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Dispersion relation in oscillatory reaction-diffusion systems with self-consistent flow in true slime mold

By H. Yamada, T. Nakagaki, Ruth E. Baker and P. K. Maini


In the large amoeboid organism Physarum, biochemical oscillators are spatially distributed throughout the organism and their collective motion exhibits phase waves, which carry physiological signals. The basic nature of this wave behaviour is not well-understood because, to date, an important effect has been neglected, namely, the shuttle streaming of protoplasm which accompanies the biochemical rhythms. Here we study the effects of self-consistent flow on the wave behaviour of oscillatory reaction-diffusion models proposed for the Physarum plasmodium, by means of numerical simulation for the dispersion relation and weakly nonlinear analysis for derivation of the phase equation. We conclude that the flow term is able to increase the speed of phase waves (similar to elongation of wave length). We compare the theoretical consequences with real waves observed in the organism and also point out the physiological roles of these effects on control mechanisms of intracellular communication

Topics: Biology and other natural sciences
Year: 2007
DOI identifier: 10.1007/s00285-006-0067-1
OAI identifier:

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  1. (2005). A coupled-oscillator model with a conservation law for the rhythmic amreboid movements of plasmodial slime moulds,
  2. (1981). ATP oscillation in Physarum plasmodium. doi
  3. (1984). ATP- and calcium-controlled contraction in a saponin model of Physarum polycephalum. doi
  4. (1996). Environment-dependent selforganization of positional information field in chemotaxis of Physarum polycephalum.
  5. (1975). Formation of dissipative structures in reaction-diffusion systems— reductive perturbation approach.
  6. (2000). Interaction between cell shape and contraction pattern in the Physarum plasmodium.
  7. (1993). Intracellular oscillations and pattern formation in the cell behavior of Physarum.
  8. (1976). Local phase and renormalized frequency in inhomogeneous chemioscillations.
  9. (2006). Mathematical model for rhythmic amoeboid movement in the true slime mold.
  10. (1999). Modulation of cellular rhythm and photoavoidance by oscillatory irradiation in the Physarum plasmodium.
  11. (1974). On a variety of wave phenomena in chemical-reactions.
  12. (1982). Oscillation in surface pH of the Physarum plasmodium.
  13. (1994). Oscillation phase dynamics in the Belousov–Zhabotinsky reaction—implementation to image-processing.
  14. (1976). Pattern formation in oscillatory chemical-reactions.
  15. (1999). Pattern formation of a reaction-diffusion system with self-consistent flow in the amoeboid organism Physarum plasmodium. doi
  16. (1973). Phase waves in oscillatory chemical reactions.
  17. (1995). Phase waves in oscillatory media.
  18. (1959). Protoplasmic streaming.
  19. (1999). Reaction-diffusion-advection model for pattern formation of rhythmic contraction in a giant amoeboid cell of the Physarum plasmodium.
  20. (1988). Reversal of thermotaxis with oscillatory stimulation in the plasmodium of Physarum polycephalum.
  21. (1979). Simple chemical-reaction systems with limit cycle behavior.
  22. (1981). Simultaneous oscillations ofCa2+ efflux and tension generation in the permealized plasmodial strand of Physarum. doi
  23. (1986). Spatial and temporal organization of intracellular adenosine nucleotide and cyclic nucleotides in relation to rhythmic motility in Physarum polycephalum.
  24. (1994). V.N.: Dynamics of the oscillation phase distribution in the BZ reaction.

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