Cell-size control and homeostasis in bacteria

Abstract

How cells control their size and maintain size homeostasis is a fundamental open question. Cell-size homeostasis has been discussed in the context of two major paradigms: "sizer," in which the cell actively monitors its size and triggers the cell cycle once it reaches a critical size, and "timer," in which the cell attempts to grow for a specific amount of time before division. These paradigms, in conjunction with the "growth law" [1] and the quantitative bacterial cell-cycle model [2], inspired numerous theoretical models [3-9] and experimental investigations, from growth [10, 11] to cell cycle and size control [12-15]. However, experimental evidence involved difficult-to-verify assumptions or population-averaged data, which allowed different interpretations [1-5, 16-20] or limited conclusions [4-9]. In particular, population-averaged data and correlations are inconclusive as the averaging process masks causal effects at the cellular level. In this work, we extended a microfluidic "mother machine" [21] and monitored hundreds of thousands of Gram-negative Escherichia coli and Gram-positive Bacillus subtilis cells under a wide range of steady-state growth conditions. Our combined experimental results and quantitative analysis demonstrate that cells add a constant volume each generation, irrespective of their newborn sizes, conclusively supporting the so-called constant Δ model. This model was introduced for E. coli [6, 7] and recently revisited [9], but experimental evidence was limited to correlations. This "adder" principle quantitatively explains experimental data at both the population and single-cell levels, including the origin and the hierarchy of variability in the size-control mechanisms and how cells maintain size homeostasis.

FIG. 1

Growth law at the population level and cell-size control at the single-cell level. (A) (Top panel) Time series of a typical cell growing in a nutrient rich medium. (Bottom panel) Sample images of dividing E. coli cells in steady-state exponential growth at 37°C in seven different growth media. (B) Partially overlapping distributions of the growth rate and the newborn size measured from individual cells in two different growth conditions. The vertical lines show the population average values. Cells in the overlap region can have the same growth rate or newborn cell size. (C) Population average of single-cell measurements demonstrates exponential dependence of newborn-cell volume on the average growth rate (red). However, s_b vs. λ of individual cells (binned data in blue empty circles; measured by following them from birth to division) show systematic deviations from the average growth law. Thus, although the cells in the overlap region in (B) can have the same growth rate or newborn cell size, the size of individual cells are controlled by a mechanism that is different from the growth law. Otherwise, all blue symbols would have fallen on top of the read line. (D) Correlations between rescaled growth parameters at the single-cell level with standard deviations from the entire set of E. coli data. Generation time vs. size at birth (left), growth rate vs. size at birth (middle), and size at division vs. size at birth (right). Dashed lines, predictions from the Δ model from this work. The first correlation falsifies the timer model, whereas the last correlation falsifies the sizer model. See also Figure S1.

FIG. 2

Experimental evidence of constancy of Δ in bacteria. (A) E. coli: average Δ with respect to the newborn size s_b, with each bin containing > 10³ cells. (B) B. subtilis (C) E. coli size mutants. All rescaled distributions conditional to different newborn size ranges collapse onto one another, demonstrating that E. coli and B. subtilis cells grow by a constant size for division, independent of the newborn cell size. See also Figures S2 and S3.

FIG. 3

Mechanism of size homeostasis by constant Δ. (A) For all newborn cells regardless of their size, if the cells always add a constant Δ and divide in the middle, their respective newborn size automatically converges to Δ. If Δ is subject to fluctuations without correlations from one generation to the next, and the cell divides in the middle with some precision, the newborn size on average still converges to 〈Δ〉. Our data confirm this size homeostasis mechanism for both E. coli (B) and B. subtilis (C). Data in (B) and (C) show the average from all growth conditions used for each organism. See also Video S1.

FIG 4

Origin and quantitative consequences of constant added size Δ. (A) Six distributions are shown in the ascending order of their relative widths. All growth parameters from different growth conditions show scale invariance, i.e., collapse when rescaled by their respective means. (B) Among the six distributions in (A), four distributions are determined by Δ (division size s_d, newborn size s_b, generation time τ_d, and Δ). See Eq. 1. Thus, ρ(Δ) and ρ(λ) are sufficient to reproduce the entire distributions for all growth conditions for both E. coli (C) and B. subtilis (SM) without any adjustable parameters. (D) Constant Δ is consistent with the “structural models” discussed in [22], which assume that the cell grows to accumulate fixed amounts of cell-cycle regulators in each generation. Since metabolism and cell cycle proteins are neither housekeeping nor ribosomal proteins, this prediction can be quantitatively tested using the proteome data [11] and the growth law in Fig. 1C. Indeed, the total P-sector proteins per cell is constant in all growth conditions (E). See also Figure S4 and Table S3.