Remodeling mechanisms determine size distributions in developing retinal vasculature.

The development of retinal blood vessels has extensively been used as a model to study vascular pattern formation. To date, various quantitative measurements, such as size distribution have been performed, but the relationship between pattern formation mechanisms and these measurements remains unclear. In the present study, we first focus on the islands (small regions subdivided by the capillary network). We quantitatively measured the island size distribution in the retinal vascular network and found that it tended to exhibit an exponential distribution. We were able to recapitulate this distribution pattern in a theoretical model by implementing the stochastic disappearance of vessel segments around arteries could reproduce the observed exponential distribution of islands. Second, we observed that the diameter distribution of the retinal artery segment obeyed a power law. We theoretically showed that an equal bifurcation branch pattern and Murray's law could reproduce this pattern. This study demonstrates the utility of examining size distribution for understanding the mechanisms of vascular pattern formation.

Critical roles of IκBα and RelA phosphorylation in transitional oscillation in NF-κB signaling module.

The transcription factor NF-κB performs various cell functions, such as regulating proliferation and differentiation and blocking apoptosis, by inducing the expression of multiple genes. The shuttling of NF-κB between the cytoplasm and nucleus is involved in its transcriptional activity in the canonical NF-κB pathway. The transcription of the NF-κB target genes is regulated by the phosphorylation of both IκBα and the RelA subunit of NF-κB, suggesting that these phosphorylation events are crucial for the oscillation. In this study, we constructed a new mathematical model of NF-κB activation to explore the modulation of the oscillation by the phosphorylation of IκBα and RelA. Based on a stability analysis around the equilibrium point, we confirmed that IκBα phosphorylation added a structure with a stable periodic solution to the phosphorylation model. The stable periodic solution appeared to transiently respond to the attenuation of the concentration of active IKKß. Because the NF-κB oscillation is caused by the periodic solution, the amplitude and period of the NF-κB oscillation in the phosphorylation model was constant regardless of the initial conditions; we defined this property as the reproducibility of the oscillation. On the other hand, the amplitude and period of the NF-κB oscillation depended on a parameter related to the RelA phosphorylation, suggesting that the oscillation period is regulated by RelA phosphorylation. In addition, the region of the periodic solution that is dependent on active IKKß also depends on a parameter related to RelA phosphorylation. Therefore, we conclude that the phosphorylation of both IκBα and RelA regulates the robustness of the NF-κB signaling module oscillation. That is, by appropriately controlling the phosphorylation process, it becomes possible to control the NF-κB oscillation and appropriately induce the NFkB-dependent expression gene. We anticipate that this study will contribute to the future elucidation of the mechanism underlying the nuclear cytoplasmic (N-C) oscillation of NF-κB.

Theta-alpha EEG phase distributions in the frontal area for dissociation of visual and auditory working memory.

Working memory (WM) is known to be associated with synchronization of the theta and alpha bands observed in electroencephalograms (EEGs). Although frontal-posterior global theta synchronization appears in modality-specific WM, local theta synchronization in frontal regions has been found in modality-independent WM. How frontal theta oscillations separately synchronize with task-relevant sensory brain areas remains an open question. Here, we focused on theta-alpha phase relationships in frontal areas using EEG, and then verified their functional roles with mathematical models. EEG data showed that the relationship between theta (6 Hz) and alpha (12 Hz) phases in the frontal areas was about 1:2 during both auditory and visual WM, and that the phase distributions between auditory and visual WM were different. Next, we used the differences in phase distributions to construct FitzHugh-Nagumo type mathematical models. The results replicated the modality-specific branching by orthogonally of the trigonometric functions for theta and alpha oscillations. Furthermore, mathematical and experimental results were consistent with regards to the phase relationships and amplitudes observed in frontal and sensory areas. These results indicate the important role that different phase distributions of theta and alpha oscillations have in modality-specific dissociation in the brain.

A ciliate memorizes the geometry of a swimming arena.

Previous studies on adaptive behaviour in single-celled organisms have given hints to the origin of their memorizing capacity. Here we report evidence that a protozoan ciliate Tetrahymena has the capacity to learn the shape and size of its swimming space. Cells confined in a small water droplet for a short period were found to recapitulate circular swimming trajectories upon release. The diameter of the circular trajectories and their duration reflected the size of the droplet and the period of confinement. We suggest a possible mechanism for this adaptive behaviour based on a Ca(2+) channel. In our model, repeated collisions with the walls of a confining droplet result in a slow rise in intracellular calcium that leads to a long-term increase in the reversal frequency of the ciliary beat.

Simple robot suggests physical interlimb communication is essential for quadruped walking.

Quadrupeds have versatile gait patterns, depending on the locomotion speed, environmental conditions and animal species. These locomotor patterns are generated via the coordination between limbs and are partly controlled by an intraspinal neural network called the central pattern generator (CPG). Although this forms the basis for current control paradigms of interlimb coordination, the mechanism responsible for interlimb coordination remains elusive. By using a minimalistic approach, we have developed a simple-structured quadruped robot, with the help of which we propose an unconventional CPG model that consists of four decoupled oscillators with only local force feedback in each leg. Our robot exhibits good adaptability to changes in weight distribution and walking speed simply by responding to local feedback, and it can mimic the walking patterns of actual quadrupeds. Our proposed CPG-based control method suggests that physical interaction between legs during movements is essential for interlimb coordination in quadruped walking.

