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Classifying enthalpy-neutral DNA strand displacement cascades: trading off desired and undesired signal propagation

Artificially designed molecular systems made of DNA can exhibit complex and programmable behaviors. One kind of building block, the enthalpy-neutral DNA strand displacement cascade, propagates signal without gaining or losing overall base pairs. This flexible and programmable component has been used for constructing molecular logic circuits, smart structures and devices, for systems with complex autonomously generated dynamics, and for diagnostics. Limiting their utility, however, these systems are susceptible to the spurious release of output even in the absence of the proper combination of inputs—so-called leak. In addition, the speed of these systems is usually affected by undesired reaction pathways such as reversible unproductive binding (toehold occlusion) or spurious displacement. We systematize the properties of the simplest enthalpy-neutral strand displacement cascades (logically linear topology). We use combinatorial arguments to show that enthalpy-neutral linear cascades can be engineered with stronger thermodynamic guarantees to leak than previously studied systematic ways to reduce leak in non-enthalpy-neutral designs. Depending on a few basic parameters, we develop a taxonomy for the desired and undesired properties and trade-offs between them. Further, we experimentally confirm the theoretical prediction of the properties on different designs. These results provide an effective guide for future designs of molecular systems. Significance Statement Molecular control circuits embedded within chemical systems to direct molecular events have transformative applications in synthetic biology, medicine, and other fields. However, due to the complexity of molecular interactions, it is challenging to understand and formally reason about the collective functions of components within larger systems. Focusing on systems composed of one type of programmable DNA strand displacement reaction, we develop a formal framework to analyze desired and undesired properties affecting speed and correctness, and experimentally confirm the predictions. The properties are derived from structural design parameters based on combinatorial arguments (counting bonds and separate complexes). This approach, analogous to the rigorous proofs of algorithm correctness in computer science, can guide the future engineering of robust and efficient molecular algorithms.