# 15Hairpin Loops

## 15.1 Folding Free Energy Change

### Hairpin loops of 4 or more unpaired nucleotides

The prediction of folding free energy changes for hairpins of 4 or more unpaired nucleotides is made with the following equation:

ΔG°37 hairpin (>3 nucleotides in loop) = ΔG°37 initiation (n) + ΔG°37 (terminal mismatch) + ΔG°37 (UU or GA first mismatch) + ΔG°37 (special GU closure) + ΔG°37 penalty (all C loops)

In this equation, n is the number of nucleotides in loop, the terminal mismatch parameter is the sequence-dependent term for the first mismatch stacking on the terminal base pair, UU and GA first mismatches receive a bonus (not applied to AG first mismatches), the special GU closure term is applied only to hairpins in which a GU closing pair (not UG) is preceded by two Gs, and finally loops with all C nucleotides receive a penalty.

The penalty for all C loops of more than three unpaired nucleotides is predicted using a linear equation:

ΔG°37 penalty (all C loops; > 3 unpaired nucleotides) = An + B

### Frequently Occuring Tetraloops

Tetraloop sequences, i.e. hairpin loops with four nucleotides, that occur frequently in the database of known secondary structures receive an enhanced stability in the form of a free energy bonus. These bonuses are sequence-dependent and appear in a lookup table.

### Short hairpin loops

The nearest neighbor rules prohibit hairpin loops with fewer than 3 nucleotides.

## 15.2 Examples

### 6 nucleotide hairpin loop with no special stacking terms

ΔG°37 = ΔG°37(Watson-Crick-Franklin Helix) + ΔG°37(Hairpin Loop)

ΔG°37 = ΔG°37(Watson-Crick-Franklin Helix) + ΔG°37(terminal mismatch) + ΔG°37 Hairpin initiation(6)

ΔG°37 = ΔG°37(CG followed by AU) + ΔG°37(AU followed by CG) + ΔG°37(CG followed by AU) + ΔG°37 AU end penalty + ΔG°37(AU followed by AA) + ΔG°37 Hairpin initiation(6)

ΔG°37 = –2.11 kcal/mol – 2.24 kcal/mol – 2.11 kcal/mol + 0.45 kcal/mol – 0.8 kcal/mol + 5.4 kcal/mol

ΔG°37 = –1.4 kcal/mol

Note that for unimolecular secondary structures, the helical intermolecular initiation does not appear.

### 5 nucleotide hairpin loop with a GA first mismatch

ΔG°37 = ΔG°37(Watson-Crick-Franklin Helix) + ΔG°37(Hairpin Loop)

ΔG°37 = ΔG°37(Watson-Crick-Franklin Helix) + ΔG°37(terminal mismatch) + ΔG°37(GA first mismatch) + ΔG°37 Hairpin initiation(5)

ΔG°37 = ΔG°37(CG followed by AU) + ΔG°37(AU followed by CG) + ΔG°37(CG followed by AU) + ΔG°37 AU end penalty+ ΔG°37(AU followed by GG) + ΔG°37(GA first mismatch) + ΔG°37 Hairpin initiation(5)

ΔG°37 = –2.11 kcal/mol – 2.24 kcal/mol – 2.11 kcal/mol + 0.45 kcal/mol – 0.8 kcal/mol – 0.8 kcal/mol + 5.6 kcal/mol

ΔG°37 = –2.0 kcal/mol

### 4 nucleotide hairpin loop with tetraloop bonus

ΔG°37 = ΔG°37(Watson-Crick-Franklin Helix) + ΔG°37(Hairpin Loop)

ΔG°37 = ΔG°37(Watson-Crick-Franklin Helix) + ΔG°37(terminal mismatch) + ΔG°37(GA first mismatch) + ΔG°37 Hairpin initiation(4) + ΔG°37 Tetraloop Bonus(CgaaaG)

ΔG°37 = ΔG°37(CG followed by AU) + ΔG°37(AU followed by CG) + ΔG°37(CG followed by CG) + ΔG°37(CG followed by GA) + ΔG°37(GA first mismatch) + ΔG°37 Hairpin initiation(4) + ΔG°37 Tetraloop Bonus(CgaaaG)

ΔG°37 = –2.11 kcal/mol – 2.24 kcal/mol – 3.26 kcal/mol – 1.4 kcal/mol – 0.8 kcal/mol + 5.6 kcal/mol – 3.0 kcal/mol

ΔG°37 = –7.2 kcal/mol

### 6 nucleotide all C loop

ΔG°37 = ΔG°37(Watson-Crick-Franklin Helix) + ΔG°37(Hairpin Loop)

