Abstract
Models of well-mixed chemical reaction networks (CRNs) have provided a solid foundation for the study of programmable molecular systems, but the importance of spatial organization in such systems has increasingly been recognized. In this paper, we explore an alternative chemical computing model introduced by Qian & Winfree in 2014, the surface CRN, which uses molecules attached to a surface such that each molecule only interacts with its immediate neighbours. Expanding on the constructions in that work, we first demonstrate that surface CRNs can emulate asynchronous and synchronous deterministic cellular automata and implement continuously active Boolean logic circuits. We introduce three new techniques for enforcing synchronization within local regions, each with a different trade-off in spatial and chemical complexity. We also demonstrate that surface CRNs can manufacture complex spatial patterns from simple initial conditions and implement interesting swarm robotic behaviours using simple local rules. Throughout all example constructions of surface CRNs, we highlight the trade-off between the ability to precisely place molecules and the ability to precisely control molecular interactions. Finally, we provide a Python simulator for surface CRNs with an easy-to-use web interface, so that readers may follow along with our examples or create their own surface CRN designs.
Highlights
We follow the definition of a surface chemical reaction networks (CRNs) as introduced in Qian & Winfree [38]: informally, it is a CRN in which individual molecules are localized to sites on a surface and can only interact with neighbouring molecules
In principle, can chemistry on a surface do? We have addressed this question with a simple asynchronous cellular-automata-like framework—the surface CRN—that serves as a tractable and comprehensible model of chemistry on a surface
Surface CRNs may not capture the full richness of all possible physics that can occur on a surface surrounded by chemicals, but we claim that they capture many of the important features of chemistry-on-a-surface in much the same way that wellmixed CRNs capture many of the important features of chemistry-in-a-tube
Summary
Turning back to engineering efforts to program chemical systems, one could imagine taking similar advantage of spatial separation by, for example, assembling molecules into polymers or tethering molecules onto a surface so that geometry will limit which molecules can reach each other (in the best case they can only touch their immediate neighbours). This prospect has engendered a considerable body of theoretical and experimental work in DNA nanotechnology [27,28,29,30,31,32,33,34,35,36]. We hope that in the future, this will encompass a wide range of chemistries using a wide range of substrates
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