High-Speed "4D" Computational Microscopy of Bacterial Surface Motility

Abstract

Bacteria exhibit surface motility modes that play pivotal roles in early-stage biofilm community development, such as type IV pili-driven "twitching" motility and flagellum-driven "spinning" and "swarming" motility. Appendage-driven motility is controlled by molecular motors, and analysis of surface motility behavior is complicated by its inherently 3D nature, the speed of which is too fast for confocal microscopy to capture. Here, we combine electromagnetic field computation and statistical image analysis to generate 3D movies close to a surface at 5 ms time resolution using conventional inverted microscopes. We treat each bacterial cell as a spherocylindrical lens and use finite element modeling to solve Maxwell's equations and compute the diffracted light intensities associated with different angular orientations of the bacterium relative to the surface. By performing cross-correlation calculations between measured 2D microscopy images and a library of computed light intensities, we demonstrate that near-surface 3D movies of Pseudomonas aeruginosa translational and rotational motion are possible at high temporal resolution. Comparison between computational reconstructions and detailed hydrodynamic calculations reveals that P. aeruginosa act like low Reynolds number spinning tops with unstable orbits, driven by a flagellum motor with a torque output of ∼2 pN μm. Interestingly, our analysis reveals that P. aeruginosa can undergo complex flagellum-driven dynamical behavior, including precession, nutation, and an unexpected taxonomy of surface motility mechanisms, including upright-spinning bacteria that diffuse laterally across the surface, and horizontal bacteria that follow helicoidal trajectories and exhibit superdiffusive movements parallel to the surface.

Keywords: Pseudomonas aeruginosa; bacteria microscopy; bacteria motility; finite element method; flagellum; hydrodynamic simulations; single-cell tracking.

Figure 1

Light-scattering simulations of tilted bacteria. (A) Modified spherical coordinate system used to specify the three-dimensional orientation of a tilted bacterium. θ represents the polar tilt angle measured with respect to the XY plane, and ϕ represents the azimuthal angle measured with respect to the positive X axis. (B) Diagram of the meshed simulation volume in FEM, including the bacterium, surrounding medium, and perfectly matched layer. The bacterium is modeled as a spherocylinder of length 3 μm and diameter 1 μm, which sits within a surrounding sphere of water with a radius of 3 μm. The perfectly matched layer is a thin outer shell of thickness 0.2 μm that absorbs light scattering off the artificial boundary. (C) Horizontal image slices obtained from the FEM-simulated light scattering. Multiple 2D slices spaced by Δd = 0.05 μm are taken from −2.5 μm below to +2.5 μm above the central plane (z = 0 μm). The final FEM image is a composite of these simulation slices. (D) We measured the spectral power distribution of our microscope light source to determine the dominant emission wavelengths (top). 260 total light-scattering simulations of tilted bacteria were conducted, spanning 10 different tilt angles (0–90°), 13 different wavelengths (400–700 nm), and two orthogonal light polarizations (purple arrows, left). Colors correspond to the wavelength of light used in the simulation, and the different tilt states are represented by the green spherocylinders. We show three example snapshots of FEM simulation results for bacteria tilted at 30° at wavelengths λ = 550, 600, and 650 nm averaged across polarizations (bottom). The final look-up table of composed images corresponding to each tilt angle (right) are obtained by summing over all simulated wavelengths according to the power spectrum and averaging the results for two orthogonal polarizations (left, purple arrows), which simulate unpolarized light.

Figure 2

3D reconstruction of the trajectory and flagellar orientation of a spinning bacterium. (A) Series of five sequential bright field snapshots (bottom) of a spinning bacterium are matched with their corresponding FEM simulated images (top) based on maximum cross-correlation value (2 μm scale bar). The location of the contact point is labeled with a red dot for each bright-field image. (B) Schematic of a reconstructed orientation and location for a bacterium bright-field image. A spherocylinder is used to visualize the long axis, distal, and proximal pole for each bacterium (see the Methods) (C) Location and orientation of the flagellum filament relative to the surface and the bacterium body is identified by fluorescence microscopy after staining of the cell membrane and flagellum. Parallel z-slices were taken at Δz = 0.2 μm, in the GFP channel, from the surface. A set of five sequential slices (z = 0.0, 0.4, 0.8, 1.2, and 1.6 μm) show that the flagellum is attached to the pole distal from the surface (3 μm scale bar). Furthermore, the flagellum axis is aligned at a non-zero angle with respect to the long axis of the body. The body–flagellum misalignment can be easily visualized in (D), the 3D render generated from the fluorescence z-scan (see the Methods). The (i–v) labeled points on z correspond to the (i–v) images in (C). (E) A 20 s reconstruction of the full 3D trajectory traced out by the poles of a single freely spinning bacterium. (F) Histogram of the tilt angles θ at which every detected reversal event occurred, generated using 60 reversals across 13 bacteria. 95% of the detected reversal events occur below a tilt angle θ = 70°.

Figure 3

Misalignment between flagellum and cell body axes lead to fast transitions in tilt angle θ. (A) Simulated trajectory of a bacterium exploring a range of polar tilt angles. The proximal pole is touching the surface, while the flagellum is connected to the pole distal to the surface. Inset shows the top view of the simulated trajectory. (B) As the flagellum spins, the hook that connects it to the body allows it to adopt different angles with respect to the body. The resulting misalignment angle between the body long axis and the flagellum (β) oscillates between β = 1.7–61° as the body tilts up and down. Larger β angles between the body and the flagellum will generally yield faster polar tilt speeds, |dθ/dt|. (C) Fluorescent labeling of the body and flagellum allows for calculation of β as the body rotates on the surface, t1–t4 with times 0.0, 0.15, 0.30, and 0.45 s, respectively (3 μm scale bar). Arrows point to flagellum location. (D) Using cross-covariance (function “xcov” in MATLAB), a simulated rising trajectory (k = 4 pN μm, τ = 2 pN μm) of a bacterium rotating on a surface (orange) is used to identify similar rises in multiple experimentally tracked trajectories (blue). The identified trajectories that closely matched the hydrodynamic model are illustrated on the right.

Figure 4

Bacteria exhibit diverse flagellum-driven translational and rotational motion while exploring surfaces during early biofilm formation. (A) Two reconstructed 3D trajectories of vertical-spinning bacteria, where the pole in contact with the surface can “slip” and make lateral excursions. These excursions result in relatively diffusive motion on the surface. (B) Two reconstructed 3D trajectories of horizontal-spinning bacteria, where the bodies’ spinning axes are predominantly parallel to the surface, their motion is highly superdiffusive, and their poles trace out a helical trajectory while alternating contact with the surface. (C) MSD versus time of the contact point for the four reconstructed trajectories in A and B. The vertical-spinning cells, A1 (top) and A2 (bottom), translate approximately diffusively on the surface with MSD slope of 0.99 and 0.83, respectively; horizontal-spinning cells, B1 (top) and B2 (bottom), translate superdiffusively with MSD slopes 1.45 and 1.48, respectively. Inset triangles represent the reference line slopes. (D) Sequential time-series snapshots, Δt = 0.12 s, of fluorescently labeled membrane and flagellum, for a horizontal-spinning cell moving on the surface. The head and flagellum maintain a misalignment angle β as it spins/translates. A diagram convention next to each snapshot illustrates the rotating V-shape maintained by the cell: The head and flagellum are each represented by a triangle pointing in the direction distal to the surface.