PairFold user interface. (A) The sequences R₁=GGCCACCUGACAGUCCUCUCC and R₂=GGAGAGAGAAGUCAACCAGAGAAACACACCAACCCAUUGCACUCCGGGUUGGUGGUAUAUUACCUGGUACGGGGGAAACUUCGUGGUGGCCG are entered in simple text boxes. In this example, the sequences form a hairpin ribozyme (8). (B) The dot-parenthesis representation of the minimum free energy secondary structure as predicted by PairFold. (C) The dot-parenthesis representation of the secondary structure found in the crystallization construct, as reported by Rupert and Ferré-D'Amaré (10). The structure reported by PairFold for the pair (R₁, R₂) contains the four stems found in the crystallization construct. The difference in the secondary structure for (R₁, R₂) of (B) and the secondary structure of (C) (highlighted in orange in B) can be attributed to the fact that the non-standard base pairings A-A, G-A and C-A found in the true structure are not accounted for in the Turner thermodynamic parameters and thus cannot be predicted by software based on these parameters.

CombFold user interface. (A) Web interface for CombFold input. The input is the combinatorial set of Figure 3B specified using IUPAC code. (B) Partial view of web interface for CombFold output, reporting that for the given input, the sequence AUGCAAUGCGCAUGCAC has the minimum free energy structure, namely ((((….))))…., with free energy −2.70 kcal/mol.

RNA Secondary structure. (A) Graphical depiction of the predicted minimum free energy secondary structure S for sequence R=GCCGCACGCGAGACCGCGCACUCCGCGGGAUG CCCAUAGGAGAAGCGGCAUUACCUGUAGCCAAGCCAGUA, plus the list of associated base pairs. S is pseudoknot free. (B) Free energy calculation for structure S. Contributions of the labeled stems and loops (hairpins, bulges, internal loops, external loop and multiloops) to the free energy are summed to obtain the total free energy, which for this strand is the minimum free energy. (C) Dot-parenthesis representation of secondary structure S. (D) Graphical depiction of two possible secondary structures for the pair of sequences (R₁, R₂)=(GCCGCACGCGAGACCGCGCA, CGCGGUCUCGCGUGCUUGGC). The structure on the left is obtained by pairing bases in matching positions of the two strands and has free energy −19.14 kcal/mol, as predicted by HYTHER^TM, but this is not the minimum free energy structure. The structure on the right is predicted by PairFold to be the minimum free energy structure, having free energy −36.70 kcal/mol.

Combinatorial sets of strands. (A) The DNA tag set of Brenner et al. (3) Each tag is obtained by concatenating eight 4mers, one chosen from each of the eight columns. Thus, each tag has length 32 and there are 8⁸=16 777 216 tags in total. One such tag is AATCTTACCAAAACATACATTCTACTTTAATC. Column i lists the strands in the set S_i, for i between 1 and 8. Also in this example, n_i=4 and N_i=8 for each i. (B) A simple combinatorial set used in the screen shots of Figure 4. This set can also be represented using IUPAC code, as 5′-AURCAAUGCSNAUGCAC-3′.

RNA Designer user interface. (A) Web interface for RNA Designer input, with input structure as in Figure 1C. (B) Partial view of web interface for RNA Designer output.