Reaction-diffusion-advection model for pattern formation of rhythmic contraction in a giant amoeboid cell of the physarum plasmodium

The plasmodium of Physarum polycephalum is a large amoeboid organism showing rhythmic contraction everywhere within an organism, and moves by forming spatio-temporal patterns of the rhythmic contraction. We propose a reaction-diffusion-advection model for the pattern formation. This model is constructed under physiological suggestions that the chemical oscillator acts as a clock regulating the rhythmic contraction and interacts spatially not only by diffusion but also by advection of protoplasm. Behavior of the model is studied by numerical calculation, especially the effects of the advection term on a simple reaction-diffusion system. The advection effect reproduces experimentally observed phenomena of fluctuating propagation of the contraction wave. Concept of the reaction-diffusion-advection system is promising for modeling the mechanism of amoeboid behaviour in the Physarum plasmodium. Copyright 1999 Academic Press.     

Information processing for the organization of chemotactic behavior ofPhysarum polycephalum studied by micro-thermography

Summary The spatial and temporal pattern of oscillating temperatures on the cell surface of a plasmodial strand ofPhysarum polycephalum was measured with a sensitive thermal image camera. The longitudinal tension of the strand was studied simultaneously. In the absence of chemical stimulation, the phases of the temperature oscillation observed at various portions of the strand were entrained with almost coincidental phase. The temperature and tension oscillation were synchronized, although the phase difference between them was occasionally changed. With local chemical stimulation, the phase of the temperature oscillation advanced in the portion to which the plasmodium would be induced to migrate. The phases between temperature and tension oscillations then became constant. The mechanism by which the plasmodium processes local information of chemical stimulus to global information for the migration is discussed.     

Environment-dependent morphology in plasmodium of true slime mold Physarum polycephalum and a network growth model

Branching network growth patterns, depending on environmental conditions, in plasmodium of true slime mold Physarum polycephalum were investigated. Surprisingly, the patterns resemble those in bacterial colonies even though the biological mechanisms differ greatly. Bacterial colonies are collectives of microorganisms in which individual organisms have motility and interact through nutritious and chemical fields. In contrast, the plasmodium is a giant amoeba-like multinucleated unicellular organism that forms a network of tubular structures through which protoplasm streams. The cell motility of the plasmodium is generated by oscillation phenomena observed in the partial bodies, which interact through the tubular structures. First, we analyze characteristics of the morphology quantitatively, then we abstract local rules governing the growing process to construct a simple network growth model. This model is independent of specific systems, in which only two rules are applied. Finally, we discuss the mechanism of commonly observed biological pattern formations through comparison with the system of bacterial colonies.     

Control of interaction strength in a network of the true slime mold by a microfabricated structure

The plasmodium of the true slime mold, Physarum polycephalum, which shows various nonlinear oscillatory phenomena, for example, in its thickness, protoplasmic streaming and concentration of intracellular chemicals, can be regarded as a collective of nonlinear oscillators. The plasmodial oscillators are interconnected by microscale tubes whose dimensions can be closely related to the strength of interaction between the oscillators. Investigation of the collective behavior of the oscillators under the conditions in which the interaction strength can be systematically controlled gives significant information on the characteristics of the system. In this study, we proposed a living model system of a coupled oscillator system in the Physarum plasmodium. We patterned the geometry and dimensions of the microscale tube structure in the plasmodium by a microfabricated structure (microstructure). As the first step, we constructed a two-oscillator system for the plasmodium that has two wells (oscillator part) and a channel (coupling part). We investigated the oscillation behavior by monitoring the thickness oscillation of the plasmodium in the microstructure with various channel widths. It was found that the oscillation behavior of two oscillators dynamically changed depending on the channel width. Based on the results of measurements of the tube dimensions and the velocity of the protoplasmic streaming in the tube, we discuss how the channel width relates to the interaction strength of the coupled oscillator system.     

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.     

