Red dashed line: Spheres follow S = 6 2 / 3 π 1 / 3 V 2 / 3. Gray dashed line: Filamentous cells with constant cell width follow the scaling law: S ∼ V. Black dashed line: Small, medium, and large rod-shaped cells with a conserved aspect ratio of 4 follow the relation: S = 2 π V 2 / 3. ( D) S- V relation for various bacterial cell shapes. Model line uses S = 2 π V 2 / 3 and the nutrient growth law ( Equation 1). Best fit from ( A) shown with horizontal green band gives aspect ratio 4.14 ± 0.17. (Inset) Relationship between γ and aspect ratio η for a sphero-cylinder (red line). ( B) Aspect-ratio distribution for cells growing in steady-state, corresponding to the data in ( A) ( Si et al., 2017). For single deletion Keio set ( Campos et al., 2018), the best fit curve is S = 5.79 V 2 / 3. Best fit shown in dashed black line for steady-state data from Si et al. coli cells subjected to different antibiotics, nutrient conditions, protein overexpression/depletion, and single gene deletions ( Nonejuie et al., 2013 Si et al., 2017 Harris and Theriot, 2016 Vadia et al., 2017 Campos et al., 2018 Gray et al., 2019), follow the scaling relation between population-averaged surface area ( S) and volume ( V): S = γ V 2 / 3 (legend on the right, 5011 data points Supplementary file 1). A constant γ thus defines a constant aspect ratio η = 4.14 ± 0.17 ( Figure 1B-inset), with a coefficient of variation ∼14% ( Figure 1B). Specifically, for a sphero-cylindrical bacterium, S = γ V 2 / 3 implies γ = η π ( η π 4 - π 12 ) - 2 / 3. This surface-to-volume scaling with a constant prefactor, γ, is a consequence of tight control of cell aspect ratio η (length/width) ( Figure 1D), whose mechanistic origin has been puzzling for almost half a century ( Zaritsky, 1975 Zaritsky, 2015). Specifically, during steady-state growth ( Si et al., 2017), γ = 6.24 ± 0.04, suggesting an elegant geometric relation: S ≈ 2 π V 2 / 3. Collected surface and volume data span two orders of magnitude and exhibit a single power law in this regime: S = γ V 2 / 3 ( Figure 1A). coli cells grown under different nutrient conditions, challenged with antibiotics, protein overexpression or depletion, and single gene deletions ( Nonejuie et al., 2013 Harris and Theriot, 2016 Si et al., 2017 Vadia et al., 2017 Campos et al., 2018 Gray et al., 2019). Here we investigated the relation between cell surface area ( S) and cell volume ( V) for E. However, it remains largely unknown how cell length and width are coupled to regulate rod-like bacterial shapes in diverse growth conditions ( Volkmer and Heinemann, 2011 Belgrave and Wolgemuth, 2013 Colavin et al., 2018 Shi et al., 2018). A recent study has linked the determination of cell size to a condition-dependent regulation of cell surface-to-volume ratio ( Harris and Theriot, 2016). At the single-cell level, control of cell volume in many rod-shaped cells is achieved via an adder mechanism, whereby cells elongate by a fixed length per division cycle ( Amir, 2014 Campos et al., 2014 Taheri-Araghi et al., 2015 Deforet et al., 2015 Wallden et al., 2016 Banerjee et al., 2017). When rod-shaped bacteria grow in media with different nutrient availability, both cell length and width increase with growth rate ( Schaechter et al., 1958 Si et al., 2017). This model reveals a mechanism for why bacterial aspect ratio is independent of cell size and growth conditions, and predicts cell morphological changes in response to nutrient perturbations, antibiotics, MreB or FtsZ depletion, in quantitative agreement with experimental data.Ĭell morphology is an important adaptive trait that is crucial for bacterial growth, motility, nutrient uptake, and proliferation ( Young, 2006). To explain the mechanistic origin of aspect-ratio control, we propose a quantitative model for the coupling between bacterial cell elongation and the accumulation of an essential division protein, FtsZ. In this study we uncover a conserved surface-to-volume scaling relation in Escherichia coli and other rod-shaped bacteria, resulting from the preservation of cell aspect ratio. While many recent studies have focused on the mechanisms underlying bacterial cell size control, it remains largely unknown how the coupling between cell length and width results in robust control of rod-like bacterial shapes. Rod-shaped bacterial cells can readily adapt their lengths and widths in response to environmental changes.
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