Systematic deviations and the birth-size dependence of the specific elongation rate as function of cell cycle progression.

Shown is data for E. coli cells growing on glucose. We denote the specific elongation rate by sER and an average of a variable x is denoted by (x). (A) The average specific elongation rate (sER) of single cells changes as function of their normalized cell age (age 0 corresponds to cell birth and age 1 to division). Exponential growth corresponds to the horizontal, dashed line. The inset figure shows this same trend, but as a function of the average length per normalized age, normalized by the total average length. Since the average length observed in a growing population corresponds to a cell approximately half way through its cell cycle, we note that the expected range runs from 2/3 to 4/3. (B) The coefficient of variation of the sER of single cells decreases as a function of normalized age, indicating compensatory dynamics. (Blue markers indicate the average of the biological replicates shown as grey markers.) (C) The mean sER of different birth-length bins are shown as function of the normalized cell age. The data indicates that smaller-than-average cells (dark blue) grow faster than average-sized cells (light green) while larger-than-average cells (red) grow slightly slower. The bar legend indicates the normalised ranges of the birth-length bins, and the number of individual cells included in each bin. All plots show the average from 7 independent experiments, all for cells grown on defined minimal medium (M9) with glucose as carbon source and with a total of 31,748 cells. Error bars are plotted as standard error of the mean; where they are not visible they are smaller than the plot markers.

The mean growth rate and the ribosome concentration of newborn cells correlates negatively with their size.

(A) The normalized specific growth rate of newborn cells is shown as function of the normalised birth size. Normalisation was done by division by the corresponding average value. (B) Three pairs of daughter cells are shown with fluorescently-labelled ribosomes that preferentially localise outside of the nucleoid in cell poles (Top). We quantified the ribosome concentration along the length axis (at fixed length intervals) of single cells by determining the total fluorescence orthogonal to this axis (Middle). The resulting data is shown as function of the normalised cell length (Bottom), which indicates the highest ribosome fluorescence at cell poles. Note that at the cell ends, the fluorescence drops in the periplasmic region of cells, which is devoid of ribosomes. (C) The concentration (total fluorescence divided by cell area) of the ribosome at birth and GFP are shown as function of the birth size of newborn cells, indicating that smaller-than-average cells have indeed higher ribosome concentrations than average-sized whereas larger-than-average cells have lower concentrations. The concentration of GFP proteins in newborn cells is size independent, because they spread homogeneously, like metabolic proteins. The full lines are fits of theoretical expectations for a cell that is either completely filled with a homogeneously spread protein (γ=1) or with ribosomes that occupy about half of the cytosolic volume (γ=0.52). For the GFP protein data, cells were grown on lactose as carbon source. (D) The normalised mean growth rate of newborn cells is plotted against their ribosome content (as function of their birth size; results of Figure A and C combined), showing that the growth rate of newborn cells correlates positively with their ribosome content, as expected 6.

Generic mathematical model captures the experimental data.

(A) Uneven division of a mother cell with polar ribosomes and homogeneously spread metabolic enzymes leads to daughter cells with identical metabolic enzyme concentrations, but deviating ribosome concentrations. Small newborn cells tend to have higher ribosome concentrations than large newborn cells. (B) In the model, ppGpp regulates the ratio of ribosomes to metabolic enzymes, by steering the saturation of ribosomes with their substrates to a fixed setpoint. (C) Since restoring the optimal metabolism versus biosynthesis rates (as explained in B) takes more than one cell cycle, mother cells will generally not yet be in a steady state at their division. Their daughters therefore inherit the perturbation consequences of previous generations, affecting their growth rate at birth. (D-F) A comparison of the experimental data for differently sized cells at birth, to averages of 50000 consecutive cell-cycle simulations. For ribosomes in D, metabolic enzymes in E and sER in F. (G) Birth-to-division growth rate trajectories for different length bins, from our mathematical model simulation with 50000 rod-shaped cells, based on cell-size dependent ribosome partitioning (A), saturation set-point control of ribosome expression (B), and the non-steady state mother effect (C). This figure qualitatively captures the experimental data shown in Fig. 1C. (H) A panel of three plots showing representative simulated trajectories of volumetric growth rate (μV), elongation rate and cell length. For the growth rate plot, the dashed line indicates the average growth rate for the entire simulation. For the length plot, the dashed line indicates 50% of the length of the associated mother cell. (I) Comparison and validation of experimental data with a model prediction. The growth-rate effect of polar localisation of ribosomes is less in large cells, because a relatively large fraction of ribosomal is located mid-cell, along the nucleoid 33,45, which reduces the size-dependent asymmetry in ribosome and metabolic protein concentration in non-average-sized, newborn cells.

Notations used in this work.