Swimming bacteria power microscopic gears

Abstract

Whereas the laws of thermodynamics prohibit extraction of useful work from the Brownian motion of particles in equilibrium, these motions can be "rectified" under nonequilibrium conditions, for example, in the presence of asymmetric geometrical obstacles. Here, we describe a class of systems in which aerobic bacteria Bacillus subtilis moving randomly in a fluid film power submillimeter gears and primitive systems of gears decorated with asymmetric teeth. The directional rotation is observed only in the regime of collective bacterial swimming and the gears' angular velocities depend on and can be controlled by the amount of oxygen available to the bacteria. The ability to harness and control the power of collective motions appears an important requirement for further development of mechanical systems driven by microorganisms.

Fig. 1.

Experimental design. (A) Shapes of some types of gears used in this study. (B) Scheme of the experimental setup. The film is suspended between four wires attached to a moveable frame. Film thickness is controlled by the linear motion of the frame (indicated by the red arrow). The experimental apparatus is placed in a transparent chamber with controlled atmosphere and mounted on the moving stage of inverted microscope. (C) Velocity distribution function P(V) for small fluorescent tracers (2.5 μm polystyrene microspheres, Spherotech, Inc.) advected by Bacillus subtilis bacteria in the regime of collective swimming at concentration 2 × 10¹⁰ cm^-3. Corresponding rms velocity, V_rms, of the tracers is about 13 μm/ sec. Red line gives the best fit to the Gaussian law, and blue line is a stretched exponential fit with the exponent 1.16.

Fig. 2.

Rotation of individual gears and of gear assemblies. Sequences of snapshots illustrating rotation of gears with eight external teeth (A–D) and twelve internal teeth (E–H). Images (I) and (J) show a system of two “engaged” gears rotating in opposite directions. Black arrows indicate the gears’ orientation obtained by computer processing of acquired images, and red arrows show the direction of rotation. In all cases, concentration of bacteria was 2 × 10¹⁰ cm^-3 and the film thickness was 200 µm. Contrast of the images was adjusted electronically. Movies S1, S2, and S3 correspond to images A–J.

Fig. 3.

Quantification of gear performance. (A) Gear’s rotation. Typical plots of the rotation angle vs. time for two types of gears. (B) Random motion of the center of mass. Position of the gears’ center of mass for the data shown in (A). Gears fluctuate around the center of the film due to confinement caused by the gravitational depression of the film. (C) Speed control. Plot of the rotation angle as a function of time for a gear with both internal and external teeth. The gear rotates when bacteria are exposed to air or oxygen but halt (region shaded pink) when the chamber is filled with nitrogen. (D) Synchronous rotation. Rotation angle as a function of time for a system of two gears. For approximately the first 100 sec, the gears rotate in synchrony. The inset plots the difference Δα in the rotation angles. Movies S1 and S2 accompany data in (A) and (B), Movie S4 accompanies data in (C), and Movie S3 accompanies data in (D).

Fig. 4.

Concentration dependence. Black solid line has the dependence of the gear rotation rate on the concentration of bacteria, n. Vertical error bars represent standard deviations of the rotation rate with gears decorated with 8 outward teeth. Sharp increase in the rotation rate at concentration ∼10¹⁰ cm^-3 coincides with the onset of collective motion. For concentration above 4 × 10¹⁰ cm^-3 rotation ceases due to the decrease in bacterial motility (32). For comparison, the dependence of effective viscosity ν of bacterial suspension measured at the same conditions is plotted as a red dashed line (adopted from ref. 32); ν₀ is viscosity of liquid without bacteria.

Fig. 5.

Tracer trajectories. Trajectories of 2.5 μm fluorescent tracers (green points) tracked in 180 consecutive frames (total tracking time 18 sec). Red curves represent reconstructed tracer trajectories (A). Trajectory of an individual tracer in the vicinity of gear’s tooth for 5 periods of time, t = 0,5,10,15,20 sec (B–F). The tracer spends significant amount of time trapped in the corner before it finally “escapes.” For all images, concentration of bacteria is 2 × 10¹⁰ cm^-3. Movie S5 accompanies this figure.