Control of Bacillus subtilis Replication Initiation during Physiological Transitions and Perturbations

High-throughput, quantitative approaches have enabled the discovery of fundamental principles describing bacterial physiology. These principles provide a foundation for predicting the behavior of biological systems, a widely held aspiration. However, these approaches are often exclusively applied to the best-known model organism, E. coli. In this report, we investigate to what extent quantitative principles discovered in Gram-negative E. coli are applicable to Gram-positive B. subtilis. We found that these two extremely divergent bacterial species employ deeply similar strategies in order to coordinate growth, cell size, and the cell cycle. These similarities mean that the quantitative physiological principles described here can likely provide a beachhead for others who wish to understand additional, less-studied prokaryotes.

subtilis and E. coli follow the same phenomenological principle of cell size homeostasis known as the adder principle (5,6). Furthermore, the two organisms share identical mechanistic origins of the adder principle, namely, a molecular threshold for division proteins and their balanced biosynthesis during growth (7). On the basis of these findings, we wanted to know to what extent B. subtilis and E. coli coordinate growth, size, and cell cycle in the same manner. A shared coordination framework would imply that, despite phylogenetic and molecular diversity, physiological regulation in bacteria is functionally conserved.
In order to create a full complement of the data necessary for comparative analysis, we measured the growth and cell cycle parameters of B. subtilis at both the population and single-cell levels under a wide range of conditions.
Previous population-level studies found that B. subtilis, like E. coli, initiates replication at a fixed mass, establishing a regulatory bridge between cell size and cell cycle control (8)(9)(10). We extended this avenue with single-cell methods to precisely measure the cell cycle parameters in individual B. subtilis cells across conditions (7,11). These results showed that the initiation size per ori (s i ) is constant under steady-state conditions as well as during nutrient shifts between two steady-state conditions. This strongly supports a threshold model for initiation in both static and dynamic environments (3,7,12,13).
The single-cell approach also allowed us to compare the relative levels of variability of all growth and cell cycle parameters both between conditions and between species. These measurements reveal strikingly similar hierarchies of physiological parameters between B. subtilis and E. coli in terms of the tightness of their control.
The richness of our quantitative physiological data generated in B. subtilis is comparable to that in E. coli, providing key evidence that B. subtilis and E. coli share core phenomenological and quantitative principles that govern their physiology. These principles provide a unified picture of bacterial growth, size, and cell cycle coordination.

RESULTS AND DISCUSSION
Ensuring steady-state growth in B. subtilis. Maintaining steady-state growth is essential for reproducible measurements of the physiological state of the cell (1). In steady-state growth, the total biomass of the culture increases exponentially with time and protein biosynthesis is balanced with the total biomass increase. That is, the protein production rate is the same as the growth rate of the cell. As a result, average protein concentrations are constant, whereas the total amount of proteins increases in proportion to the cell volume. The constant concentration and the proportional increase also apply to other macromolecules such as DNA, RNA, phospholipids, and the cell wall.
To achieve steady-state measurements in B. subtilis, we grew and monitored cells over many generations using a multiplex turbidostat that we had previously used for E. coli (3) (Fig. 1A). For both the population and single-cell assays, we began cultures from single colonies and precultured cells using appropriate batch methods before transferring them to continuous culture setups (see Materials and Methods). To avoid sporulation, we ensured that the precultures did not enter stationary phase. We used a B. subtilis strain which was nonmotile and nonbiofilm forming to facilitate size measurements of single cells. This was necessary because B. subtilis exhibits a temporal chaining phenotype, particularly under conditions mediating faster growth (14,15). During chaining, cells are physically connected and yet their cytoplasms are compartmentalized, obfuscating a definition of division (16,17). Our strain contained a genetic modification to abolish cell chaining, ensuring that cell separation coincided with septation (18) (Materials and Methods).
