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Intelligence: Maze-Solving by an Amoeboid Organism



The plasmodium of the slime mould Physarum polycephalum is a large amoeba-like cell consisting of a dendritic network of tube-like structures (pseudopodia). It changes its shape as it crawls over a plain agar gel and, if food is placed at two different points, it will put out pseudopodia that connect the two food sources. Here we show that this simple organism has the ability to find the minimum-length solution between two points in a labyrinth.
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Toshiyuki Nakagaki*†,
Hiroyasu Yamada*†‡, Ágota Tóth§
*Bio-Mimetic Control Research Center, RIKEN,
Shimoshidami, Moriyama, Nagoya 463-0003,
Local Spatio-Temporal Functions Laboratory,
RIKEN, Wako 351-0198, Japan
Research Institute for Electronic Science,
Hokkaido University, Sapporo 060-0812, Japan
§Department of Physical Chemistry, University
of Szeged, PO Box 105, Szeged H-6701, Hungary
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brief communications
Maze-solving by an
amoeboid organism
The plasmodium of the slime mould
Physarum polycephalum is a large
amoeba-like cell consisting of a den-
dritic network of tube-like structures
(pseudopodia). It changes its shape as it
crawls over a plain agar gel and, if food is
placed at two different points, it will put out
pseudopodia that connect the two food
sources. Here we show that this simple
organism has the ability to find the mini-
mum-length solution between two points
in a labyrinth.
We took a growing tip of an appropriate
size from a large plasmodium in a 25#35
cm culture trough and divided it into small
pieces. We then positioned these in a maze
created by cutting a plastic film and placing
it on an agar surface. The plasmodial pieces
spread and coalesced to form a single
organism that filled the maze (Fig. 1a),
avoiding the dry surface of the plastic film.
At the start and end points of the maze, we
placed 0.5#1#2 cm agar blocks contain-
ing nutrient (0.1 mg g$1of ground oat
flakes). There were four possible routes (!1,
Figure 1 Maze-solving by
Physarum polycephalum
. a, Structure of the organism before finding the shortest path. Blue lines indicate the
shortest paths between two agar blocks containing nutrients: !1 (41%1 mm); !2 (33%1 mm); "1 (44%1 mm); and "2 (45%1 mm).
b, Four hours after the setting of the agar blocks (AG), the dead ends of the plasmodium shrink and the pseudopodia explore all possible con-
nections. c, Four hours later, the shortest path has been selected. Plasmodium wet weight, 90%10 mg. Yellow, plasmodium; black, ‘walls
of the maze; scale bar, 1 cm. d, Path selection. Numbers indicate the frequency with which each pathway was selected. ‘None’, no
pseudopodia (tubes) were put out. See Supplementary Information for an animated version of ac.
0 0 0
0 0 0
5 6 3
0 0
© 2000 Macmillan Magazines Ltd
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Physarum polycephalum is a protist slime mould that exhibits a high degree of responsiveness to its environment through a complex network of tubes and cytoskeletal components that coordinate behavior across its unicellular, multinucleated body. Physarum has been used to study decision making, problem solving, and mechanosensation in aneural biological systems. The robust generative and repair capacities of Physarum also enable the study of whole-body regeneration within a relatively simple model system. Here we describe methods for growing, imaging, quantifying, and sampling Physarum that are adapted for investigating regeneration and repair.
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The plasmodium of Physarum polycephalum shows two-dimensional patterns in thickness oscillation. Modulations of the oscillation pattern in response to local stimulation were studied by applying computer image processing. In a concentrically extending plasmodium, oscillations were entrained to a single frequency, and phase gradient vectors pointed radially and inward mostly. When a part of the plasmodium was exposed to different temperature or chemicals, the entrained oscillations continued but new propagating phase waves started within a few minutes around the stimulated region. Phase gradient vectors pointed away from attractive stimuli (high temperature, glucose, oatflakes) but toward repulsive ones (low temperature, salts, high osmolarity, anaerobic conditions). Thus, the sensed information seems integrated at the level of interacting oscillators.
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.
