Growth processes of a planar biological network of plasmodium of a true slime mold, Physarum polycephalum, were analyzed quantitatively. The plasmodium forms a transportation network through which protoplasm conveys nutrients, oxygen, and cellular organelles similarly to blood in a mammalian vascular network. To analyze the network structure, vertices were defined at tube bifurcation points. Then edges were defined for the tubes connecting both end vertices. Morphological analysis was attempted along with conventional topological analysis, revealing that the growth process of the plasmodial network structure depends on environmental conditions. In an attractive condition, the network is a polygonal lattice with more than six edges per vertex at the early stage and the hexagonal lattice at a later stage. Through all growing stages, the tube structure was not highly developed but an unstructured protoplasmic thin sheet was dominantly formed. The network size is small. In contrast, in the repulsive condition, the network is a mixture of polygonal lattice and tree-graph. More specifically, the polygonal lattice has more than six edges per vertex in the early stage, then a tree-graph structure is added to the lattice network at a later stage. The thick tube structure was highly developed. The network size, in the meaning of Euclidean distance but not topological one, grows considerably. Finally, the biological meaning of the environment-dependent network structure in the plasmodium is discussed.

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. (C) 2008 Elsevier Ltd. All rights reserved.

Three-oscillator systems with plasmodia of true slime mold, Physarum polycephalum, which is an oscillatory amoeba-like unicellular organism, were experimentally constructed and their spatio-temporal patterns were investigated. Three typical spatio-temporal patterns were found: rotation (R), partial in-phase (PI), and partial anti-phase with double frequency (PA). In pattern R, phase differences between adjacent oscillators were almost 120 degrees. In pattern PI, two oscillators were in-phase and the third oscillator showed anti-phase against the two oscillators. In pattern PA, two oscillators showed anti-phase and the third oscillator showed frequency doubling oscillation with small amplitude. Actually each pattern is not perfectly stable but quasi-stable. Interestingly, the system shows spontaneous switching among the multiple quasi-stable patterns. Statistical analyses revealed a characteristic in the residence time of each pattern: the histograms seem to have Gamma-like distribution form but with a sharp peak and a tail on the side of long period. That suggests the attractor of this system has complex structure composed of at least three types of sub-attractors: a "Gamma attractor"-involved with several Poisson processes, a "deterministic attractor"-the residence time is deterministic, and a "stable attractor"-each pattern is stable. When the coupling strength was small, only the Gamma attractor was observed and switching behavior among patterns R, PI, and PA almost always via an asynchronous pattern named O. A conjecture is as follows: Internal/external noise exposes each pattern of R, PI, and PA coexisting around bifurcation points: That is observed as the Gamma attractor. As coupling strength increases, the deterministic attractor appears then followed by the stable attractor, always accompanied with the Gamma attractor. Switching behavior could be caused by regular existence of the Gamma attractor. (c) 2006 Elsevier B.V. All rights reserved.

We experimentally investigated spatiotemporal patterns in chains of coupled biological oscillators with boundaries and found hidden symmetric patterns that are not straightforwardly derived from explicit geometrical symmetry of the systems. We propose a model of coupled oscillators in chains with a hidden oscillator interconnecting its boundaries. The model can explain all observed patterns including the hidden symmetric ones, while other models such as discrete analogs of Neumann boundary conditions in continuous systems cannot.

Spatiotemporal patterns in rings of coupled biological oscillators of the plasmodial slime mold, Physarum polycephalum, were investigated by comparing with results analyzed by the symmetric Hopf bifurcation theory based on group theory. In three-, four-, and five-oscillator systems, all types of oscillation modes predicted by the theory were observed including a novel oscillation mode, a half period oscillation, which has not been reported anywhere in practical systems. Our results support the effectiveness of the symmetric Hopf bifurcation theory in practical systems.