To measure how long B. subtilis takes to reach physiological steady state, we measured growth rate continuously during time course experiments using our multiplex turbidostat. Growth rate generally stabilized after 6 generations, and the cell size distribution was reproducible (Fig. 1A). However, to be certain of steady-state growth, we typically waited for at least a total of 14 doublings before sample collection was performed in all our subsequent experiments. At collection, we split the culture for quantitative PCR (qPCR) marker frequency analysis and cell size measurement (see Table 1 for experimental conditions).
For single-cell measurements, we used the microfluidic mother machine to collect phase-contrast and fluorescent time-lapse images for at least 10 generations (7,19) (Fig. 1C). After analyzing durations of all cell lives, we limited our data to the time interval in which all measured parameters equilibrated (see Fig. S1    material). A typical experiment produced data for around 2,500 cells (see Table 2 for experimental conditions). We used custom software to extract single-cell data from raw images (20) (Materials and Methods). Growth law of cell size: B. subtilis size shows a positive but not exponential dependence on the nutrient-imposed growth rate. A foundational observation by Schaechter, Maaløe, and Kjeldgaard showed that the average cell size in E. coli increases exponentially with the nutrient-imposed growth rate (2). Previously, we investigated this "growth law of cell size" in E. coli under various growth and cell cycle inhibition conditions and showed that the exponential relationship was a special case wherein the growth rate was the only experimental variable (3). In B. subtilis, the Levin laboratory recently revisited the relationship between size and the nutrient-imposed growth rate and found that the average cell size in B. subtilis increased with the growth rate at the population level (21).
We extended our efforts in E. coli to B. subtilis. Using the multiplex turbidostat, we grew cells under 5 nutrient conditions with doubling times ranging between 28 and 62 min ( Fig. 1B; see also Materials and Methods and Table 1). Here, we used size interchangeably with volume and considered volume to be proportional to dry mass (22).
Panel A of Fig. 2 shows the average cell size versus growth rate under the 5 different growth conditions. As expected, the average cell size increased with growth rate.  The two-sided P value to reject the null hypothesis that the slope of C on growth rate is zero is 0.55 using the Wald test. The constancy is less clear for B. subtilis, with a P value of 0.13 for the same test. Though lower, it is still not enough to reject the null hypothesis that the slope is zero. However, single-cell data show that C ϩ D is proportional to generation time (Fig. S5). B. subtilis growth media are colored as described for Fig. 1B, with additional LB data in gray. The E. coli data are from previously published work (3). Red, synthetic rich; orange, glucose with 12 amino acids; yellow; glucose with 6 amino acids; green, glucose; blue, glycerol. Additional conditions are indicated in gray.
However, the exponential dependence observed for E. coli was less clear in B. subtilis. This difference in B. subtilis could have been due to changes in the durations of replication (C period) and cell division (D period) under different nutrient conditions (3). We thus measured the population average C period of B. subtilis employing qPCR marker frequency analysis (3,9,23). The two species exhibited similar maximum replication speeds (approximately 40 min for the C period). However, our data for B. subtilis are too sparse to determine if or for which growth rates the C period was constant (Fig. 2B).
Unfortunately, despite extensive efforts, we were unable to reliably measure the D period in B. subtilis from the population samples as we had done previously for E. coli (3). The main issue was a lack of consistency of fluorescence labeling of the DNA required for flow or image cytometry. Our results were variable from experiment to experiment and from protocol to protocol. We therefore concluded that the measurement of D period using population methods was not as reliable as needed to test the growth law of cell size in B. subtilis, a cautionary reminder in interpreting previous measurements in B. subtilis. For these reasons, we set out to measure the B. subtilis cell cycle explicitly at the single-cell level.
Single-cell determination of cell cycle parameters in B. subtilis. We employed a functional replisome protein fused with a fluorescent marker, DnaN-mGFPmut2, to measure cell cycle progression in single cells (7,24) (Materials and Methods). In B. subtilis, the replisomes from the two replication forks of a replicating chromosome are often colocalized; thus, most foci represent a pair of replisomes (25).
