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 P4, 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 , capturing both the decreased elongation rate with increasing activity at the population level across conditions (diamonds), as well as the binned data, that shows the increase in elongation rate with activity at the single-cell level within conditions (colored dots). (bottom) Single-cell simulations of elongation rate as a function of activity with identical parameters to (top), except without noise due to unequal partitioning of ribosomes at division (σR=0), showing that the positive slope between elongation rate and activity seen at the single-cell level (top) is driven by fluctuations in ribosome concentration at the single-cell level. (C) Simulations were performed for a fixed fraction of unnecessary proteins, fU= 0.073, and varying noise amplitudes of ribosomes due to unequal partitioning σR=(0,0.02,0.04,0.06) (light gray to black). For each condition, the resulting scattered data of activity versus elongation rate was binned as in the experiments. All simulations were implemented using rules for proteome allocation and division timing from [14], and other simulation parameters are described in SI Section 1.