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

Sperschneider, Jana; Datta, Amitava

For each recursive H-type pseudoknot, we need to evaluate the free energy with respect to the recursive structure elements. As described in Table 1 , the set of pseudoknots is divided into the three different classes according to the length of loop L 2 . To account for recursive structure elements, the loop entropies need to be recalculated. Following the notation in Cao and Chen (48) , we first calculate the effective loop lengths. The effective loop length l eff i for a pseudoknot loop L i (i ¼ 1, 2, 3) with internal structure elements is the number of unpaired nucleotides outside those internal structure elements plus the number of internal structure elements. (c) 5 3 For all pseudoknots with recursive structure elements, the loop entropy is recalculated using the effective loop lengths. Internal secondary structure elements add free energy values as given by the Turner energy model (8) . We keep only pseudoknots p i in the pseudoknot dictionary D p , which satisfy the following two conditions. First, a recursive H-type pseudoknot must have free energy ÁGðp i Þ < À5:25 kcal/mol. Second, the normalized pseudoknot free energy must fulfill ÁGðp i Þ=l i " where l i denotes the length of pseudoknot p i . Setting the threshold to " ¼ À0:25 is not too restrictive; however, it helps us to eliminate pseudoknots with high free energy (58) . For example, for the 3 0 -UTR TMV sequence with length 214 nt, we have 445 candidate stems in dictionary D s and 2026 pseudoknot candidates before filtering. After the length-normalized filtering step, only 274 pseudoknot candidates remain.