Researcher Database

Toshiyuki Nakagaki
Research Institute for Electronic Science Research Center of Mathematics for Social Creativity
Professor

Researcher Profile and Settings

Affiliation

  • Research Institute for Electronic Science Research Center of Mathematics for Social Creativity

Job Title

  • Professor

Degree

  • Ph.D(Nagoya University)
  • Master of Pharmaceutical Science(Hokkaido University)
  • Bachelor of Parmaceutical Science(Hokkaido University)

J-Global ID

Profile

  • Toshiyuki Nakagaki is a professor of Mathematical and Physical Ethology in Research Center of Mathematics for Social Creativity, Research Institute for Electronic Science (RIES), Hokkaido University (Sapporo, Japan). Currently he is director of RIES. He graduated from Faculty of Pharmaceutical Science, Hokkaido University (Bachelor in 1987, Master in 1989) and worked in Pfizer Inc. (Central Research Center, Nagoya, Japan) for 5 years. After quitting the job in Pfizer Inc., he entered Nagoya University (Graduate School of Human Informatics) and got a Ph.D in biophysics in 1997 while working as a part-time teacher in a correspondence high school. The thesis title was ‘Amoeboid cell behaviors based on self-organization of nonlinear chemical oscillators’. His post-doc research was done in Bio-mimetic Control Research Center, RIKEN institute, Japan and a study on ‘maze-solving by an amoeba’ was published. He became an associate professor in Hokkaido University in 2000 and conducted an experimental and mathematical study on how an amoeba of slime mold designed multi-functional transport network. After being a professor in Faculty of Complex and Intelligent Systems, Future University Hakodate in 2010, he came to his current position in 2013.

Research Interests

  • Theoretical and experimental cell physiology   physical ethology   

Research Areas

  • Life sciences / Biophysics / Physical ethology

Academic & Professional Experience

  • 2013/10 - Today Hokkaido University Research Institute for Electronic Science professor
  • 2010/04 - 2013/09 Future University Hakodate Faculty of Systems Information Science professor
  • 2000/11 - 2010/03 Hokkaido University Research Institute for Electronic Science associate professor
  • 2000/04 - 2000/10 RIKEN Institute Frontier Post-doc researcher
  • 1997/04 - 2000/03 RIKEN Institute Bio-Mimetic Control Research Center Special Post-doc researcher for Basic Science
  • 1995/04 - 1997/03 Aichi KYOKURYO correspondence high school part-time teacher
  • 1989/04 - 1994/05 Pfizer Inc. Central Research Center Nagoya scientist

Education

  • 1994/04 - 1997/03  Nagoya University  Graduate School of Human Informatics
  • 1987/04 - 1989/03  Hokkaido University  Graduate School of Pharmaceutical Science
  • 1982/04 - 1987/03  Hokkaido University  Faculty of Pharmaceutical Science

Association Memberships

  • THE JAPANESE SOCIETY FOR MATHEMATICAL BIOLOGY   形の科学会   日本時間生物学会   日本生物物理学会   日本原生生物学会   

Research Activities

Published Papers

  • Shigeru Kuroda, Nariya Uchida, Toshiyuki Nakagaki
    Cold Spring Harbor Laboratory 2018/05 [Refereed][Not invited]
  • Chao Gao, Chen Liu, Daniel Schenz, Xuelong Li, Zili Zhang, Marko Jusup, Zhen Wang, Madeleine Beekman, Toshiyuki Nakagaki
    Physics of Life Reviews 1571-0645 2018 [Refereed][Not invited]
     
    Physarum polycephalum, a single-celled, multinucleate slime mould, is a seemingly simple organism, yet it exhibits quasi-intelligent behaviour during extension, foraging, and as it adapts to dynamic environments. For these reasons, Physarum is an attractive target for modelling with the underlying goal to uncover the physiological mechanisms behind the exhibited quasi-intelligence and/or to devise novel algorithms for solving complex computational problems. The recent increase in modelling studies on Physarum has prompted us to review the latest developments in this field in the context of modelling and computing alike. Specifically, we cover models based on (i) morphology, (ii) taxis, and (iii) positive feedback dynamics found in top-down and bottom-up modelling techniques. We also survey the application of each of these core features of Physarum to solving difficult computational problems with real-world applications. Finally, we highlight some open problems in the field and present directions for future research.
  • Daniel Schenz, Yasuaki Shima, Shigeru Kuroda, Toshiyuki Nakagaki, Kei-Ichi Ueda
    JOURNAL OF PHYSICS D-APPLIED PHYSICS 50 (43) 434001  0022-3727 2017/11 [Refereed][Not invited]
     
    Exploring free space (scouting) efficiently is a non-trivial task for organisms of limited perception, such as the amoeboid Physarum polycephalum. However, the strategy behind its exploratory behaviour has not yet been characterised. In this organism, as the extension of the frontal part into free space is directly supported by the transport of body mass from behind, the formation of transport channels (routing) plays the main role in that strategy. Here, we study the organism's exploration by letting it expand through a corridor of constant width. When turning at a corner of the corridor, the organism constructed a main transport vein tracing a centre-in-centre line. We argue that this is efficient for mass transport due to its short length, and check this intuition with a new algorithm that can predict the main vein's position from the frontal tip's progression. We then present a numerical model that incorporates reaction-diffusion dynamics for the behaviour of the organism's growth front and current reinforcement dynamics for the formation of the vein network in its wake, as well as interactions between the two. The accuracy of the model is tested against the behaviour of the real organism and the importance of the interaction between growth tip dynamics and vein network development is analysed by studying variants of the model. We conclude by offering a biological interpretation of the well-known current reinforcement rule in the context of the natural exploratory behaviour of Physarum polycephalum.
  • Itsuki Kunita, Kei-Ichi Ueda, Dai Akita, Shigeru Kuroda, Toshiyuki Nakagaki
    JOURNAL OF PHYSICS D-APPLIED PHYSICS 50 (35) 354002  0022-3727 2017/09 [Refereed][Not invited]
     
    Organisms choose from among various courses of action in response to a wide variety of environmental conditions and the mechanism by which various behaviours are induced is an open question. Interesting behaviour was recently reported: that a unicellular organism of slime mold Physarum polycephalum known as an amoeba had multiple responses (crossing, returning, etc) when the amoeba encounters a zone with toxic levels of quinine, even under carefully controlled conditions. We here examined this elegant example in more detail to obtain insight into behavioural differentiation. We found that the statistical distribution of passage times across a quinine zone switch from unimodal to bimodal (with peaks corresponding to fast crossing and no crossing) when a periodic light stimulation to modulate a biorhythm in amoeba is applied homogeneously across the space, even under the same level of chemical stimuli. Based on a mathematical model for cell movement in amoeba, we successfully reproduced the stimulation-induced differentiation, which was observed experimentally. These dynamics may be explained by a saddle structure around a canard solution. Our results imply that the differentiation of behavioural types in amoeba is modified step-by-step via the compounding of stimulation inputs. The complex behaviour like the differentiation in amoeba may provide a basis for understanding the mechanism of behaviour selection in higher animals from an ethological perspective.
  • Takuya Umedachi, Kentaro Ito, Ryo Kobayashi, Akio Ishiguro, Toshiyuki Nakagaki
    JOURNAL OF PHYSICS D-APPLIED PHYSICS 50 (25) 0022-3727 2017/06 [Refereed][Not invited]
     
    Response to mechanical stimuli is a fundamental and critical ability for living cells to survive in hazardous conditions or to form adaptive and functional structures against force(s) from the environment. Although this ability has been extensively studied by molecular biology strategies, it is also important to investigate the ability from the viewpoint of biological rhythm phenomena so as to reveal the mechanisms that underlie these phenomena. Here, we use the plasmodium of the true slime mold Physarum polycephalum as the experimental system for investigating this ability. The plasmodium was repetitively stretched for various periods during which its locomotion speed was observed. Since the plasmodium has inherent oscillation cycles of protoplasmic streaming and thickness variation, how the plasmodium responds to various periods of external stretching stimuli can shed light on the other biological rhythm phenomena. The experimental results show that the plasmodium exhibits response to periodic mechanical stimulation and changes its locomotion speed depending on the period of the stretching stimuli.
  • Dai Akita, Daniel Schenz, Shigeru Kuroda, Katsuhiko Sato, Kei-ichi Ueda, Toshiyuki Nakagaki
    DEVELOPMENT GROWTH & DIFFERENTIATION 59 (5) 465 - 470 0012-1592 2017/06 [Refereed][Not invited]
     
    Vein networks span the whole body of the amoeboid organism in the plasmodial slime mould Physarum polycephalum, and the network topology is rearranged within an hour in response to spatio-temporal variations of the environment. It has been reported that this tube morphogenesis is capable of solving mazes, and a mathematical model, named the current reinforcement rule', was proposed based on the adaptability of the veins. Although it is known that this model works well for reproducing some key characters of the organism's maze-solving behaviour, one important issue is still open: In the real organism, the thick veins tend to trace the shortest possible route by cutting the corners at the turn of corridors, following a center-in-center trajectory, but it has not yet been examined whether this feature also appears in the mathematical model, using corridors of finite width. In this report, we confirm that the mathematical model reproduces the center-in-center trajectory of veins around corners observed in the maze-solving experiment.
  • Mark D. Fricker, Dai Akita, Luke L. M. Heaton, Nick Jones, Boguslaw Obara, Toshiyuki Nakagaki
    JOURNAL OF PHYSICS D-APPLIED PHYSICS 50 (25) 254005  0022-3727 2017/06 [Refereed][Not invited]
     
