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Division in Escherichia coli is triggered by a size-sensing rather than a timing mechanism.

Robert L, Hoffmann M, Krell N, Aymerich S, Robert J, Doumic M - BMC Biol. (2014)

Bottom Line: In contrast, a sizer model is robust and fits the data well.In addition, we tested the effect of variability in individual growth rates and noise in septum positioning and found that size control is robust to this phenotypic noise.We therefore provide the first precise quantitative assessment of different cell cycle models.

View Article: PubMed Central - HTML - PubMed

Affiliation: INRA, Micalis CNRS-UMR 1319, 78350 Jouy-en-Josas, France. lydia.robert@upmc.fr.

ABSTRACT

Background: Many organisms coordinate cell growth and division through size control mechanisms: cells must reach a critical size to trigger a cell cycle event. Bacterial division is often assumed to be controlled in this way, but experimental evidence to support this assumption is still lacking. Theoretical arguments show that size control is required to maintain size homeostasis in the case of exponential growth of individual cells. Nevertheless, if the growth law deviates slightly from exponential for very small cells, homeostasis can be maintained with a simple 'timer' triggering division. Therefore, deciding whether division control in bacteria relies on a 'timer' or 'sizer' mechanism requires quantitative comparisons between models and data.

Results: The timer and sizer hypotheses find a natural expression in models based on partial differential equations. Here we test these models with recent data on single-cell growth of Escherichia coli. We demonstrate that a size-independent timer mechanism for division control, though theoretically possible, is quantitatively incompatible with the data and extremely sensitive to slight variations in the growth law. In contrast, a sizer model is robust and fits the data well. In addition, we tested the effect of variability in individual growth rates and noise in septum positioning and found that size control is robust to this phenotypic noise.

Conclusions: Confrontations between cell cycle models and data usually suffer from a lack of high-quality data and suitable statistical estimation techniques. Here we overcome these limitations by using high precision measurements of tens of thousands of single bacterial cells combined with recent statistical inference methods to estimate the division rate within the models. We therefore provide the first precise quantitative assessment of different cell cycle models.

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Experimental and reconstructed age-size distributions for representative experiments from Stewartet al.[25](f1) and Wanget al.[26](s1).(A,B) Experimental age-size distributions for representative experiments f1 (A) and s1 (B). The frequency of cells of age a and size s in the population is represented by the color at the point of coordinate a on the x-axis and s on the y-axis, according to the scale indicated to the right of the figure. (C,D) Reconstruction of the distributions using the Age Model (C: reconstruction of the data f1 shown in panel A; D: reconstruction of the data s1 shown in panel B). These reconstructed distributions were obtained from simulations with the Age Model using a division rate estimated from the data (C: from f1, D: from s1). The growth functions used for the simulations are detailed in the Methods section. (E,F) Reconstruction of the distributions using the Size Model (E: reconstruction of the data f1 shown in panel A; F: reconstruction of the data s1 shown in panel B). These distributions were obtained from simulations with the Size Model using a division rate estimated from the data (E: from f1, F: from s1) with an exponential growth function (see Methods).
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Figure 3: Experimental and reconstructed age-size distributions for representative experiments from Stewartet al.[25](f1) and Wanget al.[26](s1).(A,B) Experimental age-size distributions for representative experiments f1 (A) and s1 (B). The frequency of cells of age a and size s in the population is represented by the color at the point of coordinate a on the x-axis and s on the y-axis, according to the scale indicated to the right of the figure. (C,D) Reconstruction of the distributions using the Age Model (C: reconstruction of the data f1 shown in panel A; D: reconstruction of the data s1 shown in panel B). These reconstructed distributions were obtained from simulations with the Age Model using a division rate estimated from the data (C: from f1, D: from s1). The growth functions used for the simulations are detailed in the Methods section. (E,F) Reconstruction of the distributions using the Size Model (E: reconstruction of the data f1 shown in panel A; F: reconstruction of the data s1 shown in panel B). These distributions were obtained from simulations with the Size Model using a division rate estimated from the data (E: from f1, F: from s1) with an exponential growth function (see Methods).

Mentions: We used both the Age Model and Size Model to fit the experimental age-size distributions, following the approach described above. The growth law below xmin and above xmax is unknown. Therefore, to test the Age Model, growth was assumed to be exponential between xmin and xmax and we tested several growth functions v(x) for x<xmin and x>xmax, such as constant (i.e. linear growth) and polynomial functions. Figure 3 shows the best fit we could obtain. Comparing the experimental data f1 shown in Figure 3A (Figure 3B for s1 data) with the reconstructed distribution shown in Figure 3C (Figure 3D for s1 data) we can see that the Age Model fails to reconstruct the experimental age-size distribution and produces a distribution with a different shape. In particular, its localization along the y-axis is very different. For instance, for f1 data (panels A and C), the red area corresponding to the maximum of the experimental distribution is around 2.4 on the y-axis whereas the maximum of the fitted distribution is around 3.9. The y-axis corresponds to cell size. The size distribution produced by the Age Model is thus very different from the size distribution of the experimental data (experimental and fitted size distributions are shown in Additional file 1: Figure S9).


Division in Escherichia coli is triggered by a size-sensing rather than a timing mechanism.

