Does being multi-headed make you better at solving problems? A survey of Physarum-based models and computations

Thoughts from the forest floor: a review of cognition in the slime mould Physarum polycephalum

Sensing, communication, navigation, decision-making, memory and learning are key components in a standard cognitive tool-kit that enhance an animal's ability to successfully survive and reproduce. However, these tools are not only useful for, or accessible to, animals-they evolved long ago in simpler organisms using mechanisms which may be either unique or widely conserved across diverse taxa. In this article, I review the recent research that demonstrates these key cognitive abilities in the plasmodial slime mould Physarum polycephalum, which has emerged as a model for non-animal cognition. I discuss the benefits and limitations of comparisons drawn between neural and non-neural systems, and the implications of common mechanisms across wide taxonomic divisions. I conclude by discussing future avenues of research that will draw the most benefit from a closer integration of Physarum and animal cognition research.

Noise-Induced Network Topologies

We analyze transport on a graph with multiple constraints and where the weight of the edges connecting the nodes is a dynamical variable. The network dynamics results from the interplay between a nonlinear function of the flow, dissipation, and Gaussian, additive noise. For a given set of parameters and finite noise amplitudes, the network self-organizes into one of several metastable configurations, according to a probability distribution that depends on the noise amplitude α. At a finite value α, we find a resonantlike behavior for which one network topology is the most probable stationary state. This specific topology maximizes the robustness and transport efficiency, it is reached with the maximal convergence rate, and it is not found by the noiseless dynamics. We argue that this behavior is a manifestation of noise-induced resonances in network self-organization. Our findings show that stochastic dynamics can boost transport on a nonlinear network and, further, suggest a change of paradigm about the role of noise in optimization algorithms.

Behavioural changes in slime moulds over time

Changes in behaviour over the lifetime of single-cell organisms have primarily been investigated in response to environmental stressors. However, growing evidence suggests that unicellular organisms undergo behavioural changes throughout their lifetime independently of the external environment. Here we studied how behavioural performances across different tasks vary with age in the acellular slime mould Physarum polycephalum. We tested slime moulds aged from 1 week to 100 weeks. First, we showed that migration speed decreases with age in favourable and adverse environments. Second, we showed that decision making and learning abilities do not deteriorate with age. Third, we revealed that old slime moulds can recover temporarily their behavioural performances if they go throughout a dormant stage or if they fuse with a young congener. Last, we observed the response of slime mould facing a choice between cues released by clone mates of different age. We found that both old and young slime moulds are attracted preferentially toward cues left by young slime moulds. Although many studies have studied behaviour in unicellular organisms, few have taken the step of looking for changes in behaviour over the lifetime of individuals. This study extends our knowledge of the behavioural plasticity of single-celled organisms and establishes slime moulds as a promising model to investigate the effect of ageing on behaviour at the cellular level. This article is part of a discussion meeting issue 'Collective behaviour through time'.

Memory capacity of adaptive flow networks

Biological flow networks adapt their network morphology to optimize flow while being exposed to external stimuli from different spatial locations in their environment. These adaptive flow networks retain a memory of the stimulus location in the network morphology. Yet, what limits this memory and how many stimuli can be stored are unknown. Here, we study a numerical model of adaptive flow networks by applying multiple stimuli subsequently. We find strong memory signals for stimuli imprinted for a long time into young networks. Consequently, networks can store many stimuli for intermediate stimulus duration, which balance imprinting and aging.

A survey on physarum polycephalum intelligent foraging behaviour and bio-inspired applications

In recent years, research on Physarum polycephalum has become more popular after Nakagaki (AIR 407: 6803-470, 2000) performed their famous experiment showing that Physarum was able to find the shortest route through a maze. Subsequent researches have confirmed the ability of Physarum-inspired algorithms to solve a wide range of real-world applications. In contrast to previous reviews that either focus on biological aspects or bio-inspired applications, here we present a comprehensive review that highlights recent Physarum polycephalum biological aspects, mathematical models, and Physarum bio-inspired algorithms and their applications. The novelty of this review stems from our exploration of Physarum intelligent behaviour in competition settings. Further, we have presented our new model to simulate Physarum in competition, where multiple Physarum interact with each other and with their environments. The bio-inspired Physarum in competition algorithms proved to have great potentials for future research.

Optimal control of the reaction-diffusion process on directed networks

Reaction-diffusion processes organized in networks have attracted much interest in recent years due to their applications across a wide range of disciplines. As one type of most studied solutions of reaction-diffusion systems, patterns broadly exist and are observed from nature to human society. So far, the theory of pattern formation has made significant advances, among which a novel class of instability, presented as wave patterns, has been found in directed networks. Such wave patterns have been proved fruitful but significantly affected by the underlying network topology, and even small topological perturbations can destroy the patterns. Therefore, methods that can eliminate the influence of network topology changes on wave patterns are needed but remain uncharted. Here, we propose an optimal control framework to steer the system generating target wave patterns regardless of the topological disturbances. Taking the Brusselator model, a widely investigated reaction-diffusion model, as an example, numerical experiments demonstrate our framework's effectiveness and robustness. Moreover, our framework is generally applicable, with minor adjustments, to other systems that differential equations can depict.

