Thrust and Power Output of the Bacterial Flagellar Motor: A Micromagnetic Tweezers Approach

Abstract

One of the most common swimming strategies employed by microorganisms is based on the use of rotating helical filaments, called flagella, that are powered by molecular motors. Determining the physical properties of this propulsive system is crucial to understanding the behavior of these organisms. Furthermore, the ability to dynamically monitor the activity of the flagellar motor is a valuable indicator of the overall energetics of the cell. In this work, inherently magnetic bacteria confined in micromagnetic CoFe traps are used to directly and noninvasively determine the flagellar thrust force and swimming speed of motile cells. The technique permits determination of the ratio of propulsive force/swimming speed (the hydrodynamic resistance) and the power output of the flagellar motor for individual cells over extended time periods. Cells subjected to ultraviolet radiation are observed to experience exponential decays in power output as a function of exposure time. By noninvasively measuring thrust, velocity, and power output over time at a single-cell level, this technique can serve as the foundation for fundamental studies of bacterial hydrodynamics and also provides a novel, to our knowledge, tether-free probe of single-cell energetics over time.

Figure 1

(a) TEM image of AMB-1 showing magnetosome chain and flagella. (b) A cell is trapped over the south pole of a CoFe micro-bar magnet under the influence of an external magnetic field pointing into the surface (B_ext = B_z). In this condition, flagellar forces F_flag act in the z-direction while magnetic trap forces F_mag act in the plane and orient toward the center of the trap (circular contours indicate lines of constant force). (c) When the cell is tilted along the long axis of the bar magnet (x-direction) with an in-plane field (B_ext = B_z + B_x), a flagellar force component $F_{flag}^{xy}$ is projected into the plane, and F_mag is attenuated, allowing the relative strength of F_flag and F_mag to be tuned until, at a critical angle θ_c, the cell escapes the trap. (d) F_mag along the x-direction is shown, calculated as a function of external field angle θ. The force barrier increases and moves away from the trap center as θ is increased. To see this figure in color, go online.

Figure 2

Trap calibration. (a) A schematic of the bead launch experiment at a south pole trap under negative (top) and positive (bottom) z-fields is given. (b) Bead launch trajectories under repulsion and attraction are shown. (c) Experimental bead velocity v_bead(ρ) versus radial distance ρ from trap center for a single superparamagnetic bead repeated for six trials is shown. Solid line shows fit to magnetic point-charge model. To see this figure in color, go online.

Figure 3

Schematic illustration of UV experiment. Measurement sequences s are shown that produce F_flag (circles), V_cell (triangles), and m (squares) and are successively performed, followed by navigation of the cell back to the trap center (arrow) with external fields. Before any UV exposure, the measurement sequences $s_n^b$ are performed to establish a consistent baseline of flagellar output. Afterward, sequential pulses of UV radiation are applied, followed by measurement sequences $s_n^{p_i}$ to assess the effect of the radiation on the flagellar output and to average over stochastic effects. After a series of pulses are collected, the measurement sequence is repeated under constant UV irradiation until the cell is immobilized. This allows the flagellar power output to be plotted against the cumulative UV exposure time (violet line shown in lower graph) as seen in Fig. 5. To see this figure in color, go online.

Figure 4

Histograms showing distribution of 118 (a) magnetic moments, (b) cell body lengths, (c) swimming velocities V_cell, and (d) flagellar thrust measured from launch experiments. (e) Swimming speed V_cell versus flagellar thrust F_flag is shown for 118 individual cells. (f) Calculated drag force F_Lamb on a cylinder at low Reynold’s number versus measured thrust force F_flag is shown. Solid black line indicates perfect agreement with theoretical calculation of Lamb drag, and green dashed line indicates a linear fit to the data. To see this figure in color, go online.

Figure 5

(a) Bacterial power output versus measured magnetic moment reveals correlation. (b) Scaled flagellar power output P^∗ = P/P₀ against scaled time t^∗ = t/τ is shown for three different cells with time constants τ ∼300 s (green diamonds), 60 s (black circles), and 1000 s (purple triangles). Solid line indicates exponential curve $P^{\ast }=e^{-t^{\ast }}$. (c) Experimental flagellar thrust F_flag versus velocity V_cell for the three AMB-1 exposed to UV radiation that are depicted in (b) is shown. To see this figure in color, go online.