Observed frequency-independent torque in flagellar bacterial motors optimizes space exploration

Abstract

A surprising feature of many bacterial motors is the apparently conserved form of their torque-frequency relation. Experiments indicate that the torque provided by the bacterial rotary motor is approximately constant over a large range of angular speeds. This is observed in both monotrichous and peritrichous bacteria, independently of whether they are propelled by a proton flux or by a Na+ ion flux. If the relation between angular speed ω and swimming speed is linear, a ω-independent torque implies that the power spent in active motion is proportional to the instantaneous bacterial speed. Using realistic values of the relevant parameters, we show that a constant torque maximizes the volume of the region explored by a bacterium in a resource-depleted medium. Given that nutrients in the ocean are often concentrated in separate, ephemeral patches, we propose that the observed constancy of the torque may be a trait evolved to maximize bacterial survival in the ocean.