Mathematical Model for Rhythmic Protoplasmic Movement in the True Slime Mold

The plasmodium of the true slime mold Physarum polycephalum is a large amoeboid organism that displays “smart” behavior such as chemotaxis and the ability to solve mazes and geometrical puzzles. These amoeboid behaviors are based on the dynamics of the viscoelastic protoplasm and its biochemical rhythms. By incorporating both these aspects, we constructed a mathematical model for the dynamics of the organism as a first step towards understanding the relation between protoplasmic movement and its unusual abilities. We tested the validity of the model by comparing it with physiological observation. Our model reproduces fundamental characteristics of the spatio-temporal pattern of the rhythmic movement: (1) the antiphase oscillation between frontal tip and rear when the front is freely extending; (2) the asynchronous oscillation pattern when the front is not freely extending; and (3) the formation of protoplasmic mounds over a longer time scale. Both our model and physiological observation suggest that cell stiffness plays a primary role in plasmodial behaviors, in contrast to the conventional theory of coupled oscillator systems.     

Smart network solutions in an amoeboid organism

We present evidence that the giant amoeboid organism, the true slime mold, constructs a network appropriate for maximizing nutrient uptake. The body of the plasmodium of Physarum polycephalum contains a network of tubular elements by means of which nutrients and chemical signals circulate through the organism. When food pellets were presented at different points on the plasmodium it accumulated at each pellet with a few tubes connecting the plasmodial concentrations. The geometry of the network depended on the positions of the food sources. Statistical analysis showed that the network geometry met the multiple requirements of a smart network: short total length of tubes, close connections among all the branches (a small number of transit food-sites between any two food-sites) and tolerance of accidental disconnection of the tubes. These findings indicate that the plasmodium can achieve a better solution to the problem of network configuration than is provided by the shortest connection of Steiner's minimum tree.     

The autowave electromechanical activity of the <Emphasis Type="Italic">Physarum polycephalum</Emphasis> plasmodium

The aim of this work is to clarify the role of the electrical activity of the Physarum polycephalum plasmodium in the control of the contractile activity and self-organization of the directed locomotion. This single-celled organism with a non-excitable membrane is a classic object that is used in studies of amoeboid motility. Its patterns of motor behavior and signal systems are common for many tissue cells. The presence of 50 mM KCl in an agar substrate under half of a separate plasmodial strand strongly inhibits the formation of the frontal zone and leads to sharp morphological polarization of the strand, which suggests the involvement of electrical processes in the autowave self-organization of the plasmodial structure. The gigantic sizes of the plasmodium make it possible to record its electrical activity simultaneously at different parts of the cell. It has been established that potentials and currents at parts of the plasmodium that are distant from each other oscillate synchronously and differ only in the shape of the signals, probably due to differences in the phases or the number of excited harmonics. We recorded currents (~50 pA) of single ion channels of the plasmodial membrane using the classical local voltage-clamp method. It has been found that the oscillation spectrum of the current that is generated by the plasmodium has high-frequency fluctuations, which are probably connected with periodic detachments of the membrane from the cytoskeleton during the formation and growth of the pseudopodia. It has been also shown that neomycin, a substrate inhibitor of phospholipase C, prevents oscillations of both the mechanical and electrical activity of the plasmodium. This is consistent with its well-established ability to inhibit mechanosensitive Ca²⁺ channels, which are apparently present in the plasmodial membrane. These data indicate the presence of a general signal system that is linked with the dynamics of the membrane- cytoskeleton association, which could be involved in the galvano- and chemotaxis of amoeboid cells.     

A mathematical model for adaptive transport network in path finding by true slime mold

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.     

