Environmental and Physiological Factors Affecting High-Throughput Measurements of Bacterial Growth

How starved bacteria adapt and multiply under replete nutrient conditions is intimately linked to their history of previous growth, their physiological state, and the surrounding environment. While automated equipment has enabled high-throughput growth measurements, data interpretation and knowledge gaps regarding the determinants of growth kinetics complicate comparisons between strains. Here, we present a framework for growth measurements that improves accuracy and attenuates the effects of growth history. We determined that background absorbance quantification and multiple passaging cycles allow for accurate growth rate measurements even in carbon-poor media, which we used to reveal growth-rate increases during long-term laboratory evolution of Escherichia coli. Using mathematical modeling, we showed that maximum growth rate depends on initial cell density. Finally, we demonstrated that growth of Bacillus subtilis with glycerol inhibits the future growth of most of the population, due to lipoteichoic acid synthesis. These studies highlight the challenges of accurate quantification of bacterial growth behaviors.

These studies highlight the challenges of accurate quantification of bacterial growth behaviors.
KEYWORDS density-dependent growth, glycerol, lag phase, long-term evolution experiments, teichoic acids P recise growth measurements are fundamental to our understanding of bacterial physiology and its regulation. While some bacterial species are among the fastestgrowing organisms on the planet, others grow imperceptibly slowly, with doubling times ranging from ϳ7 min (1) to thousands of years (2). Although the need for rapid growth may drive selection in some cases, many bacteria live in complex natural environments that are often stressful and nutrient limited (3). In many environments, such as the mammalian gut, leaf litter in soil, and whale falls in the ocean, food is provided only periodically; hence, bacteria experience cycles of feast and famine. Thus, the transition from starvation to rapid growth can also act as an important selective pressure in evolution (4)(5)(6).
A classical batch laboratory assay that encompasses all phases of growth involves the initial overnight growth of a liquid culture, from either a frozen stock or a colony, which is then used to inoculate fresh medium for optical density (OD) measurements in a plate reader or spectrophotometer over time (7) (Fig. 1A). Although there are exceptions when OD does not track viable cell number (8,9), OD is widely used as a proxy for the density of cells in a culture (10,11). While traversing such a growth curve, a cell population initially takes some time to accelerate in growth, experiences a period of rapid growth, and then decelerates as nutrients are consumed, waste products accumulate, or both (7). Although there can be substantial variability in the shape of a growth curve, many species qualitatively exhibit a sigmoidal shape that can be characterized by three parameters: (i) the maximal growth rate, max , which is the largest slope of the natural log of the OD over time, (ii) the lag time required to accelerate growth from stationary phase (T lag ), and (iii) the maximum or final OD (A max ); some cultures also exhibit a death phase (7). These parameters are typically extracted from a growth curve via fitting or direct calculation (12)(13)(14)(15)(16)(17)(18)(19)(20)(21). Long-term evolution experiments (LTEEs) have demonstrated that all three can be under selection (4,22), underscoring the importance of their accurate quantification. However, we have little understanding of how the technical aspects of model fitting and the methodological aspects of inoculation affect such quantifications.
The creation of genome-wide knockout libraries (23,24) has motivated highthroughput measurements of population growth-a commonly used proxy for fitness-in microtiter plates, such as the systems biological characterization of essential gene knockdowns in Bacillus subtilis (5) and of Escherichia coli nonessential gene knockouts in liquid (25,26) or embedded in a gel (26,27). As the development of advanced genetic tools simplifies the creation of strain libraries (28)(29)(30), it is critical to ensure that OD measurements in multiwell plates provide reliable estimates of population-level growth parameters.
