A mathematical model for adaptive transport network in path finding by true slime mold

Tero, Atsushi; Kobayashi, Ryo; Nakagaki, Toshiyuki

doi:10.1016/j.jtbi.2006.07.015

Cited by 366 publications

(376 citation statements)

References 17 publications

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“…A mathematical model for cases with two FSs has previously been proposed [10]. The model consists of sets of equations for protoplasm flow and adaptability of tube thickness, respectively.…”

Section: Mathematical Model For a Tube Network Adaptive To Flowmentioning

confidence: 99%

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Flow-network adaptation in Physarum amoebae

et al. 2008

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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. The current 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 both simple and powerful.

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Section: Mathematical Model For a Tube Network Adaptive To Flowmentioning

confidence: 99%

“…For a given set of conductivities and source and sink, the flux through each of the network edges can be computed. In Physarum, the radii of the tubes change in response to this flux [10,14], and in the model the conductivities evolve according to the equation…”

Section: Mathematical Model For a Tube Network Adaptive To Flowmentioning

confidence: 99%

Flow-network adaptation in Physarum amoebae

et al. 2008

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“…(2) [7,8] for mathematical details of the model.) Here we focus on the effects of parameter a on the model behavior in order to develop an understanding of the effects of inhomogeneity in the experimental system.…”

Section: -2mentioning

confidence: 99%

Minimum-Risk Path Finding by an Adaptive Amoebal Network

et al. 2007

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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 lightavoiding 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. Introduction.-The plasmodium of Physarum polycephalum is an amoebalike organism with a body made up of a tubular network through which nutrients, signals, and body mass are transported. Studies of this organism have shown that it is able to determine the shortest path through a maze as well as ''solve'' other geometric puzzles [1][2][3]. In a maze, a starved organism forms a tube that connects food sources (FS) placed at the two exits of the maze via the shortest path, while nearly the entire protoplasm of the amoeba gathers over the two FS. The organism meets its physiological requirements in adopting this shape by absorbing nutrients from the FS as rapidly as possible while maintaining sufficient connectivity to permit intracellular communication. Such behavior in a primitive organism of this kind may offer insights into the evolutionary origins of biological information processing.Here we give the plasmodium a new type of task involving optimization behavior. Two separate FS are presented to the organism, which is illuminated by an inhomogeneous light field. Because the plasmodium is photophobic, tubes connecting the FS do not follow the simple shortest paths but form according to the illumination inhomogeneity. We report on the behavior of the organism under these conditions and discuss its physiological significance. We also propose a mathematical model for the cell dynamics and present a computational algorithm for its problem solving.Organism and methods.-The plasmodium of Physarum polycephalum, which regenerated from the sclerotia in ca. one-half day in the dark (25 C), was used in the experiments. A plastic film was placed onto a 1% agar gel, leaving a rectangular area (1 2 cm 2 ) of the gel uncovered. A few pieces (0:5 1 cm 2 ) of the regenerated plasmodium were placed in the rectangular area, and the preparation was placed in the dark for a few hours. The

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“…There is a positive feedback between flux and tube thickness, as the conductance of the sol is greater in a thicker channel. With this mechanism in mind, a mathematical model illustrating shortest path search has been constructed [56]. Suppose the shape of the network formed by the Physarum is represented by a graph, in which a plasmodial tube refers to an edge of the graph and a junction between tubes refers to a node.…”

Section: Physarum Polycephalummentioning

confidence: 99%

“…In this paper, f (Q) = |Q| is used because f (|Q ij |) = |Q| , γ = 1, the Physarum can always converge to the shortest path regardless of whether the distribution of conductivities in the initial state is random or biased [56]. With the flux calculated, the conductivity can be derived, where Eq.…”

Section: A C C E P T E Dmentioning

confidence: 99%

A Physarum-inspired approach to supply chain network design

Adamatzky

Yang

et al. 2016

Sci. China Inf. Sci.

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A supply chain is a system which moves products from a supplier to customers, which plays a very important role in all economic activities. This paper proposes a novel algorithm for a supply chain network design inspired by biological principles of nutrients' distribution in protoplasmic networks of slime mould Physarum polycephalum. The algorithm handles supply networks where capacity investments and product flows are decision variables, and the networks are required to satisfy product demands. Two features of the slime mould are adopted in our algorithm. The first is the continuity of flux during the iterative process, which is used in realtime updating of the costs associated with the supply links. The second feature is adaptivity. The supply chain can converge to an equilibrium state when costs are changed. Numerical examples are provided to illustrate the practicality and flexibility of the proposed method algorithm.

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A mathematical model for adaptive transport network in path finding by true slime mold

Cited by 366 publications

References 17 publications

Flow-network adaptation in Physarum amoebae

Flow-network adaptation in Physarum amoebae

Minimum-Risk Path Finding by an Adaptive Amoebal Network

A Physarum-inspired approach to supply chain network design

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