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

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.