Here, we provide a detailed analysis of the requirements for achieving robust high-throughput measurements of fitness parameters. We quantified the importance of accurate background subtraction and established an assay of the sensitivity of the plate reader. We determined that measurements of maximal population growth rate and lag time are both sensitive to initial inoculation density, and we developed a mathematical model based on ordinary differential equations that accurately predicts this density dependence. We showed that completely removing residual glycerol from frozen stocks as a carbon source is critical for accurate measurements of E. coli growth in carbon-limited media, and we used such a strategy to reveal that evolution in a carbon-poor medium led to significant increases in the maximal growth rate of a population. We also established that the presence of glycerol during initial outgrowth from frozen stocks can have long-term impact on B. subtilis growth, causing long apparent lag times during subsequent culturing due to growth inhibition in a large FIG 1 Well-specific blanking and establishment of the spectrophotometer limit of detection are critical for accurate measurements of population growth rate. (A) Schematic of a classical experimental setup to measure bacterial growth. (B) Raw absorbance values from a typical E. coli MG1655 growth curve (light purple curve) increased starting from just above the background absorbance of the well plus media (ϳ0.08). Subtracting the background OD resulted in absorbance values (dark purple circles) that indicate substantially different growth kinetics, which are well fit by a Gompertz function (dark purple curve). With background subtraction, the maximum growth rate was 3.7-fold higher and occured ϳ60 min earlier (dark yellow curve) than without subtraction (light yellow curve). (C) The variation in the OD of a cell-free well containing only medium (gray) was much higher across a 96-well plate than the mean variation across multiple readings from a single well (teal). (D) The variation in E. coli growth curves across a 96-well plate when blanking with the cell-free absorbance of each well (teal) was much lower than when blanking with the background absorbance of a random well (black). Shaded regions represent Ϯ1 standard deviation. (E) Instantaneous growth rates computed from growth curves in panel B were much less variable for well-specific blank subtraction (teal) than for blanking with a random well (black). (F) Well-specific blank subtraction (teal) dramatically decreased the standard deviation in the estimate of maximum growth rate compared to that with subtraction of the blank from a randomly selected well in a 96-well plate (gray). (G) A dilution series from a culture with a known OD can be used to calibrate OD readings in order to establish the range majority of cells. Using transposon mutagenesis, we discovered that the increased lag time at least partially results from incorporation of glycerol during lipoteichoic acid synthesis. For large-scale high-throughput experiments, inoculating a large number of cultures from colonies is often too cumbersome; thus, these considerations are vital. Together, these findings provide a framework for accurate quantification of growth parameters and a roadmap for identifying and controlling for physiological factors that impact growth.

RESULTS
Accuracy of population density estimation from spectrophotometer absorbance readings is sensitive to the method of background subtraction. To monitor maximum growth rate and lag time (defined here as time to reach half-maximum growth rate) during a bacterial population's exit from stationary phase, it is standard practice to dilute a stationary-phase culture sufficiently that the spent medium transferred with the cells is a small fraction of the solution relative to the fresh medium. For a 100-to 1,000-fold dilution of a stationary-phase culture with an OD of ϳ1 (typical for many species under high-nutrient conditions measured with our plate reader), the starting OD is ϳ0.001 to 0.01. Thus, for species such as E. coli for which the maximum growth rate is achieved within 2 to 3 generations (31), the corresponding OD at the time of maximum growth rate can be low (Շ0.01) (Fig. 1A), making it critical to ascertain whether OD can be accurately measured at low cell densities.
It is generally appreciated that correcting for the background absorbance improves the accuracy of growth measurements. However, the extent to which different background correction methods affect growth rate calculations has not been quantified. For a culture that is growing exponentially, the number of cells, N, grows over time as N͑t͒ ϭ N 0 2 t⁄ , where N 0 is the number of cells at t ϭ 0, and is the doubling time. Thus, the growth rate of such a culture can be defined as the constant During outgrowth from stationary phase, when cells adapt their proteome to exploit the newly available nutrients (32), or after the cell density is sufficiently high that growth modifies the environment in a manner that impacts cellular physiology, the population does not grow exponentially. Nonetheless, analogous to exponential growth, we can define an instantaneous growth rate as Assuming that the OD measured by a plate reader is linearly related to N (OD ϭ ␣N, where ␣ is a scaling factor relating cell number to OD) and measurements are taken at time points t,t ϩ ⌬t,t ϩ 2⌬t, etc., the instantaneous growth rate at time t can be estimated as To illustrate the importance of background subtraction, consider a culture in which OD raw ͑t͒ ϭ ␣N͑t͒ ϩ OD bg , where OD bg is the background absorbance in the absence of cells; OD bg is typically ϳ0.1 (Fig. 1A). Without subtraction of OD bg , the ; the estimate of growth rate would be incorrect by a factor of ␣N͑t͒ ␣N͑t͒ϩOD bg (Fig. 1A). Thus, any estimate of growth rate without background (blank) subtraction is highly underestimated when in the regime OD bg տ␣N͑t͒, which is likely given the time at which the maximum growth rate of many bacterial species is first achieved. For similar reasons, using the first time point of a growth curve as a proxy for the background absorbance leads to overestimation of the maximum growth rate, because the subtracted background is too large. Therefore, a method for correctly subtracting the background is crucial for accurate growth rate estimates. We measured growth curves of E. coli MG1655 and estimated the instantaneous growth rate over time (see Materials and Methods), with and without blank subtraction. After subtracting the well blank, the maximal growth rate was 1.83 h Ϫ1 (doubling time of 22.7 min), which occurred at t ϭ 1.52 h (Fig. 1B). Without blank subtraction, the maximal growth rate estimate was substantially lower (0.49 h Ϫ1 ), and the time at which this inaccurate estimate occurred was t ϭ 3.0 h (Fig. 1B), illustrating the effects of omitting blank subtraction on lag time. To determine whether one empty well could be used as a general proxy for background absorbance, we quantified the absorbance of each well with medium before inoculating cells (see Materials and Methods). Blank values varied by ϳ0.004 across the plate, while a single well's blank value fluctuated by Ͻ0.001 over time (Fig. 1C). Blanking with a randomly selected well from the plate led to a wide variation in blanked growth curves (Fig. 1D) and maximum growth rates (Fig. 1E), with a standard deviation in growth rate estimate of 0.52 h Ϫ1 (Fig. 1F). Background subtraction with a well-specific blank led to substantially less variation in growth rate measurements, with a standard deviation in growth rate estimates for replicate cultures across the plate of 0.15 h Ϫ1 (Fig. 1F). Well-specific blanking also decreased the variability in lag measurements (see Fig. S1A in the supplemental material). The within-plate variability was sufficient to change the rank ordering of growth rates, which can lead to erroneous inferences. Thus, well-specific blanking is critical for accurate measurements of growth rate, because even comparisons in a single plate are confounded by within-plate variability.
