Abstract
A major goal of natural computing is to design biomolecules, such as nucleic acid sequences, that can be used to perform computations. We design sequences of nucleic acids that are “guaranteed” to have long folding pathways relative to their length. This particular sequences with high probability follow low-barrier folding pathways that visit a large number of distinct structures. Long folding pathways are interesting, because they demonstrate that natural computing can potentially support long and complex computations. Formally, we provide the first scalable designs of molecules whose low-barrier folding pathways, with respect to a simple, stacked pair energy model, grow superlinearly with the molecule length, but for which all significantly shorter alternative folding pathways have an energy barrier that is 2 - epsilon times that of the low-barrier pathway for any epsilon > 0 and a sufficiently long sequence.
Highlights
Novel means for performing computations or designing nanostructures at the molecular level have been success-fully developed, that exploit base pairing interactions of nucleic acids
With respect to a simple energy model that assigns an energy of −1 to each stacked pair in a structure, we prove that for any n, our design produces a strand of length Θ(n) over a 4-letter alphabet whose shortest low-barrier pathway has length Θ(n log n)
We have argued that reaching the target structure from the initial structure is significantly more likely via a low-barrier pathway with switch reconfigurations, than by direct removal of even a single band of the lock
Summary
Novel means for performing computations or designing nanostructures at the molecular level have been success-fully developed, that exploit base pairing interactions of nucleic acids. Our work here is motivated by the goal of computing with a single RNA sequence as the nucleic acids of the sequence interact with each other. RNA sequences form folded structures in which pairs of nucleic acids biochemically bond to each other. These bonds change the physical energy of the sequence, and a given sequence prefers to assume low-energy folded structures. Folding is a dynamic process, constrained by kinetics, during which an RNA sequence will move through a sequence of structures with each differing from the previous one by the addition or removal of a single base pair. Folding pathways will tend to meander along low-energy “valleys” in the landscape of secondary structures, rather than scaling high-energy “barriers”, even if the low-barrier valleys are longer
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