A design for Eterna100's Teslagon under ViennaRNA 2

Teslagon is puzzle 100 of the Eterna100-V2 RNA design benchmark: a 381-nucleotide target fold that is mostly unpaired, with two-pair helices holding large loops around a seven-way junction. Eterna players report solving it under the ViennaRNA 2 folding engine, but the benchmark withholds their solution and no algorithm has solved it in published runs, so the benchmark offers no sequence that folds into it.

Problem

Let $y^\star$ be the Eterna100-V2 target below in dot-bracket notation (381 nt; Eterna puzzle 9479126):

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

Find a sequence $x \in \{\mathrm{A},\mathrm{C},\mathrm{G},\mathrm{U}\}^{381}$ 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. Any method is allowed; a sequence found by a program that receives only $y^\star$ is the stronger result.

The target has only 42 base pairs, all in two-pair helices, and 297 unpaired nucleotides. Repeated arms carry nine 15-nucleotide hairpin loops and seven symmetric 7×7 internal loops around the seven-way junction, with three three-way junctions and one 1×11 internal loop.

Background

Eterna player wawan151 posted Teslagon in 2015, and it is the last puzzle of Eterna100 (Anderson-Lee et al., 2016). Those authors found short stems, for which few stable sequences exist, and symmetry made of repeated elements among the main sources of design difficulty; Teslagon has both. Its original target could not be solved under ViennaRNA 2 parameters, and for V2 players made it solvable by deleting one nucleotide from an internal loop (Koodli et al., 2025).

What is known

Eterna players solved all 100 V2 targets with Vienna 2, this one included, but it is the only one whose sample solution the benchmark data does not disclose (Koodli et al., 2025).
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).
The original V1 target, one nucleotide longer, is still unsolved under Vienna 2; Eterna poses it as an "[IMPOSSIBLE?]" puzzle. Under the unique-MFE criterion, Zhou et al. could neither design it nor prove it undesignable (2024), and it is not among the 18 Eterna100 targets they proved undesignable in 2025.

What would count as progress

Any 381-nt sequence for which stock RNAfold -T 37 (ViennaRNA 2.6.4) prints exactly the target. The check takes under a second, and unlike the players' solutions it can be published.
The same from a program that receives only the target, with its code, settings, random seed and run time. A run within 24 hours on one core would add this puzzle to the Eterna100-V2 count.
For the original V1 target: a design under Vienna 2, or a proof that none exists.

References

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
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
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
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
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 100, 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.