Spontaneous deadlock breaking on amoeba-based neurocomputer

Any artificial concurrent computing system involves a potential risk of “deadlock” that its multiple processes sharing common computational resources are stuck in starved conditions, if simultaneous accesses of the processes to the resources were unconditionally permitted. To avoid the deadlock, it is necessary to set up some form of central control protocol capable of appropriately regulating the resource allocation. On the other hand, many decentralized biological systems also perform concurrent computing based on interactions of components sharing limited amounts of available resources. Despite the absence of a central control unit, they appear to be free from the deadlock implying their death, as long as they are alive. Should we consider that biological computing paradigms are essentially different from artificial ones? Here we employ a photosensitive amoeboid cell known as a model organism for studying cellular information processing and construct an experimental system to explore how the amoeba copes with deadlock-like situations induced by optical feedback control. The feedback control is implemented by a recurrent neural network algorithm for leading the amoeba to solve a particular constraint satisfaction problem. We show that the amoeba is capable of breaking through the deadlock-like situations because its oscillating cellular membrane spontaneously produces a wide variety of spatiotemporal patterns. The result implies that our system can be developed to a neurocomputer that works as logical circuit, associative memory device, combinatorial optimization problem solver, and chaotic computer capable of spontaneous transition among multiple solutions.     

Stability analysis of higher-order neural networks for combinatorial optimization

Recurrent neural networks with higher order connections, from here on referred to as higher-order neural networks (HONNs), may be used for the solution of combinatorial optimization problems. In Ref. 5 a mapping of the traveling salesman problem (TSP) onto a HONN of arbitrary order was developed, thereby creating a family of related networks that can be used to solve the TSP. In this paper, we explore the trade-off between network complexity and quality of solution that is made available by the HONN mapping of the TSP. The trade-off is investigated by undertaking an analysis of the stability of valid solutions to the TSP in a HONN of arbitrary order. The techniques used to perform the stability analysis are not new, but have been widely used elsewhere in the literature. The original contribution in this paper is the application of these techniques to a HONN of arbitrary order used to solve the TSP. The results of the stability analysis show that the quality of solution is improved by increasing the network complexity, as measured by the order of the network. Furthermore, it is shown that the Hopfield network, as the simplest network in the family of higher-order networks, is expected to produce the poorest quality of solution.     

Speed–accuracy trade-offs during foraging decisions in the acellular slime mould Physarum polycephalum

Speed–accuracy trade-offs (SATs) are thought to be a fundamental feature of biological information processing, yet most evidence of SATs comes from animals. Here, we examine SATs in the foraging decisions of an acellular, amoeboid organism: the slime mould Physarum polycephalum. Slime moulds were given a simple discrimination task: selecting the highest-quality food item from a set of three options. We investigated the effect of two stressors, light exposure and hunger, on the speed and accuracy of decision-making. We also examined the effect of task difficulty. When given a difficult discrimination task, stressed individuals tend to make faster decisions than non-stressed individuals. This effect was reversed in plasmodia given easy discrimination tasks, where stressed individuals made slower decisions than non-stressed individuals. We found evidence of SATs, such that individuals who made fast decisions were more likely to make costly errors by selecting the worst possible food option. Our results suggest that SATs occur in a wider range of taxa than previously considered.     

Emergence of morphological order in the network formation of Physarum polycephalum

Emergence in a system appears through the interaction of its components, giving rise to higher order or complexity in the system. We tested for the presence of emergent properties in a biological system using the simplest biological entity of a unicellular organism; the plasmodium of Physarum polycephalum, a giant unicellular amoeboid organism that forms a network-like tubular structure connecting its food sources. We let two plasmodium networks within a single cell interact with each other, and observed how the intracellular interaction affected the morphologenesis of the plasmodium networks. We found that the two networks developed homologous morphology. We further discuss the presence of autonomous and emergent properties in homologous network formation.     

Peroxisomal ABC transporters

Peroxisomes perform a range of different functions, dependent upon organism, tissue type, developmental stage or environmental conditions, many of which are connected with lipid metabolism. This review summarises recent research on ATP binding cassette (ABC) transporters of the peroxisomal membrane (ABC subfamily D) and their roles in plants, fungi and animals. Analysis of mutants has revealed that peroxisomal ABC transporters play key roles in specific metabolic and developmental functions in different organisms. A common function is import of substrates for beta-oxidation but much remains to be determined concerning transport substrates and mechanisms which appear to differ significantly between phyla.     

