16  Bulge 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.