Panels A and B of Fig. 3 show representative cells under two growth conditions, succinate and glycerol rich, respectively. Under the condition mediating slower growth (succinate), cells were normally generated with one replicating chromosome. Replication initiation begins synchronously in the mother cell for two chromosomes. At that time, the origins are located toward the cell poles. Replication proceeds through cell division, at which point the replication forks reside near the midcell of the newly generated cell. Chromosome segregation is concurrent with replication. By the time the replication forks reach the terminus region, which is still at the midcell, the previously duplicated origins have already migrated to the cell poles (26).
It is common for initiation to have occurred in the previous generation even under conditions of slow growth (i.e., the total of the combined C and D periods [C ϩ D] is greater than the doubling time []). Yet cells rarely exhibit multifork replication. In multifork replication, initiation begins before the previous termination event completes, such that a single replicating chromosome possesses four or even eight copies of ori. Instead, B. subtilis normally initiates when the cell contains complete, homologous chromosomes where the copy number represents a power of 2. In fact, replication initiation often proceeds immediately after the previous termination event. This may be due to the role of YabA in B. subtilis replication initiation control, which ties DnaA activity to DnaN availability (27,28). Multifork replication is comparatively common in E. coli, where Hda is thought to play a similar but mechanistically distinct role in reducing initiation potential during ongoing replication (7,29).
Under conditions mediating faster growth (glycerol-rich conditions), cells are large and often born with two replicating chromosomes. These large cells then simultaneously initiate replication at four ori. However, the relative levels of variability between division size (S d ) and C ϩ D were greater under this rich condition. This means that a substantial fraction of the population was smaller and born with one replicating chromosome and consequently initiated at two ori (Fig. S8). Moreover, transient filamentation and asymmetrical septation are more common under conditions mediating fast growth, leading to the generation of cells born with numbers of replicating chromosomes which do not represent a power of 2.
Complementary ensemble determination of cell cycle parameters in B. subtilis. The main advantage of the single-cell approach is that it allows direct comparisons of the relationships between growth parameters, providing mechanistic insights (6).
However, it can be difficult to determine the cell cycle parameters directly, particularly when the foci are clumped or the signal is weak. This is especially true under conditions mediating faster growth. To ensure an unbiased analysis of the cell cycle, we also employed an ensemble method, compiling data from many individual cells and extracting the average cell cycle parameters (11) (Fig. 3C). We used the focus count at a given size as a proxy for the replication state (Materials and Methods). This method produces data similar to those generated by the original schematics used by Cooper and Helmstetter when they first elucidated the E. coli cell cycle (30). Under all conditions except those mediating the slowest growth, the measured average number of foci monotonically increases because initiation almost immediately follows termination, as discussed above. Unlike data corresponding to a theoretical single cell, the ensemble plots do not display a strict step-like behavior; we interpret this as variability in the initiation size. Ensemble plots determined under all conditions, along with the focus localization patterns, are presented in Fig. S4. The data are in good agreement with the average initiation size as measured from individual cells. We used these complementary methods to test whether the initiation size in B. subtilis is as invariant as in E. coli (3).
Invariance of initiation size: B. subtilis initiates at a fixed cell size per ori. The concept of a conserved initiation size in E. coli and S. enterica serovar Typhimurium was first explained by Donachie as a consequence of the growth law of cell size and the constant C ϩ D (2,8,30). The upshot is that, at a fixed size per origin (ori), all origins of replication fire simultaneously. Recent high-throughput work performed at both the single-cell and population levels (3,7,11) conclusively showed that the early insight reported by Donachie was correct. In fact, the initiation size per ori is invariant not only across nutrient conditions but also under conditions of antibiotic inhibition and genetic perturbations (3).
The constancy of initiation size in B. subtilis at the population level under nutrient limitation conditions was previously tested by several groups (9,10,31). In nutrient limitation, the initiation size was found to be constant, though it can be decreased in some mutants. We measured the initiation size using single-cell methods under nutrient limitation and translational inhibition conditions ( Table 2). We found that the initiation size per ori in B. subtilis is indeed invariant across conditions, even for individual cells (Fig. 4A).