Sensitivity limit of the spectrophotometer also impacts the accuracy of growth rate measurements. The ability to accurately measure changes in OD across a range of cell densities spanning several orders of magnitude is equally important for growthrate calculations. Thus, we sought a general protocol for quantifying the limit of sensitivity and linear range of a given spectrophotometer. We inoculated serial dilutions of an overnight culture of E. coli MG1655 into fresh LB and measured the OD values. At low dilutions (OD Ͼ 0.63), the absorbance measured by the plate reader was not linearly related to cell density ( Fig. 1G and H). Nonetheless, high OD measurements were able to be converted to cell-density estimates with a measured calibration curve (Fig. 1G), because the measurement coefficient of variation (CV; standard deviation/ mean) remained very low (Fig. 1I). To determine the precision of plate reader measurements at high density, we converted the spread in growth curve replicates at the same dilution into standard deviations of cell density estimates and found that the range of accurate measurement was reliably extended up to the maximum tested expected OD of ϳ3.5 (Fig. 1G), which is substantially higher than the typical corrected OD of ϳ1 for a stationary-phase E. coli culture grown in LB.
For OD values less than ϳ1, absorbances after well-specific blanking were linearly related to the dilution factor ( Fig. 1G) and had a CV of Ͻ0.2 ( Fig. 1I) down to a blank-corrected OD of ϳ0.006, well below the plate background OD bg . For larger dilutions (OD Ͻ 0.006), the CV increased sharply (Fig. 1I), indicating that growth rate measurements in our spectrophotometer are likely to be very noisy for an OD of Ͻ0.006. We conclude that any growth curve should be initialized with an inoculum such that the maximum growth rate is achieved above a blank-corrected value of 0.006. This strategy is likely effective for calibrating and determining the sensitivity limit of any spectrophotometer.
Maximum growth rates can depend strongly on initial inoculation density. We previously found that the instantaneous population growth rate strongly correlated with OD across a library of B. subtilis mutants, despite their widely varied lag times, suggesting that cell density plays a major role in determining the population's growth rate (5). Thus, to determine the optimal dilution for initializing growth curves, we systematically quantified how the inoculum cell density affects the trajectory of outgrowth from stationary phase. We diluted an overnight culture of E. coli MG1655 into fresh LB at ratios ranging from 1:12.5 to 1:6,400 in a 96-well plate and monitored the growth curves ( Fig. 2A). To examine the relationship between OD and growth rate, we plotted each curve as growth rate versus OD (Fig. 2B). After correcting for the nonlinearity at high ODs (Fig. 1G) and subtracting the well-specific backgrounds, we found that the maximum growth rate achieved at low dilutions (e.g., 1:12.5) was lower than that at larger dilutions (Fig. 2B). As expected, each curve started at a different initial OD FIG 2 Growth rate is intrinsically linked to cell density due to nutrient depletion. (A) Growth curves of a dilution series from a single overnight culture of E. coli MG1655 displayed distinct growth behaviors, with slower initial growth for lower dilutions (higher initial cell density). (B) Instantaneous growth rates as a function of OD for the curves in panel B showed that lower dilutions resulted in lower maximum growth rates. Curves followed a common approximately linear downward trajectory after reaching their maximum growth rates, indicating that the entry to stationary phase is less affected by initial OD than lag time or maximum growth rate. (C) Nutrient depletion was sufficient to recapitulate experimental growth curves. Simulated growth curves for a model of growth based on nutrient depletion in equations 4 to 6 were similar to experimental data in panel A. (D) Nutrient depletion was sufficient to recapitulate the experimental relationship between OD and instantaneous growth rate. Instantaneous growth rate as a function of OD for the curves in panel C exhibited similar behaviors to the experimental data in panel B. (E) Nutrient depletion was sufficient to recapitulate the experimental relationship between initial inoculum size and maximum growth rate. The maximum growth rates of the experimental (B) and simulated growth curves (D) exhibited a quantitatively similar decrease with increasing initial inoculum density. (F) For a library of MreB mutants (34), the maximum growth rate computed from a growth curve initialized with a 1:100 dilution of an overnight culture (teal) decreased strongly with the mean cell width, while curves initialized from a 1:10,000 dilution (black) displayed higher, roughly constant maximum growth rates. The teal and black lines are least-squares linear fits to the data. with a growth rate near 0 (Fig. 2B). Growth rate then increased and, for large dilutions (1:6,400), reached max Ϸ 2 h Ϫ1 (Fig. 2B). However, for lower dilutions, max was substantially less than 2 h Ϫ1 and was attained at a higher OD (Fig. 2B). In each case, after reaching max , the growth rate declined approximately linearly as a function of log 10 (OD) along a common trajectory (Fig. 2B). Thus, before a population reaches its maximum growth rate, its growth rate trajectory is dependent on the initial cell density; thereafter, the growth curve follows a prescribed path independent of initial cell density.
