Overview of the video sets

For the baseline video set (video set A), we used Mtb CDC1551 strain harbouring the SSB–GFP reporter, which was grown in unbuffered (pH ~6.8) standard (supplemented Middlebrook 7H9) growth medium at 37 °C. Time-lapse imaging was conducted for 96 h, with images taken every hour.

Two additional video sets were made using the fluorescent d-amino acid (FDAA) pulse-labelled CDC1551 wild-type strain. Videos were made in neutral (pH 7.0, video set B) or acidic (pH 5.9, video set C) standard (supplemented 7H9) growth medium at 37 °C. Time-lapse imaging was conducted for 140 h, with images captured every hour. All the videos were made inside a biosafety level 3 facility.

Bacterial strain

Mtb CDC1551 strain (video sets B and C) and its transformant with a hygromycin-resistant replicating plasmid expressing SSB fused to a green fluorescent protein (SSB–GFP) and smyc′::mCherry (video set A) were used in this study56. All live-cell work with these strains was performed inside a biosafety level 3 facility.

Bacterial culture

Mtb was grown in a standard medium consisting of 7H9 broth (ThermoFisher; DF0713-17-9) with 0.05% Tween 80 (ThermoFisher; BP338-500), 0.2% glycerol (ThermoFisher; G33-1) and 10% Middlebrook OADC (ThermoFisher; B12351). For the SSB–GFP reporter strain (video set A), 50 µg ml−1 of hygromycin (ThermoFisher; 10687010) was added to maintain SSB–GFP, smyc′::mCherry. The Mtb strain was grown to an OD600 of 0.5–1.0 from frozen aliquots at 37 °C with mild agitation. Cultures were subcultured via back dilution to an OD600 0.05 and grown to the mid-log phase (OD600 0.5–0.7) before experimental use. For videos in which polar growth is assessed (video sets B and C), Mtb cells were backdiluted to an OD600 of 0.2 in 10 ml 7H9 medium (unbuffered) supplemented with 100 µM HADA (see below) for 24 h. Labelled cells were washed twice with PBS (ThermoFisher; 20012-027) + 0.2% Tween 80 (PBST) and resuspended in pH 5.9 or 7.0-adjusted fresh 7H9 medium that was supplemented with sterile spent medium (50:50) for loading into the microfluidic devices for time-lapse imaging.

FDAA labelling

The blue FDAA, HADA (Tocris; 6647), was used for video set B and C. HADA powder was dissolved in DMSO to a stock concentration of 100 mM and stored for a short period at −80 °C. Cells were incubated in 100 µM HADA for 24 h before the start of the imaging.

Microfluidic device

The highest-throughput microfluidics for studying cell growth in rod-shaped bacteria require that the bacteria are loaded into thin channels40,74,75. However, mycobacteria cannot be loaded into these channels because they are coated in a thick mycolic acid layer in their cell wall, making them too sticky for these devices (Supplementary Fig. 1a).

We overcame this challenge by optimizing protocols and using a custom microfluidic device to achieve long-term time-lapse imaging of Mtb in a biosafety level 3 laboratory. We used devices previously designed to study M. smegmatis to ensure freedom of movement in polar growth and v-snapping23,25. We observed that, whereas M. smegmatis grows with a new medium constantly flowing in the microfluidic devices, Mtb enters growth arrest. Culture filtrate is required to enable Mtb single cells to grow under constant flow; therefore, we supplemented the new medium flowing into the device with culture filtrate at a ratio of 1:1 to avoid growth arrest. With these protocols, we were able to achieve a consistent growth pattern in Mtb over 4 days of imaging with a doubling time (~17 h) that is consistent with the doubling times of Mtb in bulk culture76,77,78.

Live-cell microscopy

Before loading Mtb cells into a custom polydimethylsiloxane microfluidic device, cells were filtered through a 10 μm membrane filter to remove clumps. Mtb cells were loaded into a microfluidic device through the outlet port using a syringe that contains filtered Mtb cell culture23. The devices contain a main microfluidic feeding channel with a height of 10–17 μm and viewing chambers with a diameter of 60 μm and a height of 0.8–0.9 μm. Fresh medium was delivered to cells at a flow rate of 5 μl min−1 using a microfluidic syringe pump. The device was placed on an automated microscope stage within an environmental chamber maintained at 37 °C. Mtb cells were imaged at ×60 magnification using a widefield Deltavision PersonalDV (Applied Precision), which is located inside a biosafety level 3 facility. For video set A, cells were illuminated with an InsightSSI Solid State Illumination System every hour for 96 h. Cells were imaged using transmitted light bright-field microscopy, GFP (475 nm/525 nm) and mCherry (575 nm/625 nm). mCherry was imaged to ensure the presence of the plasmid and was not used for analysis. The videos were performed in biological triplicate, with each replicate performed separately in different microfluidic devices on different days. For FDAA pulse-labelled videos (video sets B and C), cells were imaged every hour for 140 h using transmitted light bright-field microscopy, and HADA was visualized with a cyan fluorescent protein filter (433 nm/475 nm).