This constant initiation size is in stark contrast to the varying C period seen under different growth conditions (Fig. S5A). In fact, initiation size is one of the least variable physiological parameters along with septum position and width (Fig. S8). The single-cell approach also allowed us to measure the correlations between all growth and cell cycle parameters. The initiation size was found to correlate only weakly with other measured parameters (Fig. S9).
These observations are consistent with a threshold model for replication initiation (3,7,32). Within that framework, initiator molecules accumulate in a manner proportional to the growth rate. This mechanism is employed in single cells and is in turn apparent at the population level.
Initiation size is invariant at the single-cell level even during nutrient shifts. Because individual cells had shown a constant initiation size in the previous steadystate experiments, we wondered how cells would behave in a changing environment. Nutrient shift experiments have provided important insight into the coordination of biosynthesis and the cell cycle (33)(34)(35). We revisited this paradigm at the single-cell level, shifting cells from minimal media (time [] ϭ 65 min) to rich conditions ( ϭ 30 min) and back again (Fig. S6). By using the mother machine, we could add and remove nutrients immediately while measuring the cell cycle and all other physiological parameters (Materials and Methods).
The most drastic results occurred upon the shift down (Fig. 5). When nutrient supplements were removed, growth immediately paused. The crash in the growth rate caused a drastic increase in generation and cell cycle times for the cells which experienced the shift down. Replicating chromosomes were stalled, and division ceased (although division did occur immediately after the shift for the replication cycles already in D period). Strikingly, the growth pause led to an absence of initiation events until after cells restarted elongation and attained the requisite initiation size. Thus, individual cells maintained a constant initiation size through the transition.
Division also resumed after growth recommenced, but at a smaller cell size commensurate with the growth rate seen after the shift down. During the shift down, and despite the growth pause, the division rate per unit growth increases, while the initiation rate per unit growth stays constant. This means that the ori/cell ratio, which is high under conditions of fast growth, decreases until a new steady-state level is reached. The duration of the C ϩ D periods is also not constant during this time (Fig. S6).
The decoupling of initiation and division supports the idea that they are controlled by independent threshold mechanisms (7). That is, the cell builds up a pool of dedicated molecules for each task to reach a certain level (7,12,(36)(37)(38). For initiation, this threshold and the accumulation rate are conserved across growth conditions. For division, the threshold or the accumulation rate is set by the growth condition (39). In the generation after the shift down, cells grow much more slowly and therefore accumulate threshold molecules at a similarly depressed rate. As a result, both initiation and division are delayed. For division, active degradation or antagonization of FtsZ could further hinder the triggering of constriction (40,41).
E. coli and B. subtilis change cell shape differently under different growth conditions but maintain a constant initiation size. One of the major differences between E. coli and B. subtilis is that their cells change shape differently under different nutrient conditions. Data from our laboratory and others have shown that the aspect ratio of E. coli is nearly constant (at a value of approximately 4) under conditions of different nutrient-imposed growth rates (3,42). In contrast, the average width of B. subtilis remains relatively constant (Fig. S2) (10, 43).
Nevertheless, for initiation control in B. subtilis, we found that the volume per ori is more highly conserved than the length per ori at initiation. While we found length to be a good proxy for initiation size under conditions of nutrient limitation, our data show that chloramphenicol treatment decreased cell width in B. subtilis. Thus, across all growth conditions, only the initiation volume was constant (Fig. S5B to D).  (44). We extended previous analysis to include the cell cycle-related parameters C period, D period, initiation size, and added size (Δ d ) at initiation for both B. subtilis and E. coli. We found that the two evolutionarily distant organisms shared the same order of their physiological parameters in terms of CV (Fig. 6). Width, septum position, initiation size, and growth rate represented the most tightly controlled parameters. The D period was significantly more variable than the C period, and they are inversely correlated. In fact, the CVs of a particular physiological parameter were found to be extremely similar across growth conditions, species, and strains (Fig. S7). Because the imaging frequency    Fig. S6.