A new primitive protozoan devouring centric diatoms in the plankton

A new primitive protozoan Asterocaelum algophilum gen. et sp. nov., is described from the plankton of Loch Leven, Scotland where it was found primarily feeding on the centric diatoms Stephanodiscus rotula (Kütz) Hendey and Cyclotella pseudostelligera Hustedt. Stages in its life cycle consist of a trophic amoeba, a cyst from which the protoplasm emerges as one or several units similar to the amoeboid stage and a resting cyst containing a double walled resting spore. The amoeboid stage produces numerous clear hyaline pseudopodia which are often broad based and taper apically and within which a core of denser material, possibly an axial filament, is sometimes seen. The cyst and resting cyst stages externally bear long tapering empty spines formed by the laying down of a wall and subsequent emptying of the protoplasm from a number of rather stiff radiating processes produced by the amoeboid stage. All external surfaces are surrounded by an envelope of mucilage and the walls laid down by this organism give a positive reaction for cellulose. The similarity of its life cycle to that of the vampyrellids is noted.     

Dispersion relation in oscillatory reaction-diffusion systems with self-consistent flow in true slime mold

In the large amoeboid organism Physarum, biochemical oscillators are spatially distributed throughout the organism and their collective motion exhibits phase waves, which carry physiological signals. The basic nature of this wave behaviour is not well-understood because, to date, an important effect has been neglected, namely, the shuttle streaming of protoplasm which accompanies the biochemical rhythms. Here we study the effects of self-consistent flow on the wave behaviour of oscillatory reaction-diffusion models proposed for the Physarum plasmodium, by means of numerical simulation for the dispersion relation and weakly nonlinear analysis for derivation of the phase equation. We conclude that the flow term is able to increase the speed of phase waves (similar to elongation of wave length). We compare the theoretical consequences with real waves observed in the organism and also point out the physiological roles of these effects on control mechanisms of intracellular communication.     

When to use public information for breeding habitat selection? The role of environmental predictability and density dependence

To select their future breeding site, individuals usually have to assess local quality by using environmental cues. One optimal cue may be ‘public information’, the local reproductive success of conspecifics in a breeding patch (patch reproductive success) because it integrates the effect of all environmental factors on breeding success. However, the quality of information conveyed by patch reproductive success is likely to depend on (1) environmental predictability and (2) interactions between individuals. We investigated how these two factors, ignored by previous models, affect the performance of individuals using patch reproductive success for breeding habitat selection compared with other information. We built a two-patch, game-theoretical model to compare the success of a strategy of breeding habitat selection based on patch reproductive success relative to four other strategies: (1) random patch choice; (2) philopatry; (3) choice based on the presence of conspecifics the previous year (conspecific attraction); and (4) choice based on intrinsic patch quality the previous year. The results illustrate how the efficiency of strategies in tracking variations in patch quality depend on environmental predictability and costs linked to density dependence, themselves linked to the dynamics of spatial aggregation of individuals. In particular, strategies based on measures of patch reproductive success perform the best for intermediate and high temporal predictability of patch quality, whereas philopatry and conspecific attraction then perform poorly. The ‘conspecific attraction’ strategy always coexists with other strategies by efficiently parasitizing the information they use. We discuss the implications of a better understanding of breeding habitat selection behaviours for evolutionary and conservation biology. Copyright 2003 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved.      

The life cycle of the amoeboid alga Synchroma grande (Synchromophyceae, Heterokontophyta)--highly adapted yet equally equipped for rapid diversification in benthic habitats

Synchroma grande (Synchromophyceae, Heterokontophyta) is a marine amoeboid alga, which was isolated from a benthic habitat. This species has sessile cell stages (amoeboid cells with lorica and cysts) and non‐sessile cell stages (migrating and floating amoebae) during its life cycle. The different cell types and their transitions within the life cycle are described, as are their putative functions. Cell proliferation was observed only in cells attached to the substrate but not in free‐floating or migrating cells. We also characterised the phagotrophy of the meroplasmodium in comparison to other amoeboid algae and the formation of the lorica. The functional adaptations of S. grande during its life cycle were compared to the cell stages of other amoeboid algae of the red and green chloroplast lineages. S. grande was found to be highly adapted to the benthic habitat. One sexual and two asexual reproductive strategies (haplo‐diploid life cycle) support the ability of this species to achieve rapid diversification and high adaptivity in its natural habitat.     

