Proteomic signals in modular transcriptional cascades: A discrete time and cellular automaton approach

A transcriptional modular network cascade with general activation/repression coupling is analysed. It is shown that in certain conditions (the Hill coefficient is unity) it is equivalent to a cascade made of the same type of gene, and moreover the dynamics is linearisable. The protein production is shown to be a travelling kink wave on the cascade showing a successive gene expression along it. Also a cellular automaton description for both open and closed (plasmid) cascades is provided.