    We evaluate different ridge-enhancement and segmentation methods to automatically extract the network architecture from time-series of Physarum plasmodia withdrawing from an arena via a single exit. Whilst all methods gave reasonable results, judged by precision-recall analysis against a ground-truth skeleton, the mean phase angle (Feature Type) from intensity-independent, phase-congruency edge enhancement and watershed segmentation was the most robust to variation in threshold parameters. The resultant single pixel-wide segmented skeleton was converted to a graph representation as a set of weighted adjacency matrices containing the physical dimensions of each vein, and the inter-vein regions. We encapsulate the complete image processing and network analysis pipeline in a downloadable software package, and provide an extensive set of metrics that characterise the network structure, including hierarchical loop decomposition to analyse the nested structure of the developing network. In addition, the change in volume for each vein and intervening plasmodial sheet was used to predict the net flow across the network. The scaling relationships between predicted current, speed and shear force with vein radius were consistent with predictions from Murray's law. This work was presented at PhysNet 2015.
  • Makoto Iima, Hiroshi Kori, Toshiyuki Nakagaki
    JOURNAL OF PHYSICS D-APPLIED PHYSICS 50 (15) 0022-3727 2017/04 [Refereed][Not invited]
     
    The boundary of a cell is the interface with its surroundings and plays a key role in controlling the cell movement adaptations to different environments. We propose a study of the boundary effects on the patterns and waves of the rhythmic contractions in plasmodia of Physarum polycephalum, a tractable model organism of the amoeboid type. Boundary effects are defined as the effects of both the boundary conditions and the boundary shape. The rhythmicity of contraction can be modulated by local stimulation of temperature, light and chemicals, and by local deformation of cell shape via mechanosensitive ion channels as well. First, we examined the effects of boundary cell shapes in the case of a special shape resembling a tadpole, while requiring that the natural frequency in the proximity of the boundary is slightly higher and uniform. The simulation model reproduced the approximate propagated wave, from the tail to the head, while the inward waves were observed only near the periphery of the head section of the tadpole-shape. A key finding was that the frequency of the rhythmic contractions depended on the local shape of cell boundary. This implies that the boundary conditions of the phase were not always homogeneous. To understand the dependency, we reduced the two-dimensional model into a one-dimensional continuum model with Neumann boundary conditions. Here, the boundary conditions reflect the frequency distribution at the boundary. We described the analytic solutions and calculated the relationship between the boundary conditions and the wave propagation for a one-dimensional model of the continuous oscillatory field and a discrete coupled oscillator system. The results obtained may not be limited to cell movement of Physarum, but may be applicable to the other physical systems since the analysis used a generic phase diffusion equation.
  • K. Sato, I. Kunita, Y. Takikawa, D. Takeuchi, Y. Tanaka, T. Nakagaki, H. Orihara
    SOFT MATTER 13 (14) 2708 - 2716 1744-683X 2017/04 [Refereed][Not invited]
     
    Shear banding is frequently observed in complex fluids. However, the configuration of macromolecules in solutions undergoing shear banding has not yet been directly observed. In this study, by using the fact that F-actin solutions exhibit shear banding and actin filaments are visualized by fluorescent labels, we directly observed the intrinsic states of an actin solution undergoing shear banding. By combining the 3D imaging of labeled actin filaments and particle image velocimetry (PIV), we obtained orientation distributions of actin filaments in both high and low shear rate regions, whose quantitative differences are indicated. In addition, by using the orientation distributions and applying stress expression for rod-like polymers, we estimated stress tensors in both high and low shear rate regions. This evaluation indicates that different orientation distributions of filamentous macromolecules can exhibit a common shear stress.
  • Bernd Meyer, Cedrick Ansorge, Toshiyuki Nakagaki
    PLOS ONE 12 (3) 1932-6203 2017/03 [Refereed][Not invited]
     
    Self-organized mechanisms are frequently encountered in nature and known to achieve flexible, adaptive control and decision-making. Noise plays a crucial role in such systems: It can enable a self-organized system to reliably adapt to short-term changes in the environment while maintaining a generally stable behavior. This is fundamental in biological systems because they must strike a delicate balance between stable and flexible behavior. In the present paper we analyse the role of noise in the decision-making of the true slime mold Physarum polycephalum, an important model species for the investigation of computational abilities in simple organisms. We propose a simple biological experiment to investigate the reaction of P. polycephalum to time-variant risk factors and present a stochastic extension of an established mathematical model for P. polycephalum to analyze this experiment. It predicts that-due to the mechanism of stochastic resonance D noise can enable P. polycephalum to correctly assess time-variant risk factors, while the corresponding noise-free system fails to do so. Beyond the study of P. polycephalum we demonstrate that the influence of noise on self-organized decision-making is not tied to a specific organism. Rather it is a general property of the underlying process dynamics, which appears to be universal across a wide range of systems. Our study thus provides further evidence that stochastic resonance is a fundamental component of the decision-making in self-organized macroscopic and microscopic groups and organisms.
  • Dai Akita, Itsuki Kunita, Mark D. Fricker, Shigeru Kuroda, Katsuhiko Sato, Toshiyuki Nakagaki
    JOURNAL OF PHYSICS D-APPLIED PHYSICS 50 (2) 024001  0022-3727 2017/01 [Refereed][Not invited]
     
    Transport networks are ubiquitous in multicellular organisms and include leaf veins, fungal mycelia and blood vessels. While transport of materials and signals through the network plays a crucial role in maintaining the living system, the transport capacity of the network can best be understood in terms of hydrodynamics. We report here that plasmodium from the large, single-celled amoeboid Physarum was able to construct a hydrodynamically optimized veinnetwork when evacuating biomass from confined arenas of various shapes through a narrow exit. Increasingly thick veins developed towards the exit, and the network spanned the arena via repetitive bifurcations to give a branching tree. The Hausdorff distance from all parts of the plasmodium to the vein network was kept low, whilst the hydrodynamic conductivity from distal parts of the network to the exit was equivalent, irrespective of the arena shape. This combination of spatial patterning and differential vein thickening served to evacuate biomass at an equivalent rate across the entire arena. The scaling relationship at the vein branches was determined experimentally to be 2.53-3.29, consistent with predictions from Murray's law. Furthermore, we show that mathematical models for self-organised, adaptive transport in Physarum simulate the experimental network organisation well if the scaling coefficient of the current-reinforcement rule is set to 3. In simulations, this resulted in rapid development of an optimal network that minimised the combined volume and frictional energy in comparison with other scaling coefficients. This would predict that the boundary shear forces within each vein are constant throughout the network, and would be consistent with a feedback mechanism based on a sensing a threshold shear at the vein wall.
  • Physical ethology of unicellular organism
    S. Kuroda, S. Takagi, T. Saigusa, T. Nakagaki
    Brain evolution by design -From Neural origin to cognitive architecture- (Ed. by S. Shigeno, Y. Murakami, T. Nomura) ISBN: 978-4-431-56467-6, Springer-Verlag 3 - 23 2017 [Refereed][Not invited]
  • Physical ethology of single-celled organism
    Toshiyuki Nakagaki
    INTERNATIONAL JOURNAL OF PSYCHOLOGY 51 574 - 574 0020-7594 2016/07 [Refereed][Not invited]
  • Itsuki Kunita, Tatsuya Yamaguchi, Atsushi Tero, Masakazu Akiyama, Shigeru Kuroda, Toshiyuki Nakagaki
    JOURNAL OF THE ROYAL SOCIETY INTERFACE 13 (118) 20160155  1742-5689 2016/05 [Refereed][Not invited]
     
    Previous studies on adaptive behaviour in single-celled organisms have given hints to the origin of their memorizing capacity. Here we report evidence that a protozoan ciliate Tetrahymena has the capacity to learn the shape and size of its swimming space. Cells confined in a small water droplet for a short period were found to recapitulate circular swimming trajectories upon release. The diameter of the circular trajectories and their duration reflected the size of the droplet and the period of confinement. We suggest a possible mechanism for this adaptive behaviour based on a Ca2+ channel. In our model, repeated collisions with the walls of a confining droplet result in a slow rise in intracellular calcium that leads to a long-term increase in the reversal frequency of the ciliary beat.
  • 粘菌の用不用適応能に倣った形状最適化設計法の検討
    吉原一詞, 中垣俊之
    土木学会論文集 A2(応用力学) 72 (2) 3 - 11 2016 [Not refereed][Invited]
  • Shigeru Kuroda, Seiji Takagi, Toshiyuki Nakagaki, Tetsuo Ueda
    JOURNAL OF EXPERIMENTAL BIOLOGY 218 (23) 3729 - 3738 0022-0949 2015/12 [Refereed][Not invited]
     