In rodents and swine, individual differences in a broad range of characteristics correlate with intrauterine position during fetal life. By identifying the intrauterine position of mice at cesarean delivery, we can predict reliably postnatal reproductive traits such as genital morphology, timing of puberty, length of estrous cycles, timing of reproductive senescence, sexual attractiveness, sexual behavior, aggressiveness, daily activity level, body weight and tissue enzyme activity in females; in males we can predict genital and brain morphology, sexual behavior, aggressiveness, daily activity level, body weight, and tissue enzyme activity. In mice, as in all mammals, male fetuses have greater concentrations of testosterone than do females. In addition, female mouse fetuses have greater circulating concentrations of estradiol than do male fetuses, a condition not found in all mammals. A mouse fetus positioned between males has greater concentrations of testosterone than does a fetus of the same sex positioned between females, and a fetus positioned between females has greater concentrations of estradiol than does a fetus of the same sex positioned between males. Gonadal steroids regulate differentiation of secondary sexual characteristics. Studies in which the effects of intrauterine position have been eliminated by exposing fetuses to steroid receptor blockers reveal the critical role of steroids in mediating this phenomenon. The intrauterine position phenomenon provides the only mammalian model for relating postnatal traits to concentrations of endogenous hormones to which individuals are exposed during fetal life. Results from studies using this naturally occurring experimental system in litter-bearing species have given insights concerning the consequences of individual differences in steroid concentrations during sexual differentiation that likely apply to all mammals. One specific hypothesis is that circulating estradiol may interact with testosterone in mediating some aspects of sexual differentiation in rodents and, thus, possibly in other mammals.
The relationship between intracellular period modulation and external environment change was investigated from the viewpoint of internal information coding in Physarum plasmodium. For the external conditions, concentration changes of attractant (galactose) and repellent (KCl) were used, and the internal responses were measured as the thickness oscillation of the plasmodium. (i) Period of the intracellular oscillation decreased when the concentration of attractant was increased and when the concentration of repellent was decreased. (ii) The period increased when the attractant was decreased and when the repellent was increased. (iii) The larger concentration change induced the larger period modulation. (iv) These responses were observed when the change of concentration was greater than a threshold value. From these results, it was clarified that the relative change in environmental condition is encoded on the relative period modulation in intracellular oscillation. This means that the period change does not directly represent the environment itself but represents the change of its condition. Thus, it is further suggested that the plasmodium estimates the environmental condition based on the relationship between the previous external condition and the present one.
The properties of spiral-wave propagation in oscillatory and finite media are considered. Several different types of trajectories of the spiral core are seen, as the distance from the boundaries is increased. The size and the location of obstacles modify the motion of the spiral cores.
The plasmodium of Physarum polycephalum is a large amoeboid organism showing rhythmic contraction everywhere within an organism, and moves by forming spatio-temporal patterns of the rhythmic contraction. We propose a reaction-diffusion-advection model for the pattern formation. This model is constructed under physiological suggestions that the chemical oscillator acts as a clock regulating the rhythmic contraction and interacts spatially not only by diffusion but also by advection of protoplasm. Behavior of the model is studied by numerical calculation, especially the effects of the advection term on a simple reaction-diffusion system. The advection effect reproduces experimentally observed phenomena of fluctuating propagation of the contraction wave. Concept of the reaction-diffusion-advection system is promising for modeling the mechanism of amoeboid behaviour in the Physarum plasmodium. Copyright 1999 Academic Press.
The relationship between cell shape and rhythmic contractile activity in the large amoeboid organism Physarum polycephalum was studied. The organism develops intricate networks of veins in which protoplasmic sol moved to and fro very regularly. When migrating on plain agar, the plasmodium extends like a sheet and develops dendritic veins toward the rear. After a particular stimulation, the vein organization changes into veinless or vein-network structures. In both structures, the mixing rate of the protoplasm, which is related to communication among contraction oscillators, decreased compared with that of the dendritic one. Accompanying these changes in vein structure, the spatio-temporal pattern of the rhythmic contraction changed into a small-structured pattern from a synchronized one. In the above process, cell shape affects the contraction pattern, but, conversely, the contraction pattern effects the cell shape. To demonstrate this, a phase difference in the rhythmic contraction was induced artificially by entraining the intrinsic rhythm to external temperature oscillations. New veins then formed along the direction parallel to the phase difference of the rhythm. Consequently, the vein organization of the cell interacts with the contractile activity to form a feedback loop in a mechanism of contraction pattern formation.