Increased DnaA concentration under hyperosmotic stress. One of the major physiological differences between cells growing in normal osmolarity and those growing at high osmolarity is the cellular water content. We added betaine, a strong osmoprotectant, to the high-osmolarity medium to restore the water content of E. coli (19). Since normal LB medium consists of betaine (24), we managed to perform the study in the morpholinepropanesulfonic acid (MOPS) glucose medium. As shown in Fig. 4A, the addition of betaine restored the initiation volume of cells growing at high osmolarity. Moreover, the cell growth, cell size, and cell cycle parameters were also restored by betaine (Fig. S4). Those results indicate a potential role of water in regulating bacterial cell size.
The decreased initiation volume suggests acceleration in the process of chromosome replication initiation at high osmolarity. One possibility is that the cellular concentration of the DnaA protein, the master regulator of chromosome replication initiation of E. coli, increases at high osmolarity. Previous studies have demonstrated that alterations in the DnaA levels could perturb the timing of the chromosome initiation process of E. coli (9,(25)(26)(27). To test the above-mentioned hypothesis, we measured the DnaA protein content using mass spectrometry. The DnaA content per optical density at 600 nm (OD 600 ) remains almost constant at different osmolarities (Fig. 4B). To obtain the DnaA concentration, we further deduced the relative water content of cells at different osmolarities. The product of the cell size and cell number per OD was used as the proxy of the water content (Fig. S5). As shown in Fig. S5B and F, the water content of E. coli decreases dramatically at high osmolarity, consistent with previous findings (19,21). Therefore, the relative DnaA concentration corresponds to the DnaA content per OD 600 normalized by the water content. As shown in Fig. 4C, the cellular DnaA concentration dramatically increases with higher osmolarity.  (Fig. 5B), while the cell size increased slightly (Fig. 5C). Strikingly, the C period increases strongly upon DnaA overexpression, being similar to the case of hyperosmotic stress (Fig. 5D). This indicates that DnaA can also affect the process of replication elongation. Instead, the D period is largely independent of the DnaA concentrations (Fig. 5E). The invariance of growth rate and delayed cell cycle (CϩD) with DnaA overexpression further lead to a 1.5-fold increase in the DNA content per cell and a Ͼ2-fold increase in the origins per cell ( Fig. 5F and G). The origins per cell increase strongly while the cell size changes only slightly upon DnaA overexpression, indicating a remarkable reduction in initiation volume. As shown in Fig. 5H, the initiation volume indeed significantly decreases under low degrees of DnaA overexpression, consistent with previous findings (26,27). Moreover, initiation volume reaches a lower bound at higher DnaA concentrations, similar to the finding under hyperosmotic stress (Fig. 3A).
If DnaA is indeed the limiting factor of initiation volume under hyperosmotic stress, artificial knockdown of DnaA expression is expected to restore the initiation volume. To test this hypothesis, we applied CRISPR-dcas9 system to repress the expression of DnaA protein using a tunable CRISPR interference (tCRISPRi)-dnaA strain (Fig. 6A) (28). The expression of DnaA protein (per OD 600 quantity) is repressed by the CRISPR-dcas9 system in an arabinose-dose-dependent manner at a fixed high osmolarity (LB plus 0.6 M NaCl). From 0% to 0.08% arabinose, the repression of DnaA expression is ϳ3-fold (red symbols in Fig. 6A). Moreover, in the absence of arabinose, the DnaA abundances (per OD quantity) of the tCRISPRi-dnaA strain at both normal osmolarity and high osmolarity are similar to those of wild-type cells (blue triangle and purple diamond in Fig. 6A). We next investigated related cell cycle parameters of the tCRISPRi-dnaA strain growing at a fixed high osmolarity (LB plus 0.6 M NaCl medium). The growth rate of E. coli cells remains constant while cell size increases slightly upon DnaA knockdown. Strikingly, DnaA knockdown at high osmolarity completely restores the C period (99 min) to its value at normal osmolarity (ϳ35 min) (Fig. 4D). This finding is consistent with the finding in DnaA overexpression study that DnaA inhibits the chromosome replication elongation. In contrast, the D period increases only slightly upon DnaA knockdown (Fig. 6E). The invariance of the growth rate and shortened CϩD period upon DnaA knockdown further lead to a 1.5-fold decrease in the DNA content per cell and a 2.5-fold decrease in the origins per cell (Fig. 6F and G). These measurements of cell cycle parameters allowed us to deduce the effect of DnaA knockdown on initiation volume. Under zero-arabinose conditions, the initiation volume of the tCRISPRi-dnaA strain at normal osmolarity (in LB medium) is half of what it is at high osmolarity (in LB plus 0.6 M NaCl medium) (Fig. 6H), the same as the case of wild-type cells (Fig. 3A). Strikingly, DnaA knockdown increases the initiation volume of E. coli by nearly 3-fold at high osmolarity. The initiation volume even exceeds the value of wild-type cells at normal osmolarity (ϳ0.6 M 3 ), reaching 0.85 M 3 at 0.08% arabinose. As a reference, we plotted the DnaA concentration (DnaA per OD normalized by water content, as shown in Fig. S5F) together with initiation volume (Fig. 6H). The plot clearly shows that initiation volume remarkably increases with decreasing level of DnaA.