    Physarum plasmodium is a giant unicellular organism whose length can vary by more than three orders of magnitude. Using plasmodia ranging in size from 100 mu m to 10 cm, we investigated the size dependency of their thickness distributions and locomotion speeds during free locomotion. (1) In the longitudinal direction, the organism is thickest close to the front, and decreases exponentially in thickness towards the rear. The slenderness ratio varies with body size according to a power law, such that large plasmodia are long and flat, whereas small plasmodia are short and thick. (2) The mean locomotion speed is proportional to the mean maximum thickness of the frontal part. By conducting a dimensional analysis, possible physical models are discussed. (3) The intrinsic period of the thickness oscillation, which is related to shuttle streaming (period 1-2 min), increases logarithmically with body size. (4) Various characteristics exhibit size-independent, long-period (20 +/- 10 min) oscillations, including speed, shape and intrinsic thickness oscillation period. These variations are closely coupled to formation of the entire cell shape, including undulation of thickness along the longitudinal axis and timing of branching of the frontal tip. Based on these experimental results and those reported previously, we propose a simple mathematical model for cell locomotion.
  • Jean-Paul Rieu, Helene Delanoe-Ayari, Seiji Takagi, Yoshimi Tanaka, Toshiyuki Nakagaki
    Journal of the Royal Society Interface 12 (106) 1742-5689 2015/05 [Refereed][Not invited]
     
    The slime mould Physarum polycephalum is a giant multinucleated cell exhibiting well-known Ca2+-dependent actomyosin contractions of its vein network driving the so-called cytoplasmic shuttle streaming. Its actomyosin network forms both a filamentous cortical layer and large fibrils. In order to understand the role of each structure in the locomotory activity, we performed birefringence observations and traction force microscopy on excised fragments of Physarum. After several hours, these microplasmodia adopt three main morphologies: flat motile amoeba, chain types with round contractile heads connected by tubes and motile hybrid types. Each type exhibits oscillations with a period of about 1.5 min of cell area, traction forces and fibril activity (retardance) when fibrils are present. The amoeboid types show only peripheral forces while the chain types present a never-reported force pattern with contractile rings far from the cell boundary under the spherical heads. Forces are mostly transmitted where the actomyosin cortical layer anchors to the substratum, but fibrils maintain highly invaginated structures and contribute to forces by increasing the length of the anchorage line. Microplasmodia are motile only when there is an asymmetry in the shape and/or the force distribution.
  • Itsuki Kunita, Shigeru Kuroda, Kaito Ohki, Toshiyuki Nakagaki
    FRONTIERS IN MICROBIOLOGY 5 1664-302X 2014/06 [Refereed][Not invited]
     
    We have observed how the ciliate Paramecium attempts to retreat from the dead-end of a long capillary that is too narrow for turning. After many trial-and-error episodes of short-term backward swimming (SBS), which is the conventional avoidance behavior exhibited in free swimming when an obstacle is faced, long-term backward swimming (LBS) that lasted five to ten times longer was developed. LBS may have a beneficial effect for complete withdrawal from the capillary space, although in our experiment it was impossible for the organism to do so due to the capillary length. In order to identify a physically possible mechanism for LBS, we propose model equations for the membrane potential of Hodgkin Huxley type, which describe the control of ciliary movement. The physiological implications and physical mechanism of the development of LBS are discussed.
  • Shigeru Kuroda, Itsuki Kunita, Yoshimi Tanaka, Akio Ishiguro, Ryo Kobayashi, Toshiyuki Nakagaki
    JOURNAL OF THE ROYAL SOCIETY INTERFACE 11 (95) 20140205  1742-5689 2014/06 [Refereed][Not invited]
     
    Crawling using muscular waves is observed in many species, including planaria, leeches, nemertea, aplysia, snails, chitons, earthworms and maggots. Contraction or extension waves propagate along the antero-posterior axis of the body as the crawler pushes the ground substratum backward. However, the observation that locomotory waves can be directed forward or backward has attracted much attention over the past hundred years. Legged organisms such as centipedes and millipedes exhibit parallel phenomena; leg tips form density waves that propagate backward or forward. Mechanical considerations reveal that leg-density waves play a similar role to locomotory waves in limbless species, and that locomotory waves are used by a mechanism common to both legged and limbless species to achieve crawling. Here, we report that both mode switching of the wave direction and friction control were achieved when backward motion was induced in the laboratory. We show that the many variations of switching in different animals can essentially be classified in two types according to mechanical considerations. We propose that during their evolution, limbless crawlers first moved in a manner similar to walking before legs were obtained. Therefore, legged crawlers might have learned the mechanical mode of movement involved in walking long before obtaining legs.
  • Qi Ma, Anders Johansson, Atsushi Tero, Toshiyuki Nakagaki, David J.T. Sumpter
    Journal of the Royal Society Interface 10 (80) 1742-5662 2013/03/06 [Refereed][Not invited]
     
    Biological systems that build transport networks, such as trail-laying ants and the slime mould Physarum, can be described in terms of reinforced random walks. In a reinforced random walk, the route taken by 'walking' particles depends on the previous routes of other particles. Here, we present a novel form of random walk in which the flow of particles provides this reinforcement. Starting from an analogy between electrical networks and random walks, we show how to include current reinforcement. We demonstrate that current-reinforcement results in particles converging on the optimal solution of shortest path transport problems, and avoids the selfreinforcing loops seen in standard density-based reinforcement models. We further develop a variant of the model that is biologically realistic, in the sense that the particles can be identified as ants and their measured density corresponds to those observed in maze-solving experiments on Argentine ants. For network formation, we identify the importance of nonlinear current reinforcement in producing networks that optimize both network maintenance and travel times. Other than ant trail formation, these random walks are also closely related to other biological systems, such as blood vessels and neuronal networks, which involve the transport of materials or information. We argue that current reinforcement is likely to be a common mechanism in a range of systems where network construction is observed. © 2013 The Authors.
  • Ryo Kobayashi, Toshiyuki Nakagaki, Akio Ishiguro
    11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013, PTS 1 AND 2 (ICNAAM 2013) 1558 2440 - 2443 0094-243X 2013 [Refereed][Not invited]
     
    Why can animals show amazingly sinuous and robust motion under unpredictable complex environments ? It is because animals have a large number of degrees of freedom in their bodies and can orchestrate them very well. Even for the most advanced robots today, such abilities are difficult to attain. In order to create animal-like robots, autonomous decentralized control (ADC) is the key concept that facilitates real-time control of a large number of degrees of freedom corresponding to the changing surroundings. We propose a simple design principle of ADC, which is termed as discrepancy control; then, we test it by implementing it in various types of robots.
  • Adaptive path-finding and transport network formation by the amoeba-like organism {\it Physarum}
    Itsuki Kunita, Kazunori Yoshihara, Atsushi Tero, Kentaro Ito, Chiu Fan Lee, Mark D. Fricker, Toshiyuki Nakagaki
    Natural Computing and Beyond, Proceedings in Information and Communications Technology (PICT), Springer-Verlag, 6 14 - 29 2013 [Refereed][Not invited]
  • Ethological response to periodic stimulation in {\it Chara} and {\it Brepharisma}
    Itsuki Kunita, Sho Sato, Tetsu Saigusa, Toshiyuki Nakagaki
    Natural Computing and Beyond, Proceedings in Information and Communications Technology (PICT), Springer-Verlag 6 3 - 13 2013 [Refereed][Not invited]
  • Itsuki Kunita, Katsuhiko Sato, Yoshimi Tanaka, Yoshinori Takikawa, Hiroshi Orihara, Toshiyuki Nakagaki
    PHYSICAL REVIEW LETTERS 109 (24) 248303  0031-9007 2012/12 [Refereed][Not invited]
     
    We report herein the first evidence that an F-actin solution shows shear banding, which is characterized by the spontaneous separation of homogeneous shear flow into two macroscopic domains of different definite shear rates. The constant shear stress observed in the F-actin solution is explained by the banded flow with volume fractions that obey the lever rule. Nonhomogenous reversible flows were observed in the F-actin solution with respect to upward and downward changes in the shear rate. This is the first time shear banding has been observed in a simple biomacromolecule. The biological implications and dynamic aspects of shear flow velocity characteristic patterns are discussed.
  • Makoto Iima, Toshiyuki Nakagaki
    MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA 29 (3) 263 - 281 1477-8599 2012/09 [Refereed][Not invited]
     
    We study how the net transport and mixing of chemicals occur in a relatively large amoeba, the true slime mold Physarum polycephalum. The shuttle streaming of the amoeba is characterized by a rhythmic flow of the order of 1 mu m/s in which the protoplasm streams back and forth. To explain the experimentally observed transport of chemicals, we formulate a simplified model to consider the mechanism by which net transport can be induced by shuttle (or periodic) motion inside the amoeba. This model is independent from the details of fluid property as it is based on the mass conservation law only. Even in such a simplified model, we demonstrate that sectional oscillations play an important role in net transport and discuss the effects of the sectional boundary motion on net transport in the microorganism.
  • Kei-Ichi Ueda, Seiji Takagi, Toshiyuki Nakagaki
    PHYSICAL REVIEW E 86 (1) 011927  1539-3755 2012/07 [Refereed][Not invited]
     
