  The locomotion of Caenorhabditis elegans exhibits complex patterns. In
particular, the worm combines mildly curved runs and sharp turns to steer its
course. Both runs and sharp turns of various types are important components of
taxis behavior. The statistics of sharp turns have been intensively studied.
However, there have been few studies on runs, except for those on klinotaxis
(also called weathervane mechanism), in which the worm gradually curves toward
the direction with a high concentration of chemicals; this phenomenon was
discovered recently. We analyzed the data of runs by excluding sharp turns. We
show that the curving rate obeys long-tail distributions, which implies that
large curving rates are relatively frequent. This result holds true for
locomotion in environments both with and without a gradient of NaCl
concentration; it is independent of klinotaxis. We propose a phenomenological
computational model on the basis of a random walk with multiplicative noise.
The assumption of multiplicative noise posits that the fluctuation of the force
is proportional to the force exerted. The model reproduces the long-tail
property present in the experimental data.