ΔG°37 = ΔG°37(Watson-Crick-Franklin Helix) + ΔG°37(terminal mismatch) + ΔG°37 Hairpin initiation(6) + ΔG°37 penalty (all C loops)

ΔG°37 = ΔG°37(CG followed by AU) + ΔG°37(AU followed by CG) + ΔG°37(CG followed by AU) + ΔG°37 AU end penalty+ ΔG°37(AU followed by CC) + ΔG°37 Hairpin initiation(6) + 6×A + B

ΔG°37 = –2.11 kcal/mol – 2.24 kcal/mol – 2.11 kcal/mol + 0.45 kcal/mol – 0.7 kcal/mol + 5.4 kcal/mol + 6×0.3 kcal/mol + 1.6 kcal/mol

ΔG°37 = +2.1 kcal/mol

### 5 nucleotide loop with special GU closure

ΔG°37 = ΔG°37(Watson-Crick-Franklin Helix) + ΔG°37(Hairpin Loop)

ΔG°37 = ΔG°37(Watson-Crick-Franklin Helix) + ΔG°37(terminal mismatch) + ΔG°37 Hairpin initiation(5) + ΔG°37 (special GU closure)

ΔG°37 = ΔG°37(CG followed by GC) + ΔG°37(GC followed by GC) + ΔG°37(GC followed by GU) + ΔG°37 GU end penalty+ ΔG°37(GU followed by GG) + ΔG°37 Hairpin initiation(5) + ΔG°37 (special GU closure)

ΔG°37 = –2.36 kcal/mol – 3.26 kcal/mol – 1.53 kcal/mol + 0.45 kcal/mol – 0.8 kcal/mol + 5.6 kcal/mol – 2.2 kcal/mol

ΔG°37 = –4.1 kcal/mol

## 15.3 Parameter Tables

Length dependent initiation parameters are available in plain text or html format. Initiation parameters are based on experiments for sizes up to 9 nucleotides, but can be extrapolated to longer loops. For free energy changes, the extrapolation is ΔG°37 initiation (n>9) = ΔG°37 initiation (9) + 1.75 RT ln(n/9), where R is the gas constant and T is the absolute temperature. The plain text file already extrapolates out to lengths of 30 nucleotides.

The terminal mismatch tables are available for free energy changes in plain text. These parameters are also available in html.

The bonus/penalty terms (including the all-C loop terms) are available in html format.

The lookup table of for tertraloops with enhanced stability is available as plain text or html.

## 15.4 References

The hairpin loop nearest neighbor parameters for free energy change were reported in:

Mathews, D.H., Sabina, J., Zuker, M. and Turner, D.H. (1999) Expanded sequence dependence of thermodynamic parameters provides improved prediction of RNA secondary structure. J. Mol. Biol., 288, 911-940.

The experimental data for the fit of the parameters were taken from:

1. Groebe, D.R. and Uhlenbeck, O.C. (1988) Characterization of RNA hairpin loop stability. Nucleic Acids Res., 16, 11725-11735.
2. Antao, V.P., Lai, S.Y. and Tinoco, I., Jr. (1991) A thermodynamic study of unusually stable RNA and DNA hairpins. Nucleic Acids Res., 19, 5901-5905.
3. Antao, V.P. and Tinoco, I., Jr. (1992) Thermodynamic parameters for loop formation in RNA and DNA hairpin tetraloops. Nucleic Acids Res., 20, 819-824.
4. Serra, M.J., Lyttle, M.H., Axenson, T.J., Schadt, C.A. and Turner, D.H. (1993) RNA hairpin loop stability depends on closing pair. Nucleic Acids Res., 21, 3845-3849.
5. Serra, M.J., Axenson, T.J. and Turner, D.H. (1994) A model for the stabilities of RNA hairpins based on a study of the sequence dependence of stability for hairpins of six nucleotides. Biochemistry, 33, 14289-14296.
6. Laing, L.G. and Hall, K.B. (1996) A model of the iron responsive element RNA hairpin loop structure determined from NMR and thermodynamic data. Biochemistry, 35, 13586-13596.
7. Serra, M.J., Barnes, T.W., Betschart, K., Gutierrez, M.J., Sprouse, K.J., Riley, C.K., Stewart, L. and Temel, R.E. (1997) Improved parameters for the prediction of RNA hairpin stability. Biochemistry, 36, 4844-4851.
8. Giese, M.R., Betschart, K., Dale, T., Riley, C.K., Rowan, C., Sprouse, K.J. and Serra, M.J. (1998) Stability of RNA hairpins closed by wobble base pairs. Biochemistry, 37, 1094-1100.