    The survival of an organism can depend upon the direction in which it decides to move in response to changes in external conditions. Here we propose a physicochemical mechanism of the decision process for migration direction in the case of a giant amoebalike Physarum plasmodium. The tactical movement response could be changed by reversal of the phase wave of the rhythmic contractions that occur in any part of the plasmodium body when local stimulation is applied and the frequency of the rhythmic contractions is locally modulated in the stimulated region. The proposed model describes a physicochemical mechanism of coupling between the local modulation of frequency and the global transport of protoplasmic mass. The decision process is clarified from a rheological point of view.
  • Yoshimi Tanaka, Kentaro Ito, Toshiyuki Nakagaki, Ryo Kobayashi
    JOURNAL OF THE ROYAL SOCIETY INTERFACE 9 (67) 222 - 233 1742-5689 2012/02 [Refereed][Not invited]
     
    Limbless crawling is a fundamental form of biological locomotion adopted by a wide variety of species, including the amoeba, earthworm and snake. An interesting question from a biomechanics perspective is how limbless crawlers control their flexible bodies in order to realize directional migration. In this paper, we discuss the simple but instructive problem of peristalsis-like locomotion driven by elongation-contraction waves that propagate along the body axis, a process frequently observed in slender species such as the earthworm. We show that the basic equation describing this type of locomotion is a linear, one-dimensional diffusion equation with a time-space-dependent diffusion coefficient and a source term, both of which express the biological action that drives the locomotion. A perturbation analysis of the equation reveals that adequate control of friction with the substrate on which locomotion occurs is indispensable in order to translate the internal motion (propagation of the elongation-contraction wave) into directional migration. Both the locomotion speed and its direction (relative to the wave propagation) can be changed by the control of friction. The biological relevance of this mechanism is discussed.
  • Transport and mixing of chemicals inside the body of a micro-organism
    Makoto Iima, Toshiyuki Nakagaki
    Journal of Mathematical Medicine and Biology 29 263 - 281 2012 [Refereed][Not invited]
  • Takuya Umedachi, Ryo Idei, Toshiyuki Nakagaki, Ryo Kobayashi, Akio Ishiguro
    ADVANCED ROBOTICS 26 (7) 693 - 707 0169-1864 2012 [Refereed][Not invited]
     
    This paper presents a fluid-filled soft-bodied amoeboid robot inspired by the plasmodium of the true slime mold. The significant features of this robot are 2-fold. (i) The robot has a fluid circuit (i. e., cylinders and nylon tubes filled with fluid), and a truly soft and deformable body stemming from real-time tunable springs-the former seals protoplasm to induce global physical interaction between the body parts and the latter is used for elastic actuators. (ii) A fully decentralized control using coupled oscillators with a completely local sensory feedback mechanism is realized by exploiting the global physical interaction between the body parts stemming from the fluid circuit. The experimental results show that this robot exhibits adaptive locomotion without relying on any hierarchical structure. The results obtained are expected to shed new light on the design scheme for autonomous decentralized control systems. (C) Koninklijke Brill NV, Leiden and The Robotics Society of Japan, 2012
  • Novel control principle based on the discrepancy function
    Ryo Kobayashi, Toshiyuki Nakagaki, Akio Ishiguro
    RIMS Kokyuroku Bessatsu B31 61 - 77 2012 [Not refereed][Not invited]
  • Shin Watanabe, Atsushi Tero, Atsuko Takamatsu, Toshiyuki Nakagaki
    BIOSYSTEMS 105 (3) 225 - 232 0303-2647 2011/09 [Refereed][Not invited]
     
    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.
  • Tanya Latty, Kai Ramsch, Kentaro Ito, Toshiyuki Nakagaki, David J. T. Sumpter, Martin Middendorf, Madeleine Beekman
    JOURNAL OF THE ROYAL SOCIETY INTERFACE 8 (62) 1298 - 1306 1742-5689 2011/09 [Refereed][Not invited]
     
    Many biological systems use extensive networks for the transport of resources and information. Ants are no exception. How do biological systems achieve efficient transportation networks in the absence of centralized control and without global knowledge of the environment? Here, we address this question by studying the formation and properties of inter-nest transportation networks in the Argentine ant (Linepithema humile). We find that the formation of inter-nest networks depends on the number of ants involved in the construction process. When the number of ants is sufficient and networks do form, they tend to have short total length but a low level of robustness. These networks are topologically similar to either minimum spanning trees or Steiner networks. The process of network formation involves an initial construction of multiple links followed by a pruning process that reduces the number of trails. Our study thus illuminates the conditions under and the process by which minimal biological transport networks can be constructed.
  • Robert D. Guy, Toshiyuki Nakagaki, Grady B. Wright
    PHYSICAL REVIEW E 84 (1) 1539-3755 2011/07 [Refereed][Not invited]
     
    A model is presented to explain the development of flow channels within the cytoplasm of the plasmodium of the giant amoeba Physarum polycephalum. The formation of channels is related to the development of a self-organizing tubular network in large cells. Experiments indicate that the flow of cytoplasm is involved in the development and organization of these networks, and the mathematical model proposed here is motivated by recent experiments involving the observation of development of flow channel in small cells. A model of pressure-driven flow through a polymer network is presented in which the rate of flow increases the rate of depolymerization. Numerical solutions and asymptotic analysis of the model in one spatial dimension show that under very general assumptions this model predicts the formation of channels in response to flow.
  • Yoshimi Tanaka, Toshiyuki Nakagaki
    JOURNAL OF COMPUTATIONAL AND THEORETICAL NANOSCIENCE 8 (3) 383 - 390 1546-1955 2011/03 [Refereed][Not invited]
     
    A series of ethological experiments on the primitive unicellular amoeboid organism Physarum polycephalum has shown that it possesses an unexpectedly high ability of information processing. This organism can solve mazes and certain optimization problems, and can demonstrate both anticipatory and contemplative behavior. A number of mathematical models have been proposed to describe and understand this smart behavior. We survey the investigations that have been performed on the cell level.
  • Kei-Ichi Ueda, Seiji Takagi, Yasumasa Nishiura, Toshiyuki Nakagaki
    Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 83 (2) 021916  1539-3755 2011/02/28 [Refereed][Not invited]
     
    It has recently been reported that even single-celled organisms appear to be "indecisive" or "contemplative" when confronted with an obstacle. When the amoeboid organism Physarum plasmodium encounters the chemical repellent quinine during migration along a narrow agar lane, it stops for a period of time (typically several hours) and then suddenly begins to move again. When movement resumes, three distinct types of behavior are observed: The plasmodium continues forward, turns back, or migrates in both directions simultaneously. Here, we develop a continuum mathematical model of the cell dynamics of contemplative amoeboid movement. Our model incorporates the dynamics of the mass flow of the protoplasmic sol, in relation to the generation of pressure based on the autocatalytic kinetics of pseudopod formation and retraction (mainly, sol-gel conversion accompanying actin-myosin dynamics). The biological justification of the model is tested by comparing with experimentally measured spatiotemporal profiles of the cell thickness. The experimentally observed types of behavior are reproduced in simulations based on our model, and the core logic of the modeled behavior is clarified by means of nonlinear dynamics. An on-off transition between the refractory and activated states of the chemical reactivity that takes place at the leading edge of the plasmodium plays a key role in the emergence of contemplative behavior. © 2011 American Physical Society.
  • Takuya Umedachi, Koichi Takeda, Toshiyuki Nakagaki, Ryo Kobayashi, Akio Ishiguro
    INTERNATIONAL JOURNAL OF UNCONVENTIONAL COMPUTING 7 (6) 449 - 462 1548-7199 2011 [Refereed][Not invited]
     
    This paper presents a soft-bodied amoeboid robot inspired by plasmodium of true slime mold. The significant features of this robot are twofold: (1) the robot has truly soft and deformable body stemming from periodically expanding and contracting real-time tunable springs and a balloon, the former is used for an outer skin of the body and the latter serves as protoplasm in order to induce long-distance physical interaction between the body parts; and (2) a fully decentralized control using coupled oscillators with completely local sensory feedback mechanism is realized by exploiting the long-distance physical interaction. Experimental results show that this robot exhibits truly supple locomotion without relying on any hierarchical structure. The results obtained are expected to shed new light on how autonomous decentralized control may he designed.
  • Convergence properties for the Physarum solver
    Kentaro Ito, Anders Johansson, Toshiyuki Nakagaki, Atsushi Tero
    arXiv:1101.5249v1[math.OC] 27 Jan 2011 2011/01 [Not refereed][Not invited]
  • Takashi Yamamoto, Mitsuru Sugawara, Takashi Kikukawa, Seiji Miyauchi, Masahiro Yamaguchi, Atsushi Tero, Seiji Takagi, Toshiyuki Nakagaki
    BIOPHYSICAL CHEMISTRY 147 (1-2) 59 - 65 0301-4622 2010/03 [Refereed][Not invited]
     