Live-cell image segmentation

For video set A, ImageJ plugin ObjectJ (version 1.03x) was used to hand-annotate cell length, growth and cell cycle progression throughout the image stack (time lapse). Single cells were annotated23,25 for cell length by marking two points at each pole. Additional points (up to four points in total within a cell) are annotated when foci were present. The SSB–GFP reporter forms a green fluorescent focus during DNA replication. Newly divided cells generally did not have an SSB–GFP focus, labelled as the pre-replication period (B period). The period when one or two SSB–GFP foci were detected was defined as the replication period (C period), and the subsequent period when foci were absent was labelled as the post-replication period (D period). Some cells had one or two foci after the division period but before septation; in these cases, we labelled those occurrences as the pre-division period (E period)25,56,57. Cell poles and visible foci were annotated in each frame—two points at each pole of a single cell were annotated if no foci were detected, while three (one focus) or four (two foci) points were annotated when foci appeared. The localizations of foci were manually analysed (custom code) and used to determine cell cycle timing. The annotation in each frame was extracted, containing information on cell length and cell cycle progression over time (1 h timescale). The ObjectJ data were exported to an XML file. Information on mother–daughter and accelerator–alternator cell relationships was also collected from cell pedigree trees using custom scripts in MATLAB for analysis; specifically, these scripts calculate and collate single-cell data—length at birth and division, duration of each cell cycle period, SSB foci presence and localization, accelerator–alternator status and pedigree relationships between cells (for example, mother–daughter–sister cell relations). During time-lapse imaging, we observed a rare subpopulation in which the cells express a high intensity of GFP. We observed that these cells did not divide and entered growth arrest. This may be due to phototoxicity caused by high SSB–GFP abundance. These cells were excluded from annotation.

For FDAA pulse-labelled videos (video sets B and C), using the HADA label as a marker of old cell wall material, we annotated growth from the new and the old poles in cells born during the video (so that we could establish pole age) from birth to division (n = 248) (Fig. 3a,b). The cell poles and HADA labelling were hand annotated in each frame using ImageJ (version 1.53f) with an ObjectJ plugin. Whole-cell labelling was annotated at each pole in the first time point. When cells elongated, a non-labelled area appeared, representing the new growth site. In cases in which cells elongated from only one pole, three points were annotated. When cells elongated from both poles, four points were annotated, starting from one pole (single point), then the HADA-labelled cell body (two points) and then the other pole (single point). After annotation, the x and y coordinates of each annotation point were extracted, and the distance was calculated using the Euclidean distance formula.

Simulations

In Fig. 4, we show that Mtb growth was largely consistent with linear growth simulations. Here we describe the model used for the linear growth simulations and the simulation methodology. Simulations of linear growth were carried out for 500 cells. Elongation speeds were assumed to have a Gaussian distribution with the mean \(_}\rangle\) and standard deviation \(}_}}\langle _}\rangle\) determined using the experiments. They were calculated as the mean and standard deviation of \(\frac-}}}\) where Lb, Ld and Td are length at birth, length at division and the generation time, respectively. Values for (\(\langle _}\rangle\) in μm h−1, \(}}_}}\)) are as follows: unbuffered medium (0.1442, 0.226), acidic medium (0.0741, 0.286), neutral medium (0.069, 0.240), replicate 1 (0.1663, 0.181), replicate 2 (0.134, 0.193) and replicate 3 (0.1309, 0.220). The elongation speed was determined at the start of the cell cycle. The length at birth for each cell was sampled from a normal distribution with mean \(\langle \rm}\rangle\) and CV (CVb) fixed using the experimental data. The values (\(\langle \rm}\rangle\) in μm, CVb) are as follows: unbuffered medium (2.37, 0.19), acidic medium (2.34, 0.24), neutral medium (2.25, 0.18), replicate 1 (2.60, 0.19), replicate 2 (2.22, 0.18) and replicate 3 (2.27, 0.17). The cells divided upon reaching size \(}=2(1-\alpha )}+2\alpha \varDelta +\eta\). Here Δ is a constant and α is the size regulation strategy that can take any value from 0 to 1. When α is 1, cells divide on reaching a particular size 2Δ (sizer), and for \(\alpha =\frac\), cells divide on adding a constant size Δ from birth. α and Δ are determined using the slope and intercept of the experimental Ld versus Lb plot, which are 2(1 − α) and 2αΔ, respectively79. η is the size additive division noise with mean zero and standard deviation (σbd). Our results are independent of the nature of division noise. The values for (α, Δ in μm, σbd in μm) are as follows: unbuffered medium (0.60, 2.28, 0.57), acidic medium (0.89, 2.77, 0.85), neutral medium (0.71, 2.26, 0.41), replicate 1 (0.61, 2.40, 0.66), replicate 2 (0.72, 2.26, 0.42) and replicate 3 (0.65, 2.18, 0.37). The length of each cell was measured at 1 h intervals. The measured length is the sum of the actual length of the growing cell and a measurement error normally distributed with mean zero and standard deviation determined from experiments (Supplementary Notes Section 5). The standard deviation values in μm are as follows: unbuffered medium (0.13), acidic medium (0.12), neutral medium (0.11), replicate 1 (0.14), replicate 2 (0.15) and replicate 3 (0.12).