Finally, we analyzed the quantitative correlation between the initiation volume and DnaA concentration under hyperosmotic stress, DnaA overexpression, and DnaA knockdown. Strikingly, the correlation of initiation volume versus DnaA under those three independent conditions collapses into the same curve (Fig. 7A), demonstrating an important role of DnaA concentration in setting the initiation volume. We also find that the correlation of initiation age and initiation timing versus (CϩD) period with DnaA concentration (Fig. 7B and C) under three conditions largely overlap each other. The above-mentioned results strongly support the idea that the increased DnaA concentration underlies the decreased initiation volume of E. coli upon hyperosmotic stress.  Fig. S5F). Data are average of the results from triplicates, with standard deviations being ϳ10%.

DISCUSSION
The concept of the constant initiation volume (or initiation mass), as described in Equation 1, was originally proposed by Donachie in 1968 to explain the exponential correlation between cell size and growth rate of bacteria under nutrient limitation (8,29,30). Donachie deduced the constant initiation volume model through combining the cell size data of Salmonella enterica serovar Typhimurium and the Cooper-Helmstetter model of cell cycle (29,30). Recent extensive quantitative studies have confirmed the constancy of initiation mass in various modes of growth limitation and at single-cell levels (9)(10)(11). In this study, we find that the initiation volume for E. coli is reduced by hyperosmotic stress, a stress condition that profoundly affects the cellular water content. The reduced initiation volume is attributed to the increased DnaA concentration caused by water loss at high osmolarity, indicating a fundamental role of water content in cell size and cell cycle regulation.
It should be noted that at normal osmolarity, the term of "initiation volume" is interchangeable with "initiation mass" due to the constancy of cell mass density (constant water content) (12,31). Donachie first used the term initiation mass (8) since the cell size data he used originated from Schaechter et al. (30), who took optical cell density/cell (cell mass) to represent cell size (6). However, in the case of changing osmolarity, initiation volume is no longer strictly proportional to initiation mass because of the altered dry mass density. To investigate this issue, we measured the dry mass/OD 600 of E. coli cells growing at different osmolarities. Dry mass/OD 600 remains nearly constant at different osmolarities (black circles in Fig. S6A); therefore, the dry mass density (normalized by water content) strongly increases at high osmolarity (red circles in Fig. S6A). In this case, the initiation mass (the product of initiation volume and dry mass density) still remains constant at different osmolarities (black diamond in Fig. S6) (9), confirming that the theory of constant initiation mass holds true even if cell size changes due to altered water content.
Our study combining hyperosmotic stress, DnaA overexpression, and DnaA knockdown firmly establishes the quantitative correlation between initiation volume and  (Fig. 7A), in which the initiation volume can be modulated at a range of 3-fold by perturbing the DnaA concentrations. Those results clarify the important role of DnaA in controlling initiation volume and support the threshold initiation model regarding the regulation of the timing of chromosome replication initiation (9,32,33). In the threshold initiation model (Fig. 7D), E. coli cells reach initiation volume when they have accumulated a fixed threshold number (N i *) of chromosome replication initiators (e.g., the ATP form of DnaA). Furthermore, in normal osmolarity, the DnaA concentration (c dna ), is supposed to remain constant under different growth conditions, leading to the constant initiation volume (mass) as found in previous studies (9,(34)(35)(36). However, in the case of high osmolarity, c dna increases due to water loss. Therefore, the accumulation speed of replication initiators per cell in high osmolarity (red line in Fig. 7D) is faster than it is in normal osmolarity (green line in Fig. 7D). In this case, N i * could be reached at a smaller initiation volume in high osmolarity (red rectangle in Fig. 7D) than it could in normal osmolarity (green rectangle in Fig. 7D). The reduced initiation volume ultimately leads to a smaller cell size of E. coli at high osmolarity.