To interrogate whether factors such as nutrient depletion or waste accumulation cause this density dependence, we developed a minimal model of population growth dynamics during passage in liquid culture. We assume that cell density C grows with an instantaneous growth rate dictated by the physiological status of the cells and the external environment: Nutrients are consumed by growing cells at a rate proportional to their growth rate: where n is nutrient concentration, represents the production of nutrients by the cells, and ␤ is the nutrient consumption rate. We assume that the growth rate is a function of the nutrient concentration relative to a fixed nutrient concentration K (7); to model the transition from stationary phase into log phase, we assume that is related to the highest possible maximal growth rate * via a Gompertz relation (33): where min is the lowest growth rate attained at high nutrient concentration normalized to *, max ϭ 1 Ϫ min , governs how quickly increases, and ␦ is the time required to reach the maximum rate of growth rate change. We used single-cell growth data to obtain estimates of max , min , , and ␦ (Fig. S1B). We found that the simulated growth curves were relatively insensitive to the precise functional form of the acceleration in growth during lag phase. We simulated growth curves based on equations 4 to 6, assuming that OD is proportional to C, with different initial densities C͑t ϭ 0͒ and K ϭ 0.5 (where n ϭ 1 is the maximum nutrient level), * ϭ 2 h Ϫ1 , ␤ ϭ 0.8 h, max ϭ 0.99, min ϭ 0.01, ϭ 0.8 h Ϫ1 , and ␦ ϭ 0.5 h. The kinetics of these growth curves (Fig. 2C) and the resulting relation between growth rate and OD (Fig. 2D) recapitulated our experimental findings reasonably well (Fig. 2B), including the roughly linear decrease in growth rate with OD after reaching max . Hence, nutrient depletion can largely explain the relations between max and inoculation density (Fig. 2E), between lag and inoculation density (Fig. S1C), and more generally between growth rate and OD (Fig. 2D).
To experimentally distinguish between the effects of nutrient depletion and waste accumulation, we added 2% glucose to an E. coli culture at different times during growth in LB and monitored the effects on the growth curve (Fig. S1D). If nutrient depletion was the cause of growth rate slowdown, we surmised that the additional carbon would lead to a growth rate increase in early stationary phase. Early addition of the additional carbon before the culture saturated (Յ2 h) allowed for maintenance of a higher growth rate between ODs of ϳ0.2 to 0.5 ( Fig. S1D and E), but later addition (after Ն6 h) had no effect on the growth curve relative to that for no glucose addition, due either to the build-up of waste that inhibits nutrient uptake or to the inability to switch to metabolizing glucose.
To illustrate the importance of these results, we examined the growth of a library of E. coli cell-size mutants (34). After a 1:10,000 dilution, all mutants exhibited similar maximum growth rates (Fig. 2F). However, after a 1:100 dilution, maximum growth rate was negatively correlated with the average cell width of each mutant (Fig. 2F) (34). This effect appears to reflect differences in outgrowth that prevented many of the mutants from attaining the higher maximum growth rate achievable at lower inoculation densities. These findings illustrate the importance of initiating growth curves with as low a cell density as possible without dropping below the plate reader's limit of detection in order to avoid the region of decreasing maximum growth rate at high cell densities (Fig. 2F) that can distort comparisons between strains.
