Tuning the torque-speed characteristics of bacterial flagellar motor to enhance the swimming speed

TL;DR

This paper derives a condition to optimize bacterial swimming speed by tuning flagellar motor torque-speed characteristics, revealing that wild-type E. coli do not operate at this optimum and identifying an anomalous propulsion regime.

Contribution

It introduces a novel tuning condition for flagellar motors to maximize swimming speed, independent of geometric optimality, supported by experimental data.

Findings

Wild-type E. coli swim 2-3 times slower than maximum speed

A new condition for matching flagella geometry and motor torque-speed

Existence of an anomalous propulsion regime where speed increases with load

Abstract

In a classic paper, Edward Purcell analysed the dynamics of flagellated bacterial swimmers and derived a geometrical relationship which optimizes the propulsion efficiency. Experimental measurements for wild-type bacterial species E. coli have revealed that they closely satisfy this geometric optimality. However, the dependence of the flagellar motor speed on the load and more generally the role of the torque-speed characteristics of the flagellar motor is not considered in Purcell's original analysis. Here we derive a tuned condition representing a match between the flagella geometry and the torque-speed characteristics of the flagellar motor to maximize the bacterial swimming speed for a given load. This condition is independent of the geometric optimality condition derived by Purcell and interestingly this condition is not satisfied by wild-type E. coli which swim 2-3 times slower than the maximum possible speed given the amount of available motor torque. Our analysis also reveals the existence of an anomalous propulsion regime, where the swim speed increases with increasing load (drag). Finally, we present experimental data which supports our analysis.