A living coupled oscillator system was constructed by a cell patterning method with a plasmodial slime mold, in which parameters such as coupling strength and distance between the oscillators can be systematically controlled. Rich oscillation phenomena between the two-coupled oscillators, namely, desynchronizing and antiphase/in-phase synchronization were observed according to these parameters. Both experimental and theoretical approaches showed that these phenomena are closely related to the time delay effect in interactions between the oscillators.

Background: Bacteria have been reported to exhibit complicated morphological colony patterns on solid media, depending on intracellular, and extracellular factors such as motility, cell propagation, and cell-cell interaction. We isolated the filamentous cyanobacterium, Pseudanabaena sp. NIES-4403 (Pseudanabaena, hereafter), that forms scattered (discrete) migrating colonies on solid media. While the scattered colony pattern has been observed in some bacterial species, the mechanism underlying such a pattern still remains obscure. Results: We studied the morphology of Pseudanabaena migrating collectively and found that this species forms randomly scattered clusters varying in size and further consists of a mixture of comet-like wandering clusters and disk-like rotating clusters. Quantitative analysis of the formation of these wandering and rotating clusters showed that bacterial filaments tend to follow trajectories of previously migrating filaments at velocities that are dependent on filament length. Collisions between filaments occurred without crossing paths, which enhanced their nematic alignments, giving rise to bundle-like colonies. As cells increased and bundles aggregated, comet-like wandering clusters developed. The direction and velocity of the movement of cells in comet-like wandering clusters were highly coordinated. When the wandering clusters entered into a circular orbit, they turned into rotating clusters, maintaining a more stable location. Disk-like rotating clusters may rotate for days, and the speed of cells within a rotating cluster increases from the center to the outmost part of the cluster. Using a mathematical modeling with simplified assumption we reproduced some features of the scattered pattern including migrating clusters. Conclusion: Based on these observations, we propose that Pseudanabaena forms scattered migrating colonies that undergo a series of transitions involving several morphological patterns. A simplified model is able to reproduce some features of the observed migrating clusters.

細胞競合において、変異細胞は隣接した正常細胞によって排除される。初期に正常組織内へと導入された変異細胞は、多くの場合、完成した組織から駆逐される。しかし近年、初期に変異細胞が大規模に導入されることで、正常細胞による排除を受けながらも変異細胞がその数を増加させる場合があることが発見された。ここで、細胞競合を経た組織において、変異細胞が完全に駆逐されるか、それとも変異細胞が組織内で勢力を伸ばしてしまうのかという"組織の運命"が細胞のどのような性質によって決定されるのかが、発生過程において非常に重要な問題となる。そのため本稿では、ポピュレーションモデルに基づき細胞数の変化を記述する数理モデルを構築することで、この問題に取り組んだ、その結果、組織の運命を決定しているのは正常細胞と変異細胞が単独で組織を構成した場合に形成する組織サイズの比と、変異細胞の排除率と増殖率の比であることを数学的に明らかにした。(著者抄録)

To gain insight into the nature of biological synchronization at the microscopic scale, we here investigate the hydrodynamic synchronization between conically rotating objects termed nodal cilia. A mechanical model of three rotating cilia is proposed with consideration of variation in their shapes and geometrical arrangement. We conduct numerical estimations of both near-field and far-field hydrodynamic interactions, and we apply a conventional averaging method for weakly coupled oscillators. In the nonidentical case, the three cilia showed stable locked-phase differences around ±π/2. However, such phase locking also occurred with three identical cilia when allocated in a triangle except for the equilateral triangle. The effects of inhomogeneity in cilia shapes and geometrical arrangement on such asymmetric interaction is discussed to understand the role of biological variation in synchronization via hydrodynamic interactions.

An adaptation process in the transportation network of Physarum plasmodium was investigated by measuring oxygen consumption during network formation. Simultaneously, the fractal dimension as a measure of network structure was estimated. Oxygen consumption decreased during the development of the network, whereas the network structure changed from a thin mesh-type to a thick dendritic type. Our data suggested that the morphology of the plasmodial network governed energy consumption; a low dimensional network in the sense of the fractal dimension reduced energy consumption. These data were supported by experimental results excluding biological reasons, such as differences in starvation/nutrientfullness states, and aspects of mitochondrial distribution. Model analysis using the Physarum algorithm with volume conservation constraints confirmed the above findings.

