Scattered migrating colony formation in the filamentous cyanobacterium, Pseudanabaena sp. NIES-4403.

BACKGROUND: Bacteria have been reported to exhibit complicated morphological colony patterns on solid media, depending on intracellular, and extracellular factors such as motility, cell propagation, and cell-cell interaction. We isolated the filamentous cyanobacterium, Pseudanabaena sp. NIES-4403 (Pseudanabaena, hereafter), that forms scattered (discrete) migrating colonies on solid media. While the scattered colony pattern has been observed in some bacterial species, the mechanism underlying such a pattern still remains obscure. RESULTS: We studied the morphology of Pseudanabaena migrating collectively and found that this species forms randomly scattered clusters varying in size and further consists of a mixture of comet-like wandering clusters and disk-like rotating clusters. Quantitative analysis of the formation of these wandering and rotating clusters showed that bacterial filaments tend to follow trajectories of previously migrating filaments at velocities that are dependent on filament length. Collisions between filaments occurred without crossing paths, which enhanced their nematic alignments, giving rise to bundle-like colonies. As cells increased and bundles aggregated, comet-like wandering clusters developed. The direction and velocity of the movement of cells in comet-like wandering clusters were highly coordinated. When the wandering clusters entered into a circular orbit, they turned into rotating clusters, maintaining a more stable location. Disk-like rotating clusters may rotate for days, and the speed of cells within a rotating cluster increases from the center to the outmost part of the cluster. Using a mathematical modeling with simplified assumption we reproduced some features of the scattered pattern including migrating clusters. CONCLUSION: Based on these observations, we propose that Pseudanabaena forms scattered migrating colonies that undergo a series of transitions involving several morphological patterns. A simplified model is able to reproduce some features of the observed migrating clusters.

Mathematical model for cell competition: Predator-prey interactions at the interface between two groups of cells in monolayer tissue.

The phenomenon of 'cell competition' has been implicated in the normal development and maintenance of organs, such as in the regulation of organ size and suppression of neoplastic development. In cell competition, one group of cells competes with another group through an interaction at their interface. Which cell group "wins" is governed by a certain relative fitness within the cells. However, this idea of cellular fitness has not been clearly defined. We construct two types of mathematical models to describe this phenomenon of cell competition by considering the interaction at the interface as a predator-prey type interaction in a monolayer tissue such as epithelium. Both of these models can reproduce several typical experimental observations involving systems of mutant cells (losers) and normal cells (winners). By analyzing one of the model and defining an index for the degree of fitness in groups of cells, we show that the fate of each group mainly depends on the relative carrying capacities of certain resources and the strength of the predator-prey interaction at the interface. This contradicts the classical hypothesis in which the relative proliferation rate determines the winner.

Emergence of traveling waves in the zebrafish segmentation clock.

The spatial and temporal periodicity of somite formation is controlled by the segmentation clock, in which numerous cells cyclically express hairy-related transcriptional repressors with a posterior-to-anterior phase delay, creating 'traveling waves' of her1 expression. In zebrafish, the first traveling wave buds off from the synchronous oscillation zone in the blastoderm margin. Here we show that the emergence of a traveling wave coincides with the anterior expansion of Fgf signaling and that transplanted Fgf8b-soaked beads induce ectopic traveling waves. We thus propose that as development proceeds, the activity of Fgf signaling gradually expands anteriorly, starting from the margin, so that cells initiate her1 oscillation with a posterior-to-anterior phase delay. Furthermore, we suggest that Fgf has an essential role in establishing the period gradient that is required for the her1 spatial oscillation pattern at the emergence of the traveling wave.

Hydrodynamic phase locking in mouse node cilia.

Rotational movement of mouse node cilia generates leftward fluid flow in the node cavity, playing an important role in left-right determination in the embryo. Although rotation of numerous cilia was believed necessary to trigger the determination, recent reports indicate the action of two cilia to be sufficient. We examine cooperative cilia movement via hydrodynamic interaction. Results show cilia to be cooperative, having phases locked in a certain relation; a system with a pair of nonidentical cilia can achieve phase-locked states more easily than one with a pair of identical cilia.

Relation between learning process and morphology of transport tube network in plasmodium of Physarum polycephalum.