Current-reinforced random walks for constructing transport networks.

Biological systems that build transport networks, such as trail-laying ants and the slime mould Physarum, can be described in terms of reinforced random walks. In a reinforced random walk, the route taken by 'walking' particles depends on the previous routes of other particles. Here, we present a novel form of random walk in which the flow of particles provides this reinforcement. Starting from an analogy between electrical networks and random walks, we show how to include current reinforcement. We demonstrate that current-reinforcement results in particles converging on the optimal solution of shortest path transport problems, and avoids the self-reinforcing loops seen in standard density-based reinforcement models. We further develop a variant of the model that is biologically realistic, in the sense that the particles can be identified as ants and their measured density corresponds to those observed in maze-solving experiments on Argentine ants. For network formation, we identify the importance of nonlinear current reinforcement in producing networks that optimize both network maintenance and travel times. Other than ant trail formation, these random walks are also closely related to other biological systems, such as blood vessels and neuronal networks, which involve the transport of materials or information. We argue that current reinforcement is likely to be a common mechanism in a range of systems where network construction is observed.

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.

Kinetic study of anti-viral ribavirin uptake mediated by hCNT3 and hENT1 in Xenopus laevis oocytes.

Transport across the cell membrane is crucial in drug delivery. However, the process is complicated because nucleoside derivatives that are commonly used as anti-viral drugs are transported through two different types of specific transporters: concentrative transporters and equilibrative transporters. Cross-disciplinary approaches involving both biological experiments and theoretical considerations are therefore necessary to study the transport of nucleoside analogues such as ribavirin. Here we constructed an experimental model system using the Xenopus laevis oocyte that expressed examples of both types of transporters: human concentrative nucleoside transporter 3 and human equilibrative transporter 1. We also performed a kinetic study. Experimental results showed that the transport of ribavirin could be reduced by inhibiting one of the two types of transporters, which seems to be counterintuitive. We therefore designed a simple mathematical model of the dynamics of ribavirin uptake and analyzed the model behaviors using a numerical simulation. The theoretical results reproduced the experimentally observed phenomena and suggested a possible mechanism for the process. Based on this mechanism, we predicted some potential methods for the effective uptake of ribavirin from a dynamics point of view.

Rules for biologically inspired adaptive network design.

Transport networks are ubiquitous in both social and biological systems. Robust network performance involves a complex trade-off involving cost, transport efficiency, and fault tolerance. Biological networks have been honed by many cycles of evolutionary selection pressure and are likely to yield reasonable solutions to such combinatorial optimization problems. Furthermore, they develop without centralized control and may represent a readily scalable solution for growing networks in general. We show that the slime mold Physarum polycephalum forms networks with comparable efficiency, fault tolerance, and cost to those of real-world infrastructure networks--in this case, the Tokyo rail system. The core mechanisms needed for adaptive network formation can be captured in a biologically inspired mathematical model that may be useful to guide network construction in other domains.

A mathematical model of cleavage.

In the present paper, we propose a mathematical model of cleavage. Cleavage is a process during the early stages of development in which the fertile egg undergoes repeated division keeping the cluster size almost constant. During the cleavage process individual cells repeat cell division in an orderly manner to form a blastula, however, the mechanism which achieves such a coordination is still not very clear. In the present research, we took sea urchin as an example and focused on the diffusion of chemical substances from the animal and vegetal pole. By considering chemotactic motion of the centrosomes, we constructed a mathematical model that describes the processes in the early stages of cleavage.

Flow-network adaptation in Physarum amoebae.

Understanding how biological systems solve problems could aid the design of novel computational methods. Information processing in unicellular eukaryotes is of particular interest, as these organisms have survived for more than a billion years using a simple system. The large amoeboid plasmodium of Physarum is able to solve a maze and to connect multiple food locations via a smart network. This study examined how Physarum amoebae compute these solutions. The mechanism involves the adaptation of the tubular body, which appears to be similar to a network, based on cell dynamics. Our model describes how the network of tubes expands and contracts depending on the flux of protoplasmic streaming, and reproduces experimental observations of the behavior of the organism. The proposed algorithm based on Physarum is simple and powerful.

Amoebae anticipate periodic events.

When plasmodia of the true slime mold Physarum were exposed to unfavorable conditions presented as three consecutive pulses at constant intervals, they reduced their locomotive speed in response to each episode. When the plasmodia were subsequently subjected to favorable conditions, they spontaneously reduced their locomotive speed at the time when the next unfavorable episode would have occurred. This implied the anticipation of impending environmental change. We explored the mechanisms underlying these types of behavior from a dynamical systems perspective.

Minimum-risk path finding by an adaptive amoebal network.

When two food sources are presented to the slime mold Physarum in the dark, a thick tube for absorbing nutrients is formed that connects the food sources through the shortest route. When the light-avoiding organism is partially illuminated, however, the tube connecting the food sources follows a different route. Defining risk as the experimentally measurable rate of light-avoiding movement, the minimum-risk path is exhibited by the organism, determined by integrating along the path. A model for an adaptive-tube network is presented that is in good agreement with the experimental observations.

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.

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.