Interplay of periodic dynamics and noise: Insights from a simple adaptive system

We study the dynamics of a simple adaptive system in the presence of noise and periodic damping. The system is composed by two paths connecting a source and a sink, and the dynamics is governed by equations that usually describe food search of the paradigmatic Physarum polycephalum. In this work we assume that the two paths undergo damping whose relative strength is periodically modulated in time, and we analyze the dynamics in the presence of stochastic forces simulating Gaussian noise. We identify different responses depending on the modulation frequency and on the noise amplitude. At frequencies smaller than the mean dissipation rate, the system tends to switch to the path which minimizes dissipation. Synchronous switching occurs at an optimal noise amplitude which depends on the modulation frequency. This behavior disappears at larger frequencies, where the dynamics can be described by the time-averaged equations. Here we find metastable patterns that exhibit the features of noise-induced resonances.

A post-transcriptional regulon controlled by TtpA, the single tristetraprolin family member expressed in Dictyostelium discoideum

Post-transcriptional processes mediated by mRNA binding proteins represent important control points in gene expression. In eukaryotes, mRNAs containing specific AU-rich motifs are regulated by binding of tristetraprolin (TTP) family tandem zinc finger proteins, which promote mRNA deadenylation and decay, partly through interaction of a conserved C-terminal CNOT1 binding (CNB) domain with CCR4-NOT protein complexes. The social ameba Dictyostelium discoideum shared a common ancestor with humans more than a billion years ago, and expresses only one TTP family protein, TtpA, in contrast to three members expressed in humans. Evaluation of ttpA null-mutants identified six transcripts that were consistently upregulated compared to WT during growth and early development. The 3'-untranslated regions (3'-UTRs) of all six 'TtpA-target' mRNAs contained multiple TTP binding motifs (UUAUUUAUU), and one 3'-UTR conferred TtpA post-transcriptional stability regulation to a heterologous mRNA that was abrogated by mutations in the core TTP-binding motifs. All six target transcripts were upregulated to similar extents in a C-terminal truncation mutant, in contrast to less severe effects of analogous mutants in mice. All six target transcripts encoded probable membrane proteins. In Dictyostelium, TtpA may control an 'RNA regulon', where a single RNA binding protein, TtpA, post-transcriptionally co-regulates expression of several functionally related proteins.

Adaptive behaviour and learning in slime moulds: the role of oscillations

The slime mould Physarum polycephalum, an aneural organism, uses information from previous experiences to adjust its behaviour, but the mechanisms by which this is accomplished remain unknown. This article examines the possible role of oscillations in learning and memory in slime moulds. Slime moulds share surprising similarities with the network of synaptic connections in animal brains. First, their topology derives from a network of interconnected, vein-like tubes in which signalling molecules are transported. Second, network motility, which generates slime mould behaviour, is driven by distinct oscillations that organize into spatio-temporal wave patterns. Likewise, neural activity in the brain is organized in a variety of oscillations characterized by different frequencies. Interestingly, the oscillating networks of slime moulds are not precursors of nervous systems but, rather, an alternative architecture. Here, we argue that comparable information-processing operations can be realized on different architectures sharing similar oscillatory properties. After describing learning abilities and oscillatory activities of P. polycephalum, we explore the relation between network oscillations and learning, and evaluate the organism's global architecture with respect to information-processing potential. We hypothesize that, as in the brain, modulation of spontaneous oscillations may sustain learning in slime mould. This article is part of the theme issue 'Basal cognition: conceptual tools and the view from the single cell'.

Substrate and cell fusion influence on slime mold network dynamics

The acellular slime mold Physarum polycephalum provides an excellent model to study network formation, as its network is remodelled constantly in response to mass gain/loss and environmental conditions. How slime molds networks are built and fuse to allow for efficient exploration and adaptation to environmental conditions is still not fully understood. Here, we characterize the network organization of slime molds exploring homogeneous neutral, nutritive and adverse environments. We developed a fully automated image analysis method to extract the network topology and followed the slime molds before and after fusion. Our results show that: (1) slime molds build sparse networks with thin veins in a neutral environment and more compact networks with thicker veins in a nutritive or adverse environment; (2) slime molds construct long, efficient and resilient networks in neutral and adverse environments, whereas in nutritive environments, they build shorter and more centralized networks; and (3) slime molds fuse rapidly and establish multiple connections with their clone-mates in a neutral environment, whereas they display a late fusion with fewer connections in an adverse environment. Our study demonstrates that slime mold networks evolve continuously via pruning and reinforcement, adapting to different environmental conditions.

Physarum inspires research beyond biomimetic algorithms: Reply to comments on "Does being multi-headed make you better at solving problems?"

We look at a recent expansion of Physarum research from inspiring biomimetic algorithms to serving as a model organism in the evolutionary study of perception, memory, learning, and decision making.