    Transport across the cell membrane is crucial in drug delivery. However, the process is complicated because nucleoside derivatives that are commonly used its anti-viral drugs are transported through two different types of specific transporters: concentrative transporters and equilibrative transporters. Cross-disciplinary approaches involving both biological experiments and theoretical considerations are therefore necessary to study the transport of nucleoside analogues such as ribavirin. Here we constructed an experimental model system using the Xenopus laevis oocyte that expressed examples of both types of transporters: human concentrative nucleoside transporter 3 and human equilibrative transporter 1. We also performed a kinetic study. Experimental results showed that the transport of ribavirin could be reduced by inhibiting one of the two types of transporters, which seems to be counterintuitive. We therefore designed a simple mathematical model of the dynamics of ribavirin uptake and analyzed the model behaviors using a numerical simulation. The theoretical results reproduced the experimentally observed phenomena and suggested a possible mechanism for the process. Based on this mechanism, we predicted some potential methods for the effective uptake of ribavirin from a dynamics point of view. (C) 2010 Elsevier B.V. All rights reserved.
  • Takuya Umedachi, Koichi Takeda, Toshiyuki Nakagaki, Ryo Kobayashi, Akio Ishiguro
    BIOLOGICAL CYBERNETICS 102 (3) 261 - 269 0340-1200 2010/03 [Refereed][Not invited]
     
    Animals exhibit astoundingly adaptive and supple locomotion under real world constraints. In order to endow robots with similar capabilities, we must implement many degrees of freedom, equivalent to animals, into the robots' bodies. For taming many degrees of freedom, the concept of autonomous decentralized control plays a pivotal role. However a systematic way of designing such autonomous decentralized control system is still missing. Aiming at understanding the principles that underlie animals' locomotion, we have focused on a true slime mold, a primitive living organism, and extracted a design scheme for autonomous decentralized control system. In order to validate this design scheme, this article presents a soft-bodied amoeboid robot inspired by the true slime mold. Significant features of this robot are twofold: (1) the robot has a truly soft and deformable body stemming from real-time tunable springs and protoplasm, the former is used for an outer skin of the body and the latter is to satisfy the law of conservation of mass; and (2) fully decentralized control using coupled oscillators with completely local sensory feedback mechanism is realized by exploiting the long-distance physical interaction between the body parts stemming from the law of conservation of protoplasmic mass. Simulation results show that this robot exhibits highly supple and adaptive locomotion without relying on any hierarchical structure. The results obtained are expected to shed new light on design methodology for autonomous decentralized control system.
  • The Birth of Physarum Computing
    Toshiyuki Nakagaki
    INTERNATIONAL JOURNAL OF UNCONVENTIONAL COMPUTING 6 (2) 75 - 77 1548-7199 2010 [Refereed][Not invited]
  • Takuya Umedachi, Koichi Takeda, Toshiyuki Nakagaki, Ryo Kobayashi, Akio Ishiguro
    2010 IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION (ICRA) 3787 - 3792 1050-4729 2010 [Refereed][Not invited]
     
    Animals exhibit astoundingly adaptive and supple locomotion under real world constraints. In order to endow robots with similar capabilities, we must implement large degrees of freedom, equivalent to animals, into the robots' bodies. For taming large degrees of freedom, the concept of autonomous decentralized control plays a pivotal role. However, a systematic way of designing such autonomous decentralized control system is still missing. Aiming at understanding the principles that underlie animals' locomotion, in our early studies, we focused on true slime mold, a primitive living organism, and extracted a decentralized control scheme. In order to validate this control scheme, this paper presents a soft-bodied amoeboid robot inspired by true slime mold. Significant features of this robot are twofold: (1) the robot has truly soft and deformable body stemming from real-time tunable springs and a balloon, the former is used for an outer skin of the body and the latter serves as protoplasm; and (2) a fully decentralized control using coupled oscillators with completely local sensory feedback mechanism is realized by exploiting the long-distance physical interaction between the body parts stemming from both the softness of the body and the law of conservation of protoplasmic mass. Experimental results show that this robot exhibits truly supple locomotion without relying on any hierarchical structure. The results obtained are expected to shed new light on design scheme for autonomous decentralized control system.
  • Foraging Behaviors and Potential Computational Ability of Problem-Solving in an Amoeba
    Toshiyuki Nakagaki
    NATURAL COMPUTING 2 42 - 54 1867-2914 2010 [Refereed][Not invited]
     
    We study cell behaviors in the complex situations: multiple locations of food were simultaneously given. An amoeba-like organism of true slime mold gathered at the multiple food locations while body shape made of tubular network was totally changed. Then only a few tubes connected all of food locations through a network shape. By taking the network shape of body, the plasmodium could meet its own physiological requirements: as fast absorption of nutrient as possible and sufficient circulation of chemical signals and nutrients through a whole body. Optimality of network shape was evaluated in relation to a combinatorial optimization problem. Here we reviewed the potential computational ability of problem-solving in the amoeba, which was much higher than we'd though. The main message of this article is that we had better to change our stupid opinion that an amoeba is stupid.
  • Atsushi Tero, Seiji Takagi, Tetsu Saigusa, Kentaro Ito, Dan P. Bebber, Mark D. Fricker, Kenji Yumiki, Ryo Kobayashi, Toshiyuki Nakagaki
    SCIENCE 327 (5964) 439 - 442 0036-8075 2010/01 [Refereed][Not invited]
     
    Transport networks are ubiquitous in both social and biological systems. Robust network performance involves a complex trade-off involving cost, transport efficiency, and fault tolerance. Biological networks have been honed by many cycles of evolutionary selection pressure and are likely to yield reasonable solutions to such combinatorial optimization problems. Furthermore, they develop without centralized control and may represent a readily scalable solution for growing networks in general. We show that the slime mold Physarum polycephalum forms networks with comparable efficiency, fault tolerance, and cost to those of real-world infrastructure networks-in this case, the Tokyo rail system. The core mechanisms needed for adaptive network formation can be captured in a biologically inspired mathematical model that may be useful to guide network construction in other domains.
  • Aisushi Tero, Toshiyuki Nakagaki, Kazutaka Toyabe, Kenji Yumiki, Ryo Kobayashi
    INTERNATIONAL JOURNAL OF UNCONVENTIONAL COMPUTING 6 (2) 109 - 123 1548-7199 2010 [Refereed][Not invited]
     
    We propose a new solver for the Steiner tree problem, inspired by a true shine mold Physarum polycephalum. This problem involves finding the network that connects multiple points on a plane through the shortest total length. Such a network is known as the Steiner minimum tree (SMT). The solution of this problem is important for the design of transport and communication networks, but is not easy to obtain because the computational time required increases rapidly with the number of points. Using Melzak's algorithm, it is almost impossible to find the best solution for more than thirty points. However, it is known that an amoeboid organism, Physarum plasmodium, can construct a network on in agar plate between many Points at which food is placed. Because the Physarum network sometimes has the same topology as the SMT, we have studied how this is achieved by constructing a mathematical model for the network dynamics, based on the physiological mechanism. Our investigation enables us to propose and discuss the prospects of a new method for solving the Steiner problem.
  • Takuya Umedachi, Koichi Takeda, Toshiyuki Nakagaki, Ryo Kobayashi, Akio Ishiguro
    IEEE/RSJ 2010 INTERNATIONAL CONFERENCE ON INTELLIGENT ROBOTS AND SYSTEMS (IROS 2010) 2401 - 2406 2153-0858 2010 [Refereed][Not invited]
     
    Animals exhibit astoundingly adaptive and supple locomotion under real world constraints. In order to endow robots with similar capabilities, we must implement many degrees of freedom, equivalent to animals, into the robots' bodies. For taming many degrees of freedom, the concept of autonomous decentralized control plays a pivotal role. However, a systematic way of designing such autonomous decentralized control system is still missing. Aiming at understanding the principles that underlie animals' locomotion, in our early studies, we focused on plasmodium of true slime mold, a primitive living organism, and extracted a design scheme for autonomous decentralized control system. In order to demonstrate the relevance of this design scheme, this paper presents a soft-bodied fluid-driven amoeboid robot inspired by plasmodium of true slime mold. The significant features of this robot are twofold: (1) the robot has fluidic circuit (i.e., cylinders and nylon tubes filled with fluid) and truly soft and deformable body stemming from real-time tunable springs, the former serves as protoplasm and the latter is used for elastic actuators; and (2) a fully decentralized control using coupled oscillators with completely local sensory feedback mechanism is realized by exploiting the long-distance physical interaction between the body parts stemming from the law of conservation of protoplasmic mass. The experimental results show that this robot exhibits truly supple locomotion without relying on any hierarchical structure. The results obtained are expected to shed new light on design scheme for autonomous decentralized control system.
  • Risk management in spatio-temporally varying field by true slime mold
    Kentaro Ito, David Sumpter, Toshiyuki Nakagaki
    NOLTA (Nonlinear Theory and Application) journal, IEICE. 1 26 - 36 2010 [Refereed][Not invited]
  • 真正粘菌変形体から着想を得た自律分散制御方策の実験的検証
    梅舘拓也, 武田光一, 中垣俊之, 小林 亮, 石黒章夫
    計測自動制御学会論文集 46 (11) 706 - 712 2010 [Refereed][Not invited]
  • Time recoder system of protozoa
    Saigusa Tetsu, Tero Atushi, Nakagaki Toshiyuki
    BIOPHYSICAL JOURNAL 96 (3) 308A  0006-3495 2009/02 [Refereed][Not invited]
  • Toshiyuki Nakagaki
    Natural Computing - 4th International Workshop on Natural Computing, IWNC 2009, Himeji, Japan, September 2009, Proceedings Springer 42 - 54 2009 [Refereed][Not invited]
  • Takuya Umedachi, Thichi Kitamura, Koichi Takeda, Toshiyuki Nakagaki, Ryo Kobayashi, Akio Ishiguro
    DISTRIBUTED AUTONOMOUS ROBOTIC SYSTEMS 8 193 - + 2009 [Refereed][Not invited]
     
