Abstract
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.
B. Wang—Supported by NSF grants CCF-1618895 and CCF-1652824.
C. Thachuk—Supported by NSF grant CCF-1317694.
A.D. Ellington—Supported by NSF grant DBI-0939454, international funding agency ERASynBio 1541244, and by the Welch Foundation F-1654.
D. Soloveichik—Supported by NSF grants CCF-1618895 and CCF-1652824.
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Notes
- 1.
Although our use of the words enthalpy and entropy are meant to evoke the respective physical chemistry concepts, the mapping is not 1–1. We note especially that the contribution of forming additional base pairs to the free energy has both substantial enthalpic and entropic parts (which can be physically distinguished based on their temperature dependence).
- 2.
Roughly speaking, “one unit of enthalpic penalty” corresponds to an average of \(l \cdot 1.5\) kcal/mol, where l is the length of the domain (typically 5–10 nucleotides for a toehold). “One unit of entropic penalty” at concentration C M corresponds to \(\Delta G^\circ _\text {assoc} + RT \ln (1/C) \approx 1.96 + 0.6 \ln (1/C)\) kcal/mol [7]. With these numbers, at roughly 650 nM concentration, binding an additional \(l = 7\) domain is equal to one unit of entropy. At low concentrations the entropic penalty becomes dominant, while the enthalpic penalty prevails at high concentrations.
- 3.
Our length parameter N is related to the redundancy parameter of [10], but whereas we count the number of short domains, they count the long domains.
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Wang, B., Thachuk, C., Ellington, A.D., Soloveichik, D. (2017). The Design Space of Strand Displacement Cascades with Toehold-Size Clamps. In: Brijder, R., Qian, L. (eds) DNA Computing and Molecular Programming. DNA 2017. Lecture Notes in Computer Science(), vol 10467. Springer, Cham. https://doi.org/10.1007/978-3-319-66799-7_5
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