Can RNA fold into a "spring" (non-hairpin) helix?

  1. Consider the following sequence:

Can the end bind to the start?
Notice that this isn’t an ordinary hairpin; the molecule has to loop back on itself; creating a helix (semi-) loop.

  1. If so, does ViennaRNA (or any other package) support such structures?
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Yes, all the folding models we use in Etera support this. But they may have different predictions as to what pairings produce the lowest free energy (and hence form more often than alternate sets of pairings.

Here’s what Vienna and Vienna2 predict has the lowest free energy: 

while NUPACK predicts

You can explore these with the puzzle maker

But does this prediction really match nature? I’d expect an helix to be a better solution.

I tried different sequences, but didn’t manage to get an helix. Is it really the case that Eterna’s other solutions were better, or is it simply not able to consider helices?

I’m not sure what you have in mind. But for the purpose of making double stranded RNA without imperfections, the only base pairings that do that are C-G, U-A and U-G, just as the game allows. 

The energy models don’t allow for a helix of the sort you are suggesting. In nature, the RNA is coiled not flat as viewed in the sort of 2D presentation that Eterna and others use. The two side of an RNA stack/stem are actually coiled together as a helix much like the DNA double-helix:

I’m not sure that the bases would have the right orientation to bond in the sort of tertiary structure helix that you are proposing.

Hmm… it seems that parallel strands are possible under some conditions:

Interesting. I guess the point is that nature allows lots of possibilities (non-WC pairs, pseudo-knots, parallel strands, …) that most energy models (or at least the ones that Eterna supports) don’t allow.