    Self-reconfigurable robots are expected to exhibit various interesting abilities, such as adaptivity and fault tolerance. These remarkable abilities originate from the fact that their mechanical systems intrinsically possess very large degrees of freedom. This, however, causes a serious problem, i.e., controllability. To overcome this, autonomous decentralized control is expected to play a crucial role, as widely observed in living organisms. However, much is still not understood about how such decentralized control can be achieved. This is mainly because the logic connecting local behaviors to global behaviors is still not understood. In this study, we particularly focus on a very primitive living organism, slime mold (physarum polycepharum), since it is believed to employ a fully decentralized control based on coupled biochemical oscillators. We modeled a decentralized control algorithm based on coupled nonlinear oscillators and then implement this into a two-dimensional modular robot consisting of incompressible fluid (i.e., protoplasm) covered with an outer skin composed of a network of passive and real-time tunable springs. Preliminary simulation results showed that this modular robot exhibits significantly supple locomotion similar to amoeboid locomotion and that the exploitation of the "long-distant interaction" stemming from "the law of conservation of protoplasmic mass" performs some of the "computation" that the controller would otherwise have to carry out. As a consequence, adaptive amoeboid locomotion emerges without the need for any centralized control system. The results obtained are also expected to shed new light on how control and mechanical systems with large degrees of freedom should be coupled.
  • Protoplasmic Computing to Memorize and Recall Periodic Environmental Events
    Atsushi Tero, Tetsu Saigusa, Toshiyuku Nakagaki
    NATURAL COMPUTING, PROCEEDINGS 1 213 - 221 1867-2914 2009 [Not refereed][Not invited]
     
    Single-celled organisms might be more intelligent than previously envisaged [1]-[5]. The acts of anticipating and recalling events are higher functions performed by the brains of higher animals; their evolutionary origins and the way they self-organize, however, remain open questions. Here we show that an amoeboid organism can anticipate the timing of periodic events. The plasmodium of the true slime mold Physarum polycephalum moves rapidly under favorable conditions, but stops moving when transferred to less-favorable conditions. For example, plasmodia exposed to low temperature and low humidity, presented in three consecutive pulses at constant intervals, reduced their locomotive speed in response to each episode. When favorable conditions were subsequently reintroduced, the plasmodia spontaneously reduced their locomotive speed at the point in time when the next unfavorable episode would have occurred. This implies that the plasmodia are able to anticipate impending environmental change. After this anticipatory response had been evoked several times, the locomotion of the plasmodia returned to normal speed; however, the slowing down could subsequently be induced by a single unfavorable pulse, implying recall of the periodicity that had been memorized. We have explored the mechanisms underlying this behavior from a dynamical systems perspective. Our results suggest that this primitive intelligence is of cellular origin and that simple dynamics might be sufficient to explain its emergence. abstract environment.
  • Tetsu Saigusa, Toshiyuki Nakagaki
    COMPARATIVE BIOCHEMISTRY AND PHYSIOLOGY B-BIOCHEMISTRY & MOLECULAR BIOLOGY 151 (4) 447 - 447 1096-4959 2008/12 [Refereed][Not invited]
  • Toshiyuki Nakagaki, Atsushi Tero, Ryo Kobayashi, Isamu Onishi, Tomoyuki Miyaji
    NEW GENERATION COMPUTING 27 (1) 57 - 81 0288-3635 2008/11 [Refereed][Not invited]
     
    Learning how biological systems solve problems could help to design new methods of computation. Information processing in simple cellular organisms is interesting, as they have survived for almost 1 billion years using a simple system of information processing. Here we discuss a well-studied model system: the large amoeboid Physarum plasmodium. This amoeba can find approximate solutions for combinatorial optimization problems, such as solving a maze or a shortest network problem. In this report, we describe problem solving by the amoeba, and the computational methods that can be extracted from biological behaviors. The algorithm designed based on Physarum is both simple and useful.
  • Tomoyuki Miyaji, Isamu Ohnishi, Atsushi Tero, Toshiyuki Nakagaki
    International Journal of Dynamical Systems and Differential Equations 1 (3) 210 - 219 1752-3583 2008/07 [Refereed][Not invited]
     
    In this paper we study a mathematical model describing behaviour of Physarum polycephalum proposed by Tero et al. (2007). In the case of linear adaptive term, it has been proved that the model must solve the shortest path problem mathematically rigorously on a general planar graph in Miyaji and Ohnishi (2007, 2008). However, in a laboratory, P. polycephalum sometimes makes a mistake, for example, when there is a 'double-edge' in a graph. We study the case mathematically to show both why and how P. polycephalum makes a mistake. © 2008, Inderscience Publishers.
  • Atsushi Tero, Kenji Yumiki, Ryo Kobayashi, Tetsu Saigusa, Toshiyuki Nakagaki
    THEORY IN BIOSCIENCES 127 (2) 89 - 94 1431-7613 2008/06 [Refereed][Not invited]
     
    Understanding how biological systems solve problems could aid the design of novel computational methods. Information processing in unicellular eukaryotes is of particular interest, as these organisms have survived for more than a billion years using a simple system. The large amoeboid plasmodium of Physarum is able to solve a maze and to connect multiple food locations via a smart network. This study examined how Physarum amoebae compute these solutions. The mechanism involves the adaptation of the tubular body, which appears to be similar to a network, based on cell dynamics. Our model describes how the network of tubes expands and contracts depending on the flux of protoplasmic streaming, and reproduces experimental observations of the behavior of the organism. The proposed algorithm based on Physarum is simple and powerful.
  • Kenji Matsumoto, Seiji Takagi, Toshiyuki Nakagaki
    BIOPHYSICAL JOURNAL 94 (7) 2492 - 2504 0006-3495 2008/04 [Refereed][Not invited]
     
    We investigate how an amoeba mechanically moves its own center of gravity using the model organism Physarum plasmodium. Time-dependent velocity fields of protoplasmic streaming over the whole plasmodia were measured with a particle image velocimetry program developed for this work. Combining these data with measurements of the simultaneous movements of the plasmodia revealed a simple physical mechanism of locomotion. The shuttle streaming of the protoplasm was not truly symmetric due to the peristalsis-like movements of the plasmodium. This asymmetry meant that the transport capacity of the stream was not equal in both directions, and a net forward displacement of the center of gravity resulted. The generality of this as a mechanism for amoeboid locomotion is discussed.
  • Flow rate driven by peristaltic movement in plasmodial tube of Physarum polycephalum
    Hiroyasu Yamada, Toshiyuki Nakagaki
    COLLECTIVE DYNAMICS: TOPICS ON COMPETITION AND COOPERATION IN THE BIOSCIENCES 1028 210 - + 0094-243X 2008 [Refereed][Not invited]
     
    We report a theoretical analysis of protoplasmic streaming driven by peristaltic movement in an elastic tube of an amoeba-like organism. The plasmodium of Physarum polycephalum, a true slime mold, is a large amoeboid organism that adopts a sheet-like form with a tubular network. The network extends throughout the plasmodium and enables the transport and circulation of chemical signals and nutrients. This tubular flow is driven by periodically propagating waves of active contraction of the tube cortex, a process known as peristaltic movement. We derive the relationship between the phase velocity of the contraction wave and the flow rate, and we discuss the physiological implications of this relationship.
  • Toshiyuki Nakagaki, Robert D. Guy
    SOFT MATTER 4 (1) 57 - 67 1744-683X 2008 [Refereed][Not invited]
     
    We review how soft matter is self-organized to perform information processing at the cell level by examining the model organism Physarum plasmodium. The amoeboid organism, Physarum polycephalum, in the class of true slime molds, exhibits the intelligent behavior of foraging in complex situations. When placed in a maze with food sources at two exits, the organism develops tubular structures with its body which connect the food sources along the shortest path so that the rates of nutrient absorption and intracellular communication are maximized. This intelligent behavior results from the organism's control of a dynamic network through which mechanical and chemical information is transmitted. We review experimental studies that explore the development and adaptation of structures that make up the network. Recently a model of the dynamic network has been developed, and we review the formulation of this model and present some key results. The model captures the dynamics of existing networks, but it does not answer the question of how such networks form initially. To address the development of cell shape, we review existing mechanochemical models of the protoplasm of Physarum, present more general models of motile cells, and discuss how to adapt existing models to explore the development of intelligent networks in Physarum.
  • Tetsu Saigusa, Atsushi Tero, Toshiyuki Nakagaki, Yoshiki Kuramoto
    PHYSICAL REVIEW LETTERS 100 (1) 018101  0031-9007 2008/01 [Refereed][Not invited]
     
