Interaction between cell shape and contraction pattern in the Physarum plasmodium

The relationship between cell shape and rhythmic contractile activity in the large amoeboid organism Physarum polycephalum was studied. The organism develops intricate networks of veins in which protoplasmic sol moved to and fro very regularly. When migrating on plain agar, the plasmodium extends like a sheet and develops dendritic veins toward the rear. After a particular stimulation, the vein organization changes into veinless or vein-network structures. In both structures, the mixing rate of the protoplasm, which is related to communication among contraction oscillators, decreased compared with that of the dendritic one. Accompanying these changes in vein structure, the spatio-temporal pattern of the rhythmic contraction changed into a small-structured pattern from a synchronized one. In the above process, cell shape affects the contraction pattern, but, conversely, the contraction pattern effects the cell shape. To demonstrate this, a phase difference in the rhythmic contraction was induced artificially by entraining the intrinsic rhythm to external temperature oscillations. New veins then formed along the direction parallel to the phase difference of the rhythm. Consequently, the vein organization of the cell interacts with the contractile activity to form a feedback loop in a mechanism of contraction pattern formation.     

Modulation of cellular rhythm and photoavoidance by oscillatory irradiation in the Physarum plasmodium

We studied responses of cellular rhythm and light-induced movement to periodic irradiation in a unicellular amoeboid organism, the Physarum plasmodium. The intrinsic frequency of the contraction rhythm, which is based on biochemical oscillations, became synchronized with the frequency of periodic irradiation with light when both frequencies were close enough. In order to study the role of the synchronization in light-induced movement, periodic irradiation was applied to only part of the plasmodium. The rate of avoidance of light was modulated in the frequency band in which the synchronization occurred. The synchronization property of the contraction oscillation underlies the regulation of tactic movement in plasmodium.     

Mathematical Model for Rhythmic Protoplasmic Movement in the True Slime Mold

The plasmodium of the true slime mold Physarum polycephalum is a large amoeboid organism that displays “smart” behavior such as chemotaxis and the ability to solve mazes and geometrical puzzles. These amoeboid behaviors are based on the dynamics of the viscoelastic protoplasm and its biochemical rhythms. By incorporating both these aspects, we constructed a mathematical model for the dynamics of the organism as a first step towards understanding the relation between protoplasmic movement and its unusual abilities. We tested the validity of the model by comparing it with physiological observation. Our model reproduces fundamental characteristics of the spatio-temporal pattern of the rhythmic movement: (1) the antiphase oscillation between frontal tip and rear when the front is freely extending; (2) the asynchronous oscillation pattern when the front is not freely extending; and (3) the formation of protoplasmic mounds over a longer time scale. Both our model and physiological observation suggest that cell stiffness plays a primary role in plasmodial behaviors, in contrast to the conventional theory of coupled oscillator systems.     

Emergence of morphological order in the network formation of Physarum polycephalum

Emergence in a system appears through the interaction of its components, giving rise to higher order or complexity in the system. We tested for the presence of emergent properties in a biological system using the simplest biological entity of a unicellular organism; the plasmodium of Physarum polycephalum, a giant unicellular amoeboid organism that forms a network-like tubular structure connecting its food sources. We let two plasmodium networks within a single cell interact with each other, and observed how the intracellular interaction affected the morphologenesis of the plasmodium networks. We found that the two networks developed homologous morphology. We further discuss the presence of autonomous and emergent properties in homologous network formation.     

细弱绒泡菌的生活史

利用燕麦-琼脂培养、基物培养及扫描电镜技术研究了细弱绒泡菌的个体发育过程,在燕麦琼脂培养基上完成了从孢子到孢子的生活史。结果表明,细弱绒泡菌生活史包括单核的黏变形体或游动胞、多核的营养体原质团以及孢子形成阶段。孢子球形,表面具细小疣点。孢子萌发为裂式,释放1黏变形体。黏变形体行变形运动,在有水的条件下,可转变为游动胞。成熟原质团橘黄色。原质团类型为显型,具有扇形网络状菌脉。成熟原质团可形成多个孢囊。琼脂培养基上获得的细弱绒泡菌孢子与野生型相似,并具有可育性。     

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

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.     

