  The rotary motor of bacteria is a natural nano-technological marvel that
enables cell locomotion by powering the rotation of semi-rigid helical
flagellar filaments in fluid environments. It is well known that the motor
operates essentially at constant torque in counter-clockwise direction but past
work have reported a large range of values of this torque. Focusing on
Escherichia coli cells that are swimming and cells that are stuck on a glass
surface for which all geometrical and environmental parameters are known
(Darnton et al., J. Bacteriology, 2007, 189, 1756-1764), we use two validated
numerical methods to compute the value of the motor torque consistent with
experiments. Specifically, we use (and compare) a numerical method based on the
boundary integral representation of Stokes flow and also develop a hybrid
method combining boundary element and slender body theory to model the cell
body and flagellar filament, respectively. Using measured rotation speed of the
motor, our computations predict a value of the motor torque in the range 440
pNnm to 829 pNnm, depending critically on the distance between the flagellar
filaments and the nearby surface.
