# Synthesis and materialization of a reaction-diffusion French flag pattern

## TL;DR

This paper demonstrates the creation of a synthetic French flag pattern using DNA reaction networks, enabling autonomous pattern formation and control over colloidal organization in non-living matter.

## Contribution

It introduces a novel DNA-based reaction-diffusion system that synthesizes and materializes a French flag pattern, reprogrammable via network mutation.

## Key findings

- Successful synthesis of a sharp, long-lasting French flag pattern.
- Control of colloidal aggregation patterns through concentration gradients.
- Potential for testing reaction-diffusion models and fabricating autonomous soft materials.

## Abstract

During embryo development, patterns of protein concentration appear in response to morphogen gradients. These patterns provide spatial and chemical information that directs the fate of the underlying cells. Here, we emulate this process within non-living matter and demonstrate the autonomous structuration of a synthetic material. Firstly, we use DNA-based reaction networks to synthesize a French flag, an archetypal pattern composed of three chemically-distinct zones with sharp borders whose synthetic analogue has remained elusive. A bistable network within a shallow concentration gradient creates an immobile, sharp and long-lasting concentration front through a reaction-diffusion mechanism. The combination of two bistable circuits generates a French flag pattern whose 'phenotype' can be reprogrammed by network mutation. Secondly, these concentration patterns control the macroscopic organization of DNA-decorated particles, inducing a French flag pattern of colloidal aggregation. This experimental framework could be used to test reaction-diffusion models and fabricate soft materials following an autonomous developmental program.