Phylogeny of Physarida (Amoebozoa, Myxogastria) Based on the Small-Subunit Ribosomal RNA Gene, Redefinition of Physarum pusillum s. str. and Reinstatement of P. gravidum Morgan.

Myxomycetes (also called Myxogastria or colloquially, slime molds) are worldwide occurring soil amoeboflagellates. Among Amoebozoa, they have the notable characteristic to form, during their life cycle, macroscopic fruiting bodies, that will ultimately release spores. Some 1,000 species have been described, based on the macroscopic and microscopic characteristics of their fruiting bodies. We were interested in Physarum pusillum (Berk. & M.A. Curtis) G. Lister, a very common species described with two variants, each bearing such morphological differences that they could represent two distinct species. In order to test this, we observed key characters in a large selection of specimens attributed to P.  pusillum, to its synonyms (in particular Physarum gravidum), and to related species. In addition, the small-subunit ribosomal RNA gene was obtained from seven of these specimens. Based on these data, we provide a comprehensive phylogeny of the order Physarida (Eukaryota: Amoebozoa: Conosa: Macromycetozoa: Fuscisporidia). Morphology and phylogeny together support the reinstatement of P. gravidum Morgan 1896 with a neotype here designated, distinct from P. pusillum, here redefined.

Active poroelastic two-phase model for the motion of physarum microplasmodia.

The onset of self-organized motion is studied in a poroelastic two-phase model with free boundaries for Physarum microplasmodia (MP). In the model, an active gel phase is assumed to be interpenetrated by a passive fluid phase on small length scales. A feedback loop between calcium kinetics, mechanical deformations, and induced fluid flow gives rise to pattern formation and the establishment of an axis of polarity. Altogether, we find that the calcium kinetics that breaks the conservation of the total calcium concentration in the model and a nonlinear friction between MP and substrate are both necessary ingredients to obtain an oscillatory movement with net motion of the MP. By numerical simulations in one spatial dimension, we find two different types of oscillations with net motion as well as modes with time-periodic or irregular switching of the axis of polarity. The more frequent type of net motion is characterized by mechano-chemical waves traveling from the front towards the rear. The second type is characterized by mechano-chemical waves that appear alternating from the front and the back. While both types exhibit oscillatory forward and backward movement with net motion in each cycle, the trajectory and gel flow pattern of the second type are also similar to recent experimental measurements of peristaltic MP motion. We found moving MPs in extended regions of experimentally accessible parameters, such as length, period and substrate friction strength. Simulations of the model show that the net speed increases with the length, provided that MPs are longer than a critical length of ≈ 120 µm. Both predictions are in line with recent experimental observations.

Liquid brains, solid brains.

Cognitive networks have evolved a broad range of solutions to the problem of gathering, storing and responding to information. Some of these networks are describable as static sets of neurons linked in an adaptive web of connections. These are 'solid' networks, with a well-defined and physically persistent architecture. Other systems are formed by sets of agents that exchange, store and process information but without persistent connections or move relative to each other in physical space. We refer to these networks that lack stable connections and static elements as 'liquid' brains, a category that includes ant and termite colonies, immune systems and some microbiomes and slime moulds. What are the key differences between solid and liquid brains, particularly in their cognitive potential, ability to solve particular problems and environments, and information-processing strategies? To answer this question requires a new, integrative framework. This article is part of the theme issue 'Liquid brains, solid brains: How distributed cognitive architectures process information'.

The life cycles of two species of Myxomycetes in Physarales, Physarum rigidum and Didymium squamulosum.

Myxomycetes are eukaryotic microorganisms containing characteristics akin to both fungi and amoebae. They can complete their whole life cycles while being cultured on agar media, and under-laboratory conditions, which favors taxonomic, phylogenetic, and cytological researches. Here, we describe the life cycles of two such species: Didymium squamulosum collected from the field and Physarum rigidum cultured from moist chamber both belonging to the Order Physarales. Three per cent oat-agar media (OAM) was used to culture the plasmodia until they aggregated and were almost starved. Natural light was then applied to the plasmodia to induce fructification. Their life cycles share the same common stages, namely: spore, myxamoebae, swarm cell, plasmodia, and sporulation. In this study, we describe the morphogenesis from spore to spore of two species by differential interference contrast (DIC) and stereoscopic microscopies, as well as discuss the differences between the development of both species and interspecies. We found that the spore germination method of both species was the same. However, there were differences noted in time taken and fruiting body formation. Unlike P. rigidum, the species D. squamulosum did not require natural light stimulation. Moreover, the maturation process of both species had similar color transitions but exhibited distinct morphology in each developmental stage except during the swarm cell stage.

