A Coupled Reconfiguration Mechanism for Single-Stranded DNA Strand Displacement Systems

Abstract

DNA Strand Displacement (DSD) systems model basic reaction rules, such as toehold-mediated strand displacement and 4-way branch migration, that modify complexes of bound DNA strands. DSD systems have been widely used to design and reason about the correctness of molecular programs, including implementations of logic circuits, neural networks, and Chemical Reaction Networks. Such implementations employ a valuable toolkit of mechanisms – sequences of basic reaction rules – that achieve catalysis, reduce errors (e.g., due to leak), or simulate simple computational units such as logic gates, both in solution and on surfaces. Expanding the DSD toolkit of DSD mechanisms can lead to new and better ways of programming with DNA. Here we introduce a new mechanism, which we call controlled reconfiguration . We describe one example where two single-stranded DSD complexes interact, changing the bonds in both complexes in a way that would not be possible for each independently on its own via the basic reaction rules allowed by the model. We use coupled reconfiguration to refer to instances of controlled reconfiguration in which two reactants change each other in this way. We note that our DSD model disallows pseudoknots and that properties of our coupled reconfiguration construction rely on this restriction of the model. A key feature of our coupled reconfiguration example, which distinguishes it from mechanisms (such as 3-way strand displacement or 4-way branch migration) that are typically used to implement molecular programs, is that the reactants are single-stranded. Leveraging this feature, we show how to use coupled reconfiguration to implement Chemical Reaction Networks (CRNs), with a DSD system that has both single-stranded signals (which represent the species of the CRN) and single-stranded fuels (which drive the CRN reactions). Our implementation also has other desirable properties; for example it is capable of implementing reversible CRNs and uses just two distinct toeholds. We discuss drawbacks of our implementation, particularly the reliance on pseudoknot-freeness for correctness, and suggest directions for future research that can provide further insight on the capabilities and limitations of controlled reconfiguration. computing (DSD) systems. a particularly well-studied abstract model of well-mixed chemical systems, in which many interesting programs can be and have been written [2, 3, 28, 36, 41]. Moreover, arbitrary CRNs can be transformed into DSD systems that implement the original CRN [7, 10, 30, 37, 39].