Figures and data
Relationship between instantaneous growth rate and flagellar gene activity in single cells versus population.
Left: Time traces of Class-2 activity and Size (S) measured from the same mother cell across divisions (vertical ticks). We defined Class-2 activity as the time derivative of total fluorescence normalized by size, and the elongation rate as ER(t) = (1/S)(ΔS/Δt). Direct measurements of activity and size are shown as dots, whereas lines show the exponential fit for the size and the smoothed activity (see Methods and Materials). First, we used Class-2 activity to sort data points with Δt = 5 min and then bin the pair activity-elongation rate (see Fig. S4). Finally, we average the data in each bin and display the result in the right panel. Because the averaged bins are built from pairs of elongation rate values using a 5-minute time window, this binning allows us to determine the relationship between instantaneous flagellar gene activity and growth rate in single cells. Right: Instantaneous Class-2 activity versus elongation rate for different strains with varying mean levels of flagellar expression. In such strains, the native Class-1 promoter was replaced by synthetic promoters with different strengths, P1, P2 and P3 (color coded in top panel), P3 being threefold stronger than P1 [37]. The dashed line shows the linear fit to the population average of the pair Class-2 activity-elongation rate across strains, which illustrates the well-established relationship with a negative slope (cost) between growth rate and increasing mean flagellar gene activity across strains [30]. By contrast, single-cell binned data within each distinct strain shows a positive slope between instantaneous growth rate and flagellar activity, demonstrating that cells with higher flagellar gene activity are also the ones growing faster. Only the data exhibiting Class-2 activity (excluding off-states) are considered in this plot; see Fig. S3D for all states. The number of time traces is n= 69, 107, 96, 67 for the strains with the promoter P1, WT, P2, and P3, respectively, all with a duration of ∼47 hours.
Cells grow faster during pulses.
(A) The Class-2 activity time series were divided into intervals that consisted of a pulse of activity followed by an off state and another pulse. We selected all the intervals with similar durations (within a range of no more than 6 hours). The pulses were defined by the period for which the activity is above an empirical threshold (activity = 50 arbitrary units). Then, the intervals of similar duration were normalized such that they spanned from 0 to 1, in order to average them. (B) Top: Averaged pulse-to-pulse intervals (real time rescaled to 1) of the Class-2 activity. Middle and bottom: elongation rate and division time associated with the same time intervals as the top panel. The averages were calculated by applying a sliding window mean over the overlapping data consisting of n = 103 intervals.
Short-timescale shifts in Class-2 activity correlate with immediate changes in growth.
(A) Left: Schematic of a dividing mother cell producing two daughters, one inheriting the new pole (red pole) and the other retaining the old pole (blue pole). Scatter plot of elongation rate in sister cells (new-pole / old-pole daughters. (B) Bars show the mean ratio of new-pole to old-pole daughters for elongation rate, Class-1 activity, and Class-2 activity. The gray dotted line indicates a ratio of 1, corresponding to equal values between new- and old-pole daughters and is also the mean ratio obtained from a null model based on label-shuffling permutations between the daughters. Error bars indicate 95% confidence intervals. N = 1669 pairs of the WT flagellar expression strain. (C) Elongation rates across two consecutive generations for cells experiencing an abrupt change in Class-2 activity: off to on (yellow) and on to off (green). For both cases, we plot the binned ER of the daughter cell (generation g + 1) against the ER of the previous generation (g). A positive change in activity (off to on) is accompanied by an increase in ER across generations compared to the dotted line, reflecting faster cell growth in generation g+1. A decrease in activity (on to off) is associated with a reduced ER compared to the dotted line in generation g+1 (ER is lower at g+1 than at g). The number of divisions for each subset is ∼300. The shaded regions correspond to the standard deviation for each bin, and the dotted line shows the linear fit for the entire dataset, irrespective of activity, representing a null model for ER across divisions.
Relationship between instantaneous growth and promoter activity in single cells versus population for different levels of constitutive expression of unnecessary proteins.
(A) For a set of strains expressing the fluorescent protein Venus, driven by promoters of varying strengths (P1– P6, as indicated at the top), we calculated the mean elongation rate as a function of promoter activity. The diamond markers represent the average for the entire population of each strain, and the black dotted line indicates the linear fit through these population averages. The colored dots show the binned single-cell data for each strain. In each strain, cells exhibit a positive correlation between elongation rate and constitutive promoter activity. The inset shows the same data with the x-axis plotted on a log scale. (B) (top) Single-cell simulations for increasing average allocation fraction to unnecessary protein expression 
Parameters
Simultaneous monitoring of growth and pulses of flagellar gene activity in single bacteria.
