Mechanistic Origin of Cell-Size Control and Homeostasis in Bacteria

Abstract

Evolutionarily divergent bacteria share a common phenomenological strategy for cell-size homeostasis under steady-state conditions. In the presence of inherent physiological stochasticity, cells following this "adder" principle gradually return to their steady-state size by adding a constant volume between birth and division, regardless of their size at birth. However, the mechanism of the adder has been unknown despite intense efforts. In this work, we show that the adder is a direct consequence of two general processes in biology: (1) threshold-accumulation of initiators and precursors required for cell division to a respective fixed number-and (2) balanced biosynthesis-maintenance of their production proportional to volume growth. This mechanism is naturally robust to static growth inhibition but also allows us to "reprogram" cell-size homeostasis in a quantitatively predictive manner in both Gram-negative Escherichia coli and Gram-positive Bacillus subtilis. By generating dynamic oscillations in the concentration of the division protein FtsZ, we were able to oscillate cell size at division and systematically break the adder. In contrast, periodic induction of replication initiator protein DnaA caused oscillations in cell size at initiation but did not alter division size or the adder. Finally, we were able to restore the adder phenotype in slow-growing E. coli, the only known steady-state growth condition wherein E. coli significantly deviates from the adder, by repressing active degradation of division proteins. Together, these results show that cell division and replication initiation are independently controlled at the gene-expression level and that division processes exclusively drive cell-size homeostasis in bacteria. VIDEO ABSTRACT.

Keywords: ClpXP; DnaA; FtsZ; adder; bacterial cell division; balanced growth; cell size; homeostatic control; replication initiation; threshold model.

Figure 1:. E. coli is both the initiation adder and division adder, robust to static inhibition of biosynthesis.

(A) Division adder vs. initiation adder. Upper: Δ_d is the added size between birth size S_b and division size S_d, and Δ_i is the total added size between two consecutive initiations. s_i is the cell size at initiation per origin, and δ_i is Δ_i per origin. Cell length is used as a proxy for cell size because cell width remains mostly constant during cell elongation [3] (Figure S4). Lower: Illustration of the replication cycle with two overlapping cell cycles. (B) Resolving overlapping foci using intensity weighting (STAR Methods). (C) Three major measured physiological parameters show 8%−20% of variation. Each dot represents measurement from a single cell. (D) Under steady-state growth, E. coli is a division and an initiation adder, with or without static biosynthetic inhibition. Symbols are the binned data and error bars indicate standard errors of mean. In the correlation plots, the variables were rescaled by their means. 6 μM chloramphenicol and 0.05 μg/ml fosfomycin were used. See sample size in Table S3. See also Figures S1 and S2, and Data S1.

Figure 2:. Survey of the 9-dimensional cell-size homeostasis space via stochastic Helmstetter-Cooper model assuming a co-regulation hypothesis between replication initiation and cell division.

(A) The schematics of single-cell simulation of cell growth and cell cycle progression. We used experimental data to introduce stochasticity to λ, τ_cyc, and s_i. (STAR Methods; Methods S1–I). We did not consider stochasticity in the septum position because its variability is the smallest (< 5%) among all measured parameters in E. coli [3]. (B) Survey results. Pearson coefficient was used to quantify both cross-correlations [e.g. corr(λ, τ_cyc)] and mother-daughter autocorrelations [e.g. corr(λⁿ, λⁿ⁺¹)]. Each 3-D plot is based on 1,000 simulations, and each simulation computed 10,000 division cycles (Methods S1–I). Purple color indicates an adder-like behavior defined as −0.1 < corr(Δ_d, S_b) < 0.1 (inset on bottom left). ^⊗ means the actual simulation took the convolution of all nine dimensions. (C) Simulations revealed that the adder phenotype would break if the initiation size autocorrelation can be modulated, and the division adder and the initiation adder should co-vary (inset). The division adderness is corr(Δ_d, S_b), and the initiation adderness is corr(δ_i, s_i). See also Figure S2, Data S1 and Methods S1.

