High-throughput 3D tracking of bacteria on a standard phase contrast microscope

Abstract

Bacteria employ diverse motility patterns in traversing complex three-dimensional (3D) natural habitats. 2D microscopy misses crucial features of 3D behaviour, but the applicability of existing 3D tracking techniques is constrained by their performance or ease of use. Here we present a simple, broadly applicable, high-throughput 3D bacterial tracking method for use in standard phase contrast microscopy. Bacteria are localized at micron-scale resolution over a range of 350 × 300 × 200 μm by maximizing image cross-correlations between their observed diffraction patterns and a reference library. We demonstrate the applicability of our technique to a range of bacterial species and exploit its high throughput to expose hidden contributions of bacterial individuality to population-level variability in motile behaviour. The simplicity of this powerful new tool for bacterial motility research renders 3D tracking accessible to a wider community and paves the way for investigations of bacterial motility in complex 3D environments.

Figure 1. Comparison of 3D and 2D tracking methods.

In 3D tracking (left column), full position information is obtained, and speed and angle measurements are correct aside from the effects of localization errors and acquisition frequency which we neglect here. 2D projection (centre column) of the same volume introduces systematic errors in speed and angle measurements. In 2D slicing (right column), observations are constrained to a thin focal plane of thickness d. If we assume that runs have to lie fully within the slice and are five times longer than d, corresponding to typical parameters in the observation of E. coli and many other bacteria, measurement errors are minimized. However, the vast majority of turning events within the focal plane are rejected, with a bias against angles near 90°. Supplementary Discussion 1 provides derivations for the data presented here.

Figure 2. Tracking bacteria in 3D by comparing their out-of-focus diffraction patterns to a reference library.

(a) A vertical slice through a reference library created by combining 73 aligned image stacks obtained for 1 μm silica beads. (b) Horizontal slices from the reference library at positions marked in a. (c) Images of a swimming E. coli bacterium at the corresponding positions. (d) Reconstructed 3D trajectory for the bacterium in c (see Supplementary Movie 3 for a rotating view). The trajectory starting point is marked by a black dot.

Figure 3. Performance of 3D tracking.

(a) The spatial range and broadness of applicability are illustrated by a compilation of example trajectories obtained by 3D tracking of a selection of bacterial species, recorded at 15 Hz. Trajectory starting points are marked by black dots. The shown volume corresponds approximately to the tracking range. (b) Throughput analysis for E. coli tracking, showing the average number of motile bacteria (defined by a median speed above 17 μm s⁻¹, see inset) per frame with a given minimum trajectory duration. Lines of different colour correspond to 100 s long recordings at 15 Hz on 6 samples with different densities (see colour map), black denotes their average. A total of 5,890 trajectories were recorded. For the run-tumble analysis in Fig. 4, we combine these data and consider only trajectories with a minimum duration of 3 s. (c) r.m.s. localization error in x, y and z across the tracking z range. Errors are determined by tracking z stacks of 48 bacteria immobilized at random positions in the sample. The average r.m.s. error is <0.7 μm in z and <0.2 μm in x, y.

Figure 4. Analysis of E. coli run-tumble motility.

The analysis is based on 6 recordings of 100 s each from 4 different days, in which 14,188 s of total trajectory time from 2,551 motile bacteria with a minimum trajectory duration of 3 s were considered. (a) Example trajectory with marked tumbles (red) and runs (alternating between dark and light blue). (b) Histogram of run (blue) and tumble (red) durations from 6,015 and 8,350 events, respectively, with exponential fit. (c) Turning angle distribution plotted for different ranges of median run speeds. Speed ranges are chosen to contain approximately equal total trajectory time. The total number of analysed tumbles is 8,058. (d) Mean turning angle (black, left axis) and directional persistence (mean cosine of the turning angle, grey, right axis) plotted against average run speed. All error bars denote the s.e.m.

Figure 5. Individuality in run-reverse-flick motility.

(a) An 8.3-s-long 3D trajectory of a V. alginolyticus bacterium displaying run-reverse-flick motility. Flicks (red) and reversals (cyan) are marked. (b) Turning angles alternate between reversals (∼180°) and smaller flicks. (c) The direction of rotation of the polar flagellum determines whether the bacterium is pushed or pulled by the flagellum. Reversals result from switching from pushing to pulling. Flicks result from buckling of the flagellar hook (red) on resuming forward movement. A smaller deflection corresponds to a larger measured flick angle. (d) Histograms showing the population distribution of all turning angles (2,180 events, dark blue), confirmed flicks (581 events, red) and confirmed reversals (771 events, cyan). (e) Body length and flick angles for 20 individuals that displayed at least 6 flicks in their trajectory. Black: mean±s.e.m., red: scatter plot of underlying data.