Dynamical colony pattern formation in motile cyanobacteria Pseudanabaena sp. was investigated. Collectives of the bodies are self-organized and form various motile colony patterns on agar plates. The coexistence of collective movements of four types was observed: translationally moving single strands, bundles, comet-like colonies, and a rotating disk. Additionally, the colony patterns switch to others. Existence of body-to-body and body-to-environment interactions were supposed through experimental observations and the analyses. Investigation by a self-propelled particle model revealed that both interactions are necessary for the diversity of colony morphologies and internal and/or external perturbations can trigger the switching phenomena among the colonies.

In this paper, we propose designing transportation network topology and traffic distribution under fluctuating conditions using a bio-inspired algorithm. The algorithm is inspired by the adaptive behavior observed in an amoeba-like organism, plasmodial slime mold, more formally known as plasmodium of Physarum plycephalum. This organism forms a transportation network to distribute its protoplasm, the fluidic contents of its cell, throughout its large cell body. In this process, the diameter of the transportation tubes adapts to the flux of the protoplasm. The Physarum algorithm, which mimics this adaptive behavior, has been widely applied to complex problems, such as maze solving and designing the topology of railroad grids, under static conditions. However, in most situations, environmental conditions fluctuate; for example, in power grids, the consumption of electric power shows daily, weekly, and annual periodicity depending on the lifestyles or the business needs of the individual consumers. This paper studies the design of network topology and traffic distribution with oscillatory input and output traffic flows. The network topology proposed by the Physarum algorithm is controlled by a parameter of the adaptation process of the tubes. We observe various rich topologies such as complete mesh, partial mesh, Y-shaped, and V-shaped networks depending on this adaptation parameter and evaluate them on the basis of three performance functions: loss, cost, and vulnerability. Our results indicate that consideration of the oscillatory conditions and the phase-lags in the multiple outputs of the network is important: The building and/or maintenance cost of the network can be reduced by introducing the oscillating condition, and when the phase-lag among the outputs is large, the transportation loss can also be reduced. We use stability analysis to reveal how the system exhibits various topologies depending on the parameter.

Breaking of left-right symmetry in mouse embryos requires fluid flow at the node, but the precise action of the flow has remained unknown. Here we show that the left-right asymmetry of Cerl2 expression around the node, a target of the flow, is determined post-transcriptionally by decay of Cerl2 mRNA in a manner dependent on its 3' untranslated region. Cerl2 mRNA is absent specifically from the apical region of crown cells on the left side of the node. Preferential decay of Cerl2 mRNA on the left is initiated by the leftward flow and further enhanced by the operation of Wnt-Cerl2 interlinked feedback loops, in which Wnt3 upregulates Wnt3 expression and promotes Cerl2 mRNA decay, whereas Cerl2 promotes Wnt degradation. Mathematical modelling and experimental data suggest that these feedback loops behave as a bistable switch that can amplify in a noise-resistant manner a small bias conferred by fluid flow.

Traffic optimization of railroad networks was considered using an algorithm that was biologically inspired by an amoeba-like organism, plasmodium of the true slime mold, Physarum polycephalum. The organism developed a transportation network consisting of a tubular structure to transport protoplasm. It was reported that plasmodium can find the shortest path interconnecting multiple food sites during an adaptation process (Nakagaki et al., 2001. Biophys. Chem. 92, 47-52). By mimicking the adaptation process a path finding algorithm was developed by Tero et al. (2007). In this paper, the algorithm is newly modified for applications of traffic distribution optimization in transportation networks of infrastructure such as railroads under the constraint that the network topology is given. Application of the algorithm to a railroad in metropolitan Tokyo, Japan is demonstrated. The results are evaluated using three performance functions related to cost, traveling efficiency, and network weakness. The traffic distribution suggests that the modified Physarum algorithm balances the performances under a certain parameter range, indicating a biological process. (C) 2011 Elsevier Ireland Ltd. All rights reserved.

