This paper proposes a control theoretic framework to model and analyze the URLanized pattern formation of molecular concentrations in biomolecular communication networks, where bio-nanomachines, or biological cells, communicate  each other using  cell-to-cell communication mechanism mediated by a diffusible signaling molecule  . We first introduce a feedback model representation of the reaction-diffusion dynamics of biomolecular communication networks. A systematic local stability/instability analysis tool is then provided based on the root locus of the feedback system. Using the instability analysis , we analytically derive the conditions for the URLanized spatial pattern formation, or Turing pattern formation, of the bio-nanomachines. 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 .
This paper proposes a control theoretic framework to model and analyze the URLanized pattern formation of molecular concentrations in biomolecular communication networks, emerging applications in synthetic biology. In biomolecular communication networks, bio-nanomachines, or biological cells, communicate with each other using a cell-to-cell communication mechanism mediated by a diffusible signaling molecule , thereby the dynamics of molecular concentrations are approximately modeled as a reaction-diffusion system with a single diffuser . We first introduce a feedback model representation of the reaction-diffusion system and provide a systematic local stability/instability analysis tool using the root locus of the feedback system. The instability analysis then allows us to analytically derive the conditions for the URLanized spatial pattern formation, or Turing pattern formation, of the bio-nanomachines. We propose a novel synthetic biocircuit motif called activator-repressor-diffuser system and show that it is one of the minimum biomolecular circuits that admit URLanized patterns over cell population .
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The theoretical results are demonstrated on a novel biochemical circuit
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