The question of whether a single-celled organism without a brain could have functions such as learning and memory has been the subject of much debate in recent years. The plasmodium of the true slime mold, Physarum polycephalum, is an ideal model organism for such a question. The plasmodium exhibits behaviors that resemble intelligence, including solving mazes, mimicking optimal rail transportation networks, predicting the weather, and solving traveling salesman problems. In addition, the plasmodium has recently been shown to have the simplest form of learning: habituation. In the experiments in which plasmodia were repeatedly allowed to cross bridges containing aversive chemicals, the habituation behavior has been confirmed. It has been shown that the habituation process involves chemicals that are stored internally. However, it is not clear how these chemicals result in change in the behavior of plasmodium during habituation learning. This study focused on the transport tube network formed in plasmodium during the above experiments. Then, the role of the network morphology in the habituation learning process was investigated. The results showed that the network morphology changes from tree to mesh type during habituation learning, and disrupting the learned network reduces habituation behavior. In addition, it was shown that the thickness oscillation frequency depends on the network morphology. The study found that in the plasmodium of P. polycephalum, a primitive organism without a brain, transport tube networks, instead of neuronal networks, play an important role in habituation learning and the resulting decision making.

Environment-dependent morphology in plasmodium of true slime mold Physarum polycephalum and a network growth model.

Branching network growth patterns, depending on environmental conditions, in plasmodium of true slime mold Physarum polycephalum were investigated. Surprisingly, the patterns resemble those in bacterial colonies even though the biological mechanisms differ greatly. Bacterial colonies are collectives of microorganisms in which individual organisms have motility and interact through nutritious and chemical fields. In contrast, the plasmodium is a giant amoeba-like multinucleated unicellular organism that forms a network of tubular structures through which protoplasm streams. The cell motility of the plasmodium is generated by oscillation phenomena observed in the partial bodies, which interact through the tubular structures. First, we analyze characteristics of the morphology quantitatively, then we abstract local rules governing the growing process to construct a simple network growth model. This model is independent of specific systems, in which only two rules are applied. Finally, we discuss the mechanism of commonly observed biological pattern formations through comparison with the system of bacterial colonies.

Synchronization and spatiotemporal patterns in coupled phase oscillators on a weighted planar network.

To reveal the relation between network structures found in two-dimensional biological systems, such as protoplasmic tube networks in the plasmodium of true slime mold, and spatiotemporal oscillation patterns emerged on the networks, we constructed coupled phase oscillators on weighted planar networks and investigated their dynamics. Results showed that the distribution of edge weights in the networks strongly affects (i) the propensity for global synchronization and (ii) emerging ratios of oscillation patterns, such as traveling and concentric waves, even if the total weight is fixed. In-phase locking, traveling wave, and concentric wave patterns were, respectively, observed most frequently in uniformly weighted, center weighted treelike, and periphery weighted ring-shaped networks. Controlling the global spatiotemporal patterns with the weight distribution given by the local weighting (coupling) rules might be useful in biological network systems including the plasmodial networks and neural networks in the brain.

Asymmetry in cilia configuration induces hydrodynamic phase locking.

To gain insight into the nature of biological synchronization at the microscopic scale, we here investigate the hydrodynamic synchronization between conically rotating objects termed nodal cilia. A mechanical model of three rotating cilia is proposed with consideration of variation in their shapes and geometrical arrangement. We conduct numerical estimations of both near-field and far-field hydrodynamic interactions, and we apply a conventional averaging method for weakly coupled oscillators. In the nonidentical case, the three cilia showed stable locked-phase differences around ±π/2. However, such phase locking also occurred with three identical cilia when allocated in a triangle except for the equilateral triangle. The effects of inhomogeneity in cilia shapes and geometrical arrangement on such asymmetric interaction is discussed to understand the role of biological variation in synchronization via hydrodynamic interactions.

Transportation network with fluctuating input/output designed by the bio-inspired Physarum algorithm.