B. subtilis Single-Cell Initiation Control
® dictates the precision of our measurements, the actual CVs of the parameters are likely slightly (1% to 2%) lower than the values presented (Materials and Methods).
The CVs of the physiological parameters are not all independent, and we previously showed analytically how the generation time (), division size (S d ), birth size (S b ), and added size (Δ d ) are related (6). Qualitatively, this can be understood because, for example, the birth length is determined by the division length and the septum position. Therefore, the CV of birth length is greater than the CV of division length due to the contribution of the small variability in the septum position. Similarly, the CV of division size S d is larger than that of the initiation size S i because of the additional contribution from the variability of the C and D periods as well as the growth rate (). This can be seen most clearly for the conditions mediating slow growth with no overlapping replication cycles, where the division size is determined as S d ϭ S i exp[(C ϩ D)]. Therefore, the variabilities of C, D, , and S i all contribute to the variability of S d ; i.e., the variability of S d must be greater than that of S i .  Ultimately, the CV of the physiological parameters represents the manifestation of molecular regulatory mechanisms. Classically, B. subtilis and E. coli provide excellent examples of both homologous and nonhomologous versions of such mechanisms. For example, major protein players controlling replication and division, such as DnaA and FtsZ, are conserved in these and most other prokaryotes (45,46). However, the regulation of those molecules in B. subtilis and E. coli is unique (47)(48)(49). More generally, the two species often use unrelated mechanisms to achieve the same regulatory goal (49,50). Because of their phylogenetic distance, the uncanny agreement between the CVs of their physiological parameters suggests that an evolutionarily ancient control framework is shared by these organisms.
Summary and outlook. We have shown that B. subtilis and E. coli, despite their historical separation represented by the Gram stain divide, share extremely similar fundamental physiological behaviors (Fig. 7). Under a wide range of nutrient and growth inhibition conditions, both species base their chromosome replication on a constant initiation size. Impressively, this constant initiation size is imposed even during dynamic growth transitions.
Mechanically, our data support previous findings showing that B. subtilis is both a division adder and initiation adder (6,7,51) and therefore suggest that initiation is controlled in a manner similar to division. That is, the invariance of initiation mass can be explained by the following two requirements for the adder phenotype (7): (i) constant production of initiator molecules at the same rate as cell elongation ("balanced biosynthesis") and (ii) their accumulation to a threshold number to trigger initiation. For example, as the growth rate changes upon nutrient shift, the production of the initiator molecules changes by the same rate such that the concentration remains nearly constant. As long as the threshold number of the initiator molecules is independent of the growth condition, the initiation mass must remain invariant.
As with E. coli, DnaA and FtsZ are among the key proteins responsible for the initiation and division threshold mechanisms in B. subtilis, respectively (7,13,52). They can be considered initiator molecules, though not necessarily to the exclusion of others with which they work in concert. The view that global biosynthesis fundamentally controls their production, and thus the replication and division rate, is also compatible with the idea that additional levels of regulation modulate or coordinate their activity in certain situations (48,53  B. subtilis Single-Cell Initiation Control evolved to increase replication and division fidelity during steady-state or are more important in dynamic environments. More single-cell shift experiments performed with mutant or even minimal genome cells will help reveal the importance of redundant regulatory systems. This line of study can also experimentally address the limits on variability of physiological processes and why some cells seem to control some processes more tightly than others (54). These deep similarities between B. subtilis and E. coli speak to a conserved control framework which both species use to coordinate growth, DNA replication, and division. In doing so, they ensure that life's essential demand of physiological homeostasis is met. In the end, it is unclear if this framework is the result of parallel evolution or of convergent evolution. In order to better address this issue, more high-quality single-cell data are needed from diverse prokaryotes. In any case, the existence of a shared control framework underscores its efficacy, providing an intriguing avenue for the development of synthetic organisms.

Strains.
