Swimming efficiency of bacterium Escherichia coli

Abstract

We use measurements of swimming bacteria in an optical trap to determine fundamental properties of bacterial propulsion. In particular, we directly measure the force required to hold the bacterium in the optical trap and determine the propulsion matrix, which relates the translational and angular velocity of the flagellum to the torques and forces propelling the bacterium. From the propulsion matrix, dynamical properties such as torques, swimming speed, and power can be obtained by measuring the angular velocity of the motor. We find significant heterogeneities among different individuals even though all bacteria started from a single colony. The propulsive efficiency, defined as the ratio of the propulsive power output to the rotary power input provided by the motors, is found to be Ϸ2%, which is consistent with the efficiency predicted theoretically for a rigid helical coil.bacterial flagellum ͉ bacterial propulsion ͉ propulsion matrix B acteria swim by rotating helical propellers called flagellar filaments. For Escherichia coli (E. coli), these filaments are several micrometers in length and 20 nm in diameter, organized in a bundle of four or five. Each flagellar filament is driven at its base by a reversible rotary engine, which turns at a frequency of Ϸ100 Hz (1). Many important properties of the swimming bacteria, such as their average swimming speed, the rotation rate of the flagellar bundle, and the torque generated by the molecular motor, have been determined (1)(2)(3)(4)(5)23). Other properties such as the translational and rotational drag coefficients of flagellar bundles, however, are difficult to measure, especially for intact cells. These parameters are significant for quantitative understanding of bacterial propulsion and are the subject of extensive mathematical analysis and computer simulations (6-10). In this work, we investigate the fundamental swimming properties of intact E. coli by using optical tweezers and an imposed external flow. We directly measure the force required to hold the bacterium and the angular velocities of the flagellar bundle and the cell body as a function of the flow velocity. The propulsion matrix, which relates the translational and angular velocity of the flagella to the forces and torques propelling the bacterium, can thus be determined one bacterium at a time. We find that the population-averaged matrix elements are in reasonable agreement with the resistive force theory for helical propellers (7), but there is a large variability even among bacteria of similar length grown from a single colony.The propulsion matrix also allows us to determine the propulsive efficiency , which is defined as the ratio of the propulsive power output (the part of the power used to push the cell body forward) to the rotary power input (the power used to rotate the flagellar bundle). We find the propulsive efficiency is strongly dependent on growth conditions but is not very sensitive to cell-body size. Despite the flexibility and internal friction between the filaments in the flagellar ...

Unlocking the secrets of multi-flagellated propulsion: drawing insights fromTritrichomonas foetus

“…Despite the sinusoidal motion of the flagella in sperm compared with the ciliary beating of the flagella in Chlamydomonas and T. foetus, the propulsive forces for linear swimming from all of these organisms fall within a similar range of magnitude, 13.5-25 pN [69][70][71]. When compared with the propulsive force generated from the rotary flagella of the bacteria E. coli and Salmonella typhimurium, 0.37 -0.57 pN, the eukaryotes have much greater force, although the body size of bacteria is much smaller, thus drag is lower [72,73]. By far the propulsive strategy that generates the most force is the ciliated swimming of Paramecium, which generates 7000 pN of force [74].…”

Self-Induced Polar Order of Active Brownian Particles in a Harmonic Trap

“…Bacteria or both active and passive colloids confined in optical traps have attracted experimental [27][28][29] as well as theoretical [24,[30][31][32][33] interest. Passive colloids are operated in non-equilibrium by switching the trapping force [31] while active particles are intrinsically out of equilibrium [24,32,33].…”

Helical motion of the cell body enhances Caulobacter crescentus motility

“…Similarly, the flagella of Spirochetes rotate between the inner and outer cell membranes, generating a helical wave that is thought to contribute to the organism's motility (7). However, most flagellated bacteria have straight, rod-shaped cell bodies, and the effect of this body shape on motility is usually either ignored or treated as a source of passive drag (8)(9)(10).…”