Cascaded pattern formation in hydrogel medium using the polymerisation approach.

Reaction-diffusion systems are one of the models of the formation process with various patterns found in nature. Inspired by natural pattern formation, several methods for designing artificial chemical reaction-diffusion systems have been proposed. DNA is a suitable building block to build such artificial systems owing to its programmability. Previously, we reported a line pattern formed due to the reaction and diffusion of synthetic DNA; however, the width of the line was too wide to be used for further applications such as parallel and multi-stage pattern formations. Here, we propose a novel method to programme a reaction-diffusion system in a hydrogel medium to realise a sharp line capable of forming superimposed and cascaded patterns. The mechanism of this system utilises a two-segment polymerisation of DNA caused by hybridisation. To superimpose the system, we designed orthogonal DNA sequences that formed two lines in different locations on the hydrogel. Additionally, we designed a reaction to release DNA and form a cascade pattern, in which the third line appears between the two lines. To explain the mechanism of our system, we modelled the system as partial differential equations, whose simulation results agreed well with the experimental data. Our method to fabricate cascaded patterns may inspire combinations of DNA-based technologies and expand the applications of artificial reaction-diffusion systems.