Phase-shift model for the aggregation of amoebae: A computer study

Abstract

A simple theoretical model for the aggregation of amoebae is presented. A random and in other cases a homogeneous distribution of amoebae in a two-dimensional array appears to become unstable when the phase of the sustained oscillation of each individual cell is perturbed by diffusion coupling. The biochemical oscillation is supposed to be caused by autocatalytic back activation of the second order and to be localized in the membrane area of the amoebae. A chemotactic movement of the amoebae is compatible with the polar activation of the membrane caused by reaching the over-threshold concentration of an attractant in the local region of the membrane. The unstable perturbation of the limit cycle represents the local “firing” of the autocatalytic reaction. This triggering of the spike occurs earlier than that which follows in the unperturbed phase of the oscillation. The spatial variability of the chemotactic movement is asserted by the sustained periodic activities and by degradation of an attractant in the medium. The amoeba being in the “ready state” after its refractory period can respond very rapidly to the rotation of the external attractant gradient. The phase-shift gradient between the pacemaker centre (with the highest phase and frequency) and the other cells is a necessary condition for the chemotactic reaction and thereafter for the aggregation. This biochemical model of the aggregation was tested by computer simulation. The developed patterns of aggregated cells are comparable with published experimental results on cellular slime mould.