A continuum model of contraction waves and protoplasm streaming in strands of Physarum plasmodium

Teplov, V. A.; Romanovsky, Y.M.; Latushkin, O.A.

doi:10.1016/0303-2647(91)90046-n

Cited by 50 publications

(40 citation statements)

References 22 publications

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“…The flux flowing out from the source node depends on pressure difference between the two FS-oscillators, which is given by amplitudes and phases of the oscillators. One FSoscillator is perturbed by the other as the sol flow mediates physical and chemical interactions between the two FS-oscillators (Oster and Odel, 1984;Teplov et al, 1991;Tero et al, 2005). This therefore represent a system of coupled oscillators with variable interaction.…”

Section: Discussionmentioning

confidence: 99%

“…There have been many studies of patterns of rhythmic contractions in relation to cell behavior (Matsumoto et al, 1988;Miyake et al, 1996;Takamatsu et al, 2001;Oster and Odell, 1984;Teplov et al, 1991;Takahashi et al, 1997;Tero et al, 2005). However we will not consider this matter further here: instead we propose to shed light on the regulation of tube thickness by flux.…”

Section: Physiological Backgroundmentioning

confidence: 99%

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A mathematical model for adaptive transport network in path finding by true slime mold

Tero

Kobayashi

Nakagaki

2007

Journal of Theoretical Biology

362

354

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We describe here a mathematical model of the adaptive dynamics of a transport network of the true slime mold Physarum polycephalum, an amoeboid organism that exhibits path-finding behavior in a maze. This organism possesses a network of tubular elements, by means of which nutrients and signals circulate through the plasmodium. When the organism is put in a maze, the network changes its shape to connect two exits by the shortest path. This process of path-finding is attributed to an underlying physiological mechanism: a tube thickens as the flux through it increases. The experimental evidence for this is, however, only qualitative. We constructed a mathematical model of the general form of the tube dynamics. Our model contains a key parameter corresponding to the extent of the feedback regulation between the thickness of a tube and the flux through it. We demonstrate the dependence of the behavior of the model on this parameter.

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Section: Discussionmentioning

confidence: 99%

Section: Physiological Backgroundmentioning

confidence: 99%

A mathematical model for adaptive transport network in path finding by true slime mold

Tero

Kobayashi

Nakagaki

2007

Journal of Theoretical Biology

362

354

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“…It may permit more quantitative comparison with experimental results. However, the detailed mechanism coupling the calcium oscillations and the mechanical contractions is still an open issue [35,39,42,43] that calls for further experimental studies.…”

Section: Discussionmentioning

confidence: 99%

“…Whereas the regulation exerted by calcium on the cytoskeleton dynamics is well established [35,36,37,38], less is known about the mechanistic details connecting the calcium oscillations with the cytoskeletal dynamics. This is reflected by the current discussion if the cytoskeleton dynamics is "merely" coupled to an autonomous, primary calcium oscillator [39,40,41] (for instance, oscillations of mitochondrial activity [40,41], which also cause the concentration of cytosolic calcium to oscillate) or if the contractility and the resulting protoplasmic flows need to be considered as a part of the feedback loop leading to calcium oscillations [35,42,43].…”

Section: Introductionmentioning

confidence: 99%

Oscillations and uniaxial mechanochemical waves in a model of an active poroelastic medium: Application to deformation patterns in protoplasmic droplets of Physarum polycephalum

Alonso

Strachauer

Radszuweit

et al. 2016

Physica D: Nonlinear Phenomena

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“…Miyake et al [14] proposed a model of the information processing system with two levels of subsystems corresponding to the endoplasmic oscillators with long-range interaction and the ectoplasmic ones with short-range interaction. From more physical viewpoints, some models based on hydrodynamics and chemical kinetics, have been presented [15,16,17]. However, we still have an issue that the streaming can be sometimes negligible, as mentioned in the former paragraph.…”

Section: Introductionmentioning

confidence: 99%

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

1999

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The amoeboid organism, the plasmodium of Physarum polycephalum, behaves on the basis of spatio-temporal pattern formation by local contraction-oscillators. This biological system can be regarded as a reaction-diffusion system which has spatial interaction by active flow of protoplasmic sol in the cell. Paying attention to the physiological evidence that the flow is determined by contraction pattern in the plasmodium, a reaction-diffusion system having self-determined flow arises. Such a coupling of reaction-diffusion-advection is a characteristic of the biological system, and is expected to relate with control mechanism of amoeboid behaviours. Hence, we have studied effects of the self-determined flow on pattern formation of simple reaction-diffusion systems. By weakly nonlinear analysis near a trivial solution, the envelope dynamics follows the complex Ginzburg-Landau type equation just after bifurcation occurs at finite wave number. The flow term affects the nonlinear term of the equation through the critical wave number squared. Contrary to this, wave number isn't explicitly effective with lack of flow or constant flow. Thus, spatial size of pattern is especially important for regulating pattern formation in the plasmodium. On the other hand, the flow term is negligible in the vicinity of bifurcation at infinitely small wave number, and therefore the pattern formation by simple reaction-diffusion will also hold. A physiological role of pattern formation as above is discussed.

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A continuum model of contraction waves and protoplasm streaming in strands of Physarum plasmodium

Cited by 50 publications

References 22 publications

A mathematical model for adaptive transport network in path finding by true slime mold

A mathematical model for adaptive transport network in path finding by true slime mold

Oscillations and uniaxial mechanochemical waves in a model of an active poroelastic medium: Application to deformation patterns in protoplasmic droplets of Physarum polycephalum

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

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