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I'm trying to get my head around what a pseudoknot is and how I can identify them given some RNA string. For example, suppose I have a string s = CGUUGUGUACACGAUAGUACAU. Suppose the two longest substring inversions are identified in bold CGUUGUGUACACGAUAGUACAU, which form the stack of the hairpin and everything after the first substring and before the start of the last substring make up the hairpin as illustrated below.

                                  U G U
                                G       A
                                 U     C
                                  C - A
                                  G - C
                                  U - G A U A G U A C A U

By definition, a pseudoknot is defined as a secondary structure formed by pairing between a loop and a region located outside of the stem flanking the loop. In this example, we would start the pairing using some substring of the outer tail and start matching bases around the hairpin. My question: is the pseduoknot the alignment of these base pairs, and what is the significance of this alignment?

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is the pseduoknot the alignment of these base pairs

I'm not exactly sure what is meant by alignment, but if you mean base pairing from the flanking RNA to the loop of the hairpin you have depicted, then you would have an H-type pseudoknot.

Since you are interested in predicting these structures, it's important to note that a nucleic acid sequence capable of forming the necessary base-pairs for a pseudoknot structure does not imply that the sequence indeed forms a pseudoknot. It's likely that the sequence has a minimum free energy (MFE) structure that is not pseudoknotted. So the base-pairing capability is necessary but not sufficient for predicting these structures.

Take a look at the following (full-text) articles on pseudoknot prediction for additional information:

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  • $\begingroup$ Are you aware of the requirements for predicting these structures? Thanks for the articles. $\endgroup$ – ChrisD Feb 27 '15 at 4:17
  • $\begingroup$ @ChrisD what do you mean by requirements; parameters?? You can read these papers for those. $\endgroup$ – WYSIWYG Feb 27 '15 at 4:58

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