A distributed cell division counter reveals growth dynamics in the gut microbiota

Abstract

Microbial population growth is typically measured when cells can be directly observed, or when death is rare. However, neither of these conditions hold for the mammalian gut microbiota, and, therefore, standard approaches cannot accurately measure the growth dynamics of this community. Here we introduce a new method (distributed cell division counting, DCDC) that uses the accurate segregation at cell division of genetically encoded fluorescent particles to measure microbial growth rates. Using DCDC, we can measure the growth rate of Escherichia coli for >10 consecutive generations. We demonstrate experimentally and theoretically that DCDC is robust to error across a wide range of temperatures and conditions, including in the mammalian gut. Furthermore, our experimental observations inform a mathematical model of the population dynamics of the gut microbiota. DCDC can enable the study of microbial growth during infection, gut dysbiosis, antibiotic therapy or other situations relevant to human health.

Figure 1. Implementing DCDC in E. coli cells.

Stimulus counters switch between discrete states in response to specific triggers, whereas distributed counters are induced and then an observable element (for example, a bright particle) autonomously segregates as cells divide (a). The number of elapsed generations is encoded as the ratio of the number of particles to the number of cells. DCDC was implemented using a self-assembling protein (SAP) fused to a red fluorescent protein (RFP) under control of an arabinose-inducible promoter (P_Ara), producing monomers that self-assemble into a bright, fluorescent particle (b). After the cells are washed, particle production ceases but existing particles remain. We started with 10 designs for DCDC, and determined the best design as outlined in the schematic (c). To verify expression, cells were imaged after 3 h of induction with 1 mM arabinose using confocal microscopy (d, scale bar, 1 μm) and analysed using flow cytometry (e). The flow cytometry data from (e) were analysed using a range of thresholds between bright and dark cells (f) to create a receiver-operating characteristic curve, which plots the true positive rate versus the false-positive rate for varying thresholds (g). The two best-performing designs were analysed by flow cytometry after an induction time course (h). To determine the optimal induction time, we calculated the area under the receiver operating characteristic curve for the P12/P9 design (i).

Figure 2. Testing DCDC in vitro.

We maintained cells in exponential growth by diluting and sampling every hour (a). We plot the log₂ of the fraction of ‘On' cells over time under standard culturing conditions that maintain exponential growth (b). Schematic of the custom turbidostat used for testing (c). Cells were grown in sealed glass bottles, mixed with a stir bar while fresh media inflow was controlled by an electromechanical valve. A constant volume was maintained using a gravity-fed waste line. Optical density was measured using a LED and photodiode, which fed back to control the fresh media valve. Samples were acquired from the turbidostats using a syringe. We calibrated individual turbidostats using serial dilutions of E. coli cultures with known optical densities (Supplementary Fig. 2b). Logarithmically plotted raw flow cytometry data (d), the log₂ of the fraction of ‘On' cells over time (e) and optical density (f) are shown over 14 consecutive generations of exponential growth in minimal media supplemented with 0.4% (w/v) glucose, 0.5% (w/v) casamino acids and 100 mM potassium nitrate. In panel (d), the data are plotted on a log-log scale. A line was fit to the black circles to determine the doubling time. We show the log₂ of the fraction of ‘On' cells across a wide range of growth rates and temperatures with n=3 replicates for each temperature and condition (g). Leucine was supplemented because the parent strain (DP10) is a leucine auxotroph. Error bars indicate one standard deviation. Lines were fit to the coloured circles to determine doubling times. CA, casamino acids; Glu, glucose; Gly, glycerol; Leu, leucine.

Figure 3. Quantitative analysis of distributing cell division counting.

To analyse the performance of DCDC, we directly observed microcolony formation under an agar pad using time-lapse microscopy. Overlays of phase (grey) and RFP (red) are shown during microcolony formation (a). Scale bar, 2 μm. In each frame of n=4 movies, we measured the number of bright particles in each frame (b). In frames with multiple bright particles, we calculated the fold-change between the brightest and second-brightest particle in a frame (c). To measure the growth burden of DCDC, we constantly induced, induced and washed, or did not induce cells (d) and measured growth curves after each of these treatments (e). Error bars indicate one standard deviation. We created a mathematical model to understand the effects of particle splitting, degradation and false production (f) on the performance of the counter. Using our model, we calculated the dynamic range in generations as a function of the false production rate (g), and the effect of growth disparities between bright and dark cells over time (h). We also determined the relative contributions of particle splitting, degradation and false production to counting error over time (i).

Figure 4. Engineering gut microbes to count cell divisions.

GFP and RFP expression from the engineered gut E. coli strain PAS418 (a) was verified using confocal microscopy (b) and flow cytometry (c) after overnight growth with 133 mM arabinose. Scale bar in b, 2 μm. DCDC was tested in PAS418 using growth in a turbidostat in minimal media supplemented with carbon sources and amino acids as indicated (d). Error bars indicate one s.d. based on two or three replicate turbidostats (there was only one replicate for the M9+Glu+Leu condition). We also measured the growth of PAS418 under more standard culturing conditions by periodically diluting cultures grown in flasks in LB medium (e–f). PAS418 cells were introduced into mice by oral gavage and the growth was monitored using DCDC by collecting faeces every 2 h (g–j). We first measured the average transit time by monitoring the presence of GFP⁺ bacteria in the faeces of n=8 mice, shown in a box and whisker plot (h). The edges of each box are the 25th and 75th percentiles, and the middle is the median. The whiskers extend to the most extreme data points that are not considered outliers. Outliers are indicated using red crosses. We then measured the growth of induced (i) and uninduced (j) PAS418 cells in the mouse gut by plotting the log₂ of the red/green fraction from n=4 mice. In i, data points are joined by lines to aid the eye.

Figure 5. A simple model of the population dynamics of the gut microbiota.

We first consider a model with constant growth and removal rates and variable death rates from 0 h⁻¹ to 1/3 h⁻¹ (a). We then consider a model with logistic growth, a constant removal rate and variable death rates from 0 h⁻¹ to 1/3 h⁻¹ (b). Finally, we consider a model with two separate species, each of which grows logistically and has a constant removal rate (c). In this model, death is mediated by positive or negative interactions between the species, which are systematically varied from −1 (strong, negative interactions) to 1 (strong, positive interactions). We also consider a model with logistic growth, constant removal and a death rate that exponentially decays to a constant rate (d). Here we vary the final death rate from 0 h⁻¹ to 1/3 h⁻¹.