(A) Schematic of flagellar components in E. coli. A cascade of flagellar promoters coordinates the assembly of the different motor elements. The master regulator (Class-1) regulates the activity of Class-2 promoters that control the genes that encode the basal body and hook molecular elements. A Class-2 gene (fliA) drives the transcription of the Class-3 genes, which encode products needed in late flagellar assembly, such as the filament-associated proteins and the motor stator. (B) In the Mother Machine device, cells are constrained into channels where they can grow and divide while being fed by a constant flow of fresh medium. The ‘mother’ cell at the bottom of the channel is monitored over many cell divisions using epifluorescence-based time-lapse microscopy. (C) Cells growing in the Mother Machine show pulses of Class-2 activity (on state) followed by long periods of no activity (off state). The activity is calculated from the fluorescence time series controlled by a Class-2 promoter, fliFp (described in Materials and Methods; [20]). The vertical ticks show cell divisions; the dashed lines show examples of on and off states. The cartoon at the top illustrates the different growth behaviors cells exhibit during on and off states, which yields the relationship between instantaneous flagellar genes activity and growth rate.
Time series of Class-2 activity and cell elongation rate in flagellar reporter strains
Typical single-cell time series for flagellar reporter strains monitored in the Mother Machine. For each reporter strain (with promoters P1, P2, and P3, which control Class-1 expression) and the wild-type (WT) strain, Class-2 activity and cell elongation rate are shown as a function of time. In each panel, gray dots correspond to the direct calculations of activity and elongation rate, as described in Materials and Methods, and colored lines show the corresponding Savitzky–Golay–smoothed traces (window size w = 35 min). Horizontal lines indicate cell-division events.
Determining motility of the synthetic flagellar series in soft agar plates and microfluidic device.
(A) Motility plate assay for strains with synthetic promoters controlling flagellar expression. Each strain (1 µL LB culture) was spotted onto a soft-agar plate (40 mL LB, 0.25% w/v Bacto agar in 150 mm petri dish) and incubated for ∼12 h at 30 °C. Strains in which the native Class-1 promoter was replaced by Pro2, Pro4, or Pro5 (P1–P3 in the main text) were assayed alongside controls: MG1655 WT, MotA E98K MG1655 (non-motile due to impaired motor rotation), MotA E98K Pro4, Pro4 ΔfliC, and MG1655 IS5 (motile strain with elevated flagellar expression [58]). (B) Kymograph of a single mother-machine channel showing cells (outlined in blue), imaged every 5 min until they abruptly leave the channel. The table below reports the fraction of lineages that exited the channels; in contrast, the non-motile MotA E98K strain showed no channel escape events. Temperature and growth media were the same of all the other experiments, as described in the Materials and Methods.
Elongation rate vs Class-2 promoter activity scatter plot and binning.
(A) The scatter plot in gray illustrates the relationship between elongation rate and Class-2 activity (WT flagellar expression, strain E98KFD), with each point representing a distinct time point. The scatter plot is divided into 10 bins according to the Class-2 activity, each bin containing an equal number of points. The mean and standard deviation for each bin are represented in blue. The dataset consists of a total of n = 57,592 data points, corresponding to n = 107 mother cell lineages monitored over approximately 47 hours. (B) The two-dimensional histogram shows the frequency of observations across binned values of Class-2 activity and elongation rate, with the color scale indicating the number of observations per bin (logarithmic scale). (C) For each vertical slice (constant activity) from (A), bin counts were normalized between 0 and 1, highlighting the relative density of elongation rate values at each bin of activity. Color intensity indicates normalized density, with 0 corresponding to minimum and 1 to maximum relative frequency within each slice. In (B) and (C) the superimposed points in white represent binned aggregates of the data from (A), illustrating the overall trend. (D) Mean binned elongation rate as a function of Class-2 activity, for different strains that have different flagellar expression levels, i.e., strains in which Class-1 activity is controlled by synthetic promoters P1, P2, or P3, and the native promoter, WT. The number of time traces per strain are n = 69, 107, 96, 67 for P1, WT, P2, and P3, respectively, all with a similar duration of ∼47 hours.
Statistical analysis of single-cell relationships between elongation rate and Class-2 activity.