Cell learning.

Although we often think of cells as small, simple building blocks of life, in fact they are highly complex and can perform a startling variety of functions. In our bodies, cells are programmed by complex differentiation pathways and are capable of responding to a bewildering range of chemical and physical signals. Free-living single-celled organisms, such as bacteria or protists, have to cope with varying environments, locate prey and potential mates, and escape from predators - all of the same tasks that a free-living animal is faced with. When animals face complex behavioral challenges, they rely on their cognitive abilities - the ability to learn from experience, to analyse a situation and choose an appropriate course of action. This ability is essential for survival and should, in principle, be a ubiquitous feature of all living things regardless of the complexity of the organism.

Network Community Detection Based on the Physarum-Inspired Computational Framework.

Community detection is a crucial and essential problem in the structure analytics of complex networks, which can help us understand and predict the characteristics and functions of complex networks. Many methods, ranging from the optimization-based algorithms to the heuristic-based algorithms, have been proposed for solving such a problem. Due to the inherent complexity of identifying network structure, how to design an effective algorithm with a higher accuracy and a lower computational cost still remains an open problem. Inspired by the computational capability and positive feedback mechanism in the wake of foraging process of Physarum, a kind of slime, a general Physarum-based computational framework for community detection is proposed in this paper. Based on the proposed framework, the inter-community edges can be identified from the intra-community edges in a network and the positive feedback of solving process in an algorithm can be further enhanced, which are used to improve the efficiency of original optimization-based and heuristic-based community detection algorithms, respectively. Some typical algorithms (e.g., genetic algorithm, ant colony optimization algorithm, and Markov clustering algorithm) and real-world datasets have been used to estimate the efficiency of our proposed computational framework. Experiments show that the algorithms optimized by Physarum-inspired computational framework perform better than the original ones, in terms of accuracy and computational cost.

Solving NP-Hard Problems with Physarum-Based Ant Colony System.

NP-hard problems exist in many real world applications. Ant colony optimization (ACO) algorithms can provide approximate solutions for those NP-hard problems, but the performance of ACO algorithms is significantly reduced due to premature convergence and weak robustness, etc. With these observations in mind, this paper proposes a Physarum-based pheromone matrix optimization strategy in ant colony system (ACS) for solving NP-hard problems such as traveling salesman problem (TSP) and 0/1 knapsack problem (0/1 KP). In the Physarum-inspired mathematical model, one of the unique characteristics is that critical tubes can be reserved in the process of network evolution. The optimized updating strategy employs the unique feature and accelerates the positive feedback process in ACS, which contributes to the quick convergence of the optimal solution. Some experiments were conducted using both benchmark and real datasets. The experimental results show that the optimized ACS outperforms other meta-heuristic algorithms in accuracy and robustness for solving TSPs. Meanwhile, the convergence rate and robustness for solving 0/1 KPs are better than those of classical ACS.

Article for the "Free-living amoebae special issue": Isolation and characterisation of various amoebophagous fungi and evaluation of their prey spectrum.

This article gives an overview on the isolation and characterisation of endoparasitic fungi invading free-living amoebae (FLA), including the ones forming thalli inside their hosts such as Cochlonema euryblastum and also the predatory fungi which capture amoebae by adhesive hyphae. Acaulopage spp. and Stylopage spp. trap, intrude, and exploit amoebal trophozoites. Previous phylogenetic studies proved Cochlonema to be a member of the Zoopagales. The genetic investigation of Acaulopage tetraceros demonstrated its close relationship to Cochlonema. Co-cultivation of A. tetraceros with a number of FLA revealed a great prey spectrum of this amoebophageous fungus. In addition it was shown that solitary amoebal stages of slime moulds such as Dictyostelium sp. and Physarum sp. are also suited as welcome prey amoebae.

Current-reinforced random walks for constructing transport networks.

