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.     

Cognition of different length by Physarum polycephalum: Weber's law in an amoeboid organism

A true slime mold, the plasmodium of Physarum polycephalum has the ability to find the shortest route between two points in a labyrinth. To find the shortest route between two points, detection of the difference in lengths can be made from two aspects: the absolute difference between the lengths or the ratio of them. We found that the ratio of two lengths, rather than the absolute difference between the two lengths, was important in discriminating the difference in the two lengths by P. polycephalum. This finding indicates that an amoeboid organism detects differences in stimulus intensity as though it is constrained by Weber's law, suggesting that Weber's law is not reliant on the presence of a neural system and is used widely even in Amoebozoa.     

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.     

Obtaining multiple separate food sources: behavioural intelligence in the Physarum plasmodium

To evaluate performance in a complex survival task, we studied the morphology of the Physarum plasmodium transportation network when presented with multiple separate food sources. The plasmodium comprises a network of tubular elements through which chemical nutrient, intracellular signals and the viscous body are transported and circulated. When three separate food sources were presented, located at the vertices of a triangle, the tubular network connected them via a short pathway, which was often analogous to the mathematically shortest route known as Steiner's minimum tree (SMT). The other common network shape had high fault tolerance against accidental disconnection of the tubes and was known as cycle (CYC). Pattern selection appeared to be a bistable system involving SMT and CYC. When more than three food sources were presented, the network pattern tended to be a patchwork of SMT and CYC. We therefore concluded that the plasmodium tube network is a well designed and intelligent system.     

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.     

Control of interaction strength in a network of the true slime mold by a microfabricated structure

The plasmodium of the true slime mold, Physarum polycephalum, which shows various nonlinear oscillatory phenomena, for example, in its thickness, protoplasmic streaming and concentration of intracellular chemicals, can be regarded as a collective of nonlinear oscillators. The plasmodial oscillators are interconnected by microscale tubes whose dimensions can be closely related to the strength of interaction between the oscillators. Investigation of the collective behavior of the oscillators under the conditions in which the interaction strength can be systematically controlled gives significant information on the characteristics of the system. In this study, we proposed a living model system of a coupled oscillator system in the Physarum plasmodium. We patterned the geometry and dimensions of the microscale tube structure in the plasmodium by a microfabricated structure (microstructure). As the first step, we constructed a two-oscillator system for the plasmodium that has two wells (oscillator part) and a channel (coupling part). We investigated the oscillation behavior by monitoring the thickness oscillation of the plasmodium in the microstructure with various channel widths. It was found that the oscillation behavior of two oscillators dynamically changed depending on the channel width. Based on the results of measurements of the tube dimensions and the velocity of the protoplasmic streaming in the tube, we discuss how the channel width relates to the interaction strength of the coupled oscillator system.     

Controlling the geometry and the coupling strength of the oscillator system in plasmodium ofPhysarum polycephalum by microfabricated structure

Summary The plasmodium of the true slime moldPhysarum polycephalum, which shows various oscillatory phenomena, can be regarded as a collective of nonlinear oscillators. Partial bodies in the plasmodium, which are assumed to be nonlinear oscillators, are mutually connected by microscale tubes named plasmodial strand. The interactions among the oscillators can be strongly affected by the geometry and the dimension of the tube network. Investigation of the collective behavior under the condition that the configuration of the network can be manipulated gives significant information on the characteristics of the plasmodium from the viewpoint of nonlinear dynamics. In this study, we have developed a new method to control the geometry and the tube dimension of the plasmodium with a microfabricated structure. It is shown that the geometry of the plasmodium can be manipulated with a microstructure which is fabricated of ultrathick photoresist resin by photolithographic processes. In order to confirm that not only the geometry but also the dimension of the tubes can be controlled with the microstructure, we observed the cross section of the patterned plasmodium with a three-dimensional internal-structure microscope. By observing the oscillatory behavior of the partial bodies of the patterned plasmodium, it was confirmed that the coupling strength between two oscillators, which corresponds to the dimension of the plasmodial strand, can be controlled by the microstructure. It is concluded that the present method is suitable for further studies of the network of Physarum plasmodium as a collective nonlinear oscillator system.     

Multiple Manifold Clustering Using Curvature Constrained Path

The problem of multiple surface clustering is a challenging task, particularly when the surfaces intersect. Available methods such as Isomap fail to capture the true shape of the surface near by the intersection and result in incorrect clustering. The Isomap algorithm uses shortest path between points. The main draw back of the shortest path algorithm is due to the lack of curvature constrained where causes to have a path between points on different surfaces. In this paper we tackle this problem by imposing a curvature constraint to the shortest path algorithm used in Isomap. The algorithm chooses several landmark nodes at random and then checks whether there is a curvature constrained path between each landmark node and every other node in the neighborhood graph. We build a binary feature vector for each point where each entry represents the connectivity of that point to a particular landmark. Then the binary feature vectors could be used as a input of conventional clustering algorithm such as hierarchical clustering. We apply our method to simulated and some real datasets and show, it performs comparably to the best methods such as K-manifold and spectral multi-manifold clustering.     

