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In multi-cellular organisms, cells and tissues coordinate biochemical signal propagation across length scales spanning micrometres to metres. Designing synthetic materials with similar capacities for coordinated signal propagation could allow these systems to adaptively regulate themselves across space and over time. Here, we combine ideas from cell signalling and electronic circuitry to propose a biochemical waveguide that transmits information in the form of a concentration of a DNA species on a directed path. The waveguide could be seamlessly integrated into a soft material because there is virtually no difference between the chemical or physical properties of the waveguide and the material it is embedded within. We propose the design of DNA strand displacement reactions to construct the system and, using reaction–diffusion models, identify kinetic and diffusive parameters that enable super-diffusive transport of DNA species via autocatalysis. Finally, to support experimental waveguide implementation, we propose a sink reaction and spatially inhomogeneous DNA concentrations that could mitigate the spurious amplification of an autocatalyst within the waveguide, allowing for controlled waveguide triggering. Chemical waveguides could facilitate the design of synthetic biomaterials with distributed sensing machinery integrated throughout their structure and enable coordinated self-regulating programmes triggered by changing environmental conditions. 

Living systems require a sustained supply of energy and nutrients to survive. These nutrients are ingested, transformed into low-energy waste products, and excreted. In contrast, synthetic DNA strand-displacement reactions typically run within closed systems provided with a finite initial supply of reactants. Once the reactants are consumed, all net reactions halt and the system ceases to function. Here we run DNA strand-displacement reactions in a continuous flow reactor, infusing fresh reactants and withdrawing waste, enabling the system to dynamically update its outputs in response to changing inputs. Running DNA strand-displacement reactions inside of continuous flow reactors allows the system to be re-used for multiple rounds of computation, which could enable the execution of more elaborate information processing tasks, including single-rail negation and sequential logic circuits