Growth in a carbon-poor medium is highly sensitive to glycerol levels. Highthroughput methods often involve inoculation directly from a frozen stock rather than passaging through colonies, which could result in the transfer of variable amounts of glycerol, a cryoprotectant that ameliorates cell death during storage at low temperature (35,36). Thus, we sought to identify factors, such as glycerol, that affect the growth of cultures inoculated directly from frozen stocks and then passaged multiple times. We hypothesized that glycerol would have persistent effects on growth, particularly in nutrient-poor media, because it can be utilized as a carbon source. Glycerol use that substantially increases the number of cells during the first passage would then perturb growth in later passages by changing the subsequent inoculation density ( Fig. 2A). Such conditions are particularly relevant for strains generated by evolution experiments, which are often carried out in media with low carbon concentrations (37). To test the effect of glycerol on growth, we measured growth curves across a range of glycerol concentrations (Fig. 3A to D). We inoculated 1 l from a Ϫ80°C freezer stock (previously grown in Davis minimal medium with 25 mg/l glucose [DM25]) of E. coli REL606 (38), the ancestral strain for the multidecade long-term evolution experiment (LTEE) carried out by Lenski and colleagues, into the evolution medium (DM25) supplemented with 0% to 10% (vol/vol) glycerol ( Fig. 3A and B). The addition of glycerol mimics various levels of glycerol carryover from frozen stocks during inoculation. (However, we emphasize that the growth rate and competitive fitness assays performed by Lenski and collaborators prevents carryover of glycerol through repeated culturing in DM25, which acclimates the bacteria to the medium and other conditions of the LTEE prior to the fitness assays [39]). When we diluted these cultures 1:200, the resulting initial ODs substantially differed across glycerol concentrations, resulting in different growth kinetics with higher final OD values for cultures coming from higher glycerol concentrations on day 2 ( Fig. 3C and E). After passaging the cultures a third time, the growth curves for the various glycerol concentrations were now quantitatively similar ( Fig. 3D) with lower final ODs, as expected (Fig. 3E). Similar glycerol-dependent effects appeared when different amounts of a frozen stock were inoculated in DM25 ( Fig. S2A and B). Thus, accurate quantification of growth requires multiple passages to eliminate the effects of glycerol on growth.
Combined with our finding that growth rate can be accurately measured even at low OD values with well-specific background subtraction (Fig. 1F), we realized that we could use multiple passaging to measure growth parameters in a high-throughput manner for the LTEE strains, enabling us to determine whether they changed systematically over the course of the LTEE. We examined 12 strains sampled from the Ara-1 population through 60,000 generations (40,41). We diluted each culture into fresh DM25 and measured their growth curves. We then rediluted these overnight cultures 1:200 in fresh DM25 and measured their growth curves for three more passages. All strains attained relatively high ODs in the first passage due to the residual glycerol (Fig. S2E). In the second passage, growth rates were higher for the strains from later generations, but the measurements were noisy due to variations in inoculum levels (Fig. 3E). By the third passage, the noise decreased substantially, allowing us to observe that the growth rate had gradually increased over the 60,000 generations (Fig. 3F). By the fourth passage, maximum growth rates of the evolved strains had converged on values close to those measured the previous day (Fig. 3G), ranging from ϳ0.65 h Ϫ1 to ϳ1.08 h Ϫ1 from the earliest to the latest sample. Notably, the low stationary-phase density in DM25 (Fig. S2E) meant that even small amounts of noise greatly affected the measurements of growth rate; hence, well-specific blanking instead of random-well blanking was critical (Fig. 3E to G).
These data demonstrate that the serial-transfer regime of the LTEE has favored higher maximum growth rate, as predicted from theory (6) and measured previously over the first 20,000 generations (42). That previous work, however, involved using a glucose concentration much higher than that in the LTEE in order to achieve OD values suitable for measuring growth rates. Our new measurements highlight the importance of accurate blanking for quantifying growth behaviors, especially at low OD values.
Growth in glycerol greatly increases B. subtilis lag time during subsequent passaging. In addition to impacting bacterial growth in carbon-limited media, we hypothesized that glycerol could have other, species-specific effects on growth. To mimic the variable amounts of frozen stock that might be used to inoculate a culture, while also avoiding confounding differences in initial cell density, we inoculated a 96-well plate with 1 l of frozen stocks of either B. subtilis 168 or E. coli MG1655 in LB supplemented with 0.1% to 10% glycerol and measured growth curves (Fig. 4A). For both species, during the first passage (day 1), all cultures exhibited approximately the same carrying capacity (Fig. 4Bi and S3Ai) and similar lag times (Fig. 4Bii and S3Aii).  Fig. S3D and E in the supplemental material) or 1 l of a frozen stock was used to inoculate LB supplemented with various concentrations of glycerol (as shown in B to D). Growth was monitored over three passages, in which the last two followed 1:200 dilutions into LB (without glycerol). (B to D) Growth curves on day 1 (Bi), day 2 (Ci), and day 3 (Di) of cultures inoculated with 1 l of a frozen stock into LB supplemented with different concentrations of glycerol (in addition to the ϳ0.075% transferred with the frozen stock). During the second passage (Ci), the cultures had similar maximum growth rates and carrying capacities, but intermediate inoculation amounts led to large increases in lag time. Growth curves were essentially identical during the third passage (Di). On day 1 (Bii), lag times were roughly constant for intermediate inoculation amounts (squares) or glycerol concentrations (circles), but lag times increased dramatically on day 2 (Cii); by day 3 (Dii) there was little difference in lag times across glycerol concentrations. These data indicate that glycerol caused the long-lag phenotype. Similar results were obtained when inoculating with different volumes of a frozen stock (Fig. S3).

