Density fluctuations, homeostasis, and reproduction effects in bacteria

Abstract

Single-cells grow by increasing their biomass and size. Here, we report that while mass and size accumulation rates of single Escherichia coli cells are exponential, their density and, thus, the levels of macromolecular crowding fluctuate during growth. As such, the average rates of mass and size accumulation of a single cell are generally not the same, but rather cells differentiate into increasing one rate with respect to the other. This differentiation yields a density homeostasis mechanism that we support mathematically. Further, we observe that density fluctuations can affect the reproduction rates of single cells, suggesting a link between the levels of macromolecular crowding with metabolism and overall population fitness. We detail our experimental approach and the "invisible" microfluidic arrays that enabled increased precision and throughput. Infections and natural communities start from a few cells, thus, emphasizing the significance of density-fluctuations when taking non-genetic variability into consideration.

Fig. 1. Quantitative-mass imaging and “invisible” microfluidics reveal cell-to-cell variability in dry-density and density fluctuations during growth.

a Cell-to-cell dry-density plotted as a function of cell size; graph plots single-cell snapshot data at various stages along the growth cycle (n = 35,000 observations). b Microcolony expansion from one cell to four generations via quantitative-mass imaging; the vertical direction, with color coding representing cell density (normalized at t = 0, where N = 1). c Microcolony density (normalized at t = 0, N = 1) during expansion using 1D and 2D growth assays; data points and error-bars represent the average and standard deviation of n = 8 independent measurements; time-dependent density differences in 2D were statistically significant (one-way ANOVA, F(6,49) = 51.8, p « 0.001); no such evidence was found for the 1D assays (one-way ANOVA, F(7,56) = 0.8 and p = 0.5). d Density, mass, and area growth curves of individual E. coli cells from birth to division; all parameters are normalized at t = 0 and color coding represents the size, mass, and density of the same cell (i.e., the curves do not represent the dynamics of multiple cells pooled together); the horizontal red line denotes the dynamics of the normalized density (with respect to t = 0) of 10 fixed E. coli cells (DH5α, fixed by overnight incubation in 2% glutaraldehyde, followed by 3× PBS washing) over time (red line denotes the average and blue-shaded area denotes the 95% confidence intervals).

Fig. 2. Single bacteria do not necessarily exhibit identical growth rates in mass and size, and are prone to asymmetric partitioning of biomolecules upon division.

a Growth differentiation with some cells maximizing area (γ_size) and others biomass (γ_mass) accumulation; graph represents the cumulative response of three replicates, with each replicate presented separately in Supplementary Fig. 4; red line corresponds the linear fit of the experimental data (shaded areas are the 95% confidence intervals) and the yellow line represents a slope of 1. b Median density fluctuations during growth (dρ/dt, y-axis) as a function of growth differentiation (γ_A/γ_M, x-axis); dρ/dt were calculated as the median value of all density fluctuations (namely: dρ = ρ_i+1 − ρ_i in the dt = t_i+1 − t_i timeframes—see Methods) during the cell cycle; similarly, the growth rates in cell mass and size were calculated by exponential fits throughout the cell cycle, as detailed in the Methods section; color coding corresponds to increased (blue) or decreased (red) density prior to division; graph plots the cumulative response of three replicates, with each replicate presented separately in Supplementary Fig-. 5. c Growth differentiation (γ_A/γ_M) dependence on cellular dry-density at birth (normalized over the median); boxcharts represent the 25–75% of the combined three replicates with each replicate plotted separately in Supplementary Fig. 6; whiskers display the 20–80% range and asterisks denotes statistical significance (Mann–Whitney test: U = 203746, p < 0.001, with additional statistical tests reported in Supplementary Table 1). In support of this finding, we also plot the differentiation dependence on the density at birth in Supplementary Fig. 7a. d Division asymmetry in dry-density, as noted by the density differences (Δρ_daughter %) between each daughter (ρ_daughter-i at birth) to its mother (ρ_mother at division), also displayed in inset. Blue (red) traces correspond to density increases (decreases) upon division, and asterisks denote statistical significance of nonzero daughter density differences from their mother (One Sample Wilcolxon Signed Rank Test, W = 554931, Z = 28.11, p « 0.001). This graph represents the cumulative response of all biological triplicates, with each replicate presented separately in Supplementary Fig. 8, along with the respective statistical tests in Supplementary Table 2. Inset plots the daughter-daughter correlation of the dry-mass differences (d₁ and d₂, %) to their mother (color coding represents each replicate).

Fig. 3. Density homeostasis and density fluctuations subsidence upon division inhibition.

a Decrease of density fluctuations under the ampicillin (AMP) pressure; legends denote the standard deviation of fluctuations before (horizontal arrow) and during the ampicillin treatment (vertical arrow); graph represents the cumulative response of three replicates with each replicate presented separately in Supplementary Fig. 9. b Density homeostasis as evidenced by the monotonic decrease of γ_mass − γ_size with respect to the newborn cell density; inset displays the decreasing ratio of cell density prior to division (ρ_division) over the cell density at birth (ρ_birth) as a function of dry-density at birth (ρ_birth). Both the main and inset graphs plot the combined three replicates, with each replicate presented separately in Supplementary Fig. 10 and Supplementary Fig. 11, respectively.

Fig. 4. Density fluctuations impact replication rates of single bacteria.

a 3D representation of growth differentiation (γ_A − γ_Μ relationship), with each single-cell observation color coded by its replication rate level; graph represents the cumulative response of three replicates with each replicate presented separately in Supplementary Fig. 13. b Single-cell replication rates plotted as a function of density fluctuations; blue and red data points represent single-cell observations (color coded by their level of differentiation); green and purple points represent the averaged binned data and minimum replication rates levels at different levels of fluctuations; similarly, graph plots the combined three replicates, with each replicate presented separately in Supplementary Fig. 15.