Emergence of behaviour in a self-organized living matter network.

What is the origin of behaviour? Although typically associated with a nervous system, simple organisms also show complex behaviours. Among them, the slime mold Physarum polycephalum, a giant single cell, is ideally suited to study emergence of behaviour. Here, we show how locomotion and morphological adaptation behaviour emerge from self-organized patterns of rhythmic contractions of the actomyosin lining of the tubes making up the network-shaped organism. We quantify the spatio-temporal contraction dynamics by decomposing experimentally recorded contraction patterns into spatial contraction modes. Notably, we find a continuous spectrum of modes, as opposed to a few dominant modes. Our data suggests that the continuous spectrum of modes allows for dynamic transitions between a plethora of specific behaviours with transitions marked by highly irregular contraction states. By mapping specific behaviours to states of active contractions, we provide the basis to understand behaviour's complexity as a function of biomechanical dynamics.

Excitable dynamics of Physarum polycephalum plasmodial nodes under chemotaxis.

Recent results show that the chemotactic response of uni-cellular decentralized systems such as amoeboid and mammalian cells, is excitable. The same observation has not yet been reported for multi-nucleated decentralized biological systems. Here we present experimental results that shows the Physarum polycephalum plasmodial nodes spatio-temporal chemotactic dynamics as an excitable response. We found a highly optimized signal synthesis method wherein the Physarum nodes employ two intensity thresholds to properly navigate the chemoattractant field and generate corresponding spike dynamics in the node count. The node spike dynamics was found to correspond to the polarized-depolarized transition in the Physarum polycephalum morphology. Validation of our experimental observations via Brownian lattice simulations yields the same quantitative results with our experiments.

Fluid flows shaping organism morphology.

A dynamic self-organized morphology is the hallmark of network-shaped organisms like slime moulds and fungi. Organisms continuously reorganize their flexible, undifferentiated body plans to forage for food. Among these organisms the slime mould Physarum polycephalum has emerged as a model to investigate how an organism can self-organize their extensive networks and act as a coordinated whole. Cytoplasmic fluid flows flowing through the tubular networks have been identified as the key driver of morphological dynamics. Inquiring how fluid flows can shape living matter from small to large scales opens up many new avenues for research. This article is part of the theme issue 'Self-organization in cell biology'.

Direct transfer of learned behaviour via cell fusion in non-neural organisms.

Cell fusion is a fundamental phenomenon observed in all eukaryotes. Cells can exchange resources such as molecules or organelles during fusion. In this paper, we ask whether a cell can also transfer an adaptive response to a fusion partner. We addressed this question in the unicellular slime mould Physarum polycephalum, in which cell-cell fusion is extremely common. Slime moulds are capable of habituation, a simple form of learning, when repeatedly exposed to an innocuous repellent, despite lacking neurons and comprising only a single cell. In this paper, we present a set of experiments demonstrating that slime moulds habituated to a repellent can transfer this adaptive response by cell fusion to individuals that have never encountered the repellent. In addition, we show that a slime mould resulting from the fusion of a minority of habituated slime moulds and a majority of unhabituated ones still shows an adaptive response to the repellent. Finally, we further reveal that fusion must last a certain time to ensure an effective transfer of the behavioural adaptation between slime moulds. Our results provide strong experimental evidence that slime moulds exhibit transfer of learned behaviour during cell fusion and raise the possibility that similar phenomena may occur in other cell-cell fusion systems.

On chirality of slime mould.

Left-right patterning and lateralised behaviour is an ubiquitous aspect of plants and animals. The mechanisms linking cellular chirality to the large-scale asymmetry of multicellular structures are incompletely understood, and it has been suggested that the chirality of living cells is hardwired in their cytoskeleton. We examined the question of biased asymmetry in a unique organism: the slime mould Physarum polycephalum, which is unicellular yet possesses macroscopic, complex structure and behaviour. In laboratory experiment using a T-shape, we found that Physarum turns right in more than 74% of trials. The results are in agreement with previously published studies on asymmetric movement of muscle cells, neutrophils, liver cells and growing neural filaments, and for the first time reveal the presence of consistently-biased laterality in the fungi kingdom. Exact mechanisms of the slime mould's direction preference remain unknown.

Patterns of cell thickness oscillations during directional migration of Physarum polycephalum.

The functional relationship between the velocity of cell locomotion and intracellular spatial patterns of thickness oscillations in the acellular slime mould Physarum polycephalum was studied. The freely migrating plasmodial cells of 300-800 µm length were tadpole-shaped and displayed thickness oscillations along their longitudinal (body) axis. Two distinct patterns of intracellular thickness oscillations were observed in dependence on the locomotive velocity. The first mode consisted of a single travelling wave that propagated from the rear to the front of the cell. This pattern occurred when the plasmodium migrated slowly. The second mode was a multinodal standing wave that was found during events of fast propagation. Transitions between these two types of cell thickness oscillation patterns took place in narrow propagation velocity intervals. We discuss the possible mechanism leading to these patterns, which are conjectured to modulate both the intracellular pressure and the velocity of free locomotion of the cell.