We used B. subtilis strains in the 3610 background with mutations to confer nonmotility and reduce biofilm formation, a kind gift from Petra Levin (6). The background strain contained comI(Q12L) to confer competence (55). Dan Kearns also graciously provided an inducible lytF construct to enable prevention of chaining (18). For the mother machine experiments in which replisomes were tracked, we used dnaN-mGFPmut2, an instrumental gift from Paul Wiggins and Alan Grossman (24,25). Strain construction was performed using single-crossover plasmid recombination or double-crossover recombination from genomic DNA (56).
For E. coli, we used a K-12 MG1655 strain containing a functional dnaN-YPet construct, considerately shared by Rodrigo Reyes-Lamothe (57). Strain genotypes for both species are provided in Table 3.
Growth media and experimental conditions. For B. subtilis, we used S7 50 medium with different carbon sources and supplements (Sigma-Alrich, MO). Importantly, we included additional iron(III) chloride and trisodium citrate. The latter acts as a siderophore for B. subtilis, and without it our strain cannot grow in the mother machine (58). To make rich conditions, we added 2 mg/ml Casamino Acids and 0.04 mg/ml tryptophan. For E. coli, we used MOPS (morpholinepropanesulfonic acid) glucose medium. Turbidostat and mother machine experiments used the same media with the following emendation: bovine serum albumin was added at 0.5 mg/ml during the mother machine experiments in order to reduce cell adherence to surfaces inside the device. Tables 4 and 5 provide detailed information on the composition of the media.  For both turbidostat and mother machine experiments, chloramphenicol was added at concentrations between 1 and 4.2 M during translational inhibition experiments. All experiments were performed at 37°C in a climate-controlled environmental room which housed the multiplex turbidostat and all optical components (Darwin Chambers Company, MO). Tables 1 and 2 enumerate experimental conditions and sample sizes for the turbidostat and mother machine experiments, respectively.
Microscopy configuration. We performed phase-contrast and fluorescent imaging on a Nikon Ti-E inverted microscope with Perfect Focus (PFS) and an LED transmission light source, controlled by Nikon Elements. For the turbidostat experiments, we used a PFS 2, CoolLED pE-100, 60ϫ, 1.4-numericalaperture (NA) Ph3 oil immersion objective (Nikon CFI Plan Apo DM Lambda 60ϫ Oil) and an Andor Technology Neo scientific complementary metal oxide semiconductor (sCMOS) camera. For fixed-cell phase-contrast imaging, we used exposure times between 50 and 100 ms and 100% transmission power.
For mother machine experiments, we used a PFS 3, Sutter Instruments TLED, 100ϫ 1.45-NA Ph3 oil immersion objective (Nikon CFI Plan Apo DM Lambda 100ϫ Oil), Photometrics Prime 95B sCMOS camera, and Coherent Obis 488LX laser for epifluorescent illumination. For laser epifluorescent illumination, we inserted a rotating diffuser in the optical train to reduce speckle. We also reduced the camera sensor region of interest to flatten the fluorescent illumination profile. We used a Chroma filter cube with a ZT488rdc dichroic mirror and an ET252/50m emission filter. For live-cell phase-contrast imaging, we used a 30-ms exposure time at 100% transmission power at an interval of 1.5 min. For fluorescent imaging, we used a 25-ms or 50-ms exposure time at 25% power and intervals of 3 min. This weak illumination minimized physiological effects due to phototoxicity effects on the cell and allowed steady-state behavior over many hours.
Turbidostat cell preparation and sample collection. We grew all precultures at 32°C or 37°C in a water bath shaker at 260 rpm. Seed cultures were inoculated into 1 to 3 ml LB medium from a single colony from an agar plate, streaked no more than 2 days before use. Cells were grown for several hours and then diluted 1,000-fold into the target media without antibiotics and grown until an optical density at 600 (OD 600 ) of 0.1 was reached. If multiple back-dilution rounds were needed to control experimental timing, they were done such that the cells did not enter stationary phase. The culture was then inoculated into each turbidostat vial with or without antibiotics to reach the target OD 600 of 0.05. Cultures were grown for a minimum of 14 doublings to ensure steady-state conditions upon sample collection. For some conditions, cells adhered to the glass culture vial, evidence of residual biofilm activity that we observed as changes in growth rate over the time course. In these cases, the sample was transferred to a clean glass vial at the end of the experiment for at least 1 additional doubling from which the growth rate was determined.