Biological systems that build transport networks, such as trail-laying ants and the slime mould Physarum, can be described in terms of reinforced random walks. In a reinforced random walk, the route taken by 'walking' particles depends on the previous routes of other particles. Here, we present a novel form of random walk in which the flow of particles provides this reinforcement. Starting from an analogy between electrical networks and random walks, we show how to include current reinforcement. We demonstrate that current-reinforcement results in particles converging on the optimal solution of shortest path transport problems, and avoids the self-reinforcing loops seen in standard density-based reinforcement models. We further develop a variant of the model that is biologically realistic, in the sense that the particles can be identified as ants and their measured density corresponds to those observed in maze-solving experiments on Argentine ants. For network formation, we identify the importance of nonlinear current reinforcement in producing networks that optimize both network maintenance and travel times. Other than ant trail formation, these random walks are also closely related to other biological systems, such as blood vessels and neuronal networks, which involve the transport of materials or information. We argue that current reinforcement is likely to be a common mechanism in a range of systems where network construction is observed.

A fluid-filled soft robot that exhibits spontaneous switching among versatile spatiotemporal oscillatory patterns inspired by the true slime mold.

Behavioral diversity is an essential feature of living systems, enabling them to exhibit adaptive behavior in hostile and dynamically changing environments. However, traditional engineering approaches strive to avoid, or suppress, the behavioral diversity in artificial systems to achieve high performance in specific environments for given tasks. The goals of this research include understanding how living systems exhibit behavioral diversity and using these findings to build lifelike robots that exhibit truly adaptive behaviors. To this end, we have focused on one of the most primitive forms of intelligence concerning behavioral diversity, namely, a plasmodium of true slime mold. The plasmodium is a large amoeba-like unicellular organism that does not possess any nervous system or specialized organs. However, it exhibits versatile spatiotemporal oscillatory patterns and switches spontaneously between these. Inspired by the plasmodium, we built a mathematical model that exhibits versatile oscillatory patterns and spontaneously transitions between these patterns. This model demonstrates that, in contrast to coupled nonlinear oscillators with a well-designed complex diffusion network, physically interacting mechanosensory oscillators are capable of generating versatile oscillatory patterns without changing any parameters. Thus, the results are expected to shed new light on the design scheme for lifelike robots that exhibit amazingly versatile and adaptive behaviors.

Mathematical model for contemplative amoeboid locomotion.

It has recently been reported that even single-celled organisms appear to be "indecisive" or "contemplative" when confronted with an obstacle. When the amoeboid organism Physarum plasmodium encounters the chemical repellent quinine during migration along a narrow agar lane, it stops for a period of time (typically several hours) and then suddenly begins to move again. When movement resumes, three distinct types of behavior are observed: The plasmodium continues forward, turns back, or migrates in both directions simultaneously. Here, we develop a continuum mathematical model of the cell dynamics of contemplative amoeboid movement. Our model incorporates the dynamics of the mass flow of the protoplasmic sol, in relation to the generation of pressure based on the autocatalytic kinetics of pseudopod formation and retraction (mainly, sol-gel conversion accompanying actin-myosin dynamics). The biological justification of the model is tested by comparing with experimentally measured spatiotemporal profiles of the cell thickness. The experimentally observed types of behavior are reproduced in simulations based on our model, and the core logic of the modeled behavior is clarified by means of nonlinear dynamics. An on-off transition between the refractory and activated states of the chemical reactivity that takes place at the leading edge of the plasmodium plays a key role in the emergence of contemplative behavior.

Tug-of-war model for the two-bandit problem: nonlocally-correlated parallel exploration via resource conservation.

We propose a model - the "tug-of-war (TOW) model" - to conduct unique parallel searches using many nonlocally-correlated search agents. The model is based on the property of a single-celled amoeba, the true slime mold Physarum, which maintains a constant intracellular resource volume while collecting environmental information by concurrently expanding and shrinking its branches. The conservation law entails a "nonlocal correlation" among the branches, i.e., volume increment in one branch is immediately compensated by volume decrement(s) in the other branch(es). This nonlocal correlation was shown to be useful for decision making in the case of a dilemma. The multi-armed bandit problem is to determine the optimal strategy for maximizing the total reward sum with incompatible demands, by either exploiting the rewards obtained using the already collected information or exploring new information for acquiring higher payoffs involving risks. Our model can efficiently manage the "exploration-exploitation dilemma" and exhibits good performances. The average accuracy rate of our model is higher than those of well-known algorithms such as the modified -greedy algorithm and modified softmax algorithm, especially, for solving relatively difficult problems. Moreover, our model flexibly adapts to changing environments, a property essential for living organisms surviving in uncertain environments.

A mathematical model for period-memorizing behavior in Physarum plasmodium.