Synchronization of mechanochemical auto-oscillations within the Physarum polycephalum plasmodium by periodical external actions

Amoeboid locomotion of huge unicellular organism, the Physarum polycephalum plasmodium, is stipulated by endoplasmic flow, which is produced by spatially highly coordinated rhythmic contractions of the ectoplasm. To describe the self-organization of the plasmodial contractile activity, we proposed a mathematical model, which is based on the hypothesis of positive feedback between the deformation of the cytoskeleton and release of a chemical regulator of the active contraction. A nonautonomous analogue of this model was used to study the synchronization of mechanochemical auto-oscillations by periodic gradient of the external pressure. Numerical computations of the system of differential equations obtained revealed a dependency of the synchronization band on the amplitude of the external pressure oscillations. On the basis of this dependence and experimental data on the band of synchronization of the shuttle endoplasmic flow by the periodic gradient of temperature obtained with the help of the laser Doppler anemometer, relative efficiency of external synchronizing action of temperature and pressure was evaluated.     

Path finding by tube morphogenesis in an amoeboid organism

We have studied how the plasmodium of Physarum polycephalum, a large amoeboid cell, is able to track the shortest path between two selected points in a labyrinth. When nutrients are supplied at these points to a sheet-like plasmodium extended fully in a maze, the organism forms a single tube which connects the two sites via the shortest route. During the path finding, plasmodial parts in dead ends of the maze shrink and finally the tube with the minimum-length is selected from the existing possibilities. A simple cellular mechanism based on interacting cellular rhythms may describe the experimental observations.     

Smart network solutions in an amoeboid organism

We present evidence that the giant amoeboid organism, the true slime mold, constructs a network appropriate for maximizing nutrient uptake. The body of the plasmodium of Physarum polycephalum contains a network of tubular elements by means of which nutrients and chemical signals circulate through the organism. When food pellets were presented at different points on the plasmodium it accumulated at each pellet with a few tubes connecting the plasmodial concentrations. The geometry of the network depended on the positions of the food sources. Statistical analysis showed that the network geometry met the multiple requirements of a smart network: short total length of tubes, close connections among all the branches (a small number of transit food-sites between any two food-sites) and tolerance of accidental disconnection of the tubes. These findings indicate that the plasmodium can achieve a better solution to the problem of network configuration than is provided by the shortest connection of Steiner's minimum tree.     

Patterns in the distribution of intracellular ATP concentration in relation to coordination of amoeboid cell behavior in Physarum polycephalum

The Physarum plasmodium reacts tactically to external stimuli. The cell behavior of this giant amoeboid cell was studied by analysing intracellular ATP concentration. The two-dimensional (2D) spatial distribution of ATP depended on cell shape: a polar pattern for a unidirectionally migrating plasmodium, a bowl shape for a circular plasmodium, a hump shape for an oval plasmodium, or a wavy pattern for plasmodia stimulated with blue light or confined in a small chamber, etc. Local external stimulation brought about new patterns of ATP distribution. The ATP concentrations around the stimulated frontal region were reduced by about a half stimulation with KCl (repellent) or casamino acids (attractant). In both cases, migration was inhibited. Migration velocity increased almost linearly with increasing concentration of intracellular ATP above the threshold (about 20 micrograms/mg protein). Under anaerobic conditions or at low temperatures, the intracellular ATP oscillated slowly with a periodicity of about 30 min. Pattern formations in the intracellular ATP concentration and amoeboid coordination are discussed in terms of coupled chemical oscillators in a self-organizing system.     

The role of phosphoinositide-3-kinase in the control of shape and directional movement of the Physarum polycephalum plasmodium

The effects of wortmannin and LY294002, specific inhibitors of phosphoinositide-3-kinase, on the shape, locomotive behavior, and glucose chemotaxis were studied using the Physarum polycephalum plasmodium, a multinuclear amoeboid cell with the self-oscillatory mode of locomotive behavior. Both inhibitors were shown to cause a reduction in the plasmodium frontal edge and a decrease in the efficiency of mass transfer during migration. They also suppressed the chemotaxis towards glucose and eliminated the characteristic changes in self-oscillatory behavior normally observed in response to the treatment of the whole plasmodium with glucose. The manifestation of these effects depended on the inhibitor concentration, treatment duration, and size of plasmodium. The involvement of phosphoinositide-3-kinase in formation of the frontal edge and control of P. polycephalum plasmodium chemotaxis suggests that the correlation of polar shape and directional movement of amoeboid cells with the distribution of phosphoinositides in the plasma membrane has a universal nature.     

Membrane biophysics of chemoreception and taxis in the plasmodium of Physarum polycephalum

The threshold phenomena observed in chemoreception and taxis of the plasmodium of Physarum polycephalum were analyzed on the basis of physical chemistry. Various physicochemical concepts and rules, e.g. the Schulze-Hardy rule, the lyotropic number and the hydrophobic interactions, were shown to be applicable reasonably well to the physiological functions in Physarum. It was stressed that the structural change of the surface membrane induced by reception of chemical stimuli plays a decisive role in recognition and sensitivity to the external stimuli as well as the appearance of tactic movement in the amoeboid motility of Physarum.     

