  Although the motility of the flagellated bacteria, Escherichia coli, has been
widely studied, the effect of viscosity on swimming speed remains
controversial. The swimming mode of wild-type E.coli is often idealized as a
"run-and- tumble" sequence in which periods of swimming at a constant speed are
randomly interrupted by a sudden change of direction at a very low speed. Using
a tracking microscope, we follow cells for extended periods of time in
Newtonian liquids of varying viscosity, and find that the swimming behavior of
a single cell can exhibit a variety of behaviors including run-and-tumble and
"slow-random-walk" in which the cells move at relatively low speed. Although
the characteristic swimming speed varies between individuals and in different
polymer solutions, we find that the skewness of the speed distribution is
solely a function of viscosity and can be used, in concert with the measured
average swimming speed, to determine the effective running speed of each cell.
We hypothesize that differences in the swimming behavior observed in solutions
of different viscosity are due to changes in the flagellar bundling time, which
increases as the viscosity rises, due to the lower rotation rate of the
flagellar motor. A numerical simulation and the use of Resistive Force theory
provide support for this hypothesis.