(A) The color map shows the density of single-cell measurements of elongation rate versus Class-2 activity, with warmer colors indicating regions containing more data points, for the WT flagellar expression, strain E98KFD. In blue is the previously described binned data. The black dashed line shows the fixed-effect prediction from the mixed-effects linear model (ER ∼ PA with random intercepts per lineage), representing the average single-cell trend after accounting for lineage-to-lineage variability. (B) Top: Block-bootstrap estimates of the Pearson correlation between Class-2 activity and elongation rate for flagellar reporter strains (P1, WT, P2, P3), resampling whole lineages to account for within-lineage dependence. Dots show correlations from the original data; vertical lines indicate 95% percentile block-bootstrap confidence intervals. Bottom: Mixed-effects linear regression of elongation rate on promoter activity for each strain. Each point shows the fixed-effect slope (change in ER per unit PA); horizontal lines indicate 95% confidence intervals from a mixed model with random intercepts per lineage. The vertical line marks zero slope. (C) Mean elongation rate as a function of the mean Class-2 Activity, the error bars show the standard error of the mean and the dotted line shows the weighted linear regression fit (weights proportional to the number of lineages per strain), illustrating the population-level trend across strains. The table summarizes the weighted linear regression of strain-averaged ER on strain-averaged PA, showing the negative slope, its 95% confidence interval, and the one-sided p-value.
Bulk measurements show a decrease in growth rate when flagellar proteins are overexpressed in E. coli.
We calculated the growth rate for a set of strains with varying levels of flagellar expression (using different synthetic promoters with various strengths controlling Class-1 expression, P1-P3; see Table S2). Strains were grown in 96-well plates, and their OD600 was measured to calculate the slope of their growth curve during exponential growth. Each strain was also grown in bulk, and flow cytometry was used to measure fluorescence, which indicates the activity of the Class-2 promoter, fliFp. The figure shows the growth rate of each strain as a function of the corresponding mean fluorescence. The dashed line represents the best linear fit of the data. The data points reflect the averages for each strain across two biological replicates, and the error bars represent the standard deviation.
Instantaneous growth rate and flagellar Class-2 promoter activity.
(A) The mean binned growth rate as a function of Class-2 activity is presented for different strains, each with varying promoters controlling Class-1 activity: synthetic promoters P1, P2, P3, and the native promoter WT. Here, the growth rate was determined as the time derivative of the logarithm of size S(t), following the methodology of Bakshi et al. [59]. This definition of the growth rate using single-cell measurements was found to be an accurate proxy for the standard bulk growth rate obtained from OD measurements. The number of time traces per strain is 69 for P1, 96 for P2, 107 for WT, and 67 for P3, with all experiments having a similar duration of 47 hours. (B) Top: Rescaled and averaged time series of successive pulse–to– pulse intervals of Class-2 activity (same intervals as in Fig. 2). Bottom: Averaged and rescaled growth rate for the same time intervals, calculated using the same approach as outlined in (A).
Class-1 activity and elongation rate correlation.
(A) The color map shows the density of single-cell measurements of elongation rate versus Class-1 activity, for the WT flagellar expression, strain E98KFD. In blue is the mean of the binned data. The dataset includes n=57,592 data points from N=107 mother cell lineages tracked over ∼47 hours. (B) Mean binned elongation rate as a function of Class-1 activity, for different strains that have different flagellar expression levels, i.e., strains in which Class-1 activity is controlled by synthetic promoters P1, P2, or P3, and the native promoter, WT. The triangles show the population average for each strain. (C) Block-bootstrap estimates of the Pearson correlation between Class-1 activity and elongation rate for each strain, resampling whole lineages to account for within-lineage dependence. Dots show correlations from the original data; vertical lines indicate 95% percentile block-bootstrap confidence intervals.
Class-2 pulse-to-pulse and elongation rate analysis.
Pulse–to–pulse segments are defined as portions of the Class–2 activity that include two consecutive pulses (on – off – on). (A) Histogram of the duration of the segments. (B) Average of different variables for pulse-to-pulse intervals of different durations, with red representing 3–8 h, blue representing 6–12 h, and green representing 8–16 h. From top to bottom: Class-2 activity, elongation rate, and division time. The number of intervals (262, 126, 103) corresponds to the time intervals between the two successive pulses ranging from 3-8 h, 6-12 h, and 8-16 h, respectively. Experiment was performed using E. coli strain E98KFD in MOPS-Gly medium.
Cross-correlation between elongation rate and Class-2 activity in strains of varying flagellar activity.
