American Institute of Mathematical Sciences

Advanced
2008, 5(3): 419-427. doi: 10.3934/mbe.2008.5.419

Input-dependent wave propagations in asymmetric cellular automata: Possible behaviors of feed-forward loop in biological reaction network

Akinori Awazu 1,

1. 

Department of Mathematical and Life Sciences, Hiroshima University, Kagami-yama 1-3-1, Higashi-Hiroshima 739-8526, Japan

Received  August 2007 Revised  May 2008 Published  June 2008

Dynamical aspects of the asymmetric cellular automata were in- vestigated to consider the signaling processes in biological systems. As a meta- model of the cascade of feed-forward loop type network motifs in biological reaction networks, we consider the one dimensional asymmetric cellular au- tomata where the state of each cell is controlled by a trio of cells, the cell itself, the nearest upstream cell and the next nearest upstream cell. Through the systematic simulations, some novel input-dependent wave propagations were found in certain asymmetric CA, which may be useful for the signaling pro- cesses like the distinction, the filtering and the memory of external stimuli.
Keywords: Dynamical systems in biology, Cellular Automata, filteriong, etc.), Applications (signal detection.
Mathematics Subject Classification: 73B15, 37N25, 60G3.
Citation: Akinori Awazu. Input-dependent wave propagations in asymmetric cellular automata: Possible behaviors of feed-forward loop in biological reaction network. Mathematical Biosciences & Engineering, 2008, 5 (3) : 419-427. doi: 10.3934/mbe.2008.5.419
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