High-Speed Imaging of Amoeboid Movements Using Light-Sheet Microscopy

Light-sheet microscopy has been developed as a powerful tool for live imaging in biological studies. The efficient illumination of specimens using light-sheet microscopy makes it highly amenable to high-speed imaging. We therefore applied this technology to the observation of amoeboid movements, which are too rapid to capture with conventional microscopy. To simplify the setup of the optical system, we utilized the illumination optics from a conventional confocal laser scanning microscope. Using this set-up we achieved high-speed imaging of amoeboid movements. Three-dimensional images were captured at the recording rate of 40 frames/s and clearly outlined the fine structures of fluorescent-labeled amoeboid cellular membranes. The quality of images obtained by our system was sufficient for subsequent quantitative analysis for dynamics of amoeboid movements. This study demonstrates the application of light-sheet microscopy for high-speed imaging of biological specimens.     

A diffusion-based theory of organism dispersal in heterogeneous populations

We develop a general theory of organism movement in heterogeneous populations that can explain the leptokurtic movement distributions commonly measured in nature. We describe population heterogeneity in a state-structured framework, employing advection-diffusion as the fundamental movement process of individuals occupying different movement states. Our general analysis shows that population heterogeneity in movement behavior can be defined as the existence of different movement states and among-individual variability in the time individuals spend in these states. A presentation of moment-based metrics of movement illustrates the role of these attributes in general dispersal processes. We also present a special case of the general theory: a model population composed of individuals occupying one of two movement states with linear transitions, or exchange, between the two states. This two-state "exchange model" can be viewed as a correlated random walk and provides a generalization of the telegraph equation. By exploiting the main result of our general analysis, we characterize the exchange model by deriving moment-based metrics of its movement process and identifying an analytical representation of the model's time-dependent solution. Our results provide general and specific theoretical explanations for empirical patterns in organism movement; the results also provide conceptual and analytical bases for extending diffusion-based dispersal theory in several directions, thereby facilitating mechanistic links between individual behavior and spatial population dynamics.     

A second, expressed thrombospondin gene (Thbs2) exists in the mouse genome.

The diverse and occasionally conflicting properties described for the extracellular, cell surface-associated protein thrombospondin (TSP) have raised the possibility that functionally distinct forms of the protein exist in the same organism. We have isolated and characterized a partial cDNA clone for mouse TSP that is clearly homologous to, but distinct from, the coding sequence for mouse TSP deduced from a mouse genomic clone (Bornstein, P., Alfi, D., Devarayalu, L., Framson, P., and Li, P. (1990) J. Biol. Chem. 265, 16691-16698). This second TSP, which we term thrombospondin 2, is the product of a separate gene (Thbs2) and is expressed in a variety of mouse tissues in a pattern that differs from that for TSP1. Based on their translated amino acid sequences, it seems likely that TSP1 and TSP2 will be found to have both common and unique properties and that the functional consequences of TSP production will reflect the ratio of the levels of these two related proteins.     

Spatial pattern of long-distance symplasmic transport and communication in trees

Symplasmic short- and long-distance communication may be regulated at different levels of plant body organization. It depends on cell-to-cell transport modulated by plasmodesmata conductivity and frequency but above all on morphogenetic fields that integrate a plant at the supracellular level. Their control of physiological and developmental processes is especially important in trees, where the continuum consists of 3-dimensional systems of: 1) stem cells in cambium, and 2) living parenchyma cells in the secondary conductive tissues. We found that long-distance symplasmic transport in trees is spatially regulated. Uneven distribution of fluorescent tracer in cambial cells along the branches examined illustrates an unknown intrinsic phenomenon that can possibly be important for plant organism integration. Here we illustrate the spatial dynamics of symplasmic transport in cambium, test and exclude the role of callose in its regulation, and discuss the mechanism that could possibly be responsible for the maintenance of this spatial pattern.     