Periodic traction in migrating large amoeba of Physarum polycephalum.

The slime mould Physarum polycephalum is a giant multinucleated cell exhibiting well-known Ca(2+)-dependent actomyosin contractions of its vein network driving the so-called cytoplasmic shuttle streaming. Its actomyosin network forms both a filamentous cortical layer and large fibrils. In order to understand the role of each structure in the locomotory activity, we performed birefringence observations and traction force microscopy on excised fragments of Physarum. After several hours, these microplasmodia adopt three main morphologies: flat motile amoeba, chain types with round contractile heads connected by tubes and motile hybrid types. Each type exhibits oscillations with a period of about 1.5 min of cell area, traction forces and fibril activity (retardance) when fibrils are present. The amoeboid types show only peripheral forces while the chain types present a never-reported force pattern with contractile rings far from the cell boundary under the spherical heads. Forces are mostly transmitted where the actomyosin cortical layer anchors to the substratum, but fibrils maintain highly invaginated structures and contribute to forces by increasing the length of the anchorage line. Microplasmodia are motile only when there is an asymmetry in the shape and/or the force distribution.

Nonlinearity in cytoplasm viscosity can generate an essential symmetry breaking in cellular behaviors.

The cytoplasms of ameboid cells are nonlinearly viscous. The cell controls this viscosity by modulating the amount, localization and interactions of bio-polymers. Here we investigated how the nonlinearity infers the cellular behaviors and whether nonlinearity-specific behaviors exist. We modeled the developed plasmodium of the slime mold Physarum polycephalum as a network of branching tubes and examined the linear and nonlinear viscous cytoplasm flows in the tubes. We found that the nonlinearity in the cytoplasm׳s viscosity induces a novel type of symmetry breaking in the protoplasmic flow. We also show that symmetry breaking can play an important role in adaptive behaviors, namely, connection of behavioral modes implemented on different time scales and transportation of molecular signals from the front to the rear of the cell during cellular locomotion.

Material approximation of data smoothing and spline curves inspired by slime mould.

The giant single-celled slime mould Physarum polycephalum is known to approximate a number of network problems via growth and adaptation of its protoplasmic transport network and can serve as an inspiration towards unconventional, material-based computation. In Physarum, predictable morphological adaptation is prevented by its adhesion to the underlying substrate. We investigate what possible computations could be achieved if these limitations were removed and the organism was free to completely adapt its morphology in response to changing stimuli. Using a particle model of Physarum displaying emergent morphological adaptation behaviour, we demonstrate how a minimal approach to collective material computation may be used to transform and summarise properties of spatially represented datasets. We find that the virtual material relaxes more strongly to high-frequency changes in data, which can be used for the smoothing (or filtering) of data by approximating moving average and low-pass filters in 1D datasets. The relaxation and minimisation properties of the model enable the spatial computation of B-spline curves (approximating splines) in 2D datasets. Both clamped and unclamped spline curves of open and closed shapes can be represented, and the degree of spline curvature corresponds to the relaxation time of the material. The material computation of spline curves also includes novel quasi-mechanical properties, including unwinding of the shape between control points and a preferential adhesion to longer, straighter paths. Interpolating splines could not directly be approximated due to the formation and evolution of Steiner points at narrow vertices, but were approximated after rectilinear pre-processing of the source data. This pre-processing was further simplified by transforming the original data to contain the material inside the polyline. These exemplary results expand the repertoire of spatially represented unconventional computing devices by demonstrating a simple, collective and distributed approach to data and curve smoothing.

An active poroelastic model for mechanochemical patterns in protoplasmic droplets of Physarum polycephalum.

Motivated by recent experimental studies, we derive and analyze a two-dimensional model for the contraction patterns observed in protoplasmic droplets of Physarum polycephalum. The model couples a description of an active poroelastic two-phase medium with equations describing the spatiotemporal dynamics of the intracellular free calcium concentration. The poroelastic medium is assumed to consist of an active viscoelastic solid representing the cytoskeleton and a viscous fluid describing the cytosol. The equations for the poroelastic medium are obtained from continuum force balance and include the relevant mechanical fields and an incompressibility condition for the two-phase medium. The reaction-diffusion equations for the calcium dynamics in the protoplasm of Physarum are extended by advective transport due to the flow of the cytosol generated by mechanical stress. Moreover, we assume that the active tension in the solid cytoskeleton is regulated by the calcium concentration in the fluid phase at the same location, which introduces a mechanochemical coupling. A linear stability analysis of the homogeneous state without deformation and cytosolic flows exhibits an oscillatory Turing instability for a large enough mechanochemical coupling strength. Numerical simulations of the model equations reproduce a large variety of wave patterns, including traveling and standing waves, turbulent patterns, rotating spirals and antiphase oscillations in line with experimental observations of contraction patterns in the protoplasmic droplets.

