ArticlePDF Available

Intelligence: Maze-Solving by an Amoeboid Organism

Authors:

Abstract

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.
Chicago Press, Chicago, 1988).
4. vom Saal, F. S., Finch, C. E. & Nelson, J. F. in Physiology of
Reproduction Vol. 2 (eds Knobil, E., Neill, J. & Pfaff, D.)
1213–1314 (Raven, New York, 1994).
5. Finch, C. E. & Kirkwood, T. B. L. Chance, Development, and
Aging (Oxford Univ. Press, 2000).
6. Matt, D. W., Lee, J., Sarver, P. L., Judd, H. L. & Lu, J. K. H.
Biol. Reprod. 34, 478–487 (1986).
7. Bernstein, L. et al. J. Natl Cancer Inst. 76, 1035–1039 (1986).
8. Bernstein, L. et al. Br. J. Cancer 58, 379–381 (1988).
9. Key, T. et al. Br. J. Cancer 73, 698–701 (1996).
10.Holliday, R. Science 238, 163–170 (1987).
11.vom Saal, F. S. et al. Proc. Natl Acad. Sci. USA 94, 2056–2061
(1997).
!2, "1, "2) between the start and end
points (Fig. 1a).
The plasmodium pseudopodia reaching
dead ends in the labyrinth shrank (Fig. 1b),
resulting in the formation of a single thick
pseudopodium spanning the minimum
length between the nutrient-containing
agar blocks (Fig. 1c). The exact position
and length of the pseudopodium was differ-
ent in each experiment, but the path
through !2 — which was about 22% short-
er than that through !1 — was always
selected (Fig. 1d). About the same number
of tubes formed through "1 and "2 as the
difference (about 2%) in their path lengths
is lost in the meandering of the tube trajec-
tory and is within experimental error.
The addition of food leads to a local
increase in the plasmodium’s contraction
frequency, initiating waves propagating
towards regions of lower frequency1–5, in
accordance with the theory of phase
dynamics6. The plasmodial tube is rein-
forced or decays when it lies parallel or per-
pendicular, respectively, to the direction of
local periodic contraction7; the final tube,
following the wave propagation, will there-
fore link food sites by the shortest path.
To maximize its foraging efficiency, and
therefore its chances of survival, the plas-
modium changes its shape in the maze to
form one thick tube covering the shortest
distance between the food sources. This
remarkable process of cellular computation
implies that cellular materials can show a
primitive intelligence8–10.
Toshiyuki Nakagaki*†,
Hiroyasu Yamada*†‡, Ágota Tóth§
*Bio-Mimetic Control Research Center, RIKEN,
Shimoshidami, Moriyama, Nagoya 463-0003,
Japan
e-mail: nakagaki@postman.riken.go.jp
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
1. Durham, A. C. & Ridgeway, E. B. J. Cell Biol. 69, 218–223
(1976).
2. Matsumoto, K., Ueda, T. & Kobatake, Y. J. Theor. Biol.122,
339–345 (1986).
3. Miyake, Y., Tada, H., Yano, M. & Shimizu, H. Cell Struct. Funct.
19, 363–370 (1994).
4. Nakagaki, T., Yamada, H. & Ito, M. J. Theor. Biol. 197, 497–506
(1999).
5. Yamada, H., Nakagaki, T. & Ito, M. Phys. Rev. E 59, 1009–1014
(1999).
6. Kuramoto, Y. in Chemical Oscillations, Waves and Turbulence
(Springer, Berlin, 1984).
7. Nakagaki, T., Yamada, H. & Ueda, T. Biophys. Chem. 84,
195–204 (2000).
8. Sepulchre, J. A., Babloyantz, A. & Steels, L. in Proc. Int. Conf. on
Artificial Neural Networks (eds Kohonen, T. et al.) 1265–1268
(Elsevier, Amsterdam, 1991).
9. Sepulchre, J. A. & Babloyantz, A. Phys. Rev. E 48, 187–195
(1993).
10.Steinbock, O., Tóth, Á. & Showalter, K. Science 267, 868–871
(1995).
Supplementary information is available on Nature’s World-Wide
Web site (http://www.nature.com).
470 NATURE
|
VOL 407
|
28 SEPTEMBER 2000
|
www.nature.com
early (soon after puberty) and very late
(approaching menopause) pregnancies are
common in humans.
Ming-Hseng Wang, Frederick S. vom Saal
Division of Biological Sciences, University of
Missouri, Columbia, Missouri 65211, USA
e-mail: vomsaalf@missouri.edu
1. vom Saal, F. S. J. Anim. Sci. 67, 1824–1840 (1989).