(A) For each flagella-reporter strain, normalized cross-correlation functions between elongation rate and promoter activity were computed separately for every lineage (top, colored lines), using the equation on the top, where ER′(t) and A’(t) denote the elongation–rate and activity time series, respectively, with their mean subtracted. The cross-correlation quantifies how strongly signals ER′(t) and A’(t) are related when the activity signal A’(t) is shifted in time (by a lag) relative to the elongation-rate signal ER′(t). These lineage-level cross-correlations were then averaged pointwise across lineages to obtain the mean cross-correlation as a function of lag (top, black line). For each lineage, the temporal delay between elongation rate and promoter activity was defined as the lag within a predefined, biologically relevant window at which the normalized cross-correlation reached its maximum. Positive delays indicate that elongation rate lags behind promoter activity, whereas negative delays indicate that elongation rate precedes promoter activity. The distribution of delays for all lineages of a given strain is shown as a histogram (bottom), where the vertical dotted line indicates zero lag, and the blue line marks the lag at which the mean cross-correlation peaks. (B) Mean cross-correlation functions for the different strains, colored as indicated. For each strain, cross-correlations were first computed for individual lineages, and the lag axis was normalized by the average division time (Tdiv) of that strain before averaging across lineages.
Class-3 activity and elongation rate correlation.
(A) Time series of flagellar promoter activity for Class-2 (blue; fliFp), Class-3 (pink; fliCp), and elongation rate (grey) in a representative mother cell across multiple divisions. promoter activity is normalized to its mean over the series. (B) Average cross-correlation between Class-2 activity and elongation rate (blue) and between Class-3 activity and elongation rate (pink). Cross-correlation was computed for each lineage (n = 68), and values were averaged across all lineages for each time lag. Shaded areas represent the standard deviation for each lag. The lag corresponding to the maximum (average) cross-correlation is 0.835 h, for Class-3, and 0.245 h for Class-2. (C) Following the procedure outlined in Fig. 2, Class-3 activity time series were segmented into intervals spanning two consecutive peaks (on-off-on states). Intervals of similar duration were selected (10-16 h; n = 55 intervals), and their duration was normalized. Activity profiles were then smoothed. For the same intervals defined by Class-3 peaks, we also averaged Class-2 activity and elongation rate (shown below). The bacterial strain used for all these analyses was E98KFC (see Strain List).
Cross-correlation analysis of elongation rate and fluorescence for various promoters and strains.
The first row displays the correlation coefficients over time lag for three promoters, each representing one of the three flagellar classes, controlling the fluorescence: Class-1 (flhDp_mVenusNB; strain E98KFD), Class-2 (fliFp_SCFP3A; strain E98KFD), and Class-3 (fliCp_mVenusNB; strain E98KFC). In the second row are the plots corresponding to constitutive expression: Constitutive promoter (Pro4_mVenusNB; strain MGPro4-Venus) encoded on a plasmid, constitutive promoter encoded in the chromosome (pRNAI_mCherry; strain E98KFC), and a constitutive promoter that controls both the Class-1 genes flhD and flhC, and the gene encoding the fluorescent protein (Pro4-flhDC_mVenusNB; strain E98KFD Pro4_T7). The Fluorescence signal is the average intensity of the cells per area, and the elongation rate is the time derivative of the Size normalized by Size, ER(t) = (1/S(t) dS(t)/dt). Both signals were smoothed using a window of 7 frames (35 min). Each plot shows the average of the correlation over many time series, and the shaded region represents the standard deviation about the mean. The fluorescent proteins used were selected for their fast maturation time, as described in [52].
Cross-correlation analysis of elongation rate and promoter activity for various promoters and strains.
The promoter activity and elongation rate were computed as described in Materials and Methods. The promoters and strain names appear in the same order as in Fig. S12. Sampaio et al. [22] monitored the correlation between growth rates and reporter expression levels from various E. coli promoters at the single-cell level, and found anticorrelation. When we calculated the cross-correlation between the elongation rate and reporter levels (mean fluorescence), instead of promoter activity, we similarly observed a negative correlation for reporters driven by constitutive promoters (Class-1 and synthetic types; Fig. S12). However, for reporters driven by Class-2 and Class-3 promoters, we observed a positive correlation between the growth rate and both reporter levels and promoter activity.
Probability of bias advantage between the elongation rate of old and new pole daughters.
Probability that old pole daughters (newly born cells at the close end of the channel which inherits the old pole (red pole in the diagram)) or new pole daughters (daughter cells born closer to the open side of the channels that inherits the mother’s new pole (dark blue)) have higher elongation rates, with and without conditioning on promoter activity. Bars show the probability that the daughter with the elongation rate of the new pole (ERnew) has a higher elongation rate than the old daughter (ERnew> ERold), or vice versa (ERold> ERnew), either unconditionally or conditional on that daughter having higher promoter activity than its sister (e.g. ERnew > ERold given PAnew > PAold). For each case is shown the probabilities of the observed data, ‘Obs.’, and the ‘Shuffled’ pairs’ bars show the corresponding probabilities under a within– pair permutation null in which elongation rates are randomly swapped between sisters with probability 0.5. Error bars indicate 95% Clopper–Pearson exact binomial confidence intervals. The horizontal dotted line indicates a probability of 0.5, corresponding to no bias between sisters.
