An algorithmic solution to Eterna100's Taraxacum officinale

Taraxacum officinale, named after the dandelion, is puzzle 68 of the Eterna100 RNA design benchmark: a 282-nucleotide target fold that Eterna players can solve under the ViennaRNA 2 folding engine but that no algorithm has solved in the benchmark's published runs. It is one of three targets that separate the best design program from human players.

Problem

Let $y^\star$ be the target below in dot-bracket notation (282 nt, the same in Eterna100-V1 and V2; Eterna puzzle 8950194):

((((....).))).((((....).))).((((....).))).((((....).))).((((....).))).((((....).))).((((((((((((((((((((((...)))).))))))).(((((..((((((((((..(((((((...))))))).))))))))))((((.((((((...)))))))))))))))...))))))))))).((((....).))).((((....).))).((((....).))).((((....).))).((((....).)))

Using a method that receives only $y^\star$, find a sequence $x \in \{\mathrm{A},\mathrm{C},\mathrm{G},\mathrm{U}\}^{282}$ with

$$\arg\min_{y} \Delta G(x, y) = y^\star,$$

where $y$ ranges over pseudoknot-free structures with A–U, G–C and G–U pairs and $\Delta G$ is the Turner 2004 nearest-neighbour free energy at 37 °C computed by ViennaRNA 2.6.4 with default settings (dangles = 2). In practice, stock RNAfold -T 37 must print exactly $y^\star$; on a tie, the printed structure counts. Player solutions and hand edits for this puzzle are not allowed.

The target has 98 base pairs. Eleven short arms each end in a four-nucleotide hairpin loop closed by a lone base pair, which a one-nucleotide bulge separates from a three-pair stem; they flank a central domain with two three-way junctions.

Background

Eterna player ariel19_89 posted this puzzle in 2012, and Anderson-Lee et al. put it in Eterna100 (2016). It is among the 81 targets kept unchanged in V2 because players could still solve them under ViennaRNA 2 (Koodli et al., 2025). Lone base pairs are a known source of difficulty: Zhou et al. (2024) traced many of the undesignable Eterna100 targets they found to lone pairs or two-pair stems. A program that solves this target would show that automated design can place eleven lone pairs in one molecule.

What is known

• Eterna players have solved it with Vienna 2; a sample player solution is in the benchmark data.
• In the benchmark authors' runs (ViennaRNA 2.6.4, one core, 24 hours), none of RNAinverse, EternaBrain, LEARNA, SentRNA, NEMO or DesiRNA solved it.
• DesiRNA's authors report 97 of the 100 V2 targets solved, and their published solutions omit this one (Wirecki et al., 2025).
• Under the stricter unique-MFE criterion, where the target must be the only lowest-energy structure, NEMO and SAMFEO did not solve it with ViennaRNA 2.5.1 parameters, and Zhou et al. (2024) could not prove it undesignable. It is not among the 18 Eterna100 targets they proved undesignable in 2025.

What would count as progress

• A 282-nt sequence for which stock RNAfold -T 37 (ViennaRNA 2.6.4) prints exactly the target, made by a program from the target alone. The check takes under a second.
• The program, settings, random seed and run time, so the run can be repeated. A run within 24 hours on one core would add this puzzle to the Eterna100-V2 count.
• A sequence for which the target is the unique MFE structure (checkable with RNAsubopt -e 0), or a proof that none exists. Either settles the question Zhou et al. left open.

References

1. R. V. Koodli et al. Redesigning the Eterna100 for the Vienna 2 folding engine. bioRxiv (2021, revised 2025). doi:10.1101/2021.08.26.457839
2. J. Anderson-Lee et al. Principles for predicting RNA secondary structure design difficulty. J. Mol. Biol. 428, 748–757 (2016). doi:10.1016/j.jmb.2015.11.013
3. T. K. Wirecki et al. DesiRNA: structure-based design of RNA sequences with a replica exchange Monte Carlo approach. Nucleic Acids Res. 53, gkae1306 (2025). doi:10.1093/nar/gkae1306
4. T. Zhou et al. Undesignable RNA structure identification via rival structure generation and structure decomposition. RECOMB 2024, pp. 270–287. doi:10.1007/978-1-0716-3989-4_17
5. T. Zhou et al. Scalable and interpretable identification of minimal undesignable RNA structure motifs with rotational invariance. RECOMB 2025, pp. 153–174. doi:10.1007/978-3-031-90252-9_10

Source

Imported from Eterna100 V2 puzzle 68, curated by Eterna / Das Lab, Stanford. Open according to the source as of 2026-10-20. The statement above is written in our own words; see the source for the original wording, history and discussion.