    When plasmodia of the true slime mold Physarum were exposed to unfavorable conditions presented as three consecutive pulses at constant intervals, they reduced their locomotive speed in response to each episode. When the plasmodia were subsequently subjected to favorable conditions, they spontaneously reduced their locomotive speed at the time when the next unfavorable episode would have occurred. This implied the anticipation of impending environmental change. We explored the mechanisms underlying these types of behavior from a dynamical systems perspective.
  • Toshiyuki Nakagaki, Makoto Iima, Tetsuo Ueda, Yasumasa Nishiura, Tetsu Saigusa, Atsushi Tero, Ryo Kobayashi, Kenneth Showalter
    PHYSICAL REVIEW LETTERS 99 (6) 068104  0031-9007 2007/08 [Refereed][Not invited]
     
    When two food sources are presented to the slime mold Physarum in the dark, a thick tube for absorbing nutrients is formed that connects the food sources through the shortest route. When the light-avoiding organism is partially illuminated, however, the tube connecting the food sources follows a different route. Defining risk as the experimentally measurable rate of light-avoiding movement, the minimum-risk path is exhibited by the organism, determined by integrating along the path. A model for an adaptive-tube network is presented that is in good agreement with the experimental observations.
  • H. Yamada, T. Nakagaki, R. E. Baker, P. K. Maini
    JOURNAL OF MATHEMATICAL BIOLOGY 54 (6) 745 - 760 0303-6812 2007/06 [Not refereed][Not invited]
     
    In the large amoeboid organism Physarum, biochemical oscillators are spatially distributed throughout the organism and their collective motion exhibits phase waves, which carry physiological signals. The basic nature of this wave behaviour is not well-understood because, to date, an important effect has been neglected, namely, the shuttle streaming of protoplasm which accompanies the biochemical rhythms. Here we study the effects of self-consistent flow on the wave behaviour of oscillatory reaction-diffusion models proposed for the Physarum plasmodium, by means of numerical simulation for the dispersion relation and weakly nonlinear analysis for derivation of the phase equation. We conclude that the flow term is able to increase the speed of phase waves (similar to elongation of wave length). We compare the theoretical consequences with real waves observed in the organism and also point out the physiological roles of these effects on control mechanisms of intracellular communication.
  • Atsushi Tero, Ryo Kobayashi, Toshiyuki Nakagaki
    JOURNAL OF THEORETICAL BIOLOGY 244 (4) 553 - 564 0022-5193 2007/02 [Refereed][Not invited]
     
    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. (c) 2006 Elsevier Ltd. All rights reserved.
  • Effects of amount of food on path selection in the transport network of an amoeboid organsim
    Toshiyuki Nakagaki, Tetsu Saigusa, Atsushi Tero, Ryo Kobayashi
    Proceedings of Int. Symp. On Topological Aspects of Critical Systems and Networks (World Scientific Publishing Co.) 94 - 100 2007 [Not refereed][Not invited]
  • Indecisive behavior of amoeba crossing an environmental barrier
    Seiji Takagi, Yasumasa Nishiura, Toshiyuki Nakagaki, Tetsuo Ueda, Kei-ichi Ueda
    Proceedings of Int. Symp. On Topological Aspects of Critical Systems and Networks (World Scientific Publishing Co.) 86 - 93 2007 [Not refereed][Not invited]
  • Hu Yan, Hatsuki Shiga, Etsuro Ito, Toshiyuki Nakagaki, Seiji Takagi, Tetsuo Ueda, Kaoru Tsujii
    Colloid. Surf. A 284-285 115 - 119 0927-7757 2006/08/15 [Refereed][Not invited]
  • Ryo Kobayashi, Atsushi Tero, Toshiyuki Nakagaki
    JOURNAL OF MATHEMATICAL BIOLOGY 53 (2) 273 - 286 0303-6812 2006/08 [Refereed][Not invited]
     
    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.
  • A Tero, R Kobayashi, T Nakagaki
    PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 363 (1) 115 - 119 0378-4371 2006/04 [Not refereed][Not invited]
     
    We have proposed a mathematical model for the adaptive dynamics of the transport network in an amoeba-like organism, the true slime mold Physarum polycephalum. The model is based on physiological observations of this species, but can also be used for path-finding in the complicated networks of mazes and road maps. In this paper, we describe the physiological basis and the formulation of the model, as well as the results of simulations of some complicated networks. The path-finding method used by Physarum is a good example of cellular computation. (c) 2006 Elsevier B.V. All rights reserved.
  • A Takamatsu, R Tanaka, H Yamada, T Nakagaki, T Fujii, Endo, I
    PHYSICAL REVIEW LETTERS 87 (7) 0031-9007 2001/08 [Refereed][Not invited]
     
    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.
  • Maze-solving by an amoeboid organism
    T Nakagaki, H Yamada, A Toth
    NATURE 407 (6803) 470 - 470 0028-0836 2000/09 [Refereed][Not invited]
  • T Nakagaki, H Yamada, T Ueda
    BIOPHYSICAL CHEMISTRY 87 (1) 85 - 86 0301-4622 2000/09 [Refereed][Not invited]
  • Modulation of cellular rhythm and photoavoidance by oscillatory irradiation in the Physarum plasmodium
    T Nakagaki, H Yamada, T Ueda
    BIOPHYSICAL CHEMISTRY 82 (1) 23 - 28 0301-4622 1999/11 [Refereed][Not invited]
     
    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. (C) 1999 Elsevier Science B.V. All rights reserved.
  • Reaction-diffusion-advection model for pattern formation of rhythmic contraction in a giant amoeboid cell of the Physarum Plasmodium
    T Nakagaki, H Yamada, M Ito
    JOURNAL OF THEORETICAL BIOLOGY 197 (4) 497 - 506 0022-5193 1999/04 [Refereed][Not invited]
     
    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 behavior in the Physarum plasmodium. (C) 1999 Academic Press.
  • Pattern formation of a reaction-diffusion system with self-consistent flow in the amoeboid organism Physarum plasmodium
    H Yamada, T Nakagaki, M Ito
    PHYSICAL REVIEW E 59 (1) 1009 - 1014 1063-651X 1999/01 [Refereed][Not invited]
     
    The amoeboid organism, the plasmodium of Physarum polycephalum, moves by forming a spatiotemporal pattern of contraction oscillators. This biological system can be regarded as a reaction-diffusion system with spatial interaction via active flow of protoplasmic sol in the cell. We present a reaction-diffusion system with self-consistent flow on the basis of the physiological evidence that the flow is determined by contraction patterns in the plasmodium. Such a coupling of reaction, diffusion, and advection is characteristic of biological systems, and is expected to be related to control mechanisms of amoeboid behavior. Using weakly nonlinear : analysis, we show that the envelope dynamics obeys the complex Ginzburg-Landau (CGL) equation when a bifurcation occurs at finite wave number. The flow term affects the nonlinear term of the CGL equation through the critical wave number squared. A physiological role of pattern formation with the flow is discussed. [S1063-651X(99)11501-0].
  • Action spectrum for sporulation and photoavoidance in the plasmodium of Physarum polycephalum, as modified differentially by temperature and starvation
    T Nakagaki, S Umemura, Y Kakiuchi, T Ueda
    PHOTOCHEMISTRY AND PHOTOBIOLOGY 64 (5) 859 - 862 0031-8655 1996/11 [Refereed][Not invited]
     
    The plasmodium of the myxomycete Physarum polycephalum sporulates in bright natural environments, suggesting a relationship between photobehavior and sporulation. Thus, the action spectra for two light-dependent phenomena as well as the effects of other environmental conditions have been studied. Sporulation like photoavoidance responded to UVC (near 270 nm) and near IR (near 750 nm) in addition to the well-documented UVA (near 350 nm) and blue (near 460 nm) regions. Sporulation and photoavoidance had similar sensitivities in the shorter wavelengths, while the former was about 100 times more sensitive in near IR. The plasmodium moved away from light in a wide spectral range. Starvation and high temperature at 31 degrees C (25 degrees C in standard conditions) reduced photoavoidance to UVA and to blue light, respectively. A high fluence rate of WC suppressed the rhythmic contraction of the plasmodium, and the action spectrum peaked at 270 nm. These results indicate that the Physarum plasmodium may stay at brighter places not by positive phototaxis but by weakening the negative phototaxis to sunlight or by other possible taxes such as hydrotaxis. There may be at least four different photosystems in the plasmodium.
  • Phase switching of oscillatory contraction in relation to the regulation of amoeboid behavior by the Plasmodium of Physarum polycephalum
    T Nakagaki, T Ueda
    JOURNAL OF THEORETICAL BIOLOGY 179 (3) 261 - 267 0022-5193 1996/04 [Refereed][Not invited]
     
