A leader cell triggers end of lag phase in populations of Pseudomonas fluorescens

Abstract

The relationship between the number of cells colonizing a new environment and time for resumption of growth is a subject of long-standing interest. In microbiology this is known as the "inoculum effect." Its mechanistic basis is unclear with possible explanations ranging from the independent actions of individual cells, to collective actions of populations of cells. Here, we use a millifluidic droplet device in which the growth dynamics of hundreds of populations founded by controlled numbers of Pseudomonas fluorescens cells, ranging from a single cell, to one thousand cells, were followed in real time. Our data show that lag phase decreases with inoculum size. The decrease of average lag time and its variance across droplets, as well as lag time distribution shapes, follow predictions of extreme value theory, where the inoculum lag time is determined by the minimum value sampled from the single-cell distribution. Our experimental results show that exit from lag phase depends on strong interactions among cells, consistent with a "leader cell" triggering end of lag phase for the entire population.

Keywords: collective behavior; extreme value theory; growth dynamics; high-throughput millifluidics; microbial population biology.

Figure 1.

Bacterial population growth in droplets. Subfigure (A) shows two droplets of 0.4 μl are separated by an air spacer (to prevent droplet coalescence) inside the tube of a millifluidic machine. Droplets are prepared by “sipping” samples from a 96-well plate. Typically, 230 droplets are produced from six seed cultures that differ solely in the number of founding cells (the inoculum). Each seed culture delivers 40 replicate droplets, but for technical reasons that last delivers 30 replicates. Droplets move back-and-forth, via changes in pressure, passing in front of a fluorescence detector every ∼18 min. Pseudomonas fluorescens SBW25 cells express GFP from a chromosomally integrated reporter, allowing changes in biomass to be determined based on intensity of the fluorescent signal (excitation at 497 nm emission at 527 nm). Signal intensity is calibrated to cell density by plate counting (Figure S8, Supporting Information). The range of detection extends from 4 × 10⁶ to 5 × 10⁹ cells ml⁻¹ (1.6 × 10³ to 2 × 10⁶ cells per droplet). The gray area in subfigures (B) and (C) denotes the region where bacterial density is below the threshold of detection. (B) Fluorescent signal across time from 40 replicate populations (in semi-logscale) in droplets prepared from the same seed culture. The average inoculum in each droplet is N₀ = 1.6 × 10⁵ cell ml⁻¹, or 64 cells per droplet (this concentration is marked by the purple dashed line that goes across (B) and (C)). In this example, the signal exceeds the detection threshold at ∼7 h, by which populations are in exponential growth phase. At ∼20 h, stationary phase is reached, marked by cessation of growth. (C) A single time series showing population growth within a single droplet coming from the set of replicates shown in (B). The left y-axis is shared between these two plots. The blue line depicts cell density derived using DropSignal (Doulcier 2019) and the shaded area represents the standard deviation (SD). Population lag time is inferred as described in text. The purple dotted line crossing N_th = 1.6 × 10⁸ cells ml⁻¹ (64 000 cells per droplet) extrapolates the exponential growth back to its intersection with the inoculum density (purple horizontal dotted line), giving τ ≈ 5 h. The red line gives the derivative of the time series, with shaded SD, and corresponding right y-axis in red.

Figure 2.

Quantitative data on lag-times are consistent with a strongly cooperative exit from lag phase. (A) Population lag time τ as a function of inoculum size for three independent experiments (colors). Symbols are the mean lag times over droplets with a given inoculum size, with error bars denoting the standard deviation (SD). The data are compared to two models (blue lines—average, shaded blue—SD). (B) Cumulative distribution (CDF) of single-cell lag times (θ) from 156 droplets inoculated with a single bacterium on average (dark line). The y-value gives the probability that cell lag times assume a value less than or equal to the x-value. The measured distribution is fitted to a log-normal distribution (red dotted line) with a mean of 6.8 h and a SD of 1.3 h. A Gaussian “de-blurring” applied to these data generates the true distribution of cell lag times (blue dotted line). Both models in (A) simulate populations founded by bacteria with lag times drawn at random from this corrected distribution: cells growing independently in droplets (dashed blue) and cells dividing according to a signal from the leader cell (solid blue).

Figure 3.

Statistical properties of lag times. For three independent experiments (colored symbols), mean lag times (A) over populations and their SD (B) are depicted as a function of inoculum size. Each point is calculated over 40 replicate populations (droplets). Inset: variance as a function of mean. The scaling relations predicted by EVT are shown in dashed lines: for the mean and for the SD. (C) Cumulative Distributions of population lag times for different inoculum sizes [N₀, colors; legend in (D)]. The curves derive from the pooled data of three independent experiments yielding at least 120 population lag times for each. (D) Same data as in (C), scaled by subtraction of empirical mean and division by SD. The white dashed line depicts the fit by the universal distribution predicted by the EVT. The y-axis is shared between (C) and (D).

Figure 4.

How many leader cells? Results of simulation in which each cell produces a growth activator as it exits lag phase, drawn from the experimental distribution. The activator accumulates to a critical threshold and triggers end of lag phase for the entire population. (A) Population lag time as a function of inoculum size (x-axis) and threshold of growth activator (y-axis). (B) Number of leader cells that have exited lag phase before the critical activating threshold was reached. Note that the color-bar corresponds to a narrow range of between 1 and 5 cells.