Solving the Towers of Hanoi – how an amoeboid organism efficiently constructs transport networks

Abstract

SUMMARYMany biological systems require extensive networks to transport resources and information. Biological networks must trade-off network efficiency with the risk of network failure. Yet, biological networks develop in the absence of centralised control from the interactions of many components. Moreover, many biological systems need to be able to adapt when conditions change and the network requires modification. We used the slime mould Physarum polycephalum (Schwein) to study how the organism adapts its network after disruption. To allow us to determine the efficiency of the constructed networks, we used a well-known shortestpath problem: the Towers of Hanoi maze. We first show that while P. polycephalum is capable of building networks with minimal length paths through the maze, most solutions are sub-optimal. We then disrupted the network by severing the main connecting path while opening a new path in the maze. In response to dynamic changes to the environment, P. polycephalum reconstructed more efficient solutions, with all replicates building networks with minimal length paths through the maze after network disruption. While P. polycephalum altered some of its existing network to accommodate changes in the environment, it also reconstructed large sections of the network from scratch. We compared the results obtained from P. polycephalum with those obtained using another distributed biological system: ant colonies. We hypothesise that network construction in ants hinges upon stronger positive feedback than for slime mould, ensuring that ants converge more accurately upon the shortest path but are more constrained by the history of their networks in dynamic environments.

Brainless but Multi-Headed: Decision Making by the Acellular Slime Mould Physarum polycephalum

“…As expected, the plasmodia then quickly connected the sources, however, not necessarily following one of the two possible shortest paths ( Figure 4, adapted from Reid and Beekman [18]). They then made the problem dynamic by blocking and opening paths forcing the slime mould to construct a new network.…”

“…All possible moves to solve the problem can be mapped on a 2D maze. By connecting this maze to its mirror image, Reid and Beekman formed a maze with a total of 32,678 unique paths between the opposing ends (see Figure 3, adapted from Reid and Beekman [18]). Only two of these paths are the shortest.…”

“…The maze could be modified by removing or adding connecting bridges. Reproduced with permission from [18]. …”

Collective strategy for obstacle navigation during cooperative transport by ants

“…This type of behavior is akin to problem solving, and has been studied primarily in individuals rather than groups. For example, maze-solving has been studied in many taxa including rats (Mulder et al, 2004;Yoder et al, 2011) and single-celled slime molds (Nakagaki et al, 2000;Reid and Beekman, 2013;Reid et al, 2012). Groups making serial decisions face the additional challenge of maintaining consensus -defined as agreeing on a single option (Sumpter and Pratt, 2009).…”

A new multi-agent system to simulate the foraging behaviors of Physarum

“…A primitive single-cell slime mold, called as Physarum Polycephalum, shows an excellent ability in network construction without central consciousness in the process of foraging (Nakagaki et al 2000;Reid and Beekman 2013;Adamatzky and Schubert 2014). Inoculating at a maze substrate, Physarum can reserve the shortest tube connecting food sources in an entrance and an exit (Nakagaki et al 2000).…”