Table 1. Free energy parameters for hairpin loop formation.
| Parameter (number of nt or sequence) | ΔG°37, kcal/mol |
|---|---|
| ΔG°37 initiation(3) | 5.4 ± 0.2 |
| ΔG°37 initiation(4) | 5.6 ± 0.1 |
| ΔG°37 initiation(5) | 5.7 ± 0.2 |
| ΔG°37 initiation(6) | 5.4 ± 0.1 |
| ΔG°37 initiation(7) | 6.0 ± 0.2 |
| ΔG°37 initiation(8) | 5.5 ± 0.2 |
| ΔG°37 initiation(9) | 6.4 ± 0.2 |
| ΔG°37 bonus(UU or GA first mismatch but not AG) | −0.9 ± 0.1 |
| ΔG°37 bonus(GG first mismatch) | −0.8 ± 0.3 |
| ΔG°37 bonus(special G-U closure) | −2.2 ± 0.2 |
| ΔG°37 penalty(C3 loop) | 1.5 ± 0.5 |
| ΔG°37 penalty(Cn loop), A | 0.3 ± 0.1 |
| ΔG°37 penalty(Cn loop), B | 1.6 ± 0.9 |
Hairpin loop stabilities are estimated with the equation ΔG°37 loop (n > 3) = ΔG°37 initiation(n) + ΔG°37(first mismatch stacking) + ΔG°37 bonus(UU or GA first mismatch but not AG) + ΔG°37 bonus(GG first mismatch) + ΔG°37 bonus(special G-U closure) + ΔG°37 penalty(oligo-C loops), where n is the number of unpaired nucleotides in the loop. ΔG°37(first mismatch stacking) is derived from studies of terminal mismatch stability as compiled previously (45, 46). Terminal mismatch free energies for UU mismatches on both GU and UG pairs were updated from Dale et al. (47). The special GU closure bonus applies to GU closed hairpins in which a 5′ closing G is preceded by two G residues. The oligo-C penalty applies only to loops composed of all C residues. The penalty for oligo-C loops >3 nt is ΔG°37 penalty(oligo-C loops, n > 3) = An + B. In addition to the terms in the above equation, the AU/GU terminal pair penalty of 0.5 kcal/mol is also applied at the ends of helices closed by hairpin loops (8, 44). Hairpin parameters were derived from linear regression on the database, excluding the stable hairpins ACAGUGCU (where closing pairs are shown and unpaired nucleotides are in bold), ACAGUGAU, ACAGUUCU, ACAGUACU, CUACGG, CUCCGG, and CUUCGG (47, 50, 86). The supporting information contains the complete database of hairpin loops used in the linear regression. Hairpin loops of lengths at 3, 4, and 6 unpaired nt with measured free energies that are either more or less stable by 0.9 kcal/mol when compared to prediction by the above model are included in a separate lookup table (Table 2). Hairpin loops of <3 nt are prohibited. ΔG°37(first mismatch stacking) and terminal mismatch bonuses apply only to hairpin loops >3 unpaired nt. For hairpin loops >9 nt, initiation free energy is approximated (74) by ΔG°37 initiation(n > 9) = ΔG°37 initiation(9) + 1.75RTIn(n/9).