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At high levels, glycerol causes catabolite repression and supports growth rates similarly to glucose (43). Hence, we speculated that glycerol could alter the physiological state of cells as they progress through another passage. To determine whether subsequent growth was affected by the prior presence of glycerol, we diluted all cultures 1:200 into fresh LB (without adding glycerol) and monitored growth in a plate reader for a second passage (day 2) (Fig. 4Ci and S3Bi). For intermediate concentrations between 0.16% and 5%, the lag time of B. subtilis cultures during this second passage increased to 6 h (Fig. 4Cii). This increased lag was specific to B. subtilis (Fig. S3Bii, Eii, and Hii), and went away during a third passage (Fig. 4D). Similar behavior was seen when inoculating a 96-well plate with fresh LB with various volumes (0.1 to 100 l) of thawed frozen stocks of B. subtilis 168 (Fig. 4A and S3D to F). These data indicate that the second passage after revival of B. subtilis from a frozen stock is very sensitive to the glycerol concentration during initial inoculation.
To confirm that cellular responses to freezing were not required for the increase in lag time, we used 1 l of an overnight culture grown from a frozen stock to inoculate LB supplemented with 0.1% to 10% glycerol; these cultures were now removed from freezing by a 24-h passage (Fig. S4A, purple). During the passage after glycerol addition, cells exhibited the expected increases in lag time (Fig. S4A, purple). Furthermore, when we inoculated the initial culture from a colony (instead of a frozen stock) into LB supplemented with glycerol, we saw similar increases in lag time during the subsequent passage (Fig. S4A, yellow) as from inoculating in various amounts of glycerol ( Fig. 4C; Fig. S4A, teal) or different amounts of a frozen stock (Fig. S3E). These findings suggest that regrowth from a frozen stock displays little to no sign of cell death. The long-lag phenotype in the presence of glycerol for B. subtilis is distinct from the effects we observed in E. coli (Fig. 3B to E), in which the glycerol was metabolized and thus led to higher carrying capacities. Altogether, these data show that growth of B. subtilis 168 in glycerol can cause dramatic lag time increases during the subsequent passage for intermediate concentrations of glycerol. They highlight the importance of controlling for glycerol levels during high-throughput growth assays, which can be readily achieved by performing an additional passage.
Glycerol has dramatic and varied effects on B. subtilis single-cell growth. We were surprised by the increased lag times in B. subtilis growth after passaging with intermediate glycerol concentrations and sought to investigate the cell physiology underlying this phenomenon. We used time-lapse microscopy to monitor the growth of cells on LB agar pads following growth in liquid LB at the glycerol concentrations associated with the longest population lag times (Fig. 4C). For cells grown in liquid LB with 0.3125% glycerol (ϳ6-h lag time) (Fig. 4Cii), we imaged an entire ϳ2 mm-diameter spot by capturing a grid of 144 overlapping fields of view (Fig. 5A). Of the ϳ10 4 cells in one spot, only a single cell grew, and its descendants took over the entire spot over 12 h of imaging (Fig. 5B). That cell exhibited growth as soon as imaging began, and after 1.7 h, its lineage exhibited a doubling time of ϳ20 min (Fig. 5C), indicating the extreme heterogeneity in this population. In other spots (n ϭ 2), we observed no growth of any cells. Such extreme bottlenecks should be avoided for most applications.
For cells grown in LB with 0.625% glycerol (ϳ6-h lag time) (Fig. 4Cii), we again observed a small fraction of growing cells (Ͻ3%) (Fig. 5D). The cells that grew showed multiple phenotypes. Some cells started growing immediately (Movie S1); some initially bulged along the cell body and then filamented for ϳ2.5 h before the first division (Fig. 5D). Other cells did not grow for Ͼ2 h (Fig. 5E) and thereafter grew more slowly than normal (Fig. 5F; see also Movie S2). A third subset periodically shrank and had a high death rate (Movie S3). For one cell, no growth was observed for the first 3 h; afterwards it engaged in short phases of growth and shrinking, with small blebs forming during growth (Fig. S5A). It eventually divided, and many of its progeny also exhibited periodic shrinking (Movie S3) and death through explosive lysis (Fig. S5A). Thus, growth in glycerol clearly disrupts cell shape as well as growth out of stationary phase in multiple ways.

A screen links glycerol-induced lag to genes involved in teichoic acid synthesis.
