Takayuki Niizato

Minimal model of a cell connecting amoebic motion and adaptive transport networks

A cell is a minimal self-sustaining system that can move and compute. Previous work has shown that a unicellular slime mold, Physarum, can be utilized as a biological computer based on cytoplasmic flow encapsulated by a membrane. Although the interplay between the modification of the boundary of a cell and the cytoplasmic flow surrounded by the boundary plays a key role in Physarum computing, no model of a cell has been developed to describe this interplay. Here we propose a toy model of a cell that shows amoebic motion and can solve a maze, Steiner minimum tree problem and a spanning tree problem. Only by assuming that cytoplasm is hardened after passing external matter (or softened part) through a cell, the shape of the cell and the cytoplasmic flow can be changed. Without cytoplasm hardening, a cell is easily destroyed. This suggests that cytoplasmic hardening and/or sol-gel transformation caused by external perturbation can keep a cell in a critical state leading to a wide variety of shapes and motion.

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.

Emergent Runaway into an Avoidance Area in a Swarm of Soldier Crabs

Emergent behavior that arises from a mass effect is one of the most striking aspects of collective animal groups. Investigating such behavior would be important in order to understand how individuals interact with their neighbors. Although there are many experiments that have used collective animals to investigate social learning or conflict between individuals and society such as that between a fish and a school, reports on mass effects are rare. In this study, we show that a swarm of soldier crabs could spontaneously enter a water pool, which are usually avoided, by forming densely populated part of a swarm at the edge of the water pool. Moreover, we show that the observed behavior can be explained by the model of collective behavior based on inherent noise that is individuals’ different velocities in a directed group. Our results suggest that inherent noise, which is widely seen in collective animals, can contribute to formation and/or maintenance of a swarm and that the dense swarm can enter the pool by means of enhanced inherent noise.

A model of network formation by Physarum plasmodium: Interplay between cell mobility and morphogenesis

The plasmodium of Physarum polycephalum has attracted much attention due its intelligent adaptive behavior. In this study, we constructed a model of the organism and attempted to simulate its locomotion and morphogenetic behavior. By modifying our previous model, we were able to get closer to the actual behavior. We also compared the behavior of the model with that of the real organism, demonstrating remarkable similarity between the two.

Inherent noise appears as a Lévy walk in fish schools

Recent experimental and observational data have revealed that the internal structures of collective animal groups are not fixed in time. Rather, individuals can produce noise continuously within their group. These individuals’ movements on the inside of the group, which appear to collapse the global order and information transfer, can enable interactions with various neighbors. In this study, we show that noise generated inherently in a school of ayus (Plecoglossus altivelis) is characterized by various power-law behaviors. First, we show that individual fish move faster than Brownian walkers with respect to the center of the mass of the school as a super-diffusive behavior, as seen in starling flocks. Second, we assess neighbor shuffling by measuring the duration of pair-wise contact and find that this distribution obeys the power law. Finally, we show that an individual’s movement in the center of a mass reference frame displays a Lévy walk pattern. Our findings suggest that inherent noise (i.e., movements and changes in the relations between neighbors in a directed group) is dynamically self-organized in both time and space. In particular, Lévy walk in schools can be regarded as a well-balanced movement to facilitate dynamic collective motion and information transfer throughout the group.

Emergence of the scale-invariant proportion in a flock from the metric-topological interaction

Recently, it has become possible to more precisely analyze flocking behavior. Such research has prompted a reconsideration of the notion of neighborhoods in the theoretical model. Flocking based on topological distance is one such result. In a topological flocking model, a bird does not interact with its neighbors on the basis of a fixed-size neighborhood (i.e., on the basis of metric distance), but instead interacts with its nearest seven neighbors. Cavagna et al., moreover, found a new phenomenon in flocks that can be explained by neither metric distance nor topological distance: they found that correlated domains in a flock were larger than the metric and topological distance and that these domains were proportional to the total flock size. However, the role of scale-free correlation is still unclear. In a previous study, we constructed a metric-topological interaction model on three-dimensional spaces and showed that this model exhibited scale-free correlation. In this study, we found that scale-free correlation in a two-dimensional flock was more robust than in a three-dimensional flock for the threshold parameter. Furthermore, we also found a qualitative difference in behavior from using the fluctuation coherence, which we observed on three-dimensional flocking behavior. Our study suggests that two-dimensional flocks try to maintain a balance between the flock size and flock mobility by breaking into several smaller flocks.

