Article

Cellular Computation Realizing Intelligence of Slime Mold Physarum Polycephalum

Authors:
To read the full-text of this research, you can request a copy directly from the authors.

Abstract

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.

No full-text available

Request Full-text Paper PDF

To read the full-text of this research,
you can request a copy directly from the authors.

... Nakagaki et. al., recently discovered an interesting behavior of slime mold; that is, its dietary action can diversify to an optimized network [4,5], but why and how such a mysterious network, a so called "slime mold computer", is realized has not been explained at all. We suspect that this network is controlled by some unknown sensory organs that perceive temperature and humidity in the surrounding environment, because we already know that slime molds have thermotactic [2,[6][7][8][9]. ...
Article
Full-text available
ARTICLE INFO ABSTRACT We measured the thermal conductivity (λ) and thermal diffusivity (α) of a myxomycete (slime mold) by the transient short-hot wire method. The measurements were conducted two times with temperatures varying from 277 to 300 K. In the results, λ = 0.489-0.572 (W/m ⋅ K), and α = 8.36× 10-8-2.48× 10-7 (m 2 /s). The thermal properties of slime molds are close to those of water. In particular, the λ is similar to that of biological materials (cells, human blood and plasma), and slightly different from that of some kinds of organic materials (lysozyme crystals, wheat, apple, and tomato), and evidently different from inorganic substances (sand and soil).
... The difficulty of biological processes' physical government is the extreme and unforeseeable, time-variable complexity. It becomes more and more clear that even unicellular organisms can solve mazes and certain optimization problems, and can demonstrate both anticipatory and contemplative behavior (Tanaka and Nakagaki 2011). Bacteria are shown to be able to solve newly encountered problems, assessing the given problem via collective sensing, recallable stored information of past experience, and solving optimization problems that are beyond even what individual human beings can readily solve (Ben-Jacob 2009). ...
... Notwithstanding, the topic of "cellular intelligence" has a rapidly growing literature (Quevli 1917;Albrecht-Buehler 1980, 1985, 1990Mathieu and Sonea 1996;di Primio, Muller and Lengeler 2000;Ben-Jacob, Becker, Shapira and Levine 2004;Ford 2004Ford , 2006Ford , 2010Hellingwerf 2005;Ben Jacob, Shapira and Tauber 2006;Shapiro 2007). Cells can demonstrate both anticipatory and contemplative behavior (Tanaka and Nakagaki 2011). Bacteria are shown to be able to solve newly encountered problems, assessing the given problem via collective sensing and recallable stored information of past experience, as well as solving optimization problems that are beyond even what individual human beings can readily solve (Ben-Jacob 2009). ...
Article
Full-text available
We point out that the origin of life cannot be understood without a closer look at the nature of life. Therefore we present here, for the first time, ten fundamental biological facts opening new avenues to address the question of the cosmic origin of cellular life. We find that all living beings, including cells, have a genuine biological autonomy that acts with the help of spontaneous, physically indeterminate or arbitrary cellular decisions that initiate quantum effects in support of biological aims. We propose that these biologically initiated spontaneous processes are assisted by vacuum processes. A natural corollary arises, telling that biological processes organize the quantum vacuum processes of living organisms from below the physical level, which in turn strongly suggests that biology is more fundamental than physics. We point out that just as the functions played by the forwards in a well-trained football team cannot be assigned externally by a series of physical forces acting on the bodies of the football players, biological aims and functions cannot be attached to physico-chemical structures of the first cell of the Cosmos by merely physico-chemical processes, but must be assigned by a more general cosmic life form pre-existing before the first cell and containing it like mother its foetus. This would indicate that the Cosmos is not only the source of stars, galaxies, and cosmic clouds, but also of biologically initiated and organized cosmic “forces“ pre-existing in the vacuum and, ultimately, the Cosmic Subject.
... Path selection by this slime mold has been investigated enthusiastically (reviewed in Nakagaki and Guy 2008;Tanaka and Nakagaki 2011). Previous studies have shown that the slime mold selects not only the mathematically shortest route but also the route of high fault tolerance against accidental disconnection of the tubes (Nakagaki et al. 2004) and minimum risk Ito et al. 2010), suggesting that this amoeba-like true slime mold is capable of "intelligent" behavior for survival task. ...
Article
A true slime mold, the plasmodium of Physarum polycephalum has the ability to find the shortest route between two points in a labyrinth. To find the shortest route between two points, detection of the difference in lengths can be made from two aspects: the absolute difference between the lengths or the ratio of them. We found that the ratio of two lengths, rather than the absolute difference between the two lengths, was important in discriminating the difference in the two lengths by P. polycephalum. This finding indicates that an amoeboid organism detects differences in stimulus intensity as though it is constrained by Weber's law, suggesting that Weber's law is not reliant on the presence of a neural system and is used widely even in Amoebozoa.
... The difficulty of biological processes' physical government is the extreme and unforeseeable, time-variable complexity. It becomes more and more clear that even unicellular organisms can solve mazes and certain optimization problems, and can demonstrate both anticipatory and contemplative behavior (Tanaka and Nakagaki 2011). Bacteria are shown to be able to solve newly encountered problems, assessing the given problem via collective sensing, recallable stored information of past experience, and solving optimization problems that are beyond even what individual human beings can readily solve (Ben-Jacob 2009). ...
Conference Paper
Full-text available