Our study has also found that hyperosmotic stress significantly prolongs the C and D periods ( Fig. 2A to C). The prolonged C period has also been observed in the case of DnaA overexpression (Fig. 5D). Moreover, knockdown of DnaA expression at high osmolarity completely restores the C period to normal value (Fig. 6D), indicating that the increased DnaA concentration plays a major role in prolonging C period at high osmolarity. This finding suggests a new role of the DnaA protein in regulating the chromosome replication elongation process beyond regulating the replication initiation. One possibility is that alteration of the DnaA protein level significantly perturbs the intracellular dinucleoside triphosphate (dNTP) substrate pools, further affecting the replication elongation rate. This effect could be achieved if DnaA directly regulates the expression of ribonucleotide reductase (RNR), the rate-limiting enzyme in dNTP synthesis, as suggested by previous studies (13,37). Another possibility is that DnaA directly binds to the chromosome, further interfering with the replication elongation process. Hyperosmotic stress also causes an increased D period, suggesting its inhibitory effect on the cell division process. Previous studies have shown that titration of cell division-related protein, such as FtsZ or MreB, could significantly perturb the D period (9,11). In light of this, it is possible that the expression of related protein decreases at high osmolarity. It is also possible that the increased intracellular osmolyte pools (potassium and glutamate) at high osmolarity have a direct inhibitory effect on the cell division process.

MATERIALS AND METHODS
Strains and growth medium. The strains used in this study include the E. coli wild-type K-12 MG1655 strain, its DnaA overexpression strain derivative, the FL68 strain, as well as the its DnaA knockdown derivative, the tCRISPRi-DnaA strain. The media used in this study are routine LB medium and MOPS-buffered glucose minimal medium (Coolaber Beijing) as described by Dai et al. (38,39) and Basan et al. (12). Different concentrations of sodium chloride (NaCl) were supplemented to the medium to adjust the osmolarity.
To construct a DnaA overexpression strain, the coding sequence of dnaA was directly fused with Plac promoter through overlapping PCR (Green golden PCR mix; Tsingke Biotech, China). The fused Plac-dnaA cassette was inserted into the HindIII/SpeI sites of the pBBR1-MCS plasmid, resulting in the pBBR1-dnaA vector. The PlacI-lacI cassette was PCR amplified using the MG1655 genome as the template and inserted into the KpnI/HindIII sites of pBBR1-dnaA to obtain the pBBR-lacI-Plac-dnaA vector. The pBBR-lacI-Plac-dnaA vector was then transformed into the wild-type MG1655 strain, generating the FL68 strain.
The tCRISPRi-DnaA strain (MG1655 background) used for DnaA knockdown study was kindly provided by Suckjoon Jun and Fangwei Si (UCSD). The detailed information of this strain is described in studies by Si et al. (9) and Li et al. (28).
Cell growth. Cell growth was performed in a 37°C air bath shaker (220 rpm). A standard cell growth procedure contains three steps, seed culture, preculture, and experimental culture. Cells from a fresh colony in the LB plate were inoculated into LB broth plus 0.3 M NaCl medium (for early adaptation to the high osmolarity) and grown for several hours as seed culture. Seed cultures were then transferred into the medium of the final experimental culture (e.g., high-osmolarity medium) and grown overnight at 37°C as preculture. In the next day, the overnight precultures were inoculated into the same medium as for the preculture at an initial OD 600 of ϳ0.015 as experimental culture. For each condition, we took at least six OD 600 points (range, 0.05 to 0.5) to obtain an exponential-growth curve for the calculation of growth rate. The OD 600 was measured using a Thermo Scientific Genesys 30 spectrophotometer.
Cell size measurement. Five microliters of cell culture at an OD 600 of ϳ0.3 was applied to a slide glass covered with a thin layer of agar (the agar immobilizes the cells). Cells were imaged using phase-contrast mode of a Nikon Eclipse Ti-80 microscope. For each condition, the images of 500 to 1,000 individual cells were taken. Cell length (L) and width (W) were extracted using the ImageJ software. The cell volume (V) was calculated using the equation V ϭ W 2 ⁄4 ϫ ͩ L Ϫ W 3 ͪ .

Measurement of cell cycle parameters and DNA content.