Mathematical models to describe period-memorizing behavior in Physarum plasmodium are reported. In constructing the model, we first examine the basic characteristics required for the class of models, then create a minimal linear model to fulfill these requirements. We also propose two modifications of the minimal model, nonlinearization and noise addition, which improve the reproducibility of experimental evidences. Differences in the mechanisms and in the reproducibility of experiments between our models and the previous models are discussed.

[Involvement of extracellular cAMP-specific phosphodiesterase in control of motile activity of Physarum polycephalum plasmodium].

Possible involvement of extracellular cAMP-specific phosphodiesterase in the control of cell motile behavior has been investigated in Physarum polycephalum plasmodium, a multinuclear amoeboid cell with the autooscillatory mode of motility. It was found that the rate of the hydrolysis of 10 mM cAMP by a partially purified preparation of cAMP-specific phosphodiesterase secreted by the plasmodium in the course of migration decreases 20-30 times under the action of 1 mM dithiothreitol. In the presence of 1-5 mM of this strong reducing agent, the onset of the plasmodium spreading and the transition to the stage of migration were delayed in a concentration-dependent manner. In accordance with the morphological pattern of motile behavior, the duration of the maintenance of high frequency autooscillations, which normally precede the increase in the rate of the spreading and appear also in response to the application of attractants at spatially uniform concentrations, strongly increased by the action of dithiothreitol. The results obtained suggest that the autocrine production of cAMP and extracellular cAMP-specific phosphodiesterase is an important constituent of the mechanism controlling the motile behavior of the Physarum polycephalum plasmodium.

[Cytomechanics of oscillatory contractions. Modeling the longitudinal dynamics of Physarum polycephalum protoplasmic strands].

A mathematical model of the longitudinal dynamics of an isolated strand of the Physarum polycephalum plasmodium has been constructed. Its contractile system is considered as a continual viscoelastic medium with passive and active components. The mathematical description of the longitudinal dynamics of the plasmodial strand is reduced to a system of three first-order differential equations, whose variables are its active stress, deformation, and the intracellular concentration of calcium ions. The model is based on the hypothesis that there exists a feedback loop, which appears because of the influence of strand stretching on the rate of the release of calcium ions, which in turn controls the active contraction and deformation of the strand. Nonlinear interactions between the variables evoke a loss of the stationary state stability and a self-excitation of mechanochemical autooscillations when the external load exceeds some critical value. The results of numerical solutions of the model with the empirically determined viscoelastic parameters are in good agreement with the available experimental data and testify to the adequacy of the description of strand dynamics by the mathematical model in which the contractile apparatus is a part of the cellular control system. In particular, this model well simulates the form and duration of transient mechanochemical processes observed under isotonic and isometric conditions immediately after strand isolation, as well as the subsequent excitation of autooscillations of the contractile activity and their activation by strand stretching.

Flow-network adaptation in Physarum amoebae.

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. This 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 simple and powerful.

Locomotive mechanism of Physarum plasmodia based on spatiotemporal analysis of protoplasmic streaming.

We investigate how an amoeba mechanically moves its own center of gravity using the model organism Physarum plasmodium. Time-dependent velocity fields of protoplasmic streaming over the whole plasmodia were measured with a particle image velocimetry program developed for this work. Combining these data with measurements of the simultaneous movements of the plasmodia revealed a simple physical mechanism of locomotion. The shuttle streaming of the protoplasm was not truly symmetric due to the peristalsis-like movements of the plasmodium. This asymmetry meant that the transport capacity of the stream was not equal in both directions, and a net forward displacement of the center of gravity resulted. The generality of this as a mechanism for amoeboid locomotion is discussed.

Physarum machines: encapsulating reaction-diffusion to compute spanning tree.

The Physarum machine is a biological computing device, which employs plasmodium of Physarum polycephalum as an unconventional computing substrate. A reaction-diffusion computer is a chemical computing device that computes by propagating diffusive or excitation wave fronts. Reaction-diffusion computers, despite being computationally universal machines, are unable to construct certain classes of proximity graphs without the assistance of an external computing device. I demonstrate that the problem can be solved if the reaction-diffusion system is enclosed in a membrane with few 'growth points', sites guiding the pattern propagation. Experimental approximation of spanning trees by P. polycephalum slime mold demonstrates the feasibility of the approach. Findings provided advance theory of reaction-diffusion computation by enriching it with ideas of slime mold computation.