    The plasmodium of the true slime mould Physarum polycephalum is a large aggregate of protoplasm and behaves like an amoeboid cell, exhibiting rhythmic contraction everywhere within the organism. Phase dynamics of these oscillations were studied in relation to the global organization of amoeboid behavior, by analysing the thickness oscillation, isotonic tension and the motive force of the streaming. Usually the plasmodium showed synchrony, the phase of the oscillation being the same everywhere excepting the peripheral part. We found several situations where this in-phase relationship switched to anti-phase. This occurred either at the early stages of the plasmodial coalescence, or when a single plasmodium was nearly separated by partition, or when the streaming of the protoplasm was hindered by applying the hydrostatic pressure. Furthermore, the motive force of the protoplasmic streaming increased once the anti-phase relationship was established. In this way, the weak interactions among plasmodial parts induce the switching of phase relationship from in-phase to anti-phase, and this transition in turn acts to increase the interaction by promoting a rapid mixing of the protoplasm. This global feedback mechanism by phase switching should help maintain a large single plasmodium without separating into parts. The possible mechanism of phase switching is discussed in terms of coupled nonlinear oscillators. (C) 1996 Academic Press Limited.
  • A NAGAHISA, R ASAI, Y KANAI, A MURASE, M TSUCHIYANAKAGAKI, T NAKAGAKI, TC SHIEH, K TANIGUCHI
    REGULATORY PEPTIDES 46 (1-2) 433 - 436 0167-0115 1993/07 [Refereed][Not invited]
  • NAGAHISA A, ASAI R, KANAI Y, MURASE A, TSUCHIYANAKAGAKI M, NAKAGAKI T, SHIEH T, TANIGUCHI K
    Regulatory Peptides 107 (2) S122 - 275 0167-0115 1992 [Refereed][Not invited]
  • T NAKAGAKI, J ODA, H KOIZUMI, T FUKAYA, C YASUI, T UEDA
    CELL STRUCTURE AND FUNCTION 15 (4) 175 - 179 0386-7196 1990/08 [Refereed][Not invited]
  • DYNAMIC ORGANIZATION OF ATP AND BIREFRINGENT FIBRILS DURING FREE LOCOMOTION AND GALVANOTAXIS IN THE PLASMODIUM OF PHYSARUM-POLYCEPHALUM
    T UEDA, T NAKAGAKI, T YAMADA
    JOURNAL OF CELL BIOLOGY 110 (4) 1097 - 1102 0021-9525 1990/04 [Refereed][Not invited]
  • ACTION SPECTRA FOR SUPEROXIDE GENERATION AND UV AND VISIBLE-LIGHT PHOTOAVOIDANCE IN PLASMODIA OF PHYSARUM-POLYCEPHALUM
    T UEDA, Y MORI, T NAKAGAKI, Y KOBATAKE
    PHOTOCHEMISTRY AND PHOTOBIOLOGY 48 (5) 705 - 709 0031-8655 1988/11 [Refereed][Not invited]
  • CHANGES IN CAMP AND CGMP CONCENTRATION, BIREFRINGENT FIBRILS AND CONTRACTILE ACTIVITY ACCOMPANYING UV AND BLUE-LIGHT PHOTOAVOIDANCE IN PLASMODIA OF AN ALBINO STRAIN OF PHYSARUM-POLYCEPHALUM
    T UEDA, Y MORI, T NAKAGAKI, Y KOBATAKE
    PHOTOCHEMISTRY AND PHOTOBIOLOGY 47 (2) 271 - 275 0031-8655 1988/02 [Refereed][Not invited]
  • Patterns in intracellular ATP distribution and rhythmic contraction in relation to amoeboid locomotion in the plasmodium of Physarum polycephalum
    Tetsuo Ueda, Toshiyuki Nakagaki, Yonosuke Kobatake
    Protoplasma Suppl 1 51 - 56 1988 [Refereed][Not invited]

Books etc

MISC

Awards & Honors

  • 2011 NHKテレビ番組「爆笑問題の日本の教養」 爆ノーベル賞
     
    受賞者: 中垣 俊之
  • 2010 函館市長賞
     
    受賞者: 中垣 俊之
  • 2010 IgNobel Prize for Transportation Planning
     
    受賞者: NAKAGAKI Toshiyuki
  • 2008 IgNobel Prize for Cognitive Science
     
    受賞者: NAKAGAKI Toshiyuki

Research Grants & Projects

  • 数理科学と生体生命情報科学との連携による生命知の基本アルゴリズムの探求
    Japan society for promotion of science:Grant-in-aid for Scientific Research
    Date (from‐to) : 2014/04 -2017/03 
    Author : 中垣俊之
  • 細胞運動における細胞レオロジーと応力場のクロストーク
    Japan society for promotion of science:Grant-in-aid for Scientific Research
    Date (from‐to) : 2013/04 -2015/03 
    Author : 中垣俊之
  • 単細胞生物に学ぶ生命知の基本アルゴリズム
    秋山記念生命科学振興財団:研究助成
    Date (from‐to) : 2013/04 -2014/03 
    Author : 中垣 俊之
  • 生物輸送ネットワークのダイナミクス
    科学技術振興機構:戦略的国際科学技術協力推進事業
    Date (from‐to) : 2011/04 -2014/03 
    Author : 中垣 俊之
  • 生物ロコモーションに学ぶ大自由度システムの新展開
    科学技術振興機構:戦略的創造研究推進事業
    Date (from‐to) : 2008/04 -2013/03 
    Author : 小林亮
  • 時間記憶能の系統進化に対する実験的評価と非線形動力学構造
    日本学術振興会:科学研究費補助金
    Date (from‐to) : 2008/04 -2012/03 
    Author : 中垣 俊之
  • Optimization in Natural System: ants, bees and slime moulds
    Human Frontier Science Program:Research Grant
    Date (from‐to) : 2007/09 -2010/08 
    Author : SUMPTER David
  • 粘菌アルゴリズム:制約条件付き最適化問題の生物模倣型解法
    日本学術振興会:科学研究費補助金
    Date (from‐to) : 2006/04 -2008/03 
    Author : 中垣 俊之
  • トポロジー理工学の創成
    文部科学省:21世紀COEプログラム
    Date (from‐to) : 2004/04 -2008/03 
    Author : 丹田 聡
  • 単細胞生物粘菌による幾何学的パズル問題の解決法と細胞内計算アルゴリズム
    日本学術振興会:科学研究費補助金
    Date (from‐to) : 2003/04 -2004/03 
    Author : 中垣 俊之
  • 粘菌における迷路解法と細胞システム構築の動的メカニズム
    日本学術振興会:科学研究費補助金
    Date (from‐to) : 2001/04 -2003/03 
    Author : 中垣 俊之
  • 粘菌行動の反応拡散移流モデルに学ぶシステムの自己組織化
    日本学術振興会:科学研究費補助金
    Date (from‐to) : 1999/04 -2001/03 
    Author : 中垣 俊之
  • 粘菌行動の反応拡散移流モデルに学ぶシステムの自己組織化
    住友財団:基礎科学研究助成
    Date (from‐to) : 1997/04 -1998/03 
    Author : 中垣 俊之

Educational Activities

Teaching Experience

  • Soft Matter Physics
    開講年度 : 2018
    課程区分 : 修士課程
    開講学部 : 生命科学院
    キーワード : 微分方程式、システム生物学、数理生物学、非線形動力学、酵素反応速度論、ミカエリス・メンテンの酵素反応スキーム、生物リズム、リミットサイクル、神経興奮、ホジキン・ハクスレーモデル
  • Functional and Regulatory Life Science
    開講年度 : 2018
    課程区分 : 修士課程
    開講学部 : 生命科学院
    キーワード : 微分方程式、システム生物学、数理生物学、非線形動力学、酵素反応速度論、ミカエリス・メンテンの酵素反応スキーム、生物リズム、リミットサイクル、神経興奮、ホジキン・ハクスレーモデル
  • Comprehensive Lecture on Mathematics I
    開講年度 : 2018
    課程区分 : 学士課程
    開講学部 : 理学部
    キーワード : 応用数学、数理生物学、動物行動学、社会行動、ヒト行動、集団運動、動物運動、力学、運動方程式、微分方程式、非線形動力学

Campus Position History

  • 2017年4月1日 
    2019年3月31日 
    教育研究評議会評議員
  • 2017年4月1日 
    2019年3月31日 
    電子科学研究所長
  • 2019年4月1日 
    2021年3月31日 
    教育研究評議会評議員
  • 2019年4月1日 
    2021年3月31日 
    電子科学研究所長

Position History

  • 2017年4月1日 
    2019年3月31日 
    教育研究評議会評議員
  • 2017年4月1日 
    2019年3月31日 
    電子科学研究所長
  • 2019年4月1日 
    2021年3月31日 
    教育研究評議会評議員
  • 2019年4月1日 
    2021年3月31日 
    電子科学研究所長


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