MICROSCOPIC SELF-ORGANIZATION IN NETWORKS AND REGULAR LATTICE

Abstract

We report our numerical studies on the microscopic self-organizations of a reaction system in three types of networks: a regular network, a small-world network, and a random network as well as on a regular lattice. Our simulation results show that the topology of the network has an important effect on the communication among reaction molecules, and plays an important role in microscopic self-organization. The correlation length among reacting molecules in a random or a small-world network is much shorter compared with that in the regular network. As a result, it is much easier to obtain a microscopic self-organization in a small-world or a random network. A phase transition from a stochastic state to a synchronized state was observed when the randomness of a small-world network was increased. We also demonstrate that good synchronization activities of enzymatic turnover cycles can be developed on a regular lattice when the correlation length created by the fast diffusion of regulatory particles is large enough.