Stochasticity and homeostasis in the E. coli replication and division cycle

Abstract

How cells correct for stochasticity to coordinate the chromosome replication and cellular division cycle is poorly understood. We used time-lapse microscopy and fluorescently labelled SeqA to determine the timing of birth, initiation, termination, and division, as well as cell size throughout the cell cycle. We found that the time between birth and initiation (B-period) compensates for stochastic variability in birth size and growth rate. The time between termination and division (D-period) also compensates for size and growth variability, invalidating the notion that replication initiation is the principal trigger for cell division. In contrast, the time between initiation and termination (C-period) did not display such compensations. Interestingly, the C-period did show small but systematic decreases for cells that spontaneously grew faster, which suggests a coupling between metabolic fluctuations and replication. An auto-regressive theoretical framework was employed to compare different possible models of sub-period control.

Figure 1. Replication and division variability in single cells.

(A) Cells grown rapidly in defined rich medium. SeqA is fluorescently labeled with mCherry (red). Foci report on replication forks. (B) Cells grown slowly in succinate minimal medium. (C) Time-lapse images of cells growing on succinate. (D) Schematic representation of the chromosomal replication cycle in slow-growing cells. Red indicates the hemimethilated DNA binding SeqA. Indicated are the time between birth and replication initiation (B period), the subsequent time until termination (C period), and the subsequent time until division (D period). (E) Position of SeqA-foci and cell length against cell age, with 0 denoting birth and 1 division. Two typical cell cycles are highlighted in color. Top and bottom lines indicate cell length determined from phase contrast images. Middle lines indicate position of SeqA foci along the cell axis. N = 81 cell cycles. F) Corresponding histograms of B,C, and D periods.

Figure 2. Compensation for size variability.

(A) Schematic diagram indicating the cell cycle periods, and the corresponding length of the cell at birth (L_birth), replication initiation (L_init), termination (L_term), and division (L_div). (B) Histogram of cell lengths at birth, and correlations with the B period. N = 81 cell cycles. (C) Histogram of cell lengths at initiation, and correlations with the C period. D) Histogram of cell lengths at termination, and correlations with the D period. E) Histogram of cell lengths at division.

Figure 3. Compensation for growth rate variability.

(A) Histogram of growth rates for individual cell cycles. The values are determined by fitting the logarithm of the cell length against time, and thus indicate a length doubling per hour. N = 81 cell cycles. (B) B period against growth rate. (C) C period against growth rate. (D) D period against growth rate.

Figure 4. Model and comparison with data.

(A) Width of the cell size distribution, and its dependence on the strength of control in the B period (k₁) and the D period (k₂). In contrast, the C period is not modulated in response to size variability, and hence acts as a pure timer (panel B). Red circle indicates the empirically determined values. Decreasing k₁ and k₂ leads to a widening distribution (cyan square, panel C). See SI Appendix for model details. (B) Values of k₁ (left) and k₂ (right) are estimated from the empirical data. μ indicates the exponential elongation rate, T_X the duration of the sub-period X. X can be either B, C, or D. The C period data is consistent with a timer (center). Black squares are averages of binned data; red line is the best linear fit; shaded region represents the standard error of the fit parameters (confidence level of 95%). N = 81 cell cycles. (C) Comparison between data and predicted birth size distribution. Using the fits of panel B, the predictions (red line) are consistent with the empirical histogram of birth sizes (histogram). For lower compensation strengths, the distribution is wider (cyan line, square in panel A). (D) Model predictions (dashed red line) for the dependence of total cell elongation on birth size is consistent with the data. E) Model predictions for the added size as a function of birth size. The three sub-periods together yield an approximately constant average added size (dashed red line), which is consistent with the empirical data.