Speed and Correctness Guarantees for Programmable Enthalpy-Neutral DNA Reactions†

Molecular control circuits embedded within chemical systems to direct molecular events have transformative applications in synthetic biology, medicine, and other fields. However, it is challenging to understand the collective behavior of components due to the combinatorial complexity of possible interactions. Some of the largest engineered molecular systems to date have been constructed using DNA strand displacement reactions, in which signals can be propagated without a net change in base pairs (enthalpy neutral). 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, strand displacement systems are susceptible to the spurious release of output in the absence of the proper combination of inputs (leak), as well as reversible unproductive binding (toehold occlusion) and spurious displacement that slow down desired kinetics. We systematize the properties of the simplest enthalpy-neutral strand displacement cascades (logically linear topology), and develop a taxonomy for the desired and undesired properties affecting speed and correctness, and trade-offs between them based on a few fundamental parameters. We also show that enthalpy-neutral linear cascades can be engineered with stronger thermodynamic guarantees to leak than non-enthalpy-neutral designs. We confirm our theoretical analysis with laboratory experiments comparing the properties of different design parameters. Our method of tackling the combinatorial complexity using mathematical proofs can guide the engineering of robust and efficient molecular algorithms.