Assessment of cell cycle phase-specific effects of zerumbone on mitotically synchronous surface cultures of Physarum polycephalum.

Zerumbone, a natural cyclic sesquiterpene, has been the focus of recent research as it has been found to exhibit selective toxicity towards cancer cells compared to normal cells. Studies on the cell cycle phase-specific effects of this interesting compound, however, remain sparse. Hence, concentration and time-dependent effects of zerumbone were evaluated employing a suitable model system, the naturally synchronous surface cultures of Physarum polycephalum. Zerumbone treatment in S, early, and late G2 phases resulted in G2 arrest. Early G2 phase exhibited the highest sensitivity (P < 0.001) to the compound. Protein profiles showed a complete inhibition of cyclin B1 expression following zerumbone treatment. Furthermore, FACS and comet analysis revealed that zerumbone inhibited DNA synthesis (P < 0.001) without being genotoxic at the concentrations tested. Differential display of mRNA showed distinct zerumbone-induced variations in transcript profiles, an analysis of which suggested a likely link between cellular networks involving stress-related gene expression and G2 arrest in P. polycephalum.

Amoeba-inspired Tug-of-War algorithms for exploration-exploitation dilemma in extended Bandit Problem.

The true slime mold Physarum polycephalum, a single-celled amoeboid organism, is capable of efficiently allocating a constant amount of intracellular resource to its pseudopod-like branches that best fit the environment where dynamic light stimuli are applied. Inspired by the resource allocation process, the authors formulated a concurrent search algorithm, called the Tug-of-War (TOW) model, for maximizing the profit in the multi-armed Bandit Problem (BP). A player (gambler) of the BP should decide as quickly and accurately as possible which slot machine to invest in out of the N machines and faces an "exploration-exploitation dilemma." The dilemma is a trade-off between the speed and accuracy of the decision making that are conflicted objectives. The TOW model 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). Owing to this nonlocal correlation, the TOW model can efficiently manage the dilemma. In this study, we extend the TOW model to apply it to a stretched variant of BP, the Extended Bandit Problem (EBP), which is a problem of selecting the best M-tuple of the N machines. We demonstrate that the extended TOW model exhibits better performances for 2-tuple-3-machine and 2-tuple-4-machine instances of EBP compared with the extended versions of well-known algorithms for BP, the ϵ-Greedy and SoftMax algorithms, particularly in terms of its short-term decision-making capability that is essential for the survival of the amoeba in a hostile environment.

[Spectral analysis of self-oscillating motility in isolated plasmodial strand of Physarum polycephalum].

In this study the experimental dependencies of the velocity of shuttle endoplasmic motion in the isolated plasmodial strand of Physarum polycephalum obtained by laser Doppler microscopy are presented. The spectral analysis of the time dependencies of the endoplasm allows obtaining two distinct harmonic components. Influence of KCN and SHAM--inhibitors of cellular respiration--leads to a complete cessation of endoplasmic motion in the strand. After removal of the inhibitors the respiratory system becomes normal, gradually restoring the activity of both harmonic oscillation sources. Based on the spectral analysis the simulated time-dependent velocity of the endoplasmic motion is rather good consistent with experimental data.

Switch-like reprogramming of gene expression after fusion of multinucleate plasmodial cells of two Physarum polycephalum sporulation mutants.

Nonlinear dynamic processes involving the differential regulation of transcription factors are considered to impact the reprogramming of stem cells, germ cells, and somatic cells. Here, we fused two multinucleate plasmodial cells of Physarum polycephalum mutants defective in different sporulation control genes while being in different physiological states. The resulting heterokaryons established one of two significantly different expression patterns of marker genes while the plasmodial halves that were fused to each other synchronized spontaneously. Spontaneous synchronization suggests that switch-like control mechanisms spread over and finally control the entire plasmodium as a result of cytoplasmic mixing. Regulatory molecules due to the large volume of the vigorously streaming cytoplasm will define concentrations in acting on the population of nuclei and in the global setting of switches. Mixing of a large cytoplasmic volume is expected to damp stochasticity when individual nuclei deliver certain RNAs at low copy number into the cytoplasm. We conclude that spontaneous synchronization, the damping of molecular noise in gene expression by the large cytoplasmic volume, and the option to take multiple macroscopic samples from the same plasmodium provide unique options for studying the dynamics of cellular reprogramming at the single cell level.

Physarum polycephalum percolation as a paradigm for topological phase transitions in transportation networks.

