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

Abstract

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.

Slime mould: The fundamental mechanisms of biological cognition

“…Tubulin isotypes relationship between P. polycephalum and different mammals, including humans [93] Intracellular communication: reaction-diffusion model [94] Decision making and "scatter" or state of indecision between different attractors for foraging [95] Control Unit microtubules for migrating towards the conductive cores plasmodium area [96] Decision making and "scattor" or state of indecision between different attractors for foraging [95] Anticipation and memory periodic pulses [97] Distribution of nutrients [4] Using his trail for spatial memory [98] A stimulus triggers the release of a signaling molecule, generating a feedback loop [99].…”

“…Rules for biologically inspired design adaptive networks [107] Reaction-diffusion model for streaming oscillation patterns [94] Composition of a set of networks basic topologies [110] Using his trail for spatial memory [98] Detection stimulus intensity differences through the Weber-Fechner Law [6] Interdependence Plasmodium to sclerotia [111], [58], [112] Relationship of flow of electric current and polarization associated with filaments and myosin microtubules, in turn coordinate current flow (streaming) and plasmodium oscillations for "mobiligence" [109] continued on next page Minimum travel toward food [115] Retroactivity negative [115] ATP at the tip of plasmodium supervenes locomotive capacity [95] Detection stimulus intensity differences through the Weber-Fechner Law [6] Selective search Rules for Biologically Inspired Design adaptive networks [107] Selective search…”

An Active Poroelastic Model for Mechanochemical Patterns in Protoplasmic Droplets of Physarum polycephalum

“…Later, several models in the form of reaction-diffusion [13] and reaction-diffusion-advection equations [14], [15] were formulated that use homogenized quantities, for instance the average strand thickness. These models describe Physarum protoplasm as an oscillatory medium and treat the mechanical feedback in a simplified, qualitative way.…”

The Evolution of Reaction-Diffusion Controllers for Minimally Cognitive Agents

“…So how is behavior generated? There is strong evidence that, at least in some species, RD systems play an important role in coordinating biosignaling between spatially distributed sensors and actuators [50]. It is also interesting to note that many of the molecular pathways used by single-celled organisms have been conserved by evolution and play key roles in brain functions in higher animals [25,27]; the biochemical mechanisms present in unicellular organisms are the origins of natural cognition.…”