Fig 1.
Simulated effects of a molecular network with an endogenous growth-regulating threshold in bacteria.
a. Simplified toxin-antitoxin module, depicting its interaction with cellular growth rate. b. Deterministic steady state model predictions for a toxin with growth feedback. A regime with no deterministic molecular steady state (labeled "Growth Arrest") arises when toxin production sufficiently exceeds the growth feedback-imposed threshold. Growth rate is normalized to the maximum = 1. c. Binomial phenotypic inheritance at a constant molecule production rate. With no effect on cellular growth rate, the population exhibits regression to the mean within a few generations of division. d. With a discrete growth arrest threshold, the population becomes increasingly skewed over time. Box and whisker plots represent median, interquartile range, and range of a population started from a single simulated cell. Details on model implementation are presented in Supplemental Materials.
Fig 2.
Growth rate of E. coli B REL606 GFP+ cells prone to stochastic growth arrest in high lactose reveals lineage dependence.
Numbers indicate time in hours. a–d. Colony grown in a commercial microfluidic device with continuous perfusion of minimal medium containing 50 mg/ml lactose as described in Methods. e–h. Colony grown with continuous perfusion of minimal medium containing 2 mg/ml glucose, which does not predispose cells to growth arrest. a, e. Growth kinetics of a selection of cells. Individual trajectories are divided by cell division or different growth rates by a least-squares fit of the data to the model L(t) = L0egt. b, f. Growth rates from exponential model fit. Vertical lines indicate cell division times for the corresponding trajectory color. c, g. Selected frames of the time-lapse microscopy experiment. d, h. Lineages derived from time-lapse microscopy. Colors indicate growth rate. Lack of color indicates insufficient data for a significant fit. Note asymmetry in d and symmetry in h.
Fig 3.
Simulated lineages over a range of toxin production rates.
Time proceeds downward in each lineage and begins at the onset of toxin production (t = 100 h). a. Lineage growth rate superimposed on the lineages. b. Free toxin concentration superimposed on the lineage. Lineages for production rates 3.5 /min and higher are plotted with wider trajectories for visibility.
Fig 4.
Growth, lineage information, and diversity of simulated cellular lineages at various rates of toxin production at 4 h.
a. Average cellular growth rates (red) and toxin concentrations (blue) 150 minutes after onset of stress are proportional to toxin production rate, with distinct growth regulation regimes. Error bars indicate standard deviation. b. Mutual information between cell pair growth rate differences, in red (or toxin concentration difference, in blue) and their lineage distance reveals a lineage-dependent effect on cellular phenotypes near the regulatable region. c. Dispersion of average growth rate for low toxin production rates. Vertical bar represents the peak mutual information depicted in panel b. d. Growth rate distributions in the population at various toxin production rates as indicated. Red represents the mean frequency at a given growth rate; blue, standard deviation in the frequency.
Fig 5.
Critical slowing down of growing cell dynamics.
a. Growing cell numbers over time in individual simulations (blue-green lines) and averaged between them (red line) reveals persistent dampening oscillations in the critical regime. b. Mean absolute autocorrelations near the critical regime. Δt, lag time after onset of toxin production. Toxin production rates with three zeroes indicate oscillatory solutions that converge slowly to the regimes of exponential growth or extinction. Vertical dashed line indicates peak lineage-growth rate mutual information; see Fig 4. N = 100 simulations for each toxin production rate.
Fig 6.
Entropy of growth rates and toxin concentrations at 250 min.
Vertical line indicates the point of highest lineage-dependent mutual information between growth rate and lineage distance. a. Fine-grained binning. b. Binary binning into growing-non growing or high-low toxin concentration. Error bars indicate standard deviation.
Fig 7.
Distribution of growth arrested cluster sizes in simulated lineages.
Clusters are exponentially distributed below the critical region (red line, simulation; gray dashed line, exponential fit ae–bc for cluster sizes c) but diverge from an exponential distribution near the critical region, eventually becoming bimodal (purple, blue, green, and orange lines). Each parameter set was simulated 10,000 times. a. Raw probability distributions. b. Probability distributions normalized to the probability of cluster size 1.