  This paper proposes a control theoretic framework to model and analyze the
self-organized pattern formation of molecular concentrations in biomolecular
communication networks, emerging applications in synthetic biology. In
biomolecular communication networks, bionanomachines, 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
self-organized spatial pattern formation, or Turing pattern formation, of the
bionanomachines. 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 self-organized patterns over cell population.
