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Robust network structures for conserving total activity in Boolean networks

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Abstract

One of the typical properties of biological systems is the law of conservation of mass, that is, the property that the mass must remain constant over time in a closed chemical reaction system. However, it is known that Boolean networks, which are a promising model of biological networks, do not always represent the conservation law. This paper thus addresses a kind of conservation law as a generic property of Boolean networks. In particular, we consider the problem of finding network structures on which, for any Boolean operation on nodes, the number of active nodes, i.e., nodes whose state is one, is constant over time. As a solution to the problem, we focus on the strongly-connected network structures and present a necessary and sufficient condition.

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Correspondence to Shun-ichi Azuma.

Additional information

This work was supported by Grant-in-Aid for Scientific Research (B) #17H03280 from the Ministry of Education, Culture, Sports, Science and Technology of Japan.

Shun-ichi AZUMA received the B.Eng. degree in Electrical Engineering from Hiroshima University, Higashi Hiroshima, Japan, in 1999, and the M.Eng. and Ph.D. degrees in Control Engineering from Tokyo Institute of Technology, Tokyo, Japan, in 2001 and 2004, respectively. He is currently a Professor in the Department of Mechanical Systems Engineering, Graduate School of Engineering, Nagoya University, Nagoya, Japan. Prior to joining Nagoya University, he was an Assistant Professor and an Associate Professor in the Department of Systems Science, Graduate School of Informatics, Kyoto University, Uji, Japan, from 2005 to 2011 and from 2011 to 2017, respectively. He serves as Associate Editors of IFAC Journal Automatica from 2014, IEEE Transactions on Automatic Control from 2019, and so on. His research interests include analysis and control of hybrid systems and applications to systems biology.

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Azuma, Si. Robust network structures for conserving total activity in Boolean networks. Control Theory Technol. 18, 143–147 (2020). https://doi.org/10.1007/s11768-020-9202-6

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  • DOI: https://doi.org/10.1007/s11768-020-9202-6

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