Although biological autonomy is widely discussed, its description in scientific terms remains elusive. I present here a series of recent evidences on the existence of genuine biological autonomy. Nevertheless, nowadays it seems that the only acceptable ground to account for any natural phenomena, including biological autonomy, is physics. But if this were the case, then arguably there would be no way to account for genuine biological autonomy. The way out of such a situation is to build up an exact theoretical biology, and one of the first steps is to clarify the basic concepts of biology, among them biological aim, function and autonomy. We found a physical mechanism to realize biological autonomy, namely, biologically initiated vacuum processes. In the newly emerging picture, biological autonomy shows up as a new, fundamental and inevitable element in our scientific world picture. It offers new perspectives for solving problems regarding the origin and nature of life, connecting ancient Greek philosophy with modern science. Namely, our proposal sheds light in what sense can the God as conceived by Xenophanes can move the material objects of the Universe by its thoughts without toil.
Article
The modes of continuously distributed mechanochemical self-sustained oscillations (autowaves) exhibited by the Physarum plasmodium under different experimental conditions are reviewed. The role of the stretch-induced activation of contractile oscillations in the spatiotemporal self-organization of the plasmodium is elucidated. Different mathematical models describing contractile autowaves in ectoplasm and the streaming of the endoplasm are considered. Our mathematical models, which are based on the hypothesis of local positive feedback between the deformation and contraction of the contractile apparatus, are also presented. The feedback is mediated through a chemical regulatory system, whose kinetics involves the coupling to the mechanical strain. The mathematical analysis and computer simulations have demonstrated that the solutions of the models agree quantitatively with the experimental data. In particular, the only hydrodynamic interactions between the different parts of the plasmodium via the streaming endoplasm can lead to globally coordinated ectoplasmic contractions and vigorous shuttle endoplasmic streaming. These models, with empirically determined values of the viscoelastic parameters, well simulate the form and duration of the transient contractile processes observed after the isolation of the strands as well as the subsequent excitation of auto-oscillations and their stretch-induced activation under isotonic and isometric conditions.
Article
We will show that ability of information processing in an amoeboid organism is higher than we had thought. The model organism is the plasmodium of Physarum polycephalum (true slime mold), which is a large aggregate of protoplasm with many nuclei. The organism found the optimal path when it obtained the multiple locations of food. A simple mathematical model for the path finding was proposed in terms of differential equations. As well as the path-finding ability, the organism was able to anticipate the next timing of periodic climate change after experienced some periodic changes of climate, and to show a kind of behaviors that seemed to be indicisive when it encountered the presence of a chemical repellent, quinine. We indicated that simple dynamics was enough to reproduce these observed behaviors. Mathematical modeling is helpful to understand the mechanism of behavioral smartness in slime mold. The behavioral smartness can be based on motion of viscoelastic body, so we discuss rheological description of smart behavior.
Article
Full-text available
Summary The nature of the oscillator controlling shuttle streaming inPhysarum polycephalum is not well understood. To examine the possibility of complex behavior in shuttle streaming, the time between reversal of streaming direction was measured over several hours in an intact plasmodium to produce a time series. Time series data were then used to analyze shuttle streaming dynamics. Complexity in shuttle streaming is revealed by an inverse frequency (1/f) power spectrum where the amplitude of reversals is plotted against their frequency. The complex dynamics of shuttle streaming is also shown by a trajectory in phase space typical of a strange attractor. Finally, shuttle streaming time series data have a dominant Lyapunov exponent of approximately zero. Dynamic systems with a Lyapunov exponent of zero exist in a state at the edge of chaos. Systems at the edge exhibit self-organized criticality, which produces complex behavior in many physical and biological systems. We propose that complex dynamics inPhysarum shuttle streaming is an example of self-organized criticality in the cytoplasm. The complex behavior ofPhysarum is an emergent phenomenon that probably results from the interaction of actin filaments, myosin, ATP, and other components involved in cell motility.
Article
Full-text available
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.
Article
Full-text available
To evaluate performance in a complex survival task, we studied the morphology of the Physarum plasmodium transportation network when presented with multiple separate food sources. The plasmodium comprises a network of tubular elements through which chemical nutrient, intracellular signals and the viscous body are transported and circulated. When three separate food sources were presented, located at the vertices of a triangle, the tubular network connected them via a short pathway, which was often analogous to the mathematically shortest route known as Steiner's minimum tree (SMT). The other common network shape had high fault tolerance against accidental disconnection of the tubes and was known as cycle (CYC). Pattern selection appeared to be a bistable system involving SMT and CYC. When more than three food sources were presented, the network pattern tended to be a patchwork of SMT and CYC. We therefore concluded that the plasmodium tube network is a well designed and intelligent system.
Article
Full-text available
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.
Article
Full-text available