Patterns of oscillation during mitosis in plasmodia ofPhysarum polycephalum

Summary The rhythmic contraction pattern in plasmodia ofPhysarum polycephalum was studied to determine whether characteristic changes occur during the synchronized nuclear division. An electrical method that measures the contraction rhythm in situ during several cell cycles was used. Biopsies of the plasmodia were taken at 17 min intervals for precise determination of the cell cycle stages and were correlated with the simultaneously measured contraction rhythm. All measurements were performed in a temperature controlled environment (27 °C) at 100% relative humidity with the plasmodia (less than 24 h old) growing on a semi-defined agar medium. A total of 14 different plasmodia have been examined, and on one occasion the plasmodium was followed through 3 subsequent mitoses. The mitotic stages were identified with aceto-orcein coloring techniques and by fluorescence methods. Except for a few cases where a mitotic asynchrony of 2–3 min was observed, the mitotic events occurred simultaneously in the nuclei within a single plasmodium. Both the occurrence of the first mitosis after inoculation and the intermitotic times were highly variable. Our study indicates that the contraction rhythm in plasmodia ofPhysarum is unperturbed during the synchronized nuclear division. However, in 5 of the 17 examined mitoses an amplitude decay was observed. We discuss possible explanations for the obtained results with emphasis on the applied techniques, interpretation of the oscillation patterns, and possible restrictions in the cell itself.     

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.     

Oscillations in cell shape and size during locomotion and in contractile activities of Physarum polycephalum, Dictyostelium discoideum, Amoeba proteus and macrophages

Changes in cell shape and size were measured during locomotion, together with the motive force of the protoplasmic streaming, in various amoeboid cells in different stages of their life cycle, and under various environmental conditions. The variations in these measurements with time were examined by Fourier spectral analysis. Notwithstanding a change in cell type in the life cycle of P. polycephalum, myxamoebae and tiny plasmodia showed a similar time pattern of locomotion, exhibiting oscillations having a mixture of several periods. A regular oscillation with protoplasmic streaming appeared in the plasmodium only above a critical cell size. D. discoideum amoebae oscillated with two periods of a few minutes in preaggregation stage, but with a period of 10 min in aggregation stage, the latter being induced by cAMP. Macrophages and A. proteus also oscillated with periods of a few minutes. Periods of all these oscillations were prolonged severalfold by respiratory inhibition with NaCN, but were unaffected by glycolytic inhibition with 2-deoxyglucose. Cell fragments of A. proteus containing fewer granules oscillated more slowly and with a larger amplitude than those containing more granules. Among the granules, the nucleus was excluded as a possible modifier of the oscillation. The oscillation in Physarum plasmodium was reversibly suppressed by combining respiratory and ATPase inhibitions in mitochondria with NaCN and oligomycin, intracellular ATP concentration being kept at an appropriate level. The present results show that amoeboid motility, as well as cell shape, is oscillatory and that mitochondria are involved in time keeping.     

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.     

Development of spatio-temporal pattern of Ca2+ on the chemotactic behaviour ofPhysarum plasmodium

Summary The development of a spatio-temporal pattern of Ca²⁺ concentration by a plasmodium ofPhysarum polycephalum during chemotaxis was studied using fura-2. Whenever the cell displayed coordinated migration in one direction as a whole body, a spatiotemporal pattern was established with a characteristic feature along the longitudinal axis. Calcium concentration oscillated with a period of a few minutes within the cell; the mean concentration at the front was higher than that at the rear. When the cell was given an attractant only at the rear end, the mean concentration rose at the site of application with an immediate increase in the frequency of oscillation. First, the change of the frequency is propagated toward the other end and then the mean level of the Ca²⁺ concentration at the non-stimulated site decreases. As a result, the Ca²⁺ gradient is reversed along the cell, which then begins to migrate in a coordinated manner in the reverse direction. This study showed that the spatiotemporal pattern of Ca²⁺ concentration is closely related to information processing for coordinated migration in chemotaxis. The role of the pattern in that process is discussed.     

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.     