Identification of retinoblastoma related genes with shortest path in a protein-protein interaction network

This paper presents a new method for identifying retinoblastoma related genes by integrating gene expression profile and shortest path in a functional linkage graph. With the existing protein-protein interaction data from STRING, a weighted functional linkage graph is constructed. 119 consistently differentially expressed genes between retinoblastoma and normal retina were obtained from the overlap of two gene expression studies of retinoblastoma. Then the shortest paths between each pair of these 119 genes were determined with Dijkstra's algorithm. Finally, all the genes present on the shortest paths were extracted and ranked according to their betweenness and the 119 shortest genes with a betweenness greater than 100 and with a p-value less than 0.05 were selected for further analysis. We also identified 53 retinoblastoma related miRNAs from published miRNA array data and most of the 238 (119 consistently differentially expressed genes and 119 shortest path genes) retinoblastoma genes were shown to be target genes of these 53 miRNAs. Interestingly, the genes we identified from both the gene expression profiles and the functional protein association network included more cancer genes than did the genes identified from the gene expression profiles alone. In addition, these genes also had greater functional similarity to the reported cancer genes than did the genes identified from the gene expression profiles alone. This study shows promising results and proves the efficiency of the proposed methods.     

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.     

Cellular and molecular analysis of plasmodium development in Physarum.

The development of an amoeba into a plasmodium involves extensive changes in cellular organisation and gene expression. The genetic basis of a number of recessive mutations that block plasmodium development has been elucidated. The stage at which development becomes abnormal has been determined for all the mutants, as has the terminal phenotype. In order to investigate the changes in gene expression that accompany plasmodium development, a cDNA library has been made using RNA isolated from cell populations in which development was occurring.     

Modulation of cellular rhythm and photoavoidance by oscillatory irradiation in the Physarum plasmodium

We studied responses of cellular rhythm and light-induced movement to periodic irradiation in a unicellular amoeboid organism, the Physarum plasmodium. The intrinsic frequency of the contraction rhythm, which is based on biochemical oscillations, became synchronized with the frequency of periodic irradiation with light when both frequencies were close enough. In order to study the role of the synchronization in light-induced movement, periodic irradiation was applied to only part of the plasmodium. The rate of avoidance of light was modulated in the frequency band in which the synchronization occurred. The synchronization property of the contraction oscillation underlies the regulation of tactic movement in plasmodium.     

Development of the Female Gametophyte in Hydrobryum griffithii (Podostemaceae)

The development of the female gametophyte in Hydrobryum griffithiiis of the Apinagia type. The chalazal megaspore nucleus of thetwo-nucleate embryo sac completely degenerates, and only themicropylar megaspore nucleus contributes to the four nucleipresent in the organized embryo sac. The female gametophyteconsists of two synergids, an egg and a haploid central cell.The latter degenerates before the entry of the pollen tube andthere is only syngamy. The nucellar cells below the embryo sacorganize into a nucellar plasmodium.     

Impact of path parameters on maze solution time

In order to compare spatial attention and visual processing capabilities of humans and rhesus macaques, we developed a visual maze task both could perform. Maze stimuli were constructed of orthogonal line segments displayed on a monitor. Each was octagonal in outline and contained a central square (the 'start box'). A single ('main') path, containing a random number of turns, extended outward from the start box, and either reached an exit in the maze's perimeter, or a blind ending within the maze. Subjects maintained ocular fixation within the start box, and indicated their judgment whether the path reached an exit or not by depressing one of two keys (humans) or foot pedals (monkeys). Successful maze solution by human subjects required a minimum viewing time. Replacing the maze with a masking stimulus after a variable interval revealed that the percent correct performance increased systematically with greater viewing time, reaching a plateau of approximately 85% correct if mazes were visible for 500 ms or more. A multiple linear regression analysis determined that the response time of both species depended upon several parameters of the main path, including the number of turns, total length, and exist status. Human and nonhuman primates required comparable time to process each turn in the path, whereas monkeys were faster than humans in processing each unit of path length. The data suggest that a covert analysis of the maze proceeds from the center outward along the main path in the absence of saccadic eye movements, and that both monkeys and humans undertake such an analysis during the solution of visual mazes.     

