title: Heterarchy in biological systems: a logic-based dynamical model of abstract biological network derived from time-state-scale re-entrant form.
abstract: Heterarchical structure is important for understanding robustness and evolvability in a wide variety of levels of biological systems. Although many studies emphasize the heterarchical nature of biological systems, only a few computational representations of heterarchy have been created thus far. We propose here the time-state-scale re-entrant form to address the self-referential property derived from setting heterarchical structure. In this paper, we apply the time-state-scale re-entrant form to abstract self-referential modeling for a functional manifestation of biological network presented by [Tsuda, I., Tadaki, K., 1997. A logic-based dynamical theory for a genesis of biological threshold. BioSystems 42, 45-64]. The numerical results of this system show different intermittent phase transitions and power-law distribution of time spent in activating functional manifestation. The Hierarchically separated time-scales obtained from spectrum analysis imply that the reactions at different levels simultaneously appear in a dynamical system. The results verify the mutual inter-relationship between heterarchical structure in biological systems and the self-referential property of computational heterarchical systems.
authors.affiliation: Graduate School of Science and Technology, Kobe University, 1-1, Nada, Kobe 657-8501, Japan. kazutosasai@mac.com
authors.forename: Kazuto
authors.initials: K
authors.lastname: Sasai
authors.forename: Yukio-Pegio
authors.initials: YP
authors.lastname: Gunji
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D016015:Logistic Models; D008954:Models, Biological; D009097:Multienzyme Complexes / Q000378:metabolism*; D020543:Proteome / Q000378:metabolism*; D015398:Signal Transduction / Q000502:physiology*
chemical_list: D009097:Multienzyme Complexes; D020543:Proteome