Quantitative examination of five stochastic cell-cycle and cell-size control models for Escherichia coli and Bacillus subtilis

We examine five quantitative models of the cell-cycle and cell-size control in Escherichia coli and Bacillus subtilis that have been proposed over the last decade to explain single-cell experimental data generated with high-throughput methods. After presenting the statistical properties of these models, we test their predictions against experimental data. Based on simple calculations of the defining correlations in each model, we first dismiss the stochastic Helmstetter-Cooper model and the Initiation Adder model, and show that both the Replication Double Adder and the Independent Double Adder model are more consistent with the data than the other models. We then apply a recently proposed statistical analysis method and obtain that the Independent Double Adder model is the most likely model of the cell cycle. By showing that the Replication Double Adder model is fundamentally inconsistent with size convergence by the adder principle, we conclude that the Independent Double Adder model is most consistent with the data and the biology of bacterial cell-cycle and cell-size control. Mechanistically, the Independent Adder Model is equivalent to two biological principles: (i) balanced biosynthesis of the cell-cycle proteins, and (ii) their accumulation to a respective threshold number to trigger initiation and division.

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Quantitative Examination of Five Stochastic Cell-Cycle and Cell-Size Control Models for Escherichia coli and Bacillus subtilis

Frontiers in Microbiology ◽

10.3389/fmicb.2021.721899 ◽

2021 ◽

Vol 12 ◽

Author(s):

Guillaume Le Treut ◽

Fangwei Si ◽

Dongyang Li ◽

Suckjoon Jun

Keyword(s):

Experimental Data ◽

Escherichia Coli ◽

Cell Cycle ◽

Bacillus Subtilis ◽

Cell Size ◽

Size Control ◽

Statistical Analysis Method ◽

Quantitative Examination ◽

Cell Size Control ◽

Bacterial Cell Cycle

We examine five quantitative models of the cell-cycle and cell-size control in Escherichia coli and Bacillus subtilis that have been proposed over the last decade to explain single-cell experimental data generated with high-throughput methods. After presenting the statistical properties of these models, we test their predictions against experimental data. Based on simple calculations of the defining correlations in each model, we first dismiss the stochastic Helmstetter-Cooper model and the Initiation Adder model, and show that both the Replication Double Adder (RDA) and the Independent Double Adder (IDA) model are more consistent with the data than the other models. We then apply a recently proposed statistical analysis method and obtain that the IDA model is the most likely model of the cell cycle. By showing that the RDA model is fundamentally inconsistent with size convergence by the adder principle, we conclude that the IDA model is most consistent with the data and the biology of bacterial cell-cycle and cell-size control. Mechanistically, the Independent Adder Model is equivalent to two biological principles: (i) balanced biosynthesis of the cell-cycle proteins, and (ii) their accumulation to a respective threshold number to trigger initiation and division.

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Characterizing non-exponential growth and bimodal cell size distributions in Schizosaccharomyces pombe: an analytical approach

10.1101/2021.06.10.447927 ◽

2021 ◽

Author(s):

Chen Jia ◽

Abhyudai Singh ◽

Ramon Grima

Keyword(s):

Cell Cycle ◽

Fission Yeast ◽

Cell Size ◽

Control Strategy ◽

Size Control ◽

Birth Size ◽

Size Distributions ◽

Cell Size Distribution ◽

A Cell ◽

Cell Size Control

Unlike many single-celled organisms, the growth of fission yeast cells within a cell cycle is not exponential. It is rather characterized by three distinct phases (elongation, septation and fission), each with a different growth rate. Experiments also show that the distribution of cell size in a lineage is often bimodal, unlike the unimodal distributions measured for the bacterium Escherichia coli. Here we construct a detailed stochastic model of cell size dynamics in fission yeast. The theory leads to analytic expressions for the cell size and the birth size distributions, and explains the origin of bimodality seen in experiments. In particular our theory shows that the left peak in the bimodal distribution is associated with cells in the elongation phase while the right peak is due to cells in the septation and fission phases. We show that the size control strategy, the variability in the added size during a cell cycle and the fraction of time spent in each of the three cell growth phases have a strong bearing on the shape of the cell size distribution. Furthermore we infer all the parameters of our model by matching the theoretical cell size and birth size distributions to those from experimental single cell time-course data for seven different growth conditions. Our method provides a much more accurate means of determining the cell size control strategy (timer, adder or sizer) than the standard method based on the slope of the best linear fit between the birth and division sizes. We also show that the variability in added size and the strength of cell size control of fission yeast depend weakly on the temperature but strongly on the culture medium.

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Cell-cycle-specific F plasmid replication: regulation by cell size control of initiation.

