On random search: Collection kinetics of Paramecia into a trap embedded in a closed domain

Abstract

We study the kinetics of a large number of organisms initially spread uniformly in a circular two-dimensional medium, at the center of which a smaller circular trap has been introduced. We take advantage of the acidophily of Paramecium caudatum, which, coming from a neutral medium, penetrates a region of moderate acidity but moves back in the opposite situation when it meets a sharp negative acidity gradient to quantify its rate of irreversible aggregation into a spot of acidified medium in water. Two regimes are distinguished: A ballistic regime characteristic of "fresh" paramecia where the organisms swim in a straight path with a well defined velocity and a Brownian regime characteristic of older paramecia where the mean free path of the organisms is smaller than the system size. Both regimes are characterized by distinct aggregation laws. They both result from a pure random trapping process that appears to have no adaptive strategy.