Tuning bacterial hydrodynamics with magnetic fields

C. J. Pierce, E. Mumper, E. E. Brown, J. T. Brangham, B. H. Lower, S. K. Lower, F. Y. Yang, and R. Sooryakumar

Phys. Rev. E 95, 062612 – Published 30 June 2017

Abstract

Magnetotactic bacteria are a group of motile prokaryotes that synthesize chains of lipid-bound, magnetic nanoparticles called magnetosomes. This study exploits their innate magnetism to investigate previously unexplored facets of bacterial hydrodynamics at surfaces. Through use of weak, uniform, external magnetic fields and local, micromagnetic surface patterns, the relative strength of hydrodynamic, magnetic, and flagellar force components is tuned through magnetic control of the bacteria's orientation. The resulting swimming behaviors provide a means to experimentally determine hydrodynamic parameters and offer a high degree of control over large numbers of living microscopic entities. The implications of this controlled motion for studies of bacterial motility near surfaces and for micro- and nanotechnology are discussed.

Received 2 July 2016
Revised 28 March 2017

DOI:https://doi.org/10.1103/PhysRevE.95.062612

Physics Subject Headings (PhySH)

Biological fluid dynamics Biological movement Cell locomotion Micromagnetism Swimming

Bacteria Low Reynolds number swimmers Magnetic nanoparticles Microswimmers

Polymers & Soft MatterPhysics of Living SystemsFluid Dynamics

Authors & Affiliations

C. J. Pierce¹, E. Mumper², E. E. Brown², J. T. Brangham¹, B. H. Lower², S. K. Lower^2,3,4, F. Y. Yang¹, and R. Sooryakumar^1,*

¹Department of Physics, The Ohio State University, 191 W Woodruff Ave., Columbus, Ohio 43210, USA
²School of Environment and Natural Resources, The Ohio State University, 2021 Coffey Rd., Columbus, Ohio 43210, USA
³School of Earth Sciences, The Ohio State University, 125 Oval Dr. S, Columbus, Ohio 43210, USA
⁴Department of Microbial Infection and Immunity, The Ohio State University, 460 West 12th Ave., Columbus, Ohio 43210, USA

^*sooryakumar.1@osu.edu

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Issue

Vol. 95, Iss. 6 — June 2017

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Images

Figure 1
(a) Histogram of cell orientations ( $ϕ$ ) in the plane under magnetic fields oriented in the plane (at angle $ϕ = 0^{\circ}$ ; top, yellow) and in the absence of fields (bottom, blue). Inset: Transmission electron microscopy (TEM) image of M. magneticum AMB-1, with enlarged view of the flagellar attachment and a magnetosome chain. (b) Cell body orientation (arrows) and positions (points) during a typical U-turn experiment. As the field direction is rapidly reversed the cell takes a finite time $τ_{u}$ to turn. (c) Plot showing the sine of the cells' orientation as a function of time under field reversal. The cell rotates by $180^{\circ}$ in the green highlighted region. (d) Distribution of $τ_{u}$ for a collection of 100 cells.
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Figure 2
(a) Competing hydrodynamic ( $L_{H}$ ) and magnetic ( $L_{M}$ ) torques control transitions between toplike states (body in solid line) and planar states (body in dashed line) when $H_{ext}$ is oriented perpendicular to the surface. (b) Rolling forces on the cell body $F_{y}^{b}$ and flagellum $F_{y}^{f}$ lead to circular swimming in the plane. (c, d) Cell swimming under purely in-plane field $H_{x}$ , where $F_{y}^{b} = F_{y}^{f}$ . (e, f) Cell oriented at an angle $θ_{H}$ relative to surface. (f) As cell is tilted out of plane, $F_{y}^{f}$ is attenuated, yielding an unbalanced hydrodynamic force in the $y$ direction, causing the bacterium to swim to the right of $H_{x}$ . (g, h) Cell trapped by magnetic field gradient forces created by ${Co}_{0.5} {Fe}_{0.5}$ micropatterns and oriented at an angle by the external field.
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Figure 3
(a) Left: At low field strength, hydrodynamic torques are dominant, causing the cell to execute circular motion in the plane. Right: As the out of plane field ( $H_{z}$ ) is increased, magnetic torques prevail and the cell orients perpendicular to the surface (toplike state), executing an uncorrelated random walk in the plane, as it rotates about its long axis. (b) Power spectra of the $x$ -velocity component of an MTB trajectory under various $z$ -field strengths (blue), with time domain velocities inset (red). (c) The peak area integrated from 0 to 1.5 Hz. Between $H_{z} = 30$ and 40 Oe, the dramatic reduction in intensity represents the transition between the two states, allowing a critical field $H_{c}$ to be assigned to the cell in question. (d) Left: theoretical vs experimental critical fields for multiple cells, based on simple scaling. Linear fit (solid line) indicates a prefactor of 1.29. Right: Theoretical vs experimental critical fields with corrections to the drag coefficient ratio in Eq. (5).
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Figure 4
(a) Trajectories of two cells in an external field ( $H_{ext} = 90$ Oe). Cells begin swimming (bottom left) with $H_{z} = 0$ ( $θ_{H} = 0$ ), along parallel paths. When the $z$ field is turned on, the net field is tilted out of plane ( $θ_{H} = 45^{\circ}$ ) and both cells turn rightward by different amounts, causing their trajectories to differ by a constant angle of $32^{\circ}$ . Swimming velocity vs veer angle $ϕ$ for cells under purely in-plane fields (b) and fields tilted $80^{\circ}$ out of the plane (c). The panels on the bottom show the corresponding cell number as a function of $ϕ$ . The dramatically reduced velocity results from projecting the propulsive force out of the plane yet constraining the cell to remain in the plane.
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Figure 5
(a) A two-dimensional quasirandom walk of a toplike bacterium above a bare (nonmagnetic) surface. (b) Trajectory of the same cell in (a) above a ${Co}_{0.5} {Fe}_{0.5}$ micro bar magnet. The magnetic forces oriented toward the “south” pole (S) of the bar suppress the cell's lateral fluctuations, resulting in confinement for arbitrary lengths of time. (c) Round trip trajectory of the two cells near a pair of magnetic wires. A sequence of fields guides a cell off the initial trap to a neighboring trap and back (yellow trajectory). Another cell (green trajectory) deviates from the center of the trap at the wire's end, but insufficient flagellar force is projected into the plane to cause the cell to escape the wire trap.
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