The spatial and temporal periodicity of somite formation is controlled by the segmentation clock, in which numerous cells cyclically express hairy-related transcriptional repressors with a posterior-to-anterior phase delay, creating 'traveling waves' of her1 expression. In zebrafish, the first traveling wave buds off from the synchronous oscillation zone in the blastoderm margin. Here we show that the emergence of a traveling wave coincides with the anterior expansion of Fgf signaling and that transplanted Fgf8b-soaked beads induce ectopic traveling waves. We thus propose that as development proceeds, the activity of Fgf signaling gradually expands anteriorly, starting from the margin, so that cells initiate her1 oscillation with a posterior-to-anterior phase delay. Furthermore, we suggest that Fgf has an essential role in establishing the period gradient that is required for the her1 spatial oscillation pattern at the emergence of the traveling wave.

The hydrophobic beads as mimic of the living cell attachment to microchannel in fluid flow were observed and analyzed. Beads were collided to the microchannel wall by the right angle flow. We found that beads attachment in the fluid flow should be decided by the fluid velocity to the wall, and hydrophobic interaction between the channel and beads. Shear force is less effective in this case.

We present a 3-D microfluidic device that enables localized drug delivery to living slime mould, a giant amoeba-like cell. The device features a flow cell in which drugs can be introduced at several positions, allowing drugs to be delivered to the slime mould at eight different locations. This is in contrast to devices reported in the literature, which allow cells to be addressed at only a few positions. Slime mould patterning is accomplished by insertion of SU-8 structures containing mould into the flow cell. This assembly allowed us to deliver drugs to the cell to evoke a measurable change in its oscillation behaviour.

Microfluidic devices for cell culture have recently been fabricated for perfusion culture, which can provide more likely in vivo environments for cells by continuously supplying nutrition and oxygen, and removing wastes. To design integrated cell culture microfluidic devices with higher density and larger numbers of cells, a fundamental understanding of relationship between cell adhesions and fluid flow in the channel is necessary Eight types of obstacles were made in centre of the PDMS (polydimetylsyloxane) microchannel, and hydrophobic beads as mimic of living cells were introduced. We found that beads are mostly attached to certain positions of obstacles and microchannel walls, even in the high velocity gradient area. The surface of PDMS microchannel is hydrophobic, and the strong hydrophobic beads are more easily attached to the microchannel wall than that of weak hydrophobic beads. The beads are easily sedimented in the channels with square and circular obstacles, and sometimes finally blocked the fluid flow. Establishment of the evaluation method by the beads would be broadened to integrated cell devices.

The hydrophobic beads as mimic of the living cell attached to the microchannel were observed. We found that beads are mostly attached to certain positions of obstacles and microchannel walls, even in the high velocity gradient area.

Microfabrication technique was used to construct a model system with a living cell of plasmodium of the true slime mold, Physarum polycephalum, a living coupled oscillator system. Its parameters can be systematically controlled as in computer simulations, so that results are directly comparable to those of general mathematical models. As the first step, we investigated responses in oscillatory cells, the oscillators of the plasmodium, to periodic stimuli by temperature changes to elucidate characteristics of the cells as nonlinear systems whose internal dynamics are unknown because of their complexity. We observed that the forced oscillator of the plasmodium show 1: 1, 2:1, 3:1 frequency locking inside so-called Arnold tongues regions as well as in other nonlinear systems such as chemical systems and other biological systems. In addition, we found spontaneous switching behavior from certain frequency locking states to other states, even under certain fixed parameters. This technique can be applied to more complex systems with multiple elements, such as coupled oscillator systems, and would be useful to investigate complicated phenomena in biological systems such as information processing. (C) 2004 Elsevier Ireland Ltd. All rights reserved.