We also investigated the effects of NETO, OETO and BEITO dynamics on the binned data trends of growth rate versus age and elongation speed versus age plots in Fig. 5f. We conducted simulations using the information of polar growth from the fluorescent HADA-labelled experiments in both neutral and acidic pH, which we will elaborate next. The simulations have the same number of cells as the experiments, that is, n = 101 for acidic and n = 147 for neutral pH conditions. Each cell is initialized to be born at a length sampled from a normal distribution with the mean (acidic, 2.30 μm; neutral, 2.29 μm) and CV (acidic, 0.24; neutral, 0.16) determined from the experiments. Each cell starts growing as BEITO with a probability equal to the fraction of BEITO cells in the experiments (~50% for acidic and ~46% for neutral pH). The elongation speed of old and new pole growth is drawn from independent normal distributions with the mean (acidic: old, 0.044 μm h−1; new, 0.036 μm h−1; neutral: old, 0.045 μm h−1; new, 0.034 μm h−1) and CV (acidic: old, 0.38; new, 0.42; neutral: old, 0.35; new, 0.40) determined from the experiments. For the remaining non-BEITO cells, growth does not occur from the poles until a certain take-off time. To accurately simulate the take-off time distributions, we sampled the timings with equal probability and with replacement from the non-BEITO cells obtained in the experiments. It ensured that the distribution of take-off times for the old and new poles and the proportion of NETO and OETO cells are similar in the simulations and experiments. The cell cycle ends once the cell reaches a particular division size (Ld) determined solely by the birth size (Lb), that is, mathematically, Ld = 2(1 − α)Lb + 2αΔbd + ζbd. The values of α and Δbd were obtained from the experiments (α = 0.83, Δbd = 2.89 μm for acidic pH and α = 0.8, Δbd = 2.34 μm for neutral pH), and ζbd is the normally distributed noise in the division size with mean 0 and standard deviation determined such that the standard deviation of the division size is the same in simulations and experiments (acidic: 0.85 μm; neutral: 0.40 μm). The length of the cell is measured from cell birth until cell division at 1 h time intervals. A measurement noise term is added to each measurement with mean 0 and standard deviation determined using HADA-labelled cells: in these experiments, the length of the HADA-labelled part of the cell is assumed to be constant (non-growing) throughout the cell cycle and the deviation from the constancy provides an estimate of the magnitude of measurement noise (acidic: 0.099 μm; neutral: 0.078 μm). In some of the cells, it is hard to visualize the growth of the new pole because of the finite resolution limit of imaging. In these cases, the new pole appears to be non-growing until some point in the cell cycle after which it experiences a sudden change in growth. We include these non-growth biases by sampling the times from experiments for which the new pole has no measured growth. We include this bias for completeness; however, we note that its exclusion does not change the results qualitatively.

Characterizing single trajectories using AIC and BIC values

We characterize the growth at the old and new poles using FDAA (HADA) labelling (Fig. 3). Figure 3a (middle panel) shows that the cells have an unlabelled part at the old pole after the first generation. The old pole growth is measured by adding unlabelled parts to the existing unlabelled region. The growth at the new pole is marked by the appearance of an unlabelled region at the new pole and, in a few cases, the growth of unlabelled parts to the existing unlabelled region. The aim is to identify the amount of growth at each pole and the time at which the pole growth starts. However, precise measurement of single-cell polar growth is difficult because the clumping of Mtb cells (Supplementary Fig. 1a) obscures the position of the poles and, thus, complicates the determination of the HADA-unlabelled part. This section explains the statistical models used to determine the polar growth at both ends at a single-cell level.

