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.

<p>マウス胚のノード繊毛は時計回りの回転運動をする。少数繊毛系等でこの回転運動が位相同期することが観測されている。我々は繊毛間の流体的な相互作用を境界要素法により数値的に求め、振動子モデルとして繊毛間の位相差を位相縮約法により解析した。本発表では同質な繊毛パラメータの場合、2繊毛系では位相同期が起こらない一方、3繊毛系では繊毛の空間的な配置の非対称性により位相同期が起こることを報告する。</p>

The synchronized oscillation plays an important role in physiological functions in biological systems. Synchronized motion of motile cilia realizes unidirectional transport of fluid in vertebrate body. The collective behavior is believed to arise by hydrodynamic interactions via the extracellular fluid, but how this synchrony appears and develops during the embryogenesis are unknown. We analyze synchrony dynamics of nodal cilia, which determine the left-right axis, by quantifying the fluid flow and cilia rotation. We construct a model based on coupled phase oscillators explaining the offset of the synchronization of cilia after the left-right axis determination. This suggests that the synchronization of nodal cilia is governed by global and local hydrodynamic coupling.

Plasmodium of true slime mold, Physarum polycephalum, is an amoeboid<br />
organism, which spreads with developing tubular network structure and crawls on<br />
two-dimensional plane with oscillating the cell thickness. The plasmodium<br />
transforms its tubular network structure to adapt to the environment. To reveal<br />
the effect of the network structure on the oscillating behavior of the<br />
plasmodium, we constructed coupled map systems on two-dimensional weighted<br />
networks as models of the plasmodium, and investigated the relation between the<br />
distribution of weights on the network edges and the synchronization in the<br />
system. We found the probability that the system shows phase synchronization<br />
changes drastically with the weight distribution even if the total weight is<br />
constant. This implies the oscillating patterns observed in the plasmodium are<br />
controlled by the tube widths or cross-sections in the tubular networks.

Plasmodium of true slime mold, &lt;I&gt;Physarum polycephalum&lt;/I&gt;, is an amoeba-like unicellular organism. It crawls in environment with oscillating the cell thickness. The oscillating parts of the plasmodium are connected through tube structures where the protoplasm (intracellular substance) streams. Thus the plasmodium can be modeled as a network consisting of oscillating nodes (or vertices) and links (or edges). In this paper, the network geometries in various environments were analyzed with considering the relation with the spatio-temporal oscillating pattern in the each network. We show the geometry of the networks depends on environmental condition:It forms lattice networks in pleasant environment, tree-graph networks in unpleasant environment, and intermixture of them in neutral environment. The relation between the morphology and the biological function of the plasmodia is discussed in the context of spatio-temporal structure.

The MPS method is a particle method which simulates motion of continua with a finite number of particles. Thus it is relatively easy to simulate complex flows such as those in a bioreactor in which the geometry of flow is continuously modified by adhesion of cells. In this study, flows with adhesion of cells in a micro channel are simulated using the MPS method. The adhesion pattern of cells is well reproduced by the simulation.

真正粘菌変形体というアメーバ様の多核単細胞生物は,一見「単純」な生物にみえるが,実は局所的に得られた情報を細胞全体に伝達して行動するなど,複雑な情報処理や作業を行っている.単純な構造をもつ粘菌が,どのようにして複雑な情報処理を実現しているのかを理解することは,生物学,物理学,または工学の立場から見ても興味深く,我々が粘菌から学ぶべきことはまだまだ多い.しかし,生物であるがゆえに,その扱いは難しく,観測される現象は複雑である.そこで,この複雑な生物現象を系統的に扱う方法が必須となる.本稿では,その一例として,マイクロ加工技術を用いて粘菌結合振動子系を構成する方法を示し,その系の示す美しい数理的世界である,非線形振動が織りなす時空間パターンを紹介する.