Controlling the geometry and the coupling strength of the oscillator system in plasmodium ofPhysarum polycephalum by microfabricated structure

Summary The plasmodium of the true slime moldPhysarum polycephalum, which shows various oscillatory phenomena, can be regarded as a collective of nonlinear oscillators. Partial bodies in the plasmodium, which are assumed to be nonlinear oscillators, are mutually connected by microscale tubes named plasmodial strand. The interactions among the oscillators can be strongly affected by the geometry and the dimension of the tube network. Investigation of the collective behavior under the condition that the configuration of the network can be manipulated gives significant information on the characteristics of the plasmodium from the viewpoint of nonlinear dynamics. In this study, we have developed a new method to control the geometry and the tube dimension of the plasmodium with a microfabricated structure. It is shown that the geometry of the plasmodium can be manipulated with a microstructure which is fabricated of ultrathick photoresist resin by photolithographic processes. In order to confirm that not only the geometry but also the dimension of the tubes can be controlled with the microstructure, we observed the cross section of the patterned plasmodium with a three-dimensional internal-structure microscope. By observing the oscillatory behavior of the partial bodies of the patterned plasmodium, it was confirmed that the coupling strength between two oscillators, which corresponds to the dimension of the plasmodial strand, can be controlled by the microstructure. It is concluded that the present method is suitable for further studies of the network of Physarum plasmodium as a collective nonlinear oscillator system.     

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.     

Robust and emergent Physarum logical-computing

There have been many attempts for realization of emergent computing, but the notion of emergent computing is still ambiguous. In an open system, emergence and an error cannot be specified distinctly, because they are dependent on the dis-equilibration process between local and global behaviors. To manifest such an aspect, we implement a Boolean gate as a biological device made of slime mold Physarum polycephalum. A Physarum (slime mold) Boolean gate could be an internally instable machine, while it has the potential for emergent computing. First, we examined whether Physarum Boolean gate works properly, and then examined its behaviors when the gate is collapsed in terms of hardware. The behavior of Physarum changes and self-repairing computing is achieved as a result. The self-repairing against internal failure is one of attributes of emergent and robust computing.     

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.     

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。     

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.     

Relationship between endoplasmic and ectoplasmic oscillations during chemotaxis ofPhysarum polycephalum

Summary The plasmodium ofPhysarum polycephalum usually migrates coordinately as one whole body even in a complicated environment. By measuring oscillation phenomena in endoplasm and ectoplasm separately during chemotactic process, we studied the mechanism of information processing to achieve such a coordination. (1) The interaction between endoplasmic oscillators was long-range, competitive according to the length of period, and fast (18 cm/min). Ectoplasmic one was short-range. (2) After a partial stimulation of attractant to the organism, the period at the stimulated portion decreased first, and a global phase gradient appeared in endoplasm. Then ectoplasm at the non-stimulated portion was entrained to the endoplasmic pattern, and the migration direction at each part changed in accordance with the phase gradient as a whole body. (3) When the endoplasmic interaction was interrupted, the above coordinated response was not observed. These facts suggest that two-layer coupled oscillator system composed of endoplasm and ectoplasm play important roles for such an information integration.     

多头绒泡菌微原质团瞬时表达系统的构建

真核生物多头绒泡菌的原质团是研究细胞周期的好材料。但尚无合适的表达体系可供选择。本研究用多头绒泡菌ardC actin基因启动子和终止子分别替换哺乳动物细胞表达质粒pDsRed1-N1的CMVIE和SV40 polyA片段,构建了多头绒泡菌红色荧光蛋白(RFP)表达质粒pXM1;用PardC-MCS-DsRed1-TardC替换pTB38表达盒PardC-hph-TardC,构建了多头绒泡菌RFP表达质粒pXM2。将多头绒泡菌转录延伸因子类似蛋白(PELF1)基因与质粒pXM2重组,构建了PELF1红色荧光融合蛋白(PELF1-RFP)表达质粒pXM2-pelf1。通过荧光显微镜和激光扫描共聚焦显微镜观察RFP表达发现,电转参数为4kV/cm(电场)、1A(电流)、70μs(电击时间)时,质粒pXM1和pXM2电转多头绒泡菌微原质团(≤500μm)后24～48h内,RFP荧光最显著;而PELF1-RFP则主要聚集在多头绒泡菌细胞核,说明本试验建立的表达系统可以用于研究特定蛋白在多头绒泡菌内的瞬时表达。