Robert L, Hoffmann M, Krell N, Aymerich S, Robert J, Doumic M - BMC Biol. (2014)

Experimental and reconstructed age-size distributions for representative experiments from Stewartet al.[25](f1) and Wanget al.[26](s1).(A,B) Experimental age-size distributions for representative experiments f1 (A) and s1 (B). The frequency of cells of age a and size s in the population is represented by the color at the point of coordinate a on the x-axis and s on the y-axis, according to the scale indicated to the right of the figure. (C,D) Reconstruction of the distributions using the Age Model (C: reconstruction of the data f1 shown in panel A; D: reconstruction of the data s1 shown in panel B). These reconstructed distributions were obtained from simulations with the Age Model using a division rate estimated from the data (C: from f1, D: from s1). The growth functions used for the simulations are detailed in the Methods section. (E,F) Reconstruction of the distributions using the Size Model (E: reconstruction of the data f1 shown in panel A; F: reconstruction of the data s1 shown in panel B). These distributions were obtained from simulations with the Size Model using a division rate estimated from the data (E: from f1, F: from s1) with an exponential growth function (see Methods).
© Copyright Policy - open-access
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC4016582&req=5

Figure 3: Experimental and reconstructed age-size distributions for representative experiments from Stewartet al.[25](f1) and Wanget al.[26](s1).(A,B) Experimental age-size distributions for representative experiments f1 (A) and s1 (B). The frequency of cells of age a and size s in the population is represented by the color at the point of coordinate a on the x-axis and s on the y-axis, according to the scale indicated to the right of the figure. (C,D) Reconstruction of the distributions using the Age Model (C: reconstruction of the data f1 shown in panel A; D: reconstruction of the data s1 shown in panel B). These reconstructed distributions were obtained from simulations with the Age Model using a division rate estimated from the data (C: from f1, D: from s1). The growth functions used for the simulations are detailed in the Methods section. (E,F) Reconstruction of the distributions using the Size Model (E: reconstruction of the data f1 shown in panel A; F: reconstruction of the data s1 shown in panel B). These distributions were obtained from simulations with the Size Model using a division rate estimated from the data (E: from f1, F: from s1) with an exponential growth function (see Methods).
Mentions: We used both the Age Model and Size Model to fit the experimental age-size distributions, following the approach described above. The growth law below xmin and above xmax is unknown. Therefore, to test the Age Model, growth was assumed to be exponential between xmin and xmax and we tested several growth functions v(x) for x<xmin and x>xmax, such as constant (i.e. linear growth) and polynomial functions. Figure 3 shows the best fit we could obtain. Comparing the experimental data f1 shown in Figure 3A (Figure 3B for s1 data) with the reconstructed distribution shown in Figure 3C (Figure 3D for s1 data) we can see that the Age Model fails to reconstruct the experimental age-size distribution and produces a distribution with a different shape. In particular, its localization along the y-axis is very different. For instance, for f1 data (panels A and C), the red area corresponding to the maximum of the experimental distribution is around 2.4 on the y-axis whereas the maximum of the fitted distribution is around 3.9. The y-axis corresponds to cell size. The size distribution produced by the Age Model is thus very different from the size distribution of the experimental data (experimental and fitted size distributions are shown in Additional file 1: Figure S9).

Bottom Line: In contrast, a sizer model is robust and fits the data well.In addition, we tested the effect of variability in individual growth rates and noise in septum positioning and found that size control is robust to this phenotypic noise.We therefore provide the first precise quantitative assessment of different cell cycle models.

View Article: PubMed Central - HTML - PubMed

Affiliation: INRA, Micalis CNRS-UMR 1319, 78350 Jouy-en-Josas, France. lydia.robert@upmc.fr.

ABSTRACT

Background: Many organisms coordinate cell growth and division through size control mechanisms: cells must reach a critical size to trigger a cell cycle event. Bacterial division is often assumed to be controlled in this way, but experimental evidence to support this assumption is still lacking. Theoretical arguments show that size control is required to maintain size homeostasis in the case of exponential growth of individual cells. Nevertheless, if the growth law deviates slightly from exponential for very small cells, homeostasis can be maintained with a simple 'timer' triggering division. Therefore, deciding whether division control in bacteria relies on a 'timer' or 'sizer' mechanism requires quantitative comparisons between models and data.

Results: The timer and sizer hypotheses find a natural expression in models based on partial differential equations. Here we test these models with recent data on single-cell growth of Escherichia coli. We demonstrate that a size-independent timer mechanism for division control, though theoretically possible, is quantitatively incompatible with the data and extremely sensitive to slight variations in the growth law. In contrast, a sizer model is robust and fits the data well. In addition, we tested the effect of variability in individual growth rates and noise in septum positioning and found that size control is robust to this phenotypic noise.

Conclusions: Confrontations between cell cycle models and data usually suffer from a lack of high-quality data and suitable statistical estimation techniques. Here we overcome these limitations by using high precision measurements of tens of thousands of single bacterial cells combined with recent statistical inference methods to estimate the division rate within the models. We therefore provide the first precise quantitative assessment of different cell cycle models.

Show MeSH
Related in: MedlinePlus