Phenomenological understanding of aggregation and dispersion of   chemotactic cells
  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. 
Masatomo Iwasa and Ryosuke Ishiwata
physics.bio-ph q-bio.CB