Reaction–Diffusion–Advection Model for Pattern Formation of Rhythmic Contraction in a Giant Amoeboid Cell of thePhysarumPlasmodium

The plasmodium ofPhysarum polycephalumis a large amoeboid organism showing rhythmic contraction everywhere within an organism, and moves by forming spatio-temporal patterns of the rhythmic contraction. We propose a reaction–diffusion–advection model for the pattern formation. This model is constructed under physiological suggestions that the chemical oscillator acts as a clock regulating the rhythmic contraction and interacts spatially not only by diffusion but also by advection of protoplasm. Behavior of the model is studied by numerical calculation, especially the effects of the advection term on a simple reaction–diffusion system. The advection effect reproduces experimentally observed phenomena of fluctuating propagation of the contraction wave. Concept of the reaction–diffusion–advection system is promising for modeling the mechanism of amoeboid behaviour in thePhysarumplasmodium.