MG1655 and MC4100 differ in size-oscillation dynamics but not in short-timescale growth– expression coupling, which is attenuated only at flagellar Class-2 activity.
(A) Typical time series showing the Size of MG1655 background strain (EMGFD) and MC4100* (MC4100 variant with flagellar expression but non-motile). (B) Autocorrelation function (ACF) of the Size time and Elongation Rate series in MG1655 (blue) and long-term oscillating MC4100* strain (black). Averages of individual ACFs were calculated from ∼60 lineages and normalized by the mean division time. (C) Top: Density of single-cell measurements of elongation rate versus promoter activity for Class-1 and Class-2 promoters in MC4100*. Circles show the mean of the binned data. Bottom: Pearson correlation coefficients between elongation rate and promoter activity for Class-1 and Class-2 in MG1655 and MC4100, estimated by block bootstrap to account for temporal autocorrelation within time series; error bars denote 95% confidence intervals.
Statistical analysis of activity–elongation rate relationships in constitutive fluorescent reporter strains.
(A) The color map shows the density of single-cell measurements of elongation rate versus promoter activity, using the P4-Venus strain. In green is the mean of the binned data. The black dashed line shows the fixed effect prediction from the mixed-effects linear model (ER ∼ PA with random intercepts per lineage), representing the average single-cell trend after accounting for lineage-to-lineage variability. (B) Top: Block bootstrap estimates of the Pearson correlation between activity and elongation rate for the strains that overexpress Venus, resampling whole lineages to account for within lineage dependence. Dots show correlations from the original data; vertical lines indicate 95% percentile block bootstrap confidence intervals. Bottom: Mixed-effects linear regression of elongation rate on promoter activity for each strain. Each point shows the fixed-effect slope (change in ER per unit PA); horizontal lines indicate 95% confidence intervals from a mixed model with random intercepts per lineage. (C) Mean Elongation rate as a function of the mean promoter activity, the error bars show the standard error of the mean and the dotted line shows the weighted linear regression fit (weights proportional to the number of lineages per strain), illustrating the population-level trend across strains. The table summarizes the weighted linear regression of strain averaged ER on strain-averaged PA, showing the negative slope, its 95% confidence interval, and the one-sided p-value.
Elongation rate and promoter activity across constitutive expression levels and media.
(A) For a set of strains expressing the fluorescent protein Venus, driven by promoters of varying strengths (P1 to P6, as indicated at the top), and grown in two different media (labeled Rich and Poor), we calculated the mean elongation rate as a function of binned promoter activity. The black dots represent the population average for each strain, while the lines indicate the linear fit of these points for both conditions (cells grown in either rich or poor medium). (B) The average cross-correlation (see Materials and Methods for the definition) between elongation rate and promoter activity was calculated for the lineages of strains producing unnecessary proteins (same data and color-coding as in panel A), for both poor and rich media. Binning and cross-correlation analyses were performed on time-series of approximately 37 hours in duration, obtained from n = (30, 21, 19, 14, 24) lineages under poor medium and n = (12, 33, 39, 22, 40) lineages under rich medium, corresponding to strains carrying promoters P1 through P6, respectively. Poor medium consisted of Teknova MOPS EZ defined base (no ACGU) supplemented with 0.4% glycerol, 1.32 mM phosphate, and 0.85 g/L Pluronic F-108. Rich medium comprised the same MOPS base with Supplement EZ, ACGU solution, 0.5% glucose, 1.32 mM phosphate, and 0.85 g/L Pluronic F-108.
Growth-constitutive expression coupling is conserved across E. coli strains and conditions.
(A) Density of single-cell measurements of elongation rate versus promoter activity for constitutively expressed fluorescent protein in MG1655 (2 experiments, N = 508, 201 cells), B/r (2 experiments, N = 231, 932 cells), and MC4100 at 25°C and 37°C (N = 669, 259 cells). Data for MG1655 and B/r are from Wang et al. [33]; data for MC4100 are from Tanouchi et al. [44, 48]. We selected time traces for reanalysis after excluding those affected by segmentation errors. Circles show the mean of binned data. (B) Pearson correlation coefficients between elongation rate and promoter activity for each strain/condition shown in (A), estimated by block bootstrap to account for temporal autocorrelation within time series. Error bars denote 95% confidence intervals.
List of plasmids.
List of strains.
