During bacterial growth, a cell approximately doubles in size before division, after which it splits into two daughter cells. This process is subjected to the inherent perturbations of cellular noise1,2 and thus requires regulation for cell-size homeostasis. The mechanisms underlying the control and dynamics of cell size remain poorly understood owing to the difficulty in sizing individual bacteria over long periods of time in a high-throughput manner. Here we measure and analyse long-term, single-cell growth and division across different Escherichia coli strains and growth conditions3. We show that a subset of cells in a population exhibit transient oscillations in cell size with periods that stretch across several (more than ten) generations. Our analysis reveals that a simple law governing cell-size control—a noisy linear map—explains the origins of these cell-size oscillations across all strains. This noisy linear map implements a negative feedback on cell-size control: a cell with a larger initial size tends to divide earlier, whereas one with a smaller initial size tends to divide later. Combining simulations of cell growth and division with experimental data, we demonstrate that this noisy linear map generates transient oscillations, not just in cell size, but also in constitutive gene expression. Our work provides new insights into the dynamics of bacterial cell-size regulation with implications for the physiological processes involved.
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We thank S. Jun for providing the original mother machine and P. Cluzel for providing their data set on E. coli and B. subtilis growth. We also thank the Light Microscopy Core Facility at Duke University for their help in conducting microscopy experiments. This work was partially supported by a National Science Foundation Career Award (L.Y.), the National Institutes of Health (NIH) (L.Y., R01GM098642, R01GM110494), a DuPont Young Professorship (L.Y.), a David and Lucile Packard Fellowship (L.Y.), a DARPA Biochronicity Grant (DARPA-BAA-11-66, N.E.B.), a NIH Director's New Innovator Award (DP2 OD008654-01, N.E.B.), and a Burroughs Wellcome Fund CASI Award (BWF 1005769.01, N.E.B.).
The authors declare no competing financial interests.
Extended data figures and tables
a–c, Division ratio (a), growth rate (b) and doubling time (c) are plotted against initial cell length (n = 11,168). Black and red lines show binned average and trend line, respectively. In a and b, the trend lines are the linear regression line, whereas equation (4) was used in c. The error bars indicate standard deviation of each bin.
Extended Data Figure 2 A noisy linear map in E. coli cell size control across different growth temperatures and strains.
The same analysis as in Fig. 1e (LI versus LF) was performed for MC4100 grown at 27 °C (a, n = 3,772), MC4100 grown at 25 °C (b, n = 4,539), MG1655 grown at 37 °C (c, n = 10,964), and B/r strain grown at 37 °C (d, n = 5,541). The data sets for MG1655 and B/r strain were from a previous study3. Black and red lines show binned average and linear regression line, respectively. In a–d, a = 1.02, 1.08, 1.03 and 1.14, respectively. The error bars indicate standard deviation of each bin.
a, Time-frequency analysis of the noisy linear map model for LI. The top panel shows a spectrogram of 700-generation simulation constructed using 70-generation segments with 50% overlap. The bottom panel shows the temporal dynamics of LI. The same parameters as in Fig. 2a were used. b, The power spectrum of noisy linear map (X(f)). Equation (3) is plotted for different a (0 ≤ a ≤ 1.8 with 0.2 interval). X(f) = 1/(2πf)2 for a = 2 is the straight line in this log–log plot. Note that the maximum value of f is 0.5 as the time resolution is 1 generation. c, Dependence of oscillation frequencies on a simulated using the rescaled linear map (equation (2)). The noisy linear map model was simulated (Fig. 3a–c) and the distributions of oscillation frequencies are shown for four different values of a (from top to bottom, n = 24, 76, 117 and 79, respectively).
Extended Data Figure 4 Comparison of LI oscillation characteristics between all lineages (blue) and lineages without aberrant cell cycles (red).
a–g, Probability of oscillation (a), average oscillation frequency (b), and distributions of oscillation frequencies (c–g) are shown. In a and b, filled symbols represent experimental data (data shown in red are the same as Fig. 3a, b): circles are MC4100 grown at three different temperatures; squares and triangles are MG1655 and B/r strain, respectively. The unfilled circles were generated from simulations using the rescaled linear map (equation (2), the same plot as Fig. 3a, b). In a, the data shown in blue include 160 (37 °C), 54 (27 °C) and 65 (25 °C) lineages for MC4100, 158 lineages for MG1655, and 80 lineages for B/r strain. The data shown in red include 143 (37 °C), 48 (27 °C), and 57 (25 °C) lineages for MC4100, 97 lineages for MG1655, and 60 lineages for B/r strain. In b–g, only lineages that were considered oscillatory were used. For the data set in blue, n = 58 (37 °C), 21 (27 °C), and 39 (25 °C) for MC4100, 46 for MG1655, and 26 for B/r strain. For the data set in red, n = 51 (37 °C), 18 (27 °C) and 36 (25 °C) for MC4100, 34 for MG1655, and 23 for B/r strain.
Total YFP before division is plotted against total YFP at birth (n = 11,168), revealing a linear map with a = 1.05. Black and red lines show binned average and the linear regression line, respectively. The error bars indicate standard deviation of each bin.
a, Oscillation scores of YFP concentration are shown in an ascending order. The dashed line indicates a threshold for oscillation. b, For four different oscillation frequencies, ACFs with the highest oscillation scores are shown. c, The distribution of oscillation frequencies (n = 47).
The same plots as in Extended Data Fig. 6 but for MC4100 grown at 25 °C. n = 61 in c.
Extended Data Figure 10 A noisy linear map in cell size control in the data sets from ref. 12 and our experimental data of S. pombe
The same analysis as in Fig. 1e (LI versus LF) was performed. These data sets were obtained using a microfluidic device different from the mother machine. a–c, E. coli growth under three different media as indicated (n = 8,795, 4,637 and 684, respectively). d, e, Growth of B. subtilis (n = 1,592) (d) and of S. pombe (n = 85) (e). Black and red lines show binned average and the linear regression line, respectively. In a–e, a = 1.20, 0.864, 0.684, 1.41 and 0.645, respectively. Cell length (µm) (a–d) and cell area (µm2) (e) are shown. The error bars indicate standard deviation of each bin.
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Tanouchi, Y., Pai, A., Park, H. et al. A noisy linear map underlies oscillations in cell size and gene expression in bacteria. Nature 523, 357–360 (2015). https://doi.org/10.1038/nature14562
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