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DNA strand displacement, a collective name for certain behaviors of short strands of DNA, has been used to build many interesting molecular devices over the past few decades. Among those devices are general implementation schemes for Chemical Reaction Networks, suggesting a place in an abstraction hierarchy for complex molecular programming. However, the possibilities of DNA strand displacement are far from fully explored. On a theoretical level, most DNA strand displacement systems are built out of a few simple motifs, with the space of possible motifs otherwise unexplored. On a practical level, the desire for general, large-scale DNA strand displacement systems is not fulfilled. Those systems that are scalable are not general, and those that are general don't scale up well. We have recently been exploring the space of possibilities for DNA strand displacement systems where all input complexes are made out of at most two strands of DNA. As a test case, we've had an open question of whether such systems can implement general Chemical Reaction Networks, in a way that has a certain set of other desirable properties - reversible, systematic, O(1) toeholds, bimolecular reactions, and correct according to CRN bisimulation - that the state-of-the-art implementations with more than 2-stranded inputs have. Until now we've had a few results that have all but one of those desirable properties, including one based on a novel mechanism we called coupled reconfiguration, but that depended on the physically questionable assumption that pseudoknots cannot occur. We wondered whether the same type of mechanism could be done in a pseudoknot-robust way. In this work we show that in fact, coupled reconfiguration can be done in a pseudoknot-robust way, and this mechanism can implement general Chemical Reaction Networks with all inputs being single strands of DNA. Going further, the same motifs used in this mechanism can implement stacks and surface-based bimolecular reactions. Those have been previously studied as part of polymer extensions of the Chemical Reaction Network model, and on an abstract model level, the resulting extensions are Turing-complete in ways the base Chemical Reaction Network model is not. Our mechanisms are significantly different from previously tested DNA strand displacement systems, which raises questions about their ability to be implemented experimentally, but we have some reasons to believe the challenges are solvable. So we present the pseudoknot-robust coupled reconfiguration mechanism and its use for general Chemical Reaction Network implementations; we present the extensions of the mechanism to stack and surface reactions; and we discuss the possible obstacles and solutions to experimental implementation, as well as the theoretical implications of this mechanism.

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.