The discovery of B. subtilis's long lag and consequent fitness defect induced by intermediate glycerol concentrations (Fig. 4) presented the opportunity to identify genetic determinants of this phenotype, as mutants with a shorter lag would be enriched in the population. To gain insight into the underlying mechanism, we carried out an unbiased genetic screen by creating six independent pooled libraries of transposon mutants (see Materials and Methods) (44) in the wild-type strain. We grew the libraries in LB plus 1.25% glycerol, a concentration that induced a long lag time in the wild type (Fig. 5Eii). Further passaging of the libraries once in LB plus 1.25% glycerol and once more in LB revealed two libraries that evolved shorter lag times (Fig. S5B). We isolated single colonies and verified that they had a similar phenotype to the library from which they were isolated (Fig. S5C). Sequencing their transposon insertion sites identified two mutations: in sigX, which encodes a sigma factor that regulates modification of the cell envelope and resistance to cationic antimicrobial peptides (45), and in the start codon of dltA, which encodes a D-alanine ligase required for modification of wall teichoic acids (WTA) and lipoteichoic acids (LTA) (46). Note that dltA is part of the sigX regulon (Fig. 5G) (45). We verified these hits by reintroducing each transposon insertion into the parental strain ( Fig. S5D and E) and by deleting the gene (sigX or dltA) and then showing that these constructs exhibited the same reduction in lag ( Fig. 5H and I). Time-lapse imaging revealed that ΔsigX and ΔdltA cultures still exhibited regrowth heterogeneity, but with a much larger fraction (ϳ10%) of growing cells than the wild type (Fig. 5J). During stationary-phase outgrowth, ΔsigX and ΔdltA cells exhibited aberrant morphologies (Fig. S5F) similar to those taken on by the few growing wild-type cells after passaging in LB plus 0.625% glycerol (Fig. 5D and E;  Fig. S5A). The thick peptidoglycan cell wall of Gram-positive bacteria is intercalated with wall teichoic acids, which are covalently bound to peptidoglycan, and lipoteichoic acids, which are tethered to the membrane by a lipid anchor (47). Production of both wall teichoic acids and lipoteichoic acids requires substantial amounts of glycerol (48).
Thus, it appears that teichoic acid production is linked to the glycerol-dependent long-lag phenotype in B. subtilis.

DISCUSSION
As microbiology research has expanded and flourished, so has the appreciation of the sensitivity of microbial physiology and cellular structure to environmental conditions. Uncovering the details of these sensitivities will be critical to quantitative understanding of growth behaviors across microbial strains and species, as will establishing the resolution and robustness of the equipment used to measure growth. We have described a general strategy for measuring an instrument's limit of detection and range of linearity and demonstrated that, with proper protocols (see Materials and Methods), a wide range of growth behaviors can be accurately quantified.
The dependence of maximum growth rate on initial cell density presents complications similar to the antibiotic inoculum effect, whereby the sensitivity to certain drugs increases at lower cell density (49). Comparisons of growth rate and lag time between strains would ideally employ similar initial cell concentrations. However, fulfilling such a condition can be challenging due to strain differences in cell shape (50), yield in a given medium, and cell survival in and recovery from stationary phase. Moreover, some species may have growth dynamics and carrying capacities that are inoculum dependent. Given these complications, the acquisition of growth curves across a range of initial densities to map the range of growth behaviors would enhance the ability to compare strains and species. Our model based on ordinary differential equations is general and hence can be used for many microbes; in particular, it can help to correct for differences in growth rate due to variation in initial inoculum size. It is also important to note that waste accumulation should be mathematically equivalent to nutrient depletion if waste products inhibit the uptake of some nutrients, which means our model is even more broadly applicable. However, other factors may prove important for modeling growth curves, such as pH changes that are known to inhibit growth (51).
Although spectrophotometers that read microtiter plates are quite sensitive to small changes in OD (Fig. 1D and E), our analyses establish that it is critical to minimize noise that introduces complexities when calculating growth metrics; this noise minimization can be best achieved by blanking each individual well separately. This modification to protocols was relatively straightforward, and it positioned us to quantify the contribution of increased growth rate to the fitness gains observed in the LTEE with E. coli (Fig. 3). In particular, this method allowed us to show unequivocally that faster exponential growth had been selected even at the low glucose concentration and consequently low OD values of the LTEE; this conclusion was obscured without well-specific blanking (Fig. 3F to H). The ϳ66% increase in maximum growth rate that we measured is reasonably close to the ϳ70% increase in relative fitness obtained through competing late-generation samples against their ancestor (39). That relative fitness is calculated as the ratio of the realized growth rates of the evolved and ancestral bacteria over a full 24-h transfer cycle, including lag, growth, and stationary phases. Thus, other growth parameters can also affect relative fitness, including differences in lag time and carrying capacity (52), which complicates a direct comparison between maximal growth rate and relative fitness. In addition, cross-feeding interactions have evolved in some LTEE populations, and these interactions may affect the post-maximum growth rates of the competitors as cells exhaust the limiting glucose, consume by-products, and transition into stationary phase (53)(54)(55). In any case, our new protocol and growth rate measurements demonstrate the value of subtracting the blank of each well to minimize noise, especially at low OD values. These growth rate data also imply that utilization of glucose has become much faster over the LTEE, and more generally, it may be possible to evolve many bacterial species to grow at higher rates under specific nutrient conditions. Given the correlation between cell size and fitness in the LTEE (56), future studies might use these strains to explore whether the "Growth Law" that links nutrient-dependent growth rate and cell size (57) has changed over the course of evolution. In fact, it was previously shown that that the relation is not constant between the ancestor and an evolved strain isolated after just 2,000 generations (58).
