LoMAPAM—Logical Model of Autowave Processes of Amoebic Movement

Abstract

This work describes a logical discrete model of the spatiotemporal dynamics of amoebic movement (Logical Model of Autowave Processes of Amoebic Movement (LoMAPAM)) based on finite automata (homogeneous structures) and specified for Physarum polycephalum. The basic system of passing rules for the information and regulation levels of the model, describing the contractile behavior of the ectoplasmic walls of P. polycephalum, enables a rhythmic generation of contractile waves and their propagation in the ectoplasmic wall due to the created structure of the LoMAPAM model. The finite automata corresponds to elementary square planar elements. This construction is alike homogeneous structures with the only exception is its finite. The planar element is assigned to the pair of integers ( i, j). The state vector defined for every element ( i, j) in discrete time t will have three components. Each of them will be written in one of the matrices B, C, or W. The information matrix B describes the state of the matter. The regulation matrix C, the local Ca 2+ concentration. The flow matrix W describes the local flow of endoplasm or ectoplasm. The passing rules for the state vector was written in the form of Boolean functions. Six actomyosin generators placed on a circle and three and five neighbouring ectoplasmatic generators on a line and a layer of endoplasm were analysed.