We collected samples for cell size and cell cycle measurements at OD 600 of 0.2. Approximately 20 ml of cell culture was immediately put on ice to arrest growth. The culture was then split and pelleted, frozen, or fixed according to the subsequent measurement protocol. A description of our turbidostat design and function has been previously described (3).
Turbidostat growth rate measurement. The turbidostat was used to maintain cells growing exponentially between OD 600 levels of 0.05 and 0.2. In effect, it was run as a batch growth repeater by diluting the culture to an OD 600 of 0.05 when it reached an OD 600 of 0.2. An exponential line was fitted to the growth periods between consecutive dilution events. From the exponential line equation I ϭ I0 · 2 t/ , the growth rate was determined as ϭ ln 2/, where is the doubling time. The turbidostat spectrometers were blanked with the appropriate medium before each experiment.
Turbidostat cell size measurement. We fixed cells with a glutaraldehyde and paraformaldehyde mixture and imaged the results within 24 h as previously reported (59), except for the following modifications: 2 l 25% glutaraldehyde was added to 1 ml 16% paraformaldehyde, and cells were resuspended in 300 l GTE (50 mM glucose, 25 mM Tris at pH 8.0, 10 mM EDTA at pH 8.0) per sample after phosphate-buffered saline (PBS) washes.
Before imaging, we adjusted cells to an appropriate cell density as needed. Cells were pipetted onto a 2% agarose pad and briefly dried. The agarose pad was then flipped onto a Willco dish (WillCo Wells, Netherlands) and covered with a glass coverslip to reduce evaporation during imaging. A total of 80 to 200 images were generated for each experiment. Sample sizes are presented in Table 1.
We performed fixed-cell image analysis with a custom Python script using the OpenCV library. First, we detected contours using an active Snake's edge detection algorithm. We then filtered for cell contours using a priori knowledge of cell size and shape and manually checked for correctly segmented cells. Width and length were calculated from the long and short axes of the cell segments using a simple threshold analysis of the raw phase-contrast images. All segmented cells for which the width and length fell within 3 standard deviations of the mean for that measurement were kept for further analysis. To calculate cell volume, we assumed the cell was a cylinder with hemispherical ends.
Turbidostat C period measurement using qPCR. We estimated the C period using qPCR and marker frequency analysis. Genomic DNA was prepared from each turbidostat sample using a standard phenol chloroform extraction method. We amplified genomic DNA using PowerUp SYBR green master mix (Thermo Fisher Scientific). We used primer pairs targeting chromosomal loci and calculated the C period using the ratio of relative locus copy numbers as discussed previously (3). Primers are listed in Table 6.
Mother machine cell preparation and image acquisition. We prepared the cultures for the mother machine experiments using the same method as that previously described for the turbidostat experiments except for the following difference: for translational inhibition experiments, the culture was diluted into the target media with appropriate antibiotics and allowed to grow for several generations before being loaded into the device.
We performed mother machine experiments as previously described (6,7). We used a custom centrifuge to load cells into the growth channels of the mother machine. The amount of time required to remove cells from the water bath shaker, load them into the growth channels, and infuse fresh 37°C media was between 15 and 30 min. We then imaged cells for many hours under conditions of constant infusion of media via the use of a syringe pump (Harvard Apparatus, MA).
For nutrient shift experiments, two syringe pumps were used in conjunction with a manual Y valve near the device inlet. Cells experienced the change in nutrients in a time interval shorter than the imaging interval (40).