Involvement of cyclic adenosine monophosphate in the control of motile behavior of Physarum polycephalum plasmodium

Possible involvement of autocrine factors into the control of motile behavior via a receptor-mediated mechanism was investigated in Physarum polycephalum plasmodium, a multinuclear amoeboid cell with the auto-oscillatory mode of motility. Cyclic adenosine monophosphate (cAMP) and extracellular cAMP-specific phosphodiesterase, its involvement into the control of plasmodium motile behavior was proved by action of its strong inhibitor, were regarded as putative autocrine factors. It was shown that the plasmodium secreted cAMP. When it was introduced into agar support, 0.1–1 mM cAMP induced a delay of the plasmodium spreading and its transition to migration. When locally applied, cAMP at the same concentrations induced the typical for attractant action increase in oscillation frequency and the decrease of ectoplasm elasticity. The ability to exhibit positive chemotaxis in cAMP gradient and the dependence of its realization were shown to depend on the plasmodium state. Chemotaxis test specimens obtained from the migrating plasmodium, unlike those obtained from growing culture, generate alternative fronts which compete effectively with fronts oriented towards the attractant increment. The results obtained support our supposition stated earlier that advance of the Physarum polycephalum plasmodium leading edge is determined by local extracellular cAMP gradients arising from a time delay between secretion and hydrolysis of the nucleotide.     

Involvement of extracellular cAMP-specific phosphodiesterase in control of motile activity of Physarum polycephalum plasmodium

Possible involvement of extracellular cAMP-specific phosphodiesterase in the control of cell motile behavior has been investigated in Physarum polycephalum plasmodium, a multinuclear amoeboid cell with the autooscillatory mode of motility. It was found that the rate of the hydrolysis of 10 mM cAMP by a partially purified preparation of cAMP-specific phosphodiesterase secreted by the plasmodium in the course of migration decreases 20-30 times under the action of 1 mM dithiothreitol. In the presence of 1-5 mM of this strong reducing agent, the onset of the plasmodium spreading and the transition to the stage of migration were delayed in a concentration-dependent manner. In accordance with the morphological pattern of motile behavior, the duration of the maintenance of high frequency autooscillations, which normally precede the increase in the rate of the spreading and appear also in response to the application of attractants at spatially uniform concentrations, strongly increased by the action of dithiothreitol. The results obtained suggest that the autocrine production of cAMP and extracellular cAMP-specific phosphodiesterase is an important constituent of the mechanism controlling the motile behavior of the Physarum polycephalum plasmodium.     

扁绒泡菌的生活史

黏菌的生活史对于研究其营养方式的多样性以及系统发育等具有重要价值,目前国内外有关黏菌生活史的报导很少。利用燕麦-琼脂培养、基物培养及扫描电镜技术研究了扁绒泡菌的个体发育过程,在燕麦琼脂培养基上完成了从孢子到孢子的生活史。结果表明,扁绒泡菌生活史包括单核的黏变形体或游动胞、多核的营养体原质团以及孢子形成阶段。孢子球形,表面具细小疣点。孢子萌发为裂式,释放1黏变形体。原质团类型为显型。成熟原质团乳白色,可形成多个孢囊。琼脂培养基上获得的扁绒泡菌孢子与野生型相似,并具有可育性。     

Cognition of different length by Physarum polycephalum: Weber's law in an amoeboid organism

A true slime mold, the plasmodium of Physarum polycephalum has the ability to find the shortest route between two points in a labyrinth. To find the shortest route between two points, detection of the difference in lengths can be made from two aspects: the absolute difference between the lengths or the ratio of them. We found that the ratio of two lengths, rather than the absolute difference between the two lengths, was important in discriminating the difference in the two lengths by P. polycephalum. This finding indicates that an amoeboid organism detects differences in stimulus intensity as though it is constrained by Weber's law, suggesting that Weber's law is not reliant on the presence of a neural system and is used widely even in Amoebozoa.     

