Pattern formation of a reaction-diffusion system with self-consistent flow in the amoeboid organismPhysarumplasmodium

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Abstract
The amoeboid organism, the plasmodium of Physarum polycephalum, moves by forming a spatiotemporal pattern of contraction oscillators. This biological system can be regarded as a reaction-diffusion system with spatial interaction via active flow of protoplasmic sol in the cell. We present a reaction-diffusion system with self-consistent flow on the basis of the physiological evidence that the flow is determined by contraction patterns in the plasmodium. Such a coupling of reaction, diffusion, and advection is characteristic of biological systems, and is expected to be related to control mechanisms of amoeboid behavior. Using weakly nonlinear analysis, we show that the envelope dynamics obeys the complex Ginzburg-Landau (CGL) equation when a bifurcation occurs at finite wave number. The flow term affects the nonlinear term of the CGL equation through the critical wave number squared. A physiological role of pattern formation with the flow is discussed.
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