In this paper, we propose designing transportation network topology and traffic distribution under fluctuating conditions using a bio-inspired algorithm. The algorithm is inspired by the adaptive behavior observed in an amoeba-like organism, plasmodial slime mold, more formally known as plasmodium of Physarum plycephalum. This organism forms a transportation network to distribute its protoplasm, the fluidic contents of its cell, throughout its large cell body. In this process, the diameter of the transportation tubes adapts to the flux of the protoplasm. The Physarum algorithm, which mimics this adaptive behavior, has been widely applied to complex problems, such as maze solving and designing the topology of railroad grids, under static conditions. However, in most situations, environmental conditions fluctuate; for example, in power grids, the consumption of electric power shows daily, weekly, and annual periodicity depending on the lifestyles or the business needs of the individual consumers. This paper studies the design of network topology and traffic distribution with oscillatory input and output traffic flows. The network topology proposed by the Physarum algorithm is controlled by a parameter of the adaptation process of the tubes. We observe various rich topologies such as complete mesh, partial mesh, Y-shaped, and V-shaped networks depending on this adaptation parameter and evaluate them on the basis of three performance functions: loss, cost, and vulnerability. Our results indicate that consideration of the oscillatory conditions and the phase-lags in the multiple outputs of the network is important: The building and/or maintenance cost of the network can be reduced by introducing the oscillating condition, and when the phase-lag among the outputs is large, the transportation loss can also be reduced. We use stability analysis to reveal how the system exhibits various topologies depending on the parameter.

Asymmetric rotational stroke in mouse node cilia during left-right determination.

Rotational movement of isolated single cilia in mice embryo was investigated, which generates leftward fluid flow in the node cavity and plays an important role in left-right determination. The leftward unidirectional flow results from tilting of the rotational axis of the cilium to the posterior side. By combining computational fluid dynamics with experimental observations, we demonstrate that the leftward stroke can be more effective than expected for cases in which cilia tilting alone is considered with the no-slip condition under constant driving torque. Our results suggest that the driving torque is asymmetric.

Two rotating cilia in the node cavity are sufficient to break left-right symmetry in the mouse embryo.

Determination of left-right asymmetry in mouse embryos is achieved by a leftward fluid flow (nodal flow) in the node cavity that is generated by clockwise rotational movement of 200-300 cilia in the node. The precise action of nodal flow and how much flow input is required for the robust read-out of left-right determination remains unknown. Here we show that a local leftward flow generated by as few as two rotating cilia is sufficient to break left-right symmetry. Quantitative analysis of fluid flow and ciliary rotation in the node of mouse embryos shows that left-right asymmetry is already established within a few hours after the onset of rotation by a subset of nodal cilia. Examination of various ciliary mutant mice shows that two rotating cilia are sufficient to initiate left-right asymmetric gene expression. Our results suggest the existence of a highly sensitive system in the node that is able to sense an extremely weak unidirectional flow, and may favour a model in which the flow is sensed as a mechanical force.

Fluid flow and interlinked feedback loops establish left-right asymmetric decay of Cerl2 mRNA.

Breaking of left-right symmetry in mouse embryos requires fluid flow at the node, but the precise action of the flow has remained unknown. Here we show that the left-right asymmetry of Cerl2 expression around the node, a target of the flow, is determined post-transcriptionally by decay of Cerl2 mRNA in a manner dependent on its 3' untranslated region. Cerl2 mRNA is absent specifically from the apical region of crown cells on the left side of the node. Preferential decay of Cerl2 mRNA on the left is initiated by the leftward flow and further enhanced by the operation of Wnt-Cerl2 interlinked feedback loops, in which Wnt3 upregulates Wnt3 expression and promotes Cerl2 mRNA decay, whereas Cerl2 promotes Wnt degradation. Mathematical modelling and experimental data suggest that these feedback loops behave as a bistable switch that can amplify in a noise-resistant manner a small bias conferred by fluid 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.

Hidden symmetry in chains of biological coupled oscillators.

We experimentally investigated spatiotemporal patterns in chains of coupled biological oscillators with boundaries and found hidden symmetric patterns that are not straightforwardly derived from explicit geometrical symmetry of the systems. We propose a model of coupled oscillators in chains with a hidden oscillator interconnecting its boundaries. The model can explain all observed patterns including the hidden symmetric ones, while other models such as discrete analogs of Neumann boundary conditions in continuous systems cannot.