BioSystems 103 (2011) 331–341 Contents lists available at ScienceDirect BioSystems journal homepage: www.elsevier.com/locate/biosystems The emergence of synchronization behavior in Physarum polycephalum and its particle approximation Soichiro Tsuda a,b,∗,1 , Jeff Jones a,1 a Bristol Institute of Technology, University of the West of England, BS16 1QY, United Kingdom b Science and Engineering of Natural Systems Group, School of Electronics and Computer Science, University of Southampton, SO17 1BJ, United Kingdom article info Article history: Received 16 September 2010 Received in revised form 30 October 2010 Accepted 2 November 2010 Keywords: Self-organization Physarum polycephalum Phase synchronization Swarm intelligence abstract The regeneration process of contractile oscillation in the plasmodium of Physarum polycephalum is investigated experimentally and modelled computationally. When placed in a well, the Physarum cell restructures the body (fusion of small granule-like cells) and shows various complex oscillation patterns. After it completed the restructuring and regained synchronized oscillation within the body, the cell shows bilateral oscillation or rotating wave pattern. This regeneration process did not depend on the well size and all the cases tested here showed similar time course. Phase synchronization analysis based on Hilbert Transform also suggested that the cell can develop a fully synchronized oscillation within a fixed time no matter what the cell size is. A particle-based computational model was developed in order to model the emergence of oscillation patterns. Particles employing very simple and identical sensory and motor behaviors interacted with each other via the sensing and deposition of chemoattractants in a diffusive environment. From a random and almost homogeneous distribution, emergent domains of oscillatory activity emerged. By increasing the sensory radius the model simulated the regeneration process of the real plasmodium. In addition, the model replicated the rotating wave and bilateral oscillation pattern when the sensory radius was increased. The results suggest that complex emergent oscillatory behaviors (and thus the high-level systems which may utilize them, such as pumping and transport mechanisms) may be developed from simple materials inspired by Physarum slime mold. © 2010 Elsevier Ireland Ltd. All rights reserved. 1. Introduction A plasmodium of true slime mold Physarum polycephalum is a multi-nuclear single-cellular organism. In the plasmodial state, the Physarum slime mold does not have any fixed shape and it lives as an amorphous amoeba-like organism. Being a single cell, it does not have a brain, central nervous system, or neural tissue of any type. Nevertheless it is able to react to external stimuli by chang- ing the body shape without losing control as a single cell. In other words, the Physarum plasmodium is an example of natural dis- tributed computing system. Based on this fact, there has been a lot of research on “fundamental intelligence” of the cell. For exam- ple, it has been shown that the plasmodium can form an optimal tube network (Tero et al., 2010), compute planar proximity graphs (Adamatzky, 2008), and anticipate periodic events (Saigusa et al., 2008). In other cases, the cell was used to implement computa- ∗ Corresponding author at: Bristol Institute of Technology, University of the West of England, Frenchay Campus, Coldharbour Lane, Bristol BS16 1QY, United Kingdom. Tel: +44 0117 328 2068. E-mail addresses: So.Tsuda@uwe.ac.uk, soichiro.tsuda@gmail.com (S. Tsuda). 1 These authors contributed equally to this work. tional systems, such as basic logic gates (Tsuda et al., 2004), storage modification machine (Adamatzky, 2007), coupled oscillator sys- tem (Takamatsu et al., 2000b), and neural network system (Aono and Hara, 2007). So far it is known that the underlying mechanism which enables the primitive intelligent behavior is synchronization phenomena that are observed in the cell’s intrinsic cellular oscillation. The Physarum cell shows periodic contraction oscillation at 0.01 Hz (100 s per period). This is mainly caused by regular conformation changes of actin polymer for protoplasmic streaming. Synchronization is commonly observed in biological oscillators, such as circadian rhythms (Mackey and Glass, 1977) and central pattern generators (Hooper, 2001), and it makes a system more adaptive and robust against external/internal noise by dynami- cally modulating the oscillation rhythm (Kuo, 2002). Like other biological oscillators, the Physarum plasmodium is also able to mod- ulate the oscillation rhythm to behave adaptively to environmental changes. If the cell is exposed to any external stimulus (food, chemi- cal, thermal, etc.), the oscillation rhythm at a local stimulated site of the cell will be modulated because of the stimulus. The local change in oscillation frequency propagates to other unaffected parts of the cell through protoplasmic streaming and eventually forms a phase gradient within the cell through mutual entrainment (Miyake et al., 0303-2647/$ – see front matter © 2010 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.biosystems.2010.11.001