Coupled oscillator systems with oscillating cells of plasmodium of the true slime mold were constructed with a cell pattering method using microfabrication technique. Parameters in this system such as coupling strength can be systematically controlled like in computer simulations. We constructed three-oscillator systems in rings and observed spontaneous switching among typical spatio-temporal patterns even when coupling strength was fixed.

A chain of three-oscillator system was constructed with living biological oscillators of phasmodial slime mold, Physarum polycehalum and the oscillation patterns were analyzed by the symmetric Hopf bifurcation theory using group theory. Multi-stability of oscillation patterns was observed, even when the coupling strength was fixed. This suggests that the coupling strength is not an effective parameter to obtain a desired oscillation pattern among the multiple patterns. Here we propose a method to control oscillation patterns using resonance to external stimulus and demonstrate pattern switching induced by frequency resonance given to only one of oscillators in the system.

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. (C) 2000 Elsevier Science Ireland Ltd. All rights reserved.

The plasmodium of the true slime mold Physarum 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.

Gathering or escaping behavior in the plasmodium of Physarum polycephalum is considered to relate to an entrainment of the coupled nonlinear oscillators. The behavior has been explained to be caused by the formation of phase gradient between those oscillators, which results from the local frequency modulation at the stimulated site. However, it has not yet been elucidated how the formation process relates to the migration of the plasmodium. In this paper, we have introduced a model with frequency coupling besides the phase coupling in the system of coupled oscillators. By the simulation, we have shown that not only the phase gradient but also the concentration gradient of substances such as Ca2+ and ATP are self-organized and their reverse by the stimulus results in the migration of plasmodium.

The characteristics of the self-sustained oscillation in the plasmodial strand of Physarum polycephalum have been investigated in one steady and two transient conditions. An isolated Physarum strand changes its length periodically when it is suspended. In the behaviour of the self-sustained oscillation under the conditions, we provide the first demonstration that the changes in the periods of the oscillation can be ascribed to effects on the shortening phase, while the lengthening periods are almost unaffected. This result means that the asymmetric self-sustained oscillation of the Physarum strand is composed of an active contracting process, presumably due to actin filaments and myosin-like molecules in the strand, and a passive lengthening process which is merely an extension of the strand under a load.

The stochastic behavior of organelles during the recovery process of protoplasmic streaming is investigated in Nitella internodal cells at a nanometer space resolution. The motions of organelles in the components parallel and perpendicular to the alignment of actin filaments in the cell are analysed from the traces of displacement of 860 organelles in 1/30s (=video rate). The analysis of those traces shows that the generation of motive forces to the organelle follows the Poisson process. Therefore, we have been able to estimate the step size corresponding to the single force generation as similar to 100 nm. (C) 1995 Academic Press.

Ca2+ ion effect on protoplasmic streaming in an internodal cell of Nitella has been investigated for various temperatures. We have found that the protoplasmic streaming at low temperature is remarkably affected by the Ca2+ ions in the internodal cell but larger concentrations of the Ca2+ ions are needed to suppress the streaming velocity at higher temperatures. These streaming behaviors of the protoplasm, furthermore, have been elucidated on the basis of the reaction equations which take into account ATP hydrolysis due to actin-myosin molecules and inactivity of the molecules due to the Ca2+ ions.

Recovery process of protoplasmic streaming in a Nitella internodal cell has been investigated at various temperatures. It has been found that the protoplasmic streaming, after its cessation by a current stimulus to the cell, begins to occur slowly and more quickly recovers to its original steady flow with larger velocity at higher temperatures. The steady velocity exponentially decreases with increasing inverse temperature, and the recovery time, which is defined as the time required for the protoplasmic streaming to recover to the half-value of its steady velocity, shortens with increasing temperature. It has been shown that the recovery process of protoplasmic streaming is expressed by a function of nondimensional velocity and time scaled by the steady value and the recovery time, respectively. These results have been elucidated on the basis of two motional equations describing the flow dynamics of the protoplasm.