Mother machine image processing. Mother machine images were processed with custom Python software (20). The pipeline employs raw images to produce objects which represent a cell and contain all measured parameters. Briefly, the software aligns and crops images into single growth channels (cell traps), segments cells, and links segments in time to construct cell lives and lineages. Segmentation was accomplished with a convolutional neural network of the U-net architecture using manually annotated training data (60). From the constructed cells, we extracted physical parameters in space and time such as size and growth rate. The pipeline can be accessed at https://github.com/junlabucsd/mm3. After segmentation and lineage creation, the resulting cells were filtered for those with measured parameters (septum position, elongation rate, generation time, birth, division, and added length) within 4 standard deviations of their respective population means. We considered only the cells in the time interval for which the measured parameters and the fluorescent signal were in the steady state. This was normally the interval from 3 to 4 h after imaging began until imaging ceased. For the glycerol-rich growth condition with 3.5 M chloramphenicol, we excluded cells which divided at the quarter positions, which represented less than 5% of all cells. For all conditions, we further selected a subset of cells which could be followed for at least 4 to 6 consecutive generations. The later filtering step did not affect the parameter distributions but did ensure that cell cycle determinations were possible in light of the presence of overlapping cell cycles. We considered only mother cells during analysis; however, the other cells along the channel had identical elongation rates.
The variability of the physiological parameters is influenced by the imaging frequency. Thus, the CVs in the manuscript represent an upper bound on the true biological CVs. Specifically, the measurements of time were only as precise as the imaging frequency. Measurements of size were similarly limited by how much a cell was able to grow in the imaging interval. For example, we measured division length at the image time point at which we detected division, but the true division event happened somewhere between that time point and the previous time point. We used an imaging frequency of 1.5 min for phase contrast; thus, the worst case (the condition promoting fastest growth) produced 16 images per generation on average. This corresponds to a possible 4% error in measurement of the length at division. This potential error decreased as the imaging frequency increased relative to the generation time or C period. Under most of our conditions, the possible error rate was 1% to 2%. This error source does not apply to measurements of growth rate, width, or septum position.
Single-cell cycle analysis. As described in the main text, we used a functional fluorescent DnaN-mGFPmut2 fusion protein. The construct was integrated at the chromosomal locus and expressed under the native promoter. The same genetic configuration was used for E. coli with DnaN-YPet. The gene product was the ␤-clamp subunit of DNA polymerase III, which is present at high stoichiometry in active replisomes (57).
Cell cycle analysis was performed as described previously (7). Processed fluorescent images were used to determine the cell cycle parameters manually. We first identified replisome foci in the processed fluorescent images using a Laplacian of Gaussian blob detection method. We then constructed cell traces by plotting cell length versus time, with both the fluorescent signal and focus positions projected against the long axis of the cell as demonstrated in Fig. 3. Using an interactive program, we determined the start and end of replication visually based on the positions and numbers of detected foci. For the two conditions promoting fastest growth, i.e., glycerol-rich media with 0 and 1 M chloramphenicol, the termination time and thus the C period and D period were not determined separately.
Ensemble cell cycle analysis. In the ensemble method, we aligned cells by size and plotted the ensemble replication state. On the basis of measurements published by us and others (11), we chose alignment by size rather than cell age. To create the ensemble, we found the average number of foci as a function of cell size across all cells. For the slow-growth case, the number of foci is 1 at short lengths until a transition period, at which point it rises to and plateaus at 2. We take the initiation length to be the length at which the focus count rate of change is the highest, using a differentiation step corresponding to 0.2 m. By inferring the average number of overlapping cell cycles (n oc ) from the traces, we can calculate C ϩ D as follows: C ϩ D ϭ [n oc ϩ log 2 (S d /S i )] · . Data availability. Single-cell data from the steady-state mother machine experiments are provided in Data Set S1. All other data from the study are available upon request.

ACKNOWLEDGMENTS
We thank members of the Jun laboratory for comments and invaluable discussions over the years. We also thank Petra Anne Levin, Dan Kearns, Paul Wiggins, Alan