# 16Bulge Loops

## 16.1 Folding Free Energy Change

### Singe Nucleotide Bulge Loops

The prediction of folding free energy changes is made with the following equation:

ΔG°37 bulge (n=1) = ΔG°37 bulge initiation(1) + ΔG°37 (base pair stack)

In this equation, n is the number of unpaired nucleotides and the base pair stack is the stack of the closing pairs as though there is no bulge (using Watson-Crick-Franklin or GU rules as needed).

Because the helical stack continues across a single nucleotide bulge, the terminal AU/GU penalty is not applied adjacent to single bulges.

### Bulges of 2 or More Nucleotides

For bulges of 2 or more nucleotides, the following equation is used:

ΔG°37 bulge (n>1) = ΔG°37 bulge initiation(n)

Experimentally-derived parameters are available for initiation up to n = 3 and a linear extrapolation is used up to n = 6. Beyond 6, the initiation is approximated using a logarithmic function:

ΔG°37 bulge (n>6) = ΔG°37 bulge initiation(6) + 1.75 RT ln(n/6)

where R is the gas constant and T is the absolute temperature, 310.15 K.

## 16.2 Examples

### Single C bulge

ΔG°37 = ΔG°37(Watson-Crick-Franklin Pairs) + ΔG°37 intermolecular initiation + ΔG°37(Bulge Loop)

ΔG°37 = ΔG°37(GC followed by CG) + ΔG°37(CG followed by CG) + ΔG°37 intermolecular initiation + ΔG°37 bulge initiation(1) + ΔG°37(CG followed by GC)

ΔG°37 = –3.42 kcal/mol – 3.26 kcal/mol + 4.09 kcal/mol + 3.8 kcal/mol – 2.36 kcal/mol

ΔG°37 = –1.2 kcal/mol

### 3 nucleotide bulge

ΔG°37 = ΔG°37(Watson-Crick-Franklin Pairs) + ΔG°37 intermolecular initiation + ΔG°37 AU end penalty + ΔG°37(Bulge Loop)

ΔG°37 = ΔG°37(GC followed by AU) +ΔG°37 intermolecular initiation + ΔG°37 AU end penalty + ΔG°37 bulge initiation(3)

ΔG°37 = –2.35 kcal/mol + 4.09 kcal/mol + 0.45 kcal/mol + 3.2 kcal/mol

ΔG°37 = +5.4 kcal/mol

## 16.3 Parameter Tables

Bulge loop parameters are available in html or as plain text. The plain text files include an extrapolation of the initiation out to 30 unpaired nucleotides.

## 16.4 References

The bulge 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. Fink, T.R. and Crothers, D.M. (1972) Free energy of imperfect nucleic acid helices, I. The bulge defect. J. Mol. Biol., 66, 1-12.
2. Groebe, D.R. and Uhlenbeck, O.C. (1989) Thermal stability of RNA hairpins containing a four-membered loop and a bulge nucleotide. Biochemistry, 28, 742-747.
3. Longfellow, C.E., Kierzek, R. and Turner, D.H. (1990) Thermodynamic and spectroscopic study of bulge loops in oligoribonucleotides. Biochemistry, 29, 278-285.