2. Howdeshell, K. L., Hotchkiss, A. K., Thayer, K. A., Vandenbergh,
J. G. & vom Saal, F. S. Nature 401, 763–764 (1999).
3. Clutton-Brock, T. H. (ed.) Reproductive Success: Studies of
Individual Variation in Contrasting Breeding Systems (Univ.
brief communications
Intelligence
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.
a
α1
α2
β1
β2
b
AG
AG
c
d
AG
AG
None
2None
0
0
0
β1
α1
α2
β2β1,
β2
α1,
α2
0 0 0
0 0 0
5 6 3
3
0 0
© 2000 Macmillan Magazines Ltd
... However, evidence for learning in nonneural organisms is scant, and only a few unequivocal reports of learning have been described in single-cell organisms (Andersson, 2016;Ginsburg and Jablonka, 2009). Several studies showed that the nonneural organism Physarum polycephalum could be classically conditioned (Boisseau et al., 2016;Nakagaki et al., 2000Nakagaki et al., , 2004Saigusa et al., 2008), although P. polycephalum is considered a multicellular organism. ...
Article
Full-text available
Single-cell intelligence is a recent terminology suggested since it was clear that "biological intelligence" is deeply rooted in a genetic basis. The possible applications of the term conception are many where noncoding RNAs could be involved as a part to create a specific bacterial behavior through multiple gene regulation networks. Biological intelligence is the origin of the genome unit formation in all organisms, whether unicellular or multicellular. This intelligence is necessary and inevitable for the survival of the being on earth. Microbes are sensitive to some antibiotics, but they quickly acquire resistance against these antibiotics, and this degree of development or adaptation has its genetic factors that may be noncoding RNA or illegible on the genome. Perhaps the noncoding RNA could be transferred into coding RNA or vice versa. Intelligence in beings, in order to survive and/or outlive the earth, is present in its origin if it is a microbe germ, a plant pill, or a human or animal sperm. The current review aims to briefly clarify the genetic basis of classical conditioning and the probability of the connection with the noncoding RNAs and if that concept could be applied to enhance antibiotic sensitivity.
... This slime mold has several skills and behavioral patterns that could be labeled 'proto-intelligent' and that one would hardly associate with such a primitive creature. For example, it can find the minimum length between two points in a labyrinth [53]. Further research showed that P. polycephalum can minimize the network path and complexity between multiple food sources-it can solve the 'travelingsalesman problem', commonly known in both biology and computer architecture [54]. ...
Article
Full-text available
According to the current scientific paradigm, what we call ‘life’, ‘mind’, and ‘consciousness’ are considered epiphenomenal occurrences, or emergent properties or functions of matter and energy. Science does not associate these with an inherent and distinct existence beyond a materialistic/energetic conception. ‘Life’ is a word pointing at cellular and multicellular processes forming organisms capable of specific functions and skills. ‘Mind’ is a cognitive ability emerging from a matrix of complex interactions of neuronal processes, while ‘consciousness’ is an even more elusive concept, deemed a subjective epiphenomenon of brain activity. Historically, however, this has not always been the case, even in the scientific and academic context. Several prominent figures took vitalism seriously, while some schools of Western philosophical idealism and Eastern traditions promoted conceptions in which reality is reducible to mind or consciousness rather than matter. We will argue that current biological sciences did not falsify these alternative paradigms and that some forms of vitalism could be linked to some forms of idealism if we posit life and cognition as two distinct aspects of consciousness preeminent over matter. However, we will not argue in favor of vitalistic and idealistic conceptions. Rather, contrary to a physicalist doctrine, these were and remain coherent worldviews and cannot be ruled out by modern science.
... Finding optimal flow configurations in transport networks is an important problem in many real-world applications. While natural systems like river basins [1][2][3][4][5] , leaf venations [6][7][8][9] , or slime molds [10][11][12][13][14][15][16][17] involve transport of one type of mass only, e.g. water, this may not be the case in several engineering systems. ...
Article
Full-text available
Optimizing passengers routes is crucial to design efficient transportation networks. Recent results show that optimal transport provides an efficient alternative to standard optimization methods. However, it is not yet clear if this formalism has empirical validity on engineering networks. We address this issue by considering different response functions—quantities determining the interaction between passengers—in the dynamics implementing the optimal transport formulation. Particularly, we couple passengers’ fluxes by taking their sum or the sum of their squares. The first choice naturally reflects edges occupancy in transportation networks, however the second guarantees convergence to an optimal configuration of flows. Both modeling choices are applied to the Paris metro. We measure the extent of traffic bottlenecks and infrastructure resilience to node removal, showing that the two settings are equivalent in the congested transport regime, but different in the branched one. In the latter, the two formulations differ on how fluxes are distributed, with one function favoring routes consolidation, thus potentially being prone to generate traffic overload. Additionally, we compare our method to Dijkstra’s algorithm to show its capacity to efficiently recover shortest-path-like graphs. Finally, we observe that optimal transport networks lie in the Pareto front drawn by the energy dissipated by passengers, and the cost to build the infrastructure.
