Threshold accumulation of a constitutive protein explains E. coli cell-division behavior in nutrient upshifts

Abstract

Despite a boost of recent progress in dynamic single-cell measurements and analyses in Escherichia coli, we still lack a mechanistic understanding of the determinants of the decision to divide. Specifically, the debate is open regarding the processes linking growth and chromosome replication to division and on the molecular origin of the observed "adder correlations," whereby cells divide, adding roughly a constant volume independent of their initial volume. In order to gain insight into these questions, we interrogate dynamic size-growth behavior of single cells across nutrient upshifts with a high-precision microfluidic device. We find that the division rate changes quickly after nutrients change, much before growth rate goes to a steady state, and in a way that adder correlations are robustly conserved. Comparison of these data to simple mathematical models falsifies proposed mechanisms, where replication-segregation or septum completions are the limiting step for cell division. Instead, we show that the accumulation of a putative constitutively expressed "P-sector divisor" protein explains the behavior during the shift.

Keywords: E. coli; cell division; cell growth; mathematical modeling; single-cell biology.

Fig. 1.

Robust and long-term single-cell tracking through a nutritional upshift. (A) Snapshots of trapped cells in microfluidic device under stringent (Left) and rich nutrient conditions (Right) (false-colored). (B) Steady-state distributions of growth rate ${\alpha }_{cc}$ in the two growth media. (C) Steady-state distributions of birth volumes $V_0$ for the sample populations in B. (D) Sample segmentation and tracking before and after the growth medium switch is implemented; time since switch is shown in hours. (E) Tracking the change of instantaneous growth rate following the switch for cells shown above. Yellow regions indicate time range spanned by segmented images; plotted line color corresponds to the cell above with the same color segmented boundary. (F) Volume tracking of the same cell lines. Interdivision time $\tau$ is identified as the interval between dramatic volume decreases.

Fig. 2.

Near-adder behavior is conserved through a nutrient upshift, despite complex dynamics of growth and division processes. Medium shift is indicated at dotted vertical line. (A) Mean growth rate (defined by a derivative of single-cell growth curves, as illustrated by the sketch in Left) as a function of time in the experiment. The solid line indicates observable mean, and shaded regions indicate SD for all time series. (B) Interdivision time transiently increases before reaching its new (lower) steady value across the upshift. (C and D) Mean added volume shows an overshoot over more than 2 h after the shift; the mean ratio of added to initial size is one at steady states. (E) The division control shows near-adder behavior robustly across the shift. The adder plot (added size vs. initial cell size, as illustrated by the sketch on Left) quantifies division control by the slope $\zeta$ (−1 for sizer, 1 for timer, and 0 for adder) (39). Data refer to averages over biological replicates using the P5ter promoter strain (Materials and Methods).

Fig. 3.

The nonsteady data across the nutrient shift falsify commonly assumed models for division dynamics. (A) Summary of the models tested. (B–D) Dynamics of interdivision time (B) added size (C) and across the shift (D) cannot be re-created by existing size-control models. In particular, all of the tested models are too slow in reproducing the added-size dynamics and do not reproduce the initial increase in interdivision times. (E) The behavior of division control across the shift is steady across the shift for all three models considered. Data refer to averages over biological replicates using the P5ter promoter strain (Materials and Methods).

Fig. 4.

A putative divisor protein expressed from a constitutive promoter explains the shift data. (A) As model input, we used the measured instantaneous growth rates and volume-specific production rate $r$ (obtained from derivatives along lineages) from our promoters (in this case, the P5 constitutive promoter inserted close to the replication terminus). Note that this quantity has units ${\mathrm{m}\mathrm{i}\mathrm{n}}^{-1}$/$\mu {\mathrm{m}}^3$, minus a constant conversion factor from fluorescence to molecule number. The panel also shows the absolute fluorescence $F$ from the same promoter. A.u., arbitrary units. (B–D) The model predicts faithfully the size dynamics. (E) The model reproduces the observed robustness of near-adder size control. Other model variants using the production rates of different reporters fail to reproduce the observed size dynamics (SI Appendix, Figs. S6–S8). Data refer to average over biological replicates using the P5ter promoter strain (see Materials and Methods and SI Appendix, Figs. S6–S8 for the other strains).