The C period is measured by two methods. The first method is measuring the ori-to-ter ratio by qPCR. The total genomic DNA of E. coli was extracted using a bacterial total genome DNA extraction kit (Tiangen Biotech Co., Ltd.). The primers (Tsingke Biotech Co.) used for amplifying the DNA region proximal to the origin (oriC) and terminus (ter) are 3923874fw (5=-GCCCTGTGGATAACAAGGAT-3=) and 3923874rv (5=-CCTCATTCTGATCCCAGCTT-3=) for oriC, and ter-fw (5=-TCCTCG CTGTTTGTCATCTT) and ter-rv (5=-GGTCTTGCTCGAATCCCTT) for ter. The qPCR reactions were performed using a SYBR green premix (Yeasen Biotech, Shanghai, China), according to the instruction manual. The qPCR reaction was carried out in a Bio-Rad CFX96 Touch real-time PCR system with the following procedures: 95°C for 15 min, followed by 40 cycles of 95°C for 30 s, 60°C for 30 s, and 72°C for 30 s. Calculation of the C period is based on ori⁄ter ϭ 2 ͑C⁄͒ (6,13,40).
To further confirm the C period data obtained by qPCR method, we used a second method, the DNA increment method as described by Churchward and Bremer (41) and Bipatnath et al. (42), to measure the C period. This method is based on measuring the DNA increment after blocking DNA initiation of exponentially growing E. coli cells by the addition of 300 g/ml chloramphenicol or 200 g/ml rifampin (runoff experiments). The change in relative DNA amount after DNA initiation blockage corresponds to origins (ori)/genome equivalent.
The total DNA content per OD 600 was measured by the diphenylamine colorimetric method, as detailed by Basan et al. (12). DNA content per cell was obtained through measuring total DNA amount per OD and cell number per OD through plating and a bacterial counting chamber by using microscopy. The origins (ori)/cell was obtained by multiplying genome equivalents per cell by calculating the ori-to-genome equivalent ratio. The D period is calculated based on the equation ori⁄cell ϭ 2 ͑CϩD͒⁄ (6,13,40).
The average initiation timing of the population was obtained using the equation t i ϭ N_oc ϫ -(CϩD), where N_oc is the number of overlapping cell cycles, equal to ceiling [(CϩD)/]. Ceiling means the smallest integer that is larger than a specific value. The average initiation age, ␣ (0 Ͻ ␣ Ͻ 1) equals t i / (6,9).
Measurement of cellular DnaA abundance. The level of DnaA protein was measured by quantitative mass spectrometry using the 15 N-labeling method, as described by Hui et al. (43). The samples were analyzed on an AB Sciex TripleTOF 5600 system (AB Sciex, Framingham, MA). For the 15 N reference cell sample, we used the cell culture growing exponentially in MOPS glucose medium (with 15 NH 4 Cl as the nitrogen sources). Three hundred micrograms of the 15 N reference cell sample (or labeled cell sample) was mixed with 300 g of each of the 14 N cell samples (or nonlabeled cell samples) growing in LB medium supplemented with different levels of sodium chloride. The mixed sample was then subject to trichloroacetic acid (TCA) and trypsin digestion, as detailed by Hui et al. (43). The mass spectrometry experiments and raw mass spectrum data files were processed similarly to those in a study by Hui et al. (43) to obtain the ratio of the 14 N-nonlabeled to 15 N-labeled peaks for each individual detected peptide, which gives the information of the relative abundance of related protein of each condition. For the DnaA protein, the relative protein abundance data were obtained as a ratio by taking the median of the ratios of its peptides. To guarantee that the ratio data are solid, only those DnaA data with at least three peptides detected were used. In addition, for the ratio data, if one or more of its quartiles lie outside the 50% range of its median, we treat the data as poor quality data and do not use it.
Measurement of cellular dry mass/OD 600 . The measurement of cellular dry mass is performed as the same as described by Basan et al. (12). Briefly, 200 ml to 250 ml cell culture was grown to exponential phase (OD 600 , ϳ0.4) and was collected by centrifugation. The supernatant was completely and carefully removed. The cell pellets were further suspended in 2 ml double-distilled water (ddH 2 O), transferred to aluminum pans, and baked overnight under 70°C to reach constant weight, which corresponds to the dry mass. The exact OD 600 value was recorded at the beginning and further calibrated with the cell culture lost (OD 600 ) in each step to obtain the accurate OD 600 value of the cell pellet determined for dry mass.