Abstract
While current experimental demonstrations have been limited to small computational tasks, DNA strand displacement systems (DSD systems) [25] hold promise for sophisticated information processing within chemical or biological environments. A DSD system encodes designed reactions that are facilitated by three-way or four-way toehold-mediated strand displacement. However, such systems are capable of spurious displacement events that lead to leak: incorrect signal production. We have identified sources of leak pathways in typical existing DSD schemes that rely on toehold sequestration and are susceptible to toeless strand displacement (i.e. displacement reactions that occur despite the absence of a toehold). Based on this understanding, we propose a simple, domain-level motif for the design of leak-resistant DSD systems. This motif forms the basis of a number of DSD schemes that do not rely on toehold sequestration alone to prevent spurious displacements. Spurious displacements are still possible in our systems, but require multiple, low probability events to occur. Our schemes can implement combinatorial Boolean logic formulas and can be extended to implement arbitrary chemical reaction networks.
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Notes
- 1.
These assumptions include the approximate rate formulas for domain-level steps such as hybridization, fraying, 3-way and 4-way branch migration. There are also parameters set by the user that control the potential combinatorial explosion of the enumeration process, such as the granularity of domains (dividing a domain into subdomains allows the enumerator to explore more potential leak pathways, but makes the combinatorics worse), and the relevant time scales (opening a long double-stranded domain is “too slow to consider” and will not be enumerated, while a branch migration pathway may be “too fast” for considering bimolecular interactions prior to the end point).
- 2.
Each partial displacement is reversible and quickly reaches a pseudo-equilibrium proportional to two concentrations (\(F_1\) and an input). The second input then reacts, for an overall rate proportional to the product of \([F_1] \cdot [A] \cdot [B]\).
- 3.
Note that although the first reaction is reversible, the reverse reaction is bimolecular as opposed to unimolecular as is the case with the partial displacement by one input in the cooperative AND gate. Thus it is not as readily reversible, especially in low concentration regimes, and the associative gate avoids effectively trimolecular steps.
- 4.
For example, in the NLD AND gate described below, if input X is present, then there is a sequence of toehold-mediated reactions that can trigger the reporter. In particular, X displaces the top strand of \(F_1\) from the left up to the hairpin, which in turn displaces the top strand of \(F_2\) from the left up to the hairpin, and so forth. However, each of these reactions would quickly reverse because the partial displacement leaves each top strand attached. The associative hybridization AND gate of Fig. 5 also exhibits this behavior.
- 5.
The increasing length of the branch migration region is expected to lead to a linearly decreasing success probability per collision [20]. Thus each of the N strand displacement reactions slows down linearly with N. The time spent in the random walk of branch migration will increase quadratically, but will not be rate limiting for practical concentrations and values of N.
- 6.
Note that it is not enough to notice that each fuel complex has one top Y domain in excess and thus assume that to replace the top reporter strand requires all N fuel complexes. As we saw before, there are possible cascades between fuel complexes that need to be taken into account. To drive home the point, consider removing the leftmost \(X_1\) and \(X_1^*\) domains from \(F_1\). Then we could swap the top strands on \(F_1\) and \(F_2\) without decreasing the number of long domains bound, and then \(F_1\) will contain two open Y domains: \(Y_1\) and \(Y_2\). In this case, only \(N-1\) fuel complexes are sufficient to replace the top reporter strand.
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Acknowledgments
The authors are supported by a Banting Fellowship (CT), NSF CCF/HCC Grant No. 1213127, NSF CCF Grant No. 1317694, and NIGMS Systems Biology Center grant P50 GM081879 (DS). We thank Boya Wang and Robert Machinek for helpful discussions.
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Thachuk, C., Winfree, E., Soloveichik, D. (2015). Leakless DNA Strand Displacement Systems. In: Phillips, A., Yin, P. (eds) DNA Computing and Molecular Programming. DNA 2015. Lecture Notes in Computer Science(), vol 9211. Springer, Cham. https://doi.org/10.1007/978-3-319-21999-8_9
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