The dramatic increases in lag time that we observed in B. subtilis (Fig. 4C) indicate that glycerol can have lasting physiological effects that impede the future growth of cells. We did not observe this lag phenotype in E. coli (Fig. S3B). This difference is consistent with the requirement of Gram-positive bacteria for glycerol to synthesize teichoic acids, which they incorporate into the cell envelope. Without multiple dilutions to mitigate the glycerol-induced long-lag phenotype, a severe bottleneck in which very few cells are responsible for outgrowth can occur (Fig. 5B), which may complicate interpretation of experimental results. The conventional approach to streaking single colonies before starting liquid cultures avoids this problem ( Fig. S4A and B), likely due to the extreme dilution of the glycerol concentration. While streaking may be prohibitive for large strain collections or certain species and communities, washing the initial inoculum to remove the glycerol is also sufficient (Fig. S2C and D).
Our transposon mutagenesis screen linked the glycerol-induced long-lag phenotype in B. subtilis to the incorporation of glycerol into lipoteichoic acids ( Fig. 5H and I). Our data also revealed several unusual physiological and morphological impacts of glycerol in the subsequent passage, including filamentation (Fig. 5D), bulging (Fig. 5E), lysis (Fig. S5A), and repeated cycles of growth and shrinkage (Fig. S5A). Some of these phenotypes are consistent with previous observations connecting lipoteichoic acid synthesis with cell division (59). Moreover, the arrest of growth in the vast majority of cells (Fig. 5E) indicates that their physiological state was sensitized by previous exposure to even small amounts of glycerol, such that growth remained inhibited even after glycerol was no longer present. This phenomenon connects teichoic acid synthesis to growth inhibition and lag phase for the first time, and it points to a severe bottleneck that might cause additional experimental complications. This surprising phenotype also highlights the potential for other physiological history-dependent effects on growth.
In the process of dissecting the seemingly simple process of measuring bacterial growth, we developed a refined protocol that enabled precise quantitative measurements. This precision, in turn, led to the discovery of new biological phenomena. The microbial world is stunningly diverse, and we currently know very little about the growth kinetics of the vast majority of microbes. Our work provides a powerful framework to analyze the growth characteristics of microbial species in highthroughput assays.
Mapping transposon insertions using inverse PCR. Genomic DNA was extracted using the Promega Wizard Genomic DNA purification kit, digested with Sau3AI at 37°C for 90 min, and then heat-inactivated at 65°C for 20 min. The reaction mixture contained 15.5 l Milli-Q H 2 O, 2 l NEBuffer1.1, 2 l digested genomic DNA, 2 l 10X bovine serum albumin, and 0.5 l Sau3AI. The digested DNA was ligated using T4 ligase at room temperature for at least 1 h; the reaction mixture contained 2 l T4 DNA ligase buffer, 15.5 l Milli-Q H 2 O, 2 l digested DNA, and 0.5 l T4 DNA ligase. Inverse PCR was carried out with the ligated DNA using Phusion polymerase with the primers IPCR1 (5=-GCTTGTAAATTCTATCATAATTG-3=) and IPCR2 (5=-AGGGAAT CATTTGAAGGTTGG-3=). Each reaction contained 33 l Milli-Q H 2 O, 10 l 5X HF buffer, 2 l ligated DNA, 2 l IPRC1, 2 l IPCR2, 1 l 10 mM deoxynucleoside triphosphates (dNTPs), and 0.2 l Phusion polymerase. The PCR program was as follows: 98°C for 30 s, 30 cycles of 98°C for 10 s, 58°C for 30 s, and 72°C for 60 s, 72°C for 10 min, and hold at 4°C. PCR products were gel-purified and sequenced using the IPCR2 primer. The sequences were mapped onto the B. subtilis 168 genome using BLASTN.
Data availability. All data used in the manuscript are growth curves, time-lapse microscopy images, or transposon sequencing. All data are available upon request from the corresponding author.

SUPPLEMENTAL MATERIAL
Supplemental material is available online only. MOVIE S1, MOV file, 2.6 MB.