Fluctuation-Driven Flocking Movement in Three Dimensions and Scale-Free Correlation

Recent advances in the study of flocking behavior have permitted more sophisticated analyses than previously possible. The concepts of “topological distances” and “scale-free correlations” are important developments that have contributed to this improvement. These concepts require us to reconsider the notion of a neighborhood when applied to theoretical models. Previous work has assumed that individuals interact with neighbors within a certain radius (called the “metric distance”). However, other work has shown that, assuming topological interactions, starlings interact on average with the six or seven nearest neighbors within a flock. Accounting for this observation, we previously proposed a metric-topological interaction model in two dimensions. The goal of our model was to unite these two interaction components, the metric distance and the topological distance, into one rule. In our previous study, we demonstrated that the metric-topological interaction model could explain a real bird flocking phenomenon called scale-free correlation, which was first reported by Cavagna et al. In this study, we extended our model to three dimensions while also accounting for variations in speed. This three-dimensional metric-topological interaction model displayed scale-free correlation for velocity and orientation. Finally, we introduced an additional new feature of the model, namely, that a flock can store and release its fluctuations.

Information transfer in a swarm of soldier crabs

Collective behavior is broadly observed in animal groups such as insect swarm, bird flock, and fish school. Both theoretical studies and field observations have investigated possible underlying principles based on local interaction among individuals in a group without global information via conductors or leaders. Information transferred among individuals would play a key role to understand it. In this study, to investigate how individual in a swarm uses information of its own past behavior or swarm mates’ behavior, we analyzed behavior of soldier crabs Mictyris guinotae in terms of local active information storage and local transfer entropy.

Interactions between species and environments from incomplete information

There are two contradictory aspects of the adaptive process in evolution. The first is that species must optimally increase their own fitness in a given environment. The second is that species must maintain their variation to be ready to respond to changing environments. In a strict sense, these two aspects might consider to be mutually exclusive. If species are optimally adapted, then the variation in the species that is suboptimal decreases and vice versa. To resolve this dilemma, species must find a balance between optimal adaptation and robust adaptation. Finding the balance between these processes requires both the local and global complete, static information. However, the balance between the processes must be dynamic. In this study, we propose a model that illustrates dynamic negotiation between the global and local information using lattice theory. The dynamic negotiation between these two levels results in an overestimate of fitness for each species. The overestimation of fitness in our model represents the multiplicity of fitness which is sometimes discussed as the exaptation. We show that species in our model demonstrate the power law of the lifespan distribution and 1/f fluctuation for the adaptive process. Our model allows for a balance between optimal adaptation and robust adaptation without any arbitrary parameters.

A Model of Scale-Free Proportion Based on Mutual Anticipation

Recently, new empirical research of flocking behavior has been accumulated. Scale-free proportion has revealed how a flock can appear to behave as if it has one mind and body. The notion of scale-free proportion implies that the correlated domain within a flock is not constant size, but is proportional to flock size. Scale-free proportion can be explained by previous models, such as BOIDS based on the fixed radius neighborhood where an agent interacts with others if the critical valued parameter and a huge neighborhood are given. However, it is hard to explain under the normal neighborhood condition. The authors propose a new computational model that, although also based on BOIDS, incorporates mutual anticipation, which is implemented by modeling the resonance between the potential transitions available to each agent, allowing overlap between them. Via mutual anticipation, this model implements interactions not only among individuals but also between individuals and the field. The authors show that this model reveals the dynamic and robust structure of a flock or swarm, as well as scale-free proportion over a wide range of the flock sizes, comparing previous models, and that its predictions correlate well with empirical field data.