ABC inference of multi‐population divergence with admixture from unphased population genomic data

Rapidly developing sequencing technologies and declining costs have made it possible to collect genome‐scale data from population‐level samples in nonmodel systems. Inferential tools for historical demography given these data sets are, at present, underdeveloped. In particular, approximate Bayesian computation (ABC) has yet to be widely embraced by researchers generating these data. Here, we demonstrate the promise of ABC for analysis of the large data sets that are now attainable from nonmodel taxa through current genomic sequencing technologies. We develop and test an ABC framework for model selection and parameter estimation, given histories of three‐population divergence with admixture. We then explore different sampling regimes to illustrate how sampling more loci, longer loci or more individuals affects the quality of model selection and parameter estimation in this ABC framework. Our results show that inferences improved substantially with increases in the number and/or length of sequenced loci, while less benefit was gained by sampling large numbers of individuals. Optimal sampling strategies given our inferential models included at least 2000 loci, each approximately 2 kb in length, sampled from five diploid individuals per population, although specific strategies are model and question dependent. We tested our ABC approach through simulation‐based cross‐validations and illustrate its application using previously analysed data from the oak gall wasp, Biorhiza pallida.     

Dynamics of ATP-binding cassette contribute to allosteric control, nucleotide binding and energy transduction in ABC transporters

ATP-binding cassette (ABC) transporters move solutes across membranes and are associated with important diseases, including cystic fibrosis and multi-drug resistance. These molecular machines are energized by their charateristic ABC modules, molecular engines fuelled by ATP hydrolysis. A solution NMR study of a model ABC, Methanococcus jannaschii protein MJ1267, reveals that ADP-Mg binding alters the flexibilities of key ABC motifs and induces allosteric changes in conformational dynamics in the LivG insert, over 30A away from the ATPase active site. (15)N spin relaxation data support a "selected-fit" model for nucleotide binding. Transitions between rigidity and flexibility in key motifs during the ATP hydrolysis cycle may be crucial to mechanochemical energy transduction in ABC transporters. The restriction of correlated protein motions is likely a central mechanism for allosteric communications. Comparison between dynamics data from NMR and X-ray crystallography reveals their overall consistency and complementarity.     

Functional hot spots in human ATP-binding cassette transporter nucleotide binding domains

The human ATP‐binding cassette (ABC) transporter superfamily consists of 48 integral membrane proteins that couple the action of ATP binding and hydrolysis to the transport of diverse substrates across cellular membranes. Defects in 18 transporters have been implicated in human disease. In hundreds of cases, disease phenotypes and defects in function can be traced to nonsynonymous single nucleotide polymorphisms (nsSNPs). The functional impact of the majority of ABC transporter nsSNPs has yet to be experimentally characterized. Here, we combine experimental mutational studies with sequence and structural analysis to describe the impact of nsSNPs in human ABC transporters. First, the disease associations of 39 nsSNPs in 10 transporters were rationalized by identifying two conserved loops and a small α‐helical region that may be involved in interdomain communication necessary for transport of substrates. Second, an approach to discriminate between disease‐associated and neutral nsSNPs was developed and tailored to this superfamily. Finally, the functional impact of 40 unannotated nsSNPs in seven ABC transporters identified in 247 ethnically diverse individuals studied by the Pharmacogenetics of Membrane Transporters consortium was predicted. Three predictions were experimentally tested using human embryonic kidney epithelial (HEK) 293 cells stably transfected with the reference multidrug resistance transporter 4 and its variants to examine functional differences in transport of the antiviral drug, tenofovir. The experimental results confirmed two predictions. Our analysis provides a structural and evolutionary framework for rationalizing and predicting the functional effects of nsSNPs in this clinically important membrane transporter superfamily.