The autowave electromechanical activity of the <Emphasis Type="Italic">Physarum polycephalum</Emphasis> plasmodium

The aim of this work is to clarify the role of the electrical activity of the Physarum polycephalum plasmodium in the control of the contractile activity and self-organization of the directed locomotion. This single-celled organism with a non-excitable membrane is a classic object that is used in studies of amoeboid motility. Its patterns of motor behavior and signal systems are common for many tissue cells. The presence of 50 mM KCl in an agar substrate under half of a separate plasmodial strand strongly inhibits the formation of the frontal zone and leads to sharp morphological polarization of the strand, which suggests the involvement of electrical processes in the autowave self-organization of the plasmodial structure. The gigantic sizes of the plasmodium make it possible to record its electrical activity simultaneously at different parts of the cell. It has been established that potentials and currents at parts of the plasmodium that are distant from each other oscillate synchronously and differ only in the shape of the signals, probably due to differences in the phases or the number of excited harmonics. We recorded currents (~50 pA) of single ion channels of the plasmodial membrane using the classical local voltage-clamp method. It has been found that the oscillation spectrum of the current that is generated by the plasmodium has high-frequency fluctuations, which are probably connected with periodic detachments of the membrane from the cytoskeleton during the formation and growth of the pseudopodia. It has been also shown that neomycin, a substrate inhibitor of phospholipase C, prevents oscillations of both the mechanical and electrical activity of the plasmodium. This is consistent with its well-established ability to inhibit mechanosensitive Ca²⁺ channels, which are apparently present in the plasmodial membrane. These data indicate the presence of a general signal system that is linked with the dynamics of the membrane- cytoskeleton association, which could be involved in the galvano- and chemotaxis of amoeboid cells.     

圈绒泡菌的生活史

利用基物培养、燕麦-琼脂培养技术及扫描电镜技术研究了圈绒泡菌的个体发育过程, 在燕麦琼脂培养基上完成了从孢子到孢子的生活史。结果表明,生活史包括单核的黏变形体或游动胞、多核的营养体原质团以及孢子形成阶段。琼脂培养基上获得的圈绒泡菌孢子与野生型相似,并具有可育性。     

Amoeba-based computing for traveling salesman problem: Long-term correlations between spatially separated individual cells of Physarum polycephalum

A single-celled, multi-nucleated amoeboid organism, a plasmodium of the true slime mold Physarum polycephalum, can perform sophisticated computing by exhibiting complex spatiotemporal oscillatory dynamics while deforming its amorphous body. We previously devised an “amoeba-based computer (ABC)” to quantitatively evaluate the optimization capability of the amoeboid organism in searching for a solution to the traveling salesman problem (TSP) under optical feedback control. In ABC, the organism changes its shape to find a high quality solution (a relatively shorter TSP route) by alternately expanding and contracting its pseudopod-like branches that exhibit local photoavoidance behavior. The quality of the solution serves as a measure of the optimality of which the organism maximizes its global body area (nutrient absorption) while minimizing the risk of being illuminated (exposure to aversive stimuli). ABC found a high quality solution for the 8-city TSP with a high probability. However, it remains unclear whether intracellular communication among the branches of the organism is essential for computing. In this study, we conducted a series of control experiments using two individual cells (two single-celled organisms) to perform parallel searches in the absence of intercellular communication. We found that ABC drastically lost its ability to find a solution when it used two independent individuals. However, interestingly, when two individuals were prepared by dividing one individual, they found a solution for a few tens of minutes. That is, the two divided individuals remained correlated even though they were spatially separated. These results suggest the presence of a long-term memory in the intrinsic dynamics of this organism and its significance in performing sophisticated computing.     

Involvement of extracellular cAMP-specific phosphodiesterase in the control of motile activity of <Emphasis Type="Italic">Physarum polycephalum</Emphasis> plasmodium

Possible involvement of extracellular cAMP-specific phosphodiesterase in the control of cell motile behavior has been investigated in Physarum polycephalum plasmodium, a multinuclear amoeboid cell with the autooscillatory mode of motility. It was found that the rate of the hydrolysis of 10 mM cAMP by a partially purified preparation of cAMP-specific phosphodiesterase secreted by the plasmodium in the course of migration decreases 20–30 times under the action of 1 mM dithiothreitol. In the presence of 1–5 mM of this strong reducing agent, the onset of the plasmodium spreading and the transition to the stage of migration were delayed in a concentration-dependent manner. In accordance with the morphological pattern of motile behavior, the duration of the maintenance of high frequency autooscillations, which normally precede the increase in the rate of the spreading and appear also in response to the application of attractants at spatially uniform concentrations, strongly increased by the action of dithiothreitol. The results obtained suggest that the autocrine production of cAMP and extracellular cAMP-specific phosphodiesterase is an important constituent of the mechanism controlling the motile behavior of the Physarum polycephalum plasmodium.