Previous studies have determined growth at each individual pole to be linear64. Linear growth is also supported by our results in the main text (Fig. 4). Thus, to determine the growth at each pole, we fit two different models to the length versus time trajectories: (1) linear growth and (2) bilinear growth, in which the length stays constant for a certain time and then increases linearly. Bilinear growth was used to characterize NETO64, in which it was proposed that the new pole starts growing after a time delay from cell birth. We assume that some old poles may also grow bilinearly (Fig. 5c and Extended Data Fig. 4c,f).

In cells that already have an unlabelled part at the old pole, we calculate the amount of old pole growth at time t from birth as the difference between the length of the unlabelled HADA region at the old pole at time t from birth and the initial unlabelled part at birth. The measured length grown can be negative for the old pole as the unlabelled HADA region at birth can be inaccurate due to cell clumping or cell tilting along the z-plane in the microfluidic chamber. We show examples of length grown versus time for the old pole (blue and green) and new pole (red) in Fig. 5 and Extended Data Fig. 4. In most of the cells of the pulse label experiment, we do not observe a HADA-unlabelled region at the new pole at the time of birth. In these cells, the length grown at the new pole is the length of the unlabelled HADA region at the new pole. The length grown is marked as zero when we do not observe the unlabelled HADA region at a pole.

Next, we fit the two models discussed above for each single cell to the length grown at each pole versus time curves. The linear model is characterized by two parameters \(y= ax+b\), where \(a\) is the elongation speed of the pole and b is a measure of the unlabelled HADA region at cell birth. For the bilinear model, the underlying equation is

$$y=\left\b,\quad\;x\le c\\ a\left(x-c\right)+b,\quad\;x > c\end\right.$$

(1)

where \(a\), b and c are the elongation speed of the pole, the bias in determining the initial HADA-unlabelled region and the time when the pole starts growing (relative to birth), respectively. For fitting, we ignore those data points where the length grown is zero (the y-axis is zero). We minimize the squared sum of residuals (RSS); \(}=_^_-\widehat_}\right)}^\), where \(_\) is the true value of the \(}\) data point of the dependent variable and \(\widehat_}\) is the predicted value from the model. To compare which of the two models better fits the single-cell trajectories, we use the AIC and the BIC. They are defined as

$$}=2k-2\;\mathrm\left(\widehat\right)$$

(2)

$$}=\mathrm\left(N\right)k-2\;\mathrm\left(\widehat\right)$$

(3)

where k is the number of parameters in the model (k = 2 for linear, k = 3 for bilinear), N is the number of data points fitted and \(\widehat\) is the maximum value of the model’s likelihood function. In the AIC and BIC methods, a model is favoured if it has a greater maximum likelihood value, and it is penalized for having a greater number of parameters, the penalty being different for AIC and BIC as shown in equations (2) and (3). Assuming that the errors (\(_-\widehat_}\)) are drawn from an independent and identical normal distribution, the AIC and BIC values can be simplified to66

$$}=2k+N\mathrm\left(\frac}\right)+\frac$$

(4)

$$}=k\mathrm\left(N\right)+N\mathrm\left(\frac}\right)$$

(5)

The AIC and BIC values themselves have little significance. The relevant metric is the difference between AIC and BIC values of the two models being compared; in our case, they are ΔAIC = AIC(linear) − AIC(bilinear) and ΔBIC = BIC(linear) − BIC(bilinear). A model with a lower AIC and BIC value is preferred. In our case, the bilinear model is preferred if both ΔAIC and ΔBIC values are greater than zero, while the linear model is preferred if the ΔAIC and ΔBIC values are less than zero. In a few cases in which ΔAIC and ΔBIC values have opposite signs, the model with fewer parameters, that is, the linear model, is preferred.

Having chosen the appropriate model using the ΔAIC and ΔBIC values obtained upon fitting both models to the length versus time trajectories of each cell, we aim to calculate the time at which the growth at a particular pole starts, the elongation speed at that pole and the amount of growth at that pole. We discuss the calculation of these quantities for different cases of fit results obtained, first for old pole growth and subsequently for new pole growth.