A weighted constraint satisfaction approach to human goal-directed decision making

When we plan for long-range goals, proximal information cannot be exploited in a blindly myopic way, as relevant future information must also be considered. But when a subgoal must be resolved first, irrelevant future information should not interfere with the processing of more proximal, subgoal-relevant information. We explore the idea that decision making in both situations relies on the flexible modulation of the degree to which different pieces of information under consideration are weighted, rather than explicitly decomposing a problem into smaller parts and solving each part independently. We asked participants to find the shortest goal-reaching paths in mazes and modeled their initial path choices as a noisy, weighted information integration process. In a base task where choosing the optimal initial path required weighting starting-point and goal-proximal factors equally, participants did take both constraints into account, with participants who made more accurate choices tending to exhibit more balanced weighting. The base task was then embedded as an initial subtask in a larger maze, where the same two factors constrained the optimal path to a subgoal, and the final goal position was irrelevant to the initial path choice. In this more complex task, participants’ choices reflected predominant consideration of the subgoal-relevant constraints, but also some influence of the initially-irrelevant final goal. More accurate participants placed much less weight on the optimality-irrelevant goal and again tended to weight the two initially-relevant constraints more equally. These findings suggest that humans may rely on a graded, task-sensitive weighting of multiple constraints to generate approximately optimal decision outcomes in both hierarchical and non-hierarchical goal-directed tasks.     

The bacterial linear motor of Spiroplasma melliferum BC3: from single molecules to swimming cells

Spiroplasma melliferum BC3 are wall-less bacteria with internal cytoskeletons. Spiroplasma, Mycoplasma and Acholeplasma belong to the Mollicutes, which represent the smallest, simplest and minimal free-living and self-replicating forms of life. The Mollicutes are motile and chemotactic. Spiroplasma cells are, in addition, helical in shape. Based on data merging, obtained by video dark-field light microscopy of live, swimming helical Spiroplasma cells and by cryoelectron microscopy, unravelling the subcellular structure and molecular organization of the cytoskeleton, we propose a functional model in which the cytoskeleton also acts as a bacterial linear motor enabling and controlling both dynamic helicity and swimming. The cytoskeleton is a flat, monolayered ribbon constructed from seven contractile fibrils (generators) capable of changing their length differentially in a co-ordinated manner. The individual, flat, paired fibrils can be viewed as chains of tetramers approximately 100 A in diameter composed of 59 kDa monomers. The cytoskeletal ribbon is attached to the inner surface of the cell membrane (but is not an integral part of it) and follows the shortest helical line on the coiled cellular tube. We show that Spiroplasma cells can be regarded, at least in some states, as near-perfect dynamic helical tubes. Thus, the analysis of experimental data is reduced to a geometrical problem. The proposed model is based on simple structural elements and functional assumptions: rigid circular rings are threaded on a flexible, helical centreline. The rings maintain their circularity and normality to the centreline at all helical states. An array of peripheral, equidistant axial lines forms a regular cylindrical grid (membrane), by crossing the lines bounding the rings. The axial and peripheral spacing correspond to the tetramer diameter and fibril width (100 A) respectively. Based on electron microscopy data, we assign seven of the axial grid lines in the model to function as contractile generators. The generators are clustered along the shortest helical paths on the cellular coil. In the model, the shortest generator coincides with the shortest helical line. The rest, progressively longer, six generators follow to the right or to the left of the shortest generator in order to generate the maximal range of lengths. A rubbery membrane is stretched over (or represented by) the three-dimensional grid to form a continuous tube. Co-ordinated, differential length changes of the generators induce the membranal cylinder to coil and uncoil reversibly. The switch of helical sense requires equalization of the generators' length, forming a straight cylindrical tube with straight generators. The helical parameters of the cell population, obtained by light microscopy, constitute several subpopulations related, most probably, to cell size and age. The range of molecular dimensions in the active cytoskeleton inferred from light microscopy and modelling agrees with data obtained by direct measurements of subunit images on electron micrographs, scanning transmission electron microscopy (STEM) and diffraction analysis of isolated ribbons. Swimming motility and chemotactic responses are carried out by one or a combination of the following: (i). reciprocating helical extension and compression ('breathing'); (ii). propagation of a deformation (kink) along the helical path; (iii). propagation of a reversal of the helical sense along the cell body; and (iv). irregular flexing and twitching, which is functionally equivalent to standard bacterial tumbling. Here, we analyse in detail only the first case (from which all the rest are derived), including switching of the helical sense.     

