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.

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.

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. DOI: 10.1103/PhysRevLett.100.018101 PACS numbers: 87.17.Aa, 87.18.Hf, 87.23.Kg Information processing is an interesting component of biological systems. Although the brain has evolved to perform this specific function, information processing is possible without a brain, and organisms as simple as amoebae are much more intelligent than generally thought. For example, the true slime mold Physarum polycephalum can solve a maze and certain geometrical puzzles, in order to satisfy its needs for efficient absorption of nutrients and intracellular communication [1][2][3][4]. Thus, from an evolutionary perspective, information processing by unicellular organisms might represent a simple precursor of braindependent higher functions. Anticipating and recalling events are two such functions; however, the way in which they self-organize has so far remained unknown.P. polycephalum is a useful model organism for studying behavioral intelligence [5]. Its plasmodium is a large aggregate of protoplasm that possesses an intricate network of tubular structures, and can crawl over agar plates at a speed of approximately 1 cm=h at room temperature. In order to investigate primitive forms of brain function (such as learning, memory, anticipation, and recall), here we have examined the rhythmicity of cell behaviors [6,7] and the adaptability of cells to periodic environmental changes [8,9]. Our approach was to expose organisms to periodic changes in ambient conditions and to observe their behavioral responses. As there has been much controversy in recent years over the existence of nonhuman intelligence [10 -13], this subject requires evaluation by modern scientific techniques.Here we show that an amoeboid organism can anticipate the timing of periodic events. Moreover, we explore the mechanisms underlying this behavior from a dynamical systems perspective. Our results hint at the cellular origins of primitive intelligence, and imply that simple dynamics might be sufficient to explain its emergence.A large plasmodium of P. polycephalum was cultured with oat flakes in a trough (25 35 cm 2 ) on an agar plate under dim light. The tip region of an extended front was removed and placed in a narrow lane (0:5 28 cm 2 ) at 26 C and 90% humidity (hereafter referred to as standard conditions; all experiments were conducted under these ambient conditions unless otherwise specified). The organism migrated along the lane, and the position of its tip was measured every 10 min. After migrat...

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.