工学とバイオ

運動性シアノバクテリア細胞は集団化することで、円盤形の回転型運動や彗星型運動など様々なマクロ構造をとる。H23年度は、標準環境下において、束状、円盤状、彗星状のそれぞれの集団形態の運動解析を行った。その結果、コロニー形態に係わらずバクテリア密度が高いほど運動生が優れていることを見いだした。そこで、H24年度はコロニー形態毎の運動速度の解析と、バクテリアが分泌する粘液を想定した理論モデルの構築に取り組んだ。
並進運動を行うコロニー重心の運動速度は、一本鎖、束状、彗星状の順に大きいことが分かった。また、同じコロニー形態でもコロニーサイズ(設置面積)にわずかに依存して速度が大きくなる傾向が見られた。さらにコロニー速度は培地表面にバクテリア自身が分泌した粘液の有無に大きく左右されることがわかった。以上のことを纏めると、バクテリアが集合することで粘液分泌総量が増加し、それが培地から受ける抗力を低減するものと思われる。これを基に、彗星状の積層コロニーについて、底面細胞のみが駆動力を生成し、側面および底面細胞が全面、底面の水(または培地)からの抗力を受け、その他の細胞は粘液を分泌するという運動モデルを構築した。その結果、上述に見られたコロニー毎の運動特性の定性的な性質を説明することができた。
しかしながら、バクテリアが自発的に集合し、それによって多様な運動が生成するメカニズムは解明されていない。鍵となる粘液の定量化、1本鎖同士の相互作用の定量的観察を通して、より現実的な数理モデル構築を行うことが今後の課題である。

マウスの発生過程において左右差を初めて決めるメカニズムには、発生初期過程に現れるノードと呼ばれる窪みに並ぶ繊毛の回転運動が大きな役割を果たしていると考えられている。繊毛の回転運動によって、ノード流という体液の流れが生じるが、この流れを人工的に反転させるとマウスの左右も反転するという実験によって、流れ自体が、左右差を決定する2次的シグナルを生成することが示唆されてきた。ゾウリムシ表面のなどに通常良く見られる繊毛では、繊毛間の距離が非常に小さいため、繊毛同士協同的に運動することで効率的な全体の運動を生成することが良く知られている。一方、ノード繊毛は、1細胞に1本ずつという非常にまばらに生えている特殊な繊毛であり協同的な振る舞いは期待されていなかった。本研究では、ノード繊毛間の回転運動を調べ、協同性の有無を検証し、まばらで本数も少ないノード繊毛からどのようにして大局的な流れが生成されるのか、そのメカニズムを明らかにすることが目的である。
前年度までに,左右差が決まる発生の各ステージで10-50繊毛の回転運動の協同性について解析を行,協同性は初期の過程で高く流速が大きくなる後期課程では低くなることがわかった.H22年度は,協同性が生じるしくみを明らかにするために,繊毛が生える本数が劇的に少ないミュータントマウスなどを用いて,2本～5,6本のみのノードの繊毛回転運動を観察した.H21に考察した結合振動子のトイ・モデルに流体力学的な考察をさらに加え,より現実的な数理モデルを構築し,上述の少数の繊毛間の協同性解析との結果と比較した.理論考察により,繊毛間には生物学的な結合(キャップジャンクションや分子シグナル)というよりは,流体による結合が存在し,それによって生じる協同的振舞いが何らかの形で初期のステージの小さい流をサポートし,より確実な左右差形成に寄与していることが示唆された.

真正粘菌変形体(Physarum polycephalum)は多核単細胞のアメーバ様細胞である。細胞の厚みを振動させながら環境中を遣いまわり、環境からの情報を細胞の状態・形態にフィードバックしながら行動する。一見、特異な生物だが、「移動知」という概念から見た場合、生物実験系のモデル生物として最適な生物システムのうちの1つであろう。
この細胞は振動性の細胞であり、どの部分を人工的に切り取ってきても細胞の機能を失うことなく独立な細胞として振動し行動できるので、ほぼ同一の要素が集合した要素集団系(結合振動子系)として捉えることができる。この細胞全体を眺めて見ると管状構造のネットワークで構成されている。管内では原形質流動という往復流動が見られ細胞の部分間、つまり、要素間の相互作用はこの流動を通して行われている。興味深いことに、この細胞は環境の状況に応じてその形態(管ネットワークの形態)と振動周期を著しく変化させる。つまり、管ネットワークの幾何が生物としての機能に大きな影響を与えていることが予想される。
本研究の目的は、管ネットワークのトポロジーと形態に着目し、構成論的手法により、原始的な生物の形態による環境の適応機構を明らかにすることである。具体的には、外部環境に応じて輸送管ネットワーク形態が著しく変化する現象について、(1)環境依存のネットワーク構造の特徴を抽出し、(2)環境適応の観点から生物機能がどのように機能的、効率的になっているかを調べ、粘菌の輸送管ネットワークの適応機構の解明を目指した。真栄養分摂取効率,エサ探索効率,エネルギー消費量,栄養分輸送効率などの指標を計測した結果、正粘菌変形体は、各環境毎に最も適応した輸送管ネットワーク形態をとっていることが明らかとなった。