Ants find the shortest path: a mathematical proof

In the most basic application of Ant Colony Optimization (ACO), a set of artificial ants find the shortest path between a source and a destination. Ants deposit pheromone on paths they take, preferring paths that have more pheromone on them. Since shorter paths are traversed faster, more pheromone accumulates on them in a given time, attracting more ants and leading to reinforcement of the pheromone trail on shorter paths. This is a positive feedback process that can also cause trails to persist on longer paths, even when a shorter path becomes available. To counteract this persistence on a longer path, ACO algorithms employ remedial measures, such as using negative feedback in the form of uniform evaporation on all paths. Obtaining high performance in ACO algorithms typically requires fine tuning several parameters that govern pheromone deposition and removal. This paper proposes a new ACO algorithm, called EigenAnt, for finding the shortest path between a source and a destination, based on selective pheromone removal that occurs only on the path that is actually chosen for each trip. We prove that the shortest path is the only stable equilibrium for EigenAnt, which means that it is maintained for arbitrary initial pheromone concentrations on paths, and even when path lengths change with time. The EigenAnt algorithm uses only two parameters and does not require them to be finely tuned. Simulations that illustrate these properties are provided.     

STUDIES IN THE DYNAMICS OF HISTOGENESIS : I. TENSION OF DIFFERENTIAL GROWTH AS A STIMULUS TO MYOGENESIS.

1. The region of most active mitosis per mm. of cross-section in the intestine is the entodermal epithelial tube. The mitotic figures primarily follow the path of a right-handed helix. In one of the twenty embryos the mitotic figures describe the path of a right-handed helix. 2. The region of least active or relatively passive growth per mm. of cross-section is the mesenchyme, derived from the splanchnic mesoderm surrounding the epithelial tube. 3. The rapid expansion, due to epithelial growth in a rotating spiral manner, of the intestinal lumen is greater than the activity manifest in the surrounding mesenchyme. This causes a pressure in the latter resulting in a flattening and elongation of the mesenchymal cells. The successive changes in shape of these cells through the spherical, ellipsoidal, and spindle cellular phases are seen. The mesenchymal wall decreases in thickness, due to tension caused by epithelial tubular dilation. 4. The rotating spiral growth of the epithelial cells causes the formation of a series of mesenchymal cellular and fibrillar concentric rings due to the centripetal force of the former. 5. The circular, smooth muscle cells are differentiated in the outer, more condensed margins of the ring. At these points the developing tensional stresses are greater than within the ring. 6. The inner circular smooth muscle coat is the first one differentiated and is incident to the rapid growth of the epithelial tube in diameter. The former soon tends to restrict the growth of the epithelial tube in diameter. The tube, pursuing the lines of least resistance, grows in length. During the period of rapid growth in length the outer longitudinal muscle coat is in the process of formation. 7. The tensional stresses to which the elongated strained mesenchymal cells are subjected appear to be a dynamic stimulus to smooth muscle differentiation. 8. From this study of a closely graded and progressive series of sections of intestinal development, the conclusion is drawn that muscle tissue is not self-differentiating, in the strict sense of the term, but that the tension of differential growth acts as the stimulus to smooth muscle differentiation.     

Identification of three genes expressed primarily during development in Physarum polycephalum

During the life cycle of Physarum polycephalum, uninucleate amoebae develop into multinucleate syncytial plasmodia. These two cell types differ greatly in cellular organisation, behaviour and gene expression. Classical genetic analysis has identified the mating-type gene, matA, as the key gene controlling the initiation of plasmodium development, but nothing is known about the molecular events controlled by matA. In order to identify genes involved in regulating plasmodium formation, we constructed a subtracted cDNA library from cells undergoing development. Three genes that have their highest levels of expression during plasmodium development were identified: redA, redB (regulated in development) and mynD (myosin). Both redA and redB are single-copy genes and are not members of gene families. Although redA has no significant sequence similarities to known genes, redB has sequence similarity to invertebrate sarcoplasmic calcium-binding proteins. The mynD gene is closely related to type II myosin heavy-chain genes from many organisms and is one of a family of type II myosin genes in P. polycephalum. Our results indicate that many more red genes remain to be identified, some of which may play key roles in controlling plasmodium formation. Received: 21 June 1999 / Accepted: 17 August 1999     

多头绒泡菌肌球蛋白的纯化及性质的研究

从多头绒泡菌中纯化了肌球蛋白,并对其亚基组成及ＡＴＰ酶性质进行了研究。该肌球蛋白是由一种重链（２２５ｋＤ）和两种轻链（２０ｋＤ,１７．５ｋＤ）组成的大分子,其亚基之比为ＨＣ：ＬＣ１：ＬＣ２＝２：４：２。兔肌Ｆ－肌动蛋白能较大激活粘菌肌球蛋白ＡＴＰ酶活性,Ｃａ~（２＋）离子也能提高其活性,Ｍｇ~（２＋）离子无明显影响。钒酸盐,碘乙酸,对氯汞苯甲酸对其ＡＴＰ酶活性有显著抑制作用。