The Design Space of Strand Displacement Cascades with Toehold-Size Clamps

DNA strand displacement cascades have proven to be a uniquely flexible and programmable primitive for constructing molecular logic circuits, smart structures and devices, and for systems with complex autonomously generated dynamics. Limiting their utility, however, strand displacement systems are susceptible to the spurious release of output even in the absence of the proper combination of inputs—so-called leak. A common mechanism for reducing leak involves clamping the ends of helices to prevent fraying, and thereby kinetically blocking the initiation of undesired displacement. Since a clamp must act as the incumbent toehold for toehold exchange, clamps cannot be stronger than a toehold. In this paper we systematize the properties of the simplest of strand displacement cascades (a translator) with toehold-size clamps. Surprisingly, depending on a few basic parameters, we find a rich and diverse landscape for desired and undesired properties and trade-offs between them. Initial experiments demonstrate a significant reduction of leak.