Two-Gradient Model in <i>d</i> = 2

<div><p>(A) The mean threshold position fluctuates about <i>L</i>/2 due to the symmetry of the system.</p><p>(B) Variation of the width <i>w</i> as a function of averaging time.</p><p>(C) Data collapse of the width as a function of averaging time, at long times, for a range of parameter values. The full line shows <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030078#pcbi-0030078-e019" target="_blank">Equation 19</a> with <i>k~</i>_2<i>d</i> = 0.63 and Α~ = 2.5. * indicates the standard parameter values. For the other datasets, parameter values were changed as follows: open circle, <i>D</i> = 0.5 μm²s⁻¹; open square, <i>J</i> = 9 μm⁻¹s⁻¹; ×, Δ<i>x</i> = 0.02 μm; closed circle, <i>μ</i> = 1 s⁻¹; +, <i>μ</i> = 0.25 s⁻¹; diamond, <i>L</i> = 7.5 μm; and inverted triangle, <i>L</i> = 15 μm and Δ<i>x</i> = 0.02 μm. </p><p>(D) Plot of width as a function of decay length for averaging times: ×, <i>τ</i> = 30 s; open circle, <i>τ</i> = 45 s; and +, <i>τ</i> = 60 s. The full line shows the prediction from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030078#pcbi-0030078-e019" target="_blank">Equation 19</a>.</p></div

Single-Gradient Model in <i>d</i> = 2

<div><p>(A) Variation of the estimated threshold position with averaging time, with <i>x_T</i> = 2 μm and <i>λ</i> = 2 μm.</p><p>(B) Variation of the width as a function of averaging time.</p><p>(C) Data collapse of the width at large <i>τ</i> for a range of parameter values. Full line shows the prediction of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030078#pcbi-0030078-e007" target="_blank">Equation 7</a> with <i>k</i>_2<i>d</i> = 0.40 and <i>α</i> = 2.5.</p><p>(D) <i>w</i>(<i>τ</i>) as a function of decay length, with <i>x_T</i> = 2 μm. Results for three different averaging times are shown: ×, <i>τ</i> = 10 s; circle, <i>τ</i> = 15 s; and +, <i>τ</i> = 22.5 s. The full line shows the prediction from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030078#pcbi-0030078-e007" target="_blank">Equation 7</a>. At large <i>λ</i>, the simulation results deviate from the prediction since the assumption that <i>L</i> ≫ <i>λ</i> is no longer valid.</p><p>(E) Plot of the probability distribution for measuring the threshold at position <i>x</i> with an averaging time <i>τ</i> = 45 s. The full line shows a normal distribution.</p><p>(F) Scaling of the crossover time, <i>τ_×</i>, according to <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0030078#pcbi-0030078-e013" target="_blank">Equation 13</a>.</p><p>In (A), (B), and (E), the standard parameter values given in the text were used. In (C) and (F), * indicates the standard parameter values. For the other datasets, one parameter value was changed as follows: open circle, <i>D</i> = 0.5 μm²s⁻¹; open square, <i>J</i> = 6.25 μm⁻¹s⁻¹; ×, Δ<i>x</i> = 0.02 μm; closed circle, <i>μ</i> = 1 s⁻¹; +, <i>μ</i> = 0.11 s⁻¹; open diamond, <i>x_T</i> = 1 μm; and inverted triangle, <i>x_T</i> = 3 μm.</p></div

Single-Cell Dynamics Reveals Sustained Growth during Diauxic Shifts

<div><p>Stochasticity in gene regulation has been characterized extensively, but how it affects cellular growth and fitness is less clear. We study the growth of <i>E. coli</i> cells as they shift from glucose to lactose metabolism, which is characterized by an obligatory growth arrest in bulk experiments that is termed the lag phase. Here, we follow the growth dynamics of individual cells at minute-resolution using a single-cell assay in a microfluidic device during this shift, while also monitoring <i>lac</i> expression. Mirroring the bulk results, the majority of cells displays a growth arrest upon glucose exhaustion, and resume when triggered by stochastic <i>lac</i> expression events. However, a significant fraction of cells maintains a high rate of elongation and displays no detectable growth lag during the shift. This ability to suppress the growth lag should provide important selective advantages when nutrients are scarce. Trajectories of individual cells display a highly non-linear relation between <i>lac</i> expression and growth, with only a fraction of fully induced levels being sufficient for achieving near maximal growth. A stochastic molecular model together with measured dependencies between nutrient concentration, <i>lac</i> expression level, and growth accurately reproduces the observed switching distributions. The results show that a growth arrest is not obligatory in the classic diauxic shift, and underscore that regulatory stochasticity ought to be considered in terms of its impact on growth and survival.</p></div

Results of the stochastic model.

<p>(A) Example time-series of cell growth rate for a cell with fast (green), slow (blue) and very slow (red) response. (B) Fluorescence time-series for the cells shown in (A). Inset: The same data on a logarithmic scale, showing that cells with higher expression levels at the time of shift of medium tend to be induced more rapidly. (C) Histograms of growth (red) and fluorescence (green) recovery times, ΔTμ₂ and ΔT_F. In panels (C) and (D), cells at ΔTμ₂ = 0 showed a decrease in growth rate of less than 20%. (D) <i>Lac</i> expression of each lineage at t_shift plotted against growth recovery time. Cells which did not reach the induction threshold in the time of the simulations are placed at ΔTμ₂ = 500 min. Cells with initial concentrations above ∼10 nM typically have a rapid recovery of growth rate. Note that the plot range does not represent the full range of initial expression levels.</p

Stochastic model.

<p>(A) Within each cell the concentrations of lactose, LacYZ and LacI are simulated, as well as the operator state. Lactose imported from the environment or glucose lead to cell growth. (B) Each cell is simulated until it reaches a specified length, at which point it divides to produce two daughter cells. The proteins of the parent cell are partitioned randomly between the two daughters. The daughters are then simulated until their subsequent division. Growth and fluorescence recovery times (T_F and T_µ) are extracted from the reconstructed cell lineages.</p

Switching synchrony of sister cells.

<p>The growth recovery delays ΔTµ₂ are plotted for pairs of sister cells. (A) Data obtained from experiments. N = 75, r² = 0.52, p-value <0.001. (B) Data resulting from simulations. N = 660, r²≈0.13 and p<0.001. Note that in both cases lineages in which one cell switches but its sister or its progeny does not are not plotted (in total: 22 pairs for the experimental data, 146 pairs for the numerical data).</p

Dynamics at the population level and in single cells.

<p>(A) Growth curve for a typical microcolony, indicating the sum of all cell lengths within the colony. (B) Mean fluorescence intensity (per unit area) within cells, averaged over a microcolony. (C) Single-cell length over time for three different lineages, representing cases with no growth rate decrease (green), a lag phase (blue) and a longer lag phase (red). Arrows indicate cell division events. The curves are vertically shifted for clarity. (D) Elongation rates obtained by exponential fits to the length data at sub-cell cycle resolution. Drawn lines are fitted parameterized functions. ΔTµ₂ is the time difference between the time of shift and the half maximum to growth recovery after shift. (E) Fluorescence levels for the three lineages in (C) and (D). Drawn lines are fitted parameterized functions. ΔT_F is the time difference between the time of shift and the half maximum to induction after shift. Black bar: 120 min before the shift, over which data was averaged to determine the expression level prior to the shift.</p