... This alternative approach suggests evaluating intelligence according to how a system completes tasks that bring about its own goals. It is becoming increasingly recognised that plants (Baluška and Mancuso, 2009;Shemesh et al., 2010;Trewavas, 2014;Gagliano et al., 2016;Novoplansky, 2016;Calvo et al., 2020) and basal systems (Maturana and Varela, 1980;Nakagaki et al., 2000;Hellingwerf, 2005;Ben Jacob et al., 2006;Lyon, 2006;Van Duijn et al., 2006;Shapiro, 2007;Saigusa et al., 2008;Baluška and Levin, 2016;Pinto and Mascher, 2016;Reid and Latty, 2016;Levin, 2019;Bechtel and Bich, 2021;Boussard et al., 2021;Hanson, 2021;Lyon et al., 2021) display some degree of intelligence that is expressed in various manners in which they adapt to the complexity of their environments. Selective pressures and environmental stresses that challenge both homeostasis and development are fundamental existential tasks that all biological systems encounter and must adaptively respond to. ...
Article
Full-text available
Intelligence in current AI research is measured according to designer-assigned tasks that lack any relevance for an agent itself. As such, tasks and their evaluation reveal a lot more about our intelligence than the possible intelligence of agents that we design and evaluate. As a possible first step in remedying this, this article introduces the notion of “self-concern,” a property of a complex system that describes its tendency to bring about states that are compatible with its continued self-maintenance. Self-concern, as argued, is the foundation of the kind of basic intelligence found across all biological systems, because it reflects any such system's existential task of continued viability. This article aims to cautiously progress a few steps closer to a better understanding of some necessary organisational conditions that are central to self-concern in biological systems. By emulating these conditions in embodied AI, perhaps something like genuine self-concern can be implemented in machines, bringing AI one step closer to its original goal of emulating human-like intelligence.
Article
Physarum polycephalum inspired algorithm (PPA) has attracted great attention recently. By modelling real-world problems into a graph and adopting proper adaption equation, PPA could solve system optimization or user equilibrium problems. However, few PPA-based algorithms could tackle problems with capacity constraints, lacking the ability to control link flows in the PPA. To tackle this problem, a novel framework, the capacitated PPA (CPPA), is proposed to allow capacity constraints toward link flow in the PPA. To prove the validity of the CPPA, we developed three applications of the CPPA, i.e., the CPPA for the maximum-flow problem (CPPA-MF), the CPPA for the minimum-cost-maximum-flow problem (CPPA-MCMF), and the CPPA for the link-capacitated traffic assignment problem (CPPA-CTAP). In the experiments, the CPPA-MF shows competitive performance among four baseline algorithms; the CPPA-MCMF is approximately 50% faster than the baseline algorithms; the CPPA-CTAP reduce the oversaturated degree from approximately 40% to 1.5% compared to the original algorithm. The experimental results prove the validation of the CPPA framework. The CPPA is also robust since it have been successfully applied in three different scenarios. The proposed CPPA extends the PPA’s application to capacity-constrain problems and might shed some lights on its future applications in complex real-world problems.
Article
We derive a class of equations describing low Reynolds number steady flows of incompressible and viscous fluids in networks made of straight channels, with several sources and sinks, and adaptive conductivities. A graph represents the network, and the fluxes at sources and sinks control the flow. The adaptive conductivities describe the transverse channel elasticities, mirroring several network structures found in physics and biology. Minimising the dissipated energy per unit time, we have found an explicit form for the adaptation equations and, asymptotically in time, a steady-state tree geometry for the graph connecting sources and sinks is reached. A phase transition tuned by an order parameter for the adapted steady-state graph has been found.
Article
Physarum polycephalum is a unicellular slime mould that has been intensely studied owing to its ability to solve mazes, find shortest paths, generate Steiner trees, share knowledge and remember past events and the implied applications to unconventional computing. The CELL model is a cellular automaton introduced in Gunji et al . (Gunji et al. 2008 J. Theor. Biol. 253 , 659–667 ( doi:10.1016/j.jtbi.2008.04.017 )) that models Physarum ’s amoeboid motion, tentacle formation, maze solving and network creation. In the present paper, we extend the CELL model by spawning multiple CELLs, allowing us to understand the interactions between multiple cells and, in particular, their mobility, merge speed and cytoplasm mixing. We conclude the paper with some notes about applications of our work to modelling the rise of present-day civilization from the early nomadic humans and the spread of trends and information around the world. Our study of the interactions of this unicellular organism should further the understanding of how P. polycephalum communicates and shares information.
Chapter
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.
Article
Full-text available
Plasmodia migrate towards those situations which increase the frequency of their alternations in streaming, and away from those which decrease the frequency. Therefore peristalsis-like waves in Physarum move in the direction opposite from the net movement of the organism. The mechanism is fundamentally related to other known types of chemotaxis.
Article
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.
Article
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.
Article
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.
Article
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.
Article
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.
Article
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.
Article
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.