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Top1. Introduction
All living organisms have evolved to survive under some set of external conditions. Put another way, they are organized as an entity capable of sustaining further organization. The plasmodium of the true slime mold Physarum polycephalum, one of the most primitive living organisms, is no exception. The conditions of the culture medium determine the pattern of Physarum’s body formation (Takamatsu, Takaba, & Takizawa, 2009). The plasmodium quickly shows isotropic and homogeneous patterns under favorable conditions, and anisotropic and heterogeneous patterns under unfavorable conditions.
Such morphological changes can be interpreted as a balancing act between the exploration of new possibilities and the exploitation of given certainties (March, 1991). The isotropic body is suited to stable exploitation of food located near the body, a favorable condition. If food is not present near the body, however, the organism must explore. This is not an unfavorable situation, as an anisotropic body form is suited to efficient exploration, making good use of available resources (the body itself). To survive, the organism figuratively takes a gamble by narrowing itself to increase its range of exploration, an example of a living organization facing the choice between exploration and exploitation.
Protoplasm flows easily in the sol state, but less so in the gel state. In this study we focused on these aspects, simplifying the distinction between sol and gel states to the amount of protoplasm in a given location. This simplification enabled a simple model of cell motility, one that describes cytoplasmic streaming using only the amount of protoplasm. We call this integrated representation of the sol and gel states a “representation by softness.” Cell body softness is comparable to the plasticity of materials (Lundberg, Krishan, Xu, O’Hern, & Dennin, 2008).
The lack of distinction between sol and gel states invalidates the distinction between the structure of the body and the resources the structure consumes. For example, a tubular structure conveys the protoplasm, while the structure itself is composed of the conveyed protoplasm. This example represents the notion of softness well. We propose a model based on softness, which aims to represent motility in cells composed of “soft” components.
In Takamatsu, Takaba, and Takizawa (2009) the authors considered two measures, the spread angle and the contact angle, as tools for analyzing morphological patterns. The spread angle is proportional to the range of exploration in a peripheral body part. The contact angle is a representation of the body thickness. In this study the spread angle and contact angle are indirectly represented by two simple parameters that describe the softness of an aggregation of protoplasm.
Our model of cell motility is composed of protoplasm motion on a square lattice in the same manner as the model by Gunji, Shirakawa, Niizato, and Haruna (2008) in which a dot on a square lattice is regarded as a small amount of protoplasm. While that model does not treat protoplasm thickness directly, our model does.
In addition to Physarum, our model also shows morphological changes as figures that can be interpreted as a relation between exploration and exploitation. The figures were numerically analyzed by using the measures in Gunji, Shirakawa, Niizato, Yamachiyo, and Tani (2011) and indicated a trade-off between exploration and exploitation.
As Adamatzky and Jones (2008) pointed out, the plasmodium is a mass of protoplasm encapsulated in an elastic plasma membrane. Physarum computing Adamatzky (2007, 2010) and Adamatzky, DeLacyCostello, and Shirakawa (2008) precisely utilizes the amorphous and elastic nature of the organism as one of the resources that enables construction of an unconventional computer. Our model directly investigates how this elastic organism explores its surrounding space by exploiting cytoplasmic resources. Our goal is to elucidate the biological mechanism of exploration by massive cellular organisms, and to understand the underlying mechanism in adaptive plasmodium computation.