Journal of Bacteriology ◽

10.1128/jb.173.8.2673-2680.1991 ◽

1991 ◽

Vol 173 (8) ◽

pp. 2673-2680 ◽

Cited By ~ 22

Author(s):

J D Keasling ◽

B O Palsson ◽

S Cooper

Keyword(s):

Cell Cycle ◽

Cell Size ◽

Size Control ◽

Plasmid Replication ◽

F Plasmid ◽

Replication Regulation ◽

Cell Size Control

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A bimolecular mechanism for the cell size control of the cell cycle

Biosystems ◽

10.1016/0303-2647(83)90012-6 ◽

1983 ◽

Vol 16 (3-4) ◽

pp. 297-305 ◽

Cited By ~ 15

Author(s):

L. Alberghina ◽

E. Martegani ◽

L. Mariani ◽

G. Bortolan

Keyword(s):

Cell Cycle ◽

Cell Size ◽

Size Control ◽

Cell Size Control ◽

Bimolecular Mechanism

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Constriction rate modulation can drive cell size control and homeostasis inC. crescentus

10.1101/266817 ◽

2018 ◽

Cited By ~ 1

Author(s):

Ambroise Lambert ◽

Aster Vanhecke ◽

Anna Archetti ◽

Seamus Holden ◽

Felix Schaber ◽

...

Keyword(s):

Cell Cycle ◽

Cell Size ◽

Caulobacter Crescentus ◽

Size Control ◽

Time Lapse ◽

Structured Illumination ◽

Structured Illumination Microscopy ◽

Daughter Cells ◽

Division Site ◽

Cell Size Control

AbstractRod-shaped bacteria typically grow first via sporadic and dispersed elongation along their lateral walls, then via a combination of zonal elongation and constriction at the division site to form the poles of daughter cells. Although constriction comprises up to half of the cell cycle, its impact on cell size control and homeostasis has rarely been considered. To reveal the roles of cell elongation and constriction in bacterial size regulation during cell division, we captured the shape dynamics ofCaulobacter crescentuswith time-lapse structured illumination microscopy and used molecular markers as cell-cycle landmarks. We perturbed constriction rate using a hyperconstriction mutant or fosfomycin inhibition. We report that constriction rate contributes to both size control and homeostasis, by determining elongation during constriction, and by compensating for variation in pre-constriction elongation on a single-cell basis.

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Single-cell data and correlation analysis support the independent double adder model in both Escherichia coli and Bacillus subtilis

10.1101/2020.10.06.315820 ◽

2020 ◽

Author(s):

Guillaume Le Treut ◽

Fangwei Si ◽

Dongyang Li ◽

Suckjoon Jun

Keyword(s):

Escherichia Coli ◽

Cell Cycle ◽

Bacillus Subtilis ◽

Cell Division ◽

Correlation Analysis ◽

Size Control ◽

Replication Initiation ◽

Biological Models ◽

Value Analysis ◽

E Coli

AbstractThe reference point for cell-size control in the cell cycle is a fundamental biological question. We previously reported that we were unable to reproduce the conclusions of Witz et al.’s eLife paper (Witz, van Nimwegen, and Julou 2019) entitled, “Initiation of chromosome replication controls both division and replication cycles in E. coli through a double-adder mechanism”, despite extensive efforts. In this ‘replication double adder’ (RDA) model, both replication and division cycles are determined via replication initiation as the sole implementation point of size control. Witz et al. justified the RDA model using a type of correlation analysis (the “I-value analysis”) that they developed. By contrast, we previously showed that, in both Escherichia coli and Bacillus subtilis, replication initiation and cell division are determined by balanced biosynthesis of key cell cycle proteins (e.g., DnaA for initiation and FtsZ for cell division) and their accumulation to their respective threshold numbers, which Witz et al. coined the ‘independent double adder’ (IDA) model. The adder phenotype is a natural quantitative consequence of these mechanistic principles. In a recent bioRxiv response to our report, Witz and colleagues explicitly confirmed two important limitations of the I-value analysis: (1) it is only applicable to non-overlapping cell cycles, wherein E. coli is known to deviate from the adder principle, and (2) it is only applicable to select biological models and, for example, cannot evaluate the IDA model. These limitations of the I-value analysis were not explained in the original eLife paper and were overlooked during the review process. In this report, we show using data analysis, mathematical modeling, and experiments why the I-value analysis - in its current implementation - cannot compare different biological models. Furthermore, the RDA model is incompatible with the adder principle and is not broadly supported by experimental data. For completeness, we also provide a detailed point-by-point response to Witz et al.’s response (Witz, Julou, and van Nimwegen 2020) in the Supplemental Information.

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