Scattering of particle-like patterns in dissipative systems is studied, especially we focus on the issue how the input-output relation is controlled at a head-on collision where traveling pulses or spots interact strongly. It remains an open problem due to the large deformation of patterns at a colliding point. We found that a special type of unstable steady or time-periodic solutions called scattors and their stable and unstable manifolds direct the traffic flow of orbits. Such scattors are in general highly unstable even in the one-dimensional case which causes a variety of input-output relations through the scattering process. We illustrate the ubiquity of scattors by using the complex Ginzburg-Landau equation, the Gray-Scott model, and a three-component reaction diffusion model arising in gas-discharge phenomena.
Article
Full-text available
The properties of excitable media are exploited to find minimum-length paths in complex labyrinths. Optimal pathways are experimentally determined by the collection of time-lapse position information on chemical waves propagating through mazes prepared with the Belousov-Zhabotinsky reaction. The corresponding velocity fields provide maps of optimal paths from every point in an image grid to a particular target point. Collisions of waves that were temporarily separated by obstacles mark boundary lines between Significantly different paths with the same absolute distance. The pathfinding algorithm is tested in very complex mazes with a simple reaction-diffusion model.
Article
Full-text available
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.
Article
Full-text available
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.
Article
We studied the effect of the size of food sources (FSs) presented to the true slime mould Physarum polycephalum on the tubular networks formed by the organism to absorb nutrient. The amount of plasmodium gathering at an FS was shown to be proportional to both the concentration of nutrient and the surface area of the FS. We presented two FSs to test which connection the organism selected in response to varying amounts of food and derived a simple rule for connection persistence: the longer connection collapses earlier. A mathematical model for tube selection in response to amount of food was derived and predicted our experimental findings regarding the choice of connection. When three FSs were presented to the organism, the longer tubes were also the first to collapse, explained by the relative probability of disconnection. The size of the FS is thus a key parameter determining network formation.
Article
The aims of this Feature Article are to show how simple or complex isothermal autocatalytic reactions can give rise to oscillatory behavior by considering virtually the simplest possible example (A + 2B → 3B; B → C) under the simplest and most readily realizable of circumstances (cstr). Although this is only a two-dimensional scheme it vividly and clearly represents all the key aspects of many real systems, including the birth, growth, and extinction of stable oscillations. Moreover, it is a "robust" model and it does not collapse when reversibility and parallel alternative routes are added. In the recent past, mathematical schemes have usually been either too elaborate to be understood or have failed to satisfy such basic requirements as the principle of detailed balance. Yet other models have failed to conserve mass or have not represented stable oscillations. Such fatal flaws are absent not only from this prototype but also from its comparison (A + B → 2B; B → C saturating). The springs of chaotic behavior in deterministic chemical models are also touched on, but it should be noted that real cstr must fall short of perfect homogeneity and that there may still be a gap between expectation and experimental proof of chaos.
Article
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.
Article
We have studied how the plasmodium of Physarum polycephalum, a large amoeboid cell, is able to track the shortest path between two selected points in a labyrinth. When nutrients are supplied at these points to a sheet-like plasmodium extended fully in a maze, the organism forms a single tube which connects the two sites via the shortest route. During the path finding, plasmodial parts in dead ends of the maze shrink and finally the tube with the minimum-length is selected from the existing possibilities. A simple cellular mechanism based on interacting cellular rhythms may describe the experimental observations.
Article
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.
Article
We propose a new solver for the Steiner tree problem, inspired by a true slime 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 an 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.
Article
Droplets emitting surface-active chemicals exhibit chemotaxis toward low-pH regions. Such droplets are self-propelled and navigate through a complex maze to seek a source of acid placed at one of the maze's exits. In doing so, the droplets find the shortest path through the maze. Chemotaxis and maze solving are due to an interplay between acid/base chemistry and surface tension effects.
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.
Article
Even for humans it is not easy to solve a maze. But the plasmodium of true slime mold, an amoeba-like unicellular organism, has shown an amazing ability to do so. This implies that an algorithm and a high computing capacity are included in the unicellular organism. In this report, we discuss information processing in the microorganism to focus on the issue as to whether the maze-solving behavior is akin to primitive intelligence.
Article
We present evidence that the giant amoeboid organism, the true slime mold, constructs a network appropriate for maximizing nutrient uptake. The body of the plasmodium of Physarum polycephalum contains a network of tubular elements by means of which nutrients and chemical signals circulate through the organism. When food pellets were presented at different points on the plasmodium it accumulated at each pellet with a few tubes connecting the plasmodial concentrations. The geometry of the network depended on the positions of the food sources. Statistical analysis showed that the network geometry met the multiple requirements of a smart network: short total length of tubes, close connections among all the branches (a small number of transit food-sites between any two food-sites) and tolerance of accidental disconnection of the tubes. These findings indicate that the plasmodium can achieve a better solution to the problem of network configuration than is provided by the shortest connection of Steiner's minimum tree.
Article
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.
Article
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.