  We present a simple model that describes the motion of a single chemotactic
cell exposed to a traveling wave of the chemoattractant. The model incorporates
two types of responses to stimulation by the chemoattractant, i.e., change in
polarity and change in motility of the cell. The periodic change in motility is
assumed to be induced by the periodic stimulation by the chemoattractant on the
basis of previous observations. Consequently, net migration of the cell occurs
in a particular direction with respect to wave propagation, which explains the
migration of Dictyostelium cells in aggregation processes. The difference
between two time delays from the stimulation to the two responses and the wave
frequency determined by the frequency of the secretion of the chemoattractant
are important parameters that determine the direction of migration and the
effective interaction between cells in a population. This result explains the
dispersed state of a population of vegetative cells and cells in preaggregation
without the assumption of a chemorepellent, and also explains the commencement
of the aggregation. The result is extended to a general fact as follows: the
temporal oscillation of the magnitude of the random motion for gradient-sensing
particles induces spontaneous movement, even when the particles are exposed to
a periodic wave of the chemoattractant, which results in the aggregation or
dispersion of the particles communicating via their attractant.