Figure 3:. Dynamic perturbation of DnaA production breaks the initiation adder but not the division adder.

(A) Prediction of periodic induction of dnaA at every other generation (period T=2τ), based on the co-regulation hypothesis [17, 37]. Small-born cells would grow by larger added size, whereas large-born cells would grow by smaller added size, behaving like a sizer. (B) Initiation size periodically oscillated, breaking the initiation adder. The division adder remained intact, refuting the co-regulation hypothesis. The period of IPTG infusion was about 4τ, and the IPTG concentration was altered between 200 μM and 0 μM (Methods S1–III.E). The left plots show the data of periodic underexpression of dnaA. Each dot corresponds to one division cycle of a single cell. In the correlation plots, the variables were normalized by their means and the shaded area represents the 95% confidence interval of linear fit to the respective raw scatter plot. The cell images overlay phase contrast with fluorescence of replisome markers. See also Figure S3, STAR Methods, Methods S1 and Table S3.

Figure 4:. Dynamic perturbation to division breaks the division adder but not the initiation adder.

(A) Dynamic modulation of division protein FtsZ oscillates the division size but not the initiation size. (B) To periodically modulate the FtsZ production, IPTG concentration was alternated between 0 μM and 10 μM for E. coli, and xylose concentration between 0.1% w/v and 1% w/v for B. subtilis, at every 4τ. For periodic induction of sulA in E. coli, IPTG concentration was alternated between 0 μM and 40 μM, at every 4τ. The data presentation of this figure is the same as that in Figure 3 (see caption). See also Figure S4 and Methods S1.

Figure 5:. The mechanistic origin of the adder and validation.

(A) The adder phenotype requires accumulation of division proteins to a fixed amount 2N* to trigger division, and their balanced biosynthesis during growth. Under these conditions, newborn cells are born either larger or smaller than the population average, but they on average contain N* division proteins. The two adder requirements ensure that both small-born and large-born cells add a constant size (namely, N* division proteins) in each generation. (B) A typical timelapse sequence with FtsZ-mVenus. The total intensity was obtained by integrating the FtsZ-mVenus fluorescence intensity over the entire cell, which increases steadily from birth to division, tracking elongation of the cell. As a result, the FtsZ-mVenus concentration stays nearly constant within fluctuations. (C) The synthesis and accumulation of FtsZ in E. coli cells fulfills both requirements for adder. The total added FtsZ number ΔN (estimated by the added fluorescence ΔI) and the synthesis per unit volume dN/dS were constant and independent of cell size at birth. See also Figure S5 and Methods S1.

Figure 6:. Testing the mechanism of adder in the FtsZ oscillation experiments.

(A) Total FtsZ-mVenus concentration oscillates in response to the periodic induction, but the threshold amount at the septum is invariant. The amount of FtsZ accumulated in the septum ring was estimated by integrating the fluorescence intensity within a fixed area enclosing the mid-cell region (STAR Methods). The solid lines represent the prediction based on balanced biosynthesis and threshold model (Methods S1–III). (B) The total added fluorescence ΔI and the max Z-ring intensity remain invariant with respect to birth size. By contrast, the production rate of FtsZ was variable due to oscillations. Symbol colors indicate repeats of experiments, similar to Figure 5B. See also Figure S6.

Figure 7:. Restoring the division adder.

(A) Our hypothesis for why E. coli under slow growth conditions deviated from the adder towards the sizer reported in [19]. In slow-growing cells, significant amount of FtsZ is actively degraded by ClpXP [64, 65], which decreases autocorrelations of FtsZ concentration. (B) We were able to restore the adder in slow growth conditions (doubling time ≈ 4 hours) by repressing clpX expression via tCRISPRi (STAR Methods), confirming our hypothesis. Inset shows that wildtype E. coli is an initiation adder in slow growth conditions. Each shaded area represents the 95% confidence interval of linear fit to the respective raw scatter plot. See also Figure S7 and STAR Methods.