Mathematical classification of regulatory logics for compound environmental changes

• Published in: Journal of theoretical biology Vol. 251; no. 2; pp. 363 - 379
• Main Authors: Tanaka, Reiko J., Kimura, Hidenori
• Format: Journal Article
• Language: English
• Published: England Elsevier Ltd 21.03.2008
• Subjects: Adaptation, Physiological; Animals; Cell Physiological Phenomena; Compound control; Control logics; Environment; Equivalence class; Gene Expression Regulation; Gene regulatory unit; Logical functions; Logistic Models; Models, Biological; Second Messenger Systems; Control logics; Equivalence class; Logical functions; Compound control; Gene regulatory unit
• ISSN: 0022-5193; 1095-8541
• DOI: 10.1016/j.jtbi.2007.11.023

This paper is concerned with biological regulatory mechanisms in response to the simultaneous occurrence of a huge number of environmental changes. The restricted resources of cells strictly limit the number of their regulatory methods; hence, cells must adopt, as compensation, special mechanisms to deal with the simultaneous occurrence of environmental changes. We hypothesize that cells use various control logics to integrate information about independent environmental changes related to a cell task and represent the resulting effects of the different ways of integration by logical functions. Using the notion of equivalence classes in set theory, we describe the mathematical classification of the effects into biologically unequivalent ones realized by different control logics. Our purely mathematical and systematic classification of logical functions reveals three elementary control logics with different biological relevance. To better understand their biological significance, we consider examples of biological systems that use these elementary control logics.