DotKnot: pseudoknot prediction using the probability dot plot under a refined energy model

Sperschneider, Jana; Datta, Amitava

where TÁS L 1 ,L 2 ,L 3 is the purely entropic free energy for loops L 1 , L 2 and L 3 . Three different pseudoknot energy models are employed for the loop entropy calculation, each of that comprise pseudoknots with certain characteristics. The length of loop L 2 determines which energy I II III Figure 4 . Construction of a recursive H-type pseudoknot. On the first level, two stems form a core H-type pseudoknot. On the second level, recursive secondary structure elements may form in each of the three loops. On the third level, the recursive H-type pseudoknot is assembled. model is used for the respective pseudoknot candidate (Table 1) . For details on pseudoknot loop entropy calculation using the virtual bond models CC06 and CC09 see (42) and (48), respectively. For pseudoknots with long interhelix loop L 2 , there is no physical loop entropy model available and we have to employ heuristics (24) (25) (26) . This heuristic energy model (LongPK) is also used for pseudoknots with one interrupted stem regardless of the length of loop L 2 . Stems interrupted by long bulge or internal loops are likely to result in bending rather than rigid formations (48) . Therefore, the loop entropy calculation becomes intricate. We calculate the loop entropy as TÁS L 1 ,L 2 ,L 3 ¼ þ Â L, where L is the number of unpaired nucleotides in the three pseudoknot loops with ¼ 7:0 kcal/mol and ¼ 0:1 kcal/mol. For pseudoknots with regular stems and loop length L 2 of 0 or 1 nt, one can generally assume that the two pseudoknot stems are coaxially stacked. This leads to a stabilizing effect for the two base pairs at the interhelix junction. Here, coaxial stacking is calculated using the Turner energy model, multiplied by an estimated weighting parameter g < 1 and added to the free energy of a pseudoknot (7, 8, 24) . For pseudoknots with interrupted stems and absent loop L 2 , we also add the appropriate coaxial stacking energy multiplied by an estimated weighting parameter g < 1. After energy evaluation, only pseudoknots with negative free energy are stored in the pseudoknot dictionary D p . Additionally, we demand that the free energy of a core H-type pseudoknot needs to be lower than the free energies wðS 1 Þ and wðS 2 Þ of the pseudoknot stems S 1 and S 2 .