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In the Bonabeau model, chemotaxis, which is observed in social insects, such as ants, was introduced into the movement rules of agents to control the collision frequency between agents, and its effect on the mechanism of hierarchical structure formation was investigated. Like an ant, this chemotactic agent makes stochastic decisions regarding its direction of movement depending on the intensity of its released chemicals. Because of this mechanism, the agent depends on its past location history. It can perform different motions from a random walk (RW) and asymmetric attractive or repulsive interactions with other agents via the diffusion of chemotactic substances. When there is an attractive interaction between these agents, they are more likely to aggregate, which increases the effective density; thus, the disparity in the agent winning ratio is more likely to form than in a conventional model with a RW. However, in the case of repulsive interactions, the agents became more distant from each other, the effective density decreased, and a disparity in the winning ratio was less likely to form. This indicates that the disparity in the winning ratio is tunable owing to the interactions between the introduced chemotactic agents.

A model is proposed for group chase and escape using chemotactic movements only. In the proposed model, the movement depends on the concentration of the chemical substances released by each agent. Chemotaxis-based interactions propagate slower and later, and exist locally between agents, making groups chase and escape under more uncertain circumstances than in cases where agent distance measurements use electromagnetic waves, such as visible light. Numerical results with the model demonstrate that maintaining a longer distance between the chasers and targets is a better strategy for each group.

Intracellular signaling dynamics are often obscured by the spatial and temporal limitations of cell size. Here, we developed a method to enlarge Dictyostelium discoideum cells by partial cytokinesis inhibition, generating multinucleated yet functional giant cells. These cells retained chemotactic signaling, polarity, and motility, enabling high-resolution live-cell imaging. Using fluorescent probes for cAMP and Ca 2+ , we uncovered a directional, front-to-rear propagation of cAMP signaling and a biphasic Ca 2+ response coordinated with actin wave dynamics. Grid-based mapping revealed asymmetric cAMP synthesis and decay kinetics, and vesicle localization suggested spatially regulated cAMP secretion. Our findings demonstrate that intracellular signaling involves self-organized, spatially structured propagation events aligned with cellular polarity. The giant cell platform offers a powerful and generalizable strategy for dissecting the spatiotemporal logic of single-cell signaling. A method to enlarge living Dictyostelium cells by selectively inhibiting cytokinesis while preserving cellular functions enables direct visualization of directional cAMP and Ca 2+ signal propagation in single cells.

This chapter contains sections titled: Introduction Representation of Networks Classical Network Scale‐Free Network Small‐World Network Clustered Network Hierarchical Modularity Network Motif Assortativity Reciprocity Weighted Networks Network Complexity Centrality Conclusion References

Intracellular signaling dynamics are often obscured by the spatial and temporal limitations of cell size. Here, we developed a method to enlarge Dictyostelium discoideum cells by partial cytokinesis inhibition, generating multinucleated yet functional giant cells. These cells retained chemotactic signaling, polarity, and motility, enabling high-resolution live-cell imaging. Using fluorescent probes for cAMP and Ca2+, we uncovered a directional, front-to-rear propagation of cAMP signaling and a biphasic Ca2+ response coordinated with actin wave dynamics. Grid-based mapping revealed asymmetric cAMP synthesis and decay kinetics, and vesicle localization suggested spatially regulated cAMP secretion. Combining giant cells with super-resolution or electron microscopy allowed detailed visualization of intracellular local structures at high resolution. Our findings demonstrate that intracellular signaling involves self-organized, spatially structured propagation events aligned with cellular polarity. The giant cell platform offers a powerful and generalizable strategy for dissecting the spatiotemporal logic of single-cell signaling.

We examined the effects of inhomogeneity on the dynamics and structural properties using Boolean networks. Two different power-law rank outdegree distributions were embedded to determine the role of hubs. The degree of randomness and coherence of the binary sequence in the networks were measured by entropy and mutual information, depending on the number of outdegrees and types of Boolean functions for the hub. With a large number of outdegrees, the path length from the hub reduces as well as the effects of Boolean function on the hub are more prominent. These results indicate that the hubs play important roles in networks' dynamics and structural properties. By comparing the effect of the skewness of the two different power-law rank distributions, we found that networks with more uniform distribution exhibit shorter average path length and higher event probability of coherence but lower degree of coherence. Networks with more skewed rank distribution have complementary properties. These results indicate that highly connected hubs provide an effective route for propagating their signals to the entire network.

We propose a growing network model that consists of two tunable mechanisms: growth by merging modules which are represented as complete graphs and a fitness-driven preferential attachment. Our model exhibits the three prominent statistical properties are widely shared in real biological networks, for example gene regulatory, protein-protein interaction, and metabolic networks. They retain three power law relationships, such as the power laws of degree distribution, clustering spectrum, and degree-degree correlation corresponding to scale-free connectivity, hierarchical modularity, and disassortativity, respectively. After making comparisons of these properties between model networks and biological networks, we confirmed that our model has inference potential for evolutionary processes of biological networks.

We propose a model for evolving networks by merging building blocks represented as complete graphs, reminiscent of modules in biological system or communities in sociology. The model shows power-law degree distributions, power-law clustering spectra and high average clustering coefficients independent of network size. The analytical solutions indicate that a degree exponent is determined by the ratio of the number of merging nodes to that of all nodes in the blocks, demonstrating that the exponent is tunable, and are also applicable when the blocks are classical networks such as Erdős-Rényi or regular graphs. Our model becomes the same model as the Barabási-Albert model under a specific condition.

This chapter contains sections titled: Introduction Unified Evolving Network Model: Reproduction of Heterogeneous Connectivity, Hierarchical Modularity, and Disassortativity Modeling Without Parameter Tuning: A Case Study of Metabolic Networks Bipartite Relationship: A Case Study of Metabolite Distribution Conclusion References

We demonstrate the advantages of feedforward loops using a Boolean network, which is one of the discrete dynamical models for transcriptional regulatory networks. After comparing the dynamical behaviors of network embedded feedback and feedforward loops, we found that feedforward loops can provide higher temporal order (coherence) with lower entropy (randomness) in a temporal program of gene expression. In addition, complexity of the state space that increases with longer length of attractors and greater number of attractors is also reduced for networks with more feedforward loops. Feedback loops show opposite effects on dynamics of the networks. These results suggest that feedforward loops are one of the favorable local structures in biomolecular and neuronal networks.