Programmable reactions and diffusion using DNA for pattern formation in hydrogel medium

We demonstrate a method of pattern formation based on an artificial reaction diffusion system in hydrogel medium. By designing both the reaction term and the diffusion term of the system, we have succeeded in generating a sustainable DNA pattern in the gel. A DNA logic gate anchored in the gel detected the diffused molecules from distant source points to mark the equidistant region from the source points, which produced a Voronoi pattern in the gel. Combined with a diffusion modulation method for DNA molecules, the Voronoi pattern was modified as a weighted Voronoi pattern with different morphologies. The proposed framework will be useful in designing a structured gel system responsive to molecular signals.