A bilinear curve best fits the trajectory for old pole growth shown in Extended Data Fig. 4c. In these cases in which the old pole growth is bilinear, the value of parameter c (equation (1)) of the best bilinear fit denotes the time at which the pole starts elongating. The slope \(a\) is the elongation speed of the pole and the constant b is the bias in determining the initial unlabelled HADA region. Thus, the amount of polar growth during the cell cycle is the length increase within time c and Td (the doubling time). Mathematically, the amount of polar growth = \(a(}-c)\). For the old pole growth trajectories in Extended Data Fig. 4a,b, where the best fits are linear, we assume that the growth starts from time 0. The y-intercept obtained (positive in (b) and negative in (c)) can be interpreted as the error in determining the initial unlabelled HADA region. The elongation speed is the slope of the best linear fit, and the amount of growth is equal to Slope × Td.

Next, we discuss the calculations of growth parameters for the new pole growth. We fit the non-zero length grown versus time data to the two models—linear and bilinear—and choose the appropriate model based on ΔAIC and ΔBIC values. In the trajectory shown in Extended Data Fig. 4c, the best fit is linear with a negative y-intercept. On extrapolating the best fit to y = 0, we obtain a positive time Ttrans. As we do not observe the unlabelled HADA region before this time point, we interpret the time Ttrans as the time when the pole starts growing. The raw data show the new pole to have a HADA label for some time after Ttrans because the unlabelled HADA region is small and might be undetectable in the videos until it reaches a particular length. Examining the videos shows that this length is around 0.2–0.4 µm. This can also be seen in Extended Data Fig. 4a–c trajectories, in which there is a sudden jump in the length of the new pole. The elongation speed is the slope of the best linear fit, and the amount of growth is Slope × (Td − Ttrans). In Extended Data Fig. 4b, the best linear fit has a positive y-intercept. In this case, we interpret the y-intercept as an initial undetectable HADA-unlabelled region at the new pole. The new pole starts growing from the beginning of the cell cycle with an elongation speed equalling the slope of the best linear fit. The amount of growth at the new pole during a cell cycle is Slope × Td. In Extended Data Fig. 4a, in which a bilinear fit better explains the length grown as a function of time, the interpretation of the fit is similar to that of the old pole. The constant parameter b in equation (1) denotes the HADA-unlabelled region at cell birth, c denotes the time when the new pole starts growing and the slope \(a\) denotes the elongation speed. The amount of growth is given by the same equation as that of the old pole, \(a(}-c)\).

In a few cases, we observed that the new pole had an unlabelled HADA region at cell birth. In such cases, we analysed the new pole using the same method as the old pole, as discussed previously in this section.

We use the definition of BEITO as cells starting to grow from both poles within 1 h of birth. This is related to the error in estimating the value of c, the time when the pole starts growing. To calculate the accuracy in the estimation of parameter c, we generated 100 trajectories using the model (either linear or bilinear) determined for each pole and each cell. To the deterministic growth component—elongation speed and growing time—we added a noise that is normally distributed with mean 0 and standard deviation determined by the residuals. For each of the 100 trajectories, we again undertook the fitting and model selection procedure described above and obtained estimates of elongation speed and time delay before growth at that pole starts. The standard deviation of parameter c is obtained for the old pole and the new pole growth. The standard deviation for both poles in both acidic and neutral conditions is between 0.8 h and 1.1 h. Note that this is close to the time between successive measurements (Δt = 1 h) but much smaller than the mean interdivision time (35–45 h).

Statistics and reproducibility

The scatter plots are presented with median values. The two-sided, two-tailed Mann–Whitney test was performed throughout the features compared between accelerator and alternator cells within Mtb or M. smegmatis strains.

Significance between CV values was tested using an asymptotic test for the equality of coefficients of variation from k populations80. The test is commonly used to compare variation between k different groups with unequal sample sizes. In this work, we consider k = 2 because we conduct pairwise CV comparisons. P < 0.05 was considered statistically significant. The test does quite well irrespective of the underlying distribution of the data (normal, log-normal, gamma) provided that the sample size is large (n = 20).

We used the package ‘cvequality’ (version 0.2.0) in R version 4.1.2 (202 1-11-01) to compare the coefficients of variation. Simulations and data analyses were performed using MATLAB version R202lb. Three-dimensional histograms were made using Python version 3.9.

Images from Fig. 1b,d and Supplementary Fig. 1a,b are representative of three biological replicates. Images from Fig. 3a and Supplementary Fig. 1c are representative of two biological replicates. Single cells loaded into 40–60 separate microfluidic chambers were used for imaging, generating 40–60 videos per biological replicate. The videos from two biological replicates, part of which were used for Fig. 3a, include a total of 1,089 annotated single cells.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.