振動しながら環境中をはい回るアメーバ様の単細胞生物、真正粘菌(Physarun polycephalum)変形体は、環境に応じてその形態を動的に変化させる。変形体の部分間は管状構造で結ばれており、その内部には原形質の流れが観察され細胞内物質や栄養分を運んでいるる。変形体の振動している各部分を振動子(あるいはノード)、ノード間を結ぶ管状構造をリンクと定義して、変形体全体をネットワークとして捉えることができる。興味深いことに、この細胞は環境の状況に応じてその形態(管状構造ネットワークの形態)と振動周期が著しく変化する。この環境依存の形態変化は一種の適応行動と見て取ることができる。
本研究では、形態の動的な変化はこの細胞にどのように利益をもたらすのかを探るために、各環境における形態の特徴の解析と振動の時空間パターンを解析した。次に、変形体の管状構造ネットワークの形態に着目し、実験結果からネットワーク・トポロジーの特徴抽出を行った。実験結果解析で明らかにされたネットワーク・トポロジーに基づき結合セルモデルによるネットワーク形態依存の同期現象について解析し、最後に、ネットワーク形成モデルの提案を行い、非常に簡単な局所ルールだけで複雑なネットワークが生成できることが示した。これらの実験・モデル解析による構成論的手法により生物のネットワーク幾何と生物機能の関係について考察を行った。今後は、これらの実験事実に基づき、要素集合系の環境依存形態変化による適応行動のアルゴリズムの抽出を目指す。

本研究は、振動性の細胞である真正粘菌変形体細胞で構築した結合振動子系に見られる時空間パターンの遷移現象のダイナミクス解析を目的としている。
平成17年度では、これまでに研究代表者らが見出した遷移現象について、各相互作用強度毎に現れる振動パターンとその頻度、遷移規則を詳細に調べた。その結果、出現パターンの出現頻度には相互作用強度依存性があり、それに伴いパターン間の遷移確率も変化することがわかった。
また、複数見られる時空間振動の各パターンが生じるメカニズムを調べるために、数理モデルの構築に着手した。これまでの研究で位相方程式というシンプルな結合振動子モデルを想定してきたが、このモデルでは1つの安定な振動パターンしか得られない。そこで、真正粘菌細胞の振動は細胞の収縮弛緩によって引き起こされることから、系全体に原形質量保存則を適用したモデルを考案した。その結果、例えば、2振動子系、3振動子系で見られた全てのパターンを再現することができた。
平成18年度では、遷移現象の背後のメカニズムを知るために各パターンに留まる滞在時間の分布を詳細に調べ、ガンマ分布(複数のボアソン過程から生じる分布)をベースとしたものであることを見出した。この結果から、背後にある力学系として次のような描像が得られる。結合強度を制御パラメータとした分岐構造があり、それらは多重の準安定状態にある。真正粘菌を始めとした生物系は常に内外ノイズにさらされており、分岐前後の近傍ではノイズによって多重準安定状態間を跳ばされてガンマ分布を形成していると考えられる。真正粘菌のエサ探索時にはランダムな時空間パターンが現れるが、このような機構を利用して固定化した行動ではなく自発行動が可能となると考えられる。これらの実験結果を踏まえた遷移現象のモデル化については今後の課題である。

真正粘菌変形体は、アメーバ様の単細胞生物であり、様々な振動現象を示す。本研究の目的は、真正粘菌変形体を用いて、生きたままの状態で結合振動子系を構築し、粘菌における非線形振動子集団のダイナミクスを調べることにある。
これまでの研究で、申請者は2つの粘菌振動子が結合した系を構築してきた。この研究では、この方法を多数の振動子の結合系に拡張し、粘菌を2次元上にパターニングする方法を検討した。その結果、マイクロ加工技術の1つである、フォトリソグラフィーの方法を用いることで、粘菌結合振動子間の結合強度をシステマティックに制御できることがわかった。
また、この粘菌結合振動子系を用いて外部刺激を入力しその応答を調べることで、非線形ダイナミクスに関して様々な知見を得られることが期待される。本年度の研究では、刺激入力方法として光り刺激による方法を検討した。光刺激は、コンピュータで光りの強弱を空間的にパターニングしたものをデジタルプロジェクタを用いて、粘菌試料に投射して与えた。その結果、光パターンに応じて粘菌の移動行動が観察された。よって、本研究により、このようなセットアップでの光刺激入力が粘菌結合振動子系においても有効であることが確認された。さらに、この刺激入力方法によって、生きた粘菌結合振動子系における刺激応答を観察し、非線形ダイナミクスを検討していくことが、今後の課題である。