Reaction-diffusion (RD) based clock and wavefront model has long been proposed as the mechanism underlying biological pattern formation of repeated and segmented structures including somitogenesis. However, systematic molecular level understanding of the mechanism remains elusive, largely due to the lack of suitable experimental systems to probe RD quantitatively in vivo. Here we design a synthetic gene circuit that couples gene expression regulation (reaction) with quorum sensing (diffusion) to guide bacterial cells self-organizing into stripe patterns at both microscopic and colony scales. An experimentally verified mathematical model confirms that these periodic spatial structures are emerged from the integration of oscillatory gene expression as the molecular clock and the outward expanding diffusions as the propagating wavefront. Furthermore, our paired model-experiment data illustrate that the RD-based patterning is sensitive to initial conditions and can be modulated by external inducers to generate diverse patterns, including multiple-stripe pattern, target-like pattern and ring patterns with reversed fluorescence. Powered by our synthetic biology setup, we also test different topologies of gene networks and show that network motifs enabling robust oscillations are foundations of sequential stripe pattern formation. These results verified close connections between gene network topology and resulting RD driven pattern formation, offering an engineering approach to help understand biological development.
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