Before revision:  The theoretical results are demonstrated on a novel biochemical circuit called activator-repressor-diffuser system , and the Turing pattern formation is numerically confirmed. Finally, we show that the activator-repressor-diffuser system is a minimum biochemical circuit that admits URLanized patterns in biomolecular communication networks .
After revision:  The theoretical results are demonstrated on a novel biochemical circuit called activator-repressor-diffuser system and show that it is one of the minimum biomolecular circuits that admit URLanized patterns over cell population .