We study the formation of transportation networks of the true slime mold Physarum polycephalum after fragmentation by shear. Small fragments, called microplasmodia, fuse to form macroplasmodia in a percolation transition. At this topological phase transition, one single giant component forms, connecting most of the previously isolated microplasmodia. Employing the configuration model of graph theory for small link degree, we have found analytically an exact solution for the phase transition. It is generally applicable to percolation as seen, e.g., in vascular networks.

Flow-induced channel formation in the cytoplasm of motile cells.

A model is presented to explain the development of flow channels within the cytoplasm of the plasmodium of the giant amoeba Physarum polycephalum. The formation of channels is related to the development of a self-organizing tubular network in large cells. Experiments indicate that the flow of cytoplasm is involved in the development and organization of these networks, and the mathematical model proposed here is motivated by recent experiments involving the observation of development of flow channel in small cells. A model of pressure-driven flow through a polymer network is presented in which the rate of flow increases the rate of depolymerization. Numerical solutions and asymptotic analysis of the model in one spatial dimension show that under very general assumptions this model predicts the formation of channels in response to flow.

Traffic optimization in railroad networks using an algorithm mimicking an amoeba-like organism, Physarum plasmodium.

Traffic optimization of railroad networks was considered using an algorithm that was biologically inspired by an amoeba-like organism, plasmodium of the true slime mold, Physarum polycephalum. The organism developed a transportation network consisting of a tubular structure to transport protoplasm. It was reported that plasmodium can find the shortest path interconnecting multiple food sites during an adaptation process (Nakagaki et al., 2001. Biophys. Chem. 92, 47-52). By mimicking the adaptation process a path finding algorithm was developed by Tero et al. (2007). In this paper, the algorithm is newly modified for applications of traffic distribution optimization in transportation networks of infrastructure such as railroads under the constraint that the network topology is given. Application of the algorithm to a railroad in metropolitan Tokyo, Japan is demonstrated. The results are evaluated using three performance functions related to cost, traveling efficiency, and network weakness. The traffic distribution suggests that the modified Physarum algorithm balances the performances under a certain parameter range, indicating a biological process.

Rebuilding Iberian motorways with slime mould.

Plasmodium of a cellular slime mould Physarum polycephalum is a unique living substrate proved to be efficient in solving many computational problems with natural spatial parallelism. The plasmodium solves a problem represented by a configuration of source of nutrients by building an efficient foraging and intra-cellular transportation network. The transportation networks developed by the plasmodium are similar to transport networks built by social insects and simulated trails in multi-agent societies. In the paper we are attempting to answer the question "How close plasmodium of P. polycephalum approximates man-made motorway networks in Spain and Portugal, and what are the differences between existing motorway structure and plasmodium network of protoplasmic tubes?". We cut agar plates in a shape of Iberian peninsula, place oat flakes at the sites of major urban areas and analyse the foraging network developed. We compare the plasmodium network with principle motorways and also analyse man-made and plasmodium networks in a framework of planar proximity graphs.

An adaptive and robust biological network based on the vacant-particle transportation model.

A living system reveals local computing by referring to a whole system beyond the exploration-exploitation dilemma. The slime mold, Physarum polycephalum, uses protoplasmic flow to change its own outer shape, which yields the boundary condition and forms an adaptive and robust network. This observation suggests that the whole Physarum can be represented as a local protoplasmic flow system. Here, we show that a system composed of particles, which move and are modified based upon the particle transformation that contains the relationship between the parts and the whole, can emulate the network formed by Physarum. This system balances the exploration-exploitation trade-off and shows a scale-free sub-domain. By decreasing the number of particles, our model, VP-S, can emulate the Physarum adaptive network as it is attracted to a food stimulus. By increasing the number of particles, our model, VP-D, can emulate the pattern of a growing Physarum. The patterns produced by our model were compared with those of the Physarum pattern quantitatively, which showed that both patterns balance exploration with exploitation. This model should have a wide applicability to study biological collective phenomena in general.

RNase-dependent discontinuities associated with the crossovers of spontaneously formed joint DNA molecules in Physarum polycephalum.

Transient four stranded joint DNA molecules bridging sister chromatids constitute an intriguing feature of replicating genomes. Here, we studied their structure and frequency of formation in Physarum polycephalum. By "3D gels", we evidenced that they are not made of four continuous DNA strands. Discontinuities, which do not interfere with the unique propensity of the joint DNA molecules to branch migrate in vitro, are linked to the crossover, enhanced by RNaseA, and affect at most half of the DNA strands. We propose a structural model of joint DNA molecules containing ribonucleotides inserted within one strand, a gapped strand, and two continuous DNA strands. We further show that spontaneous joint DNA molecules are short-lived and are as abundant as replication forks. Our results emphasize the highly frequent formation of joint DNA molecules involving newly replicated DNA in an untreated cell and uncover a transitory mechanism connecting the sister chromatids during S phase.