# 37Bulge Loops

### Single 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(n) + ΔG°37 (special C bulge) + ΔG°37 (base pair stack) – RT ln(number of states)

In this equation, n is the number of unpaired nucleotides, a special C bulge is a bulged C adjacent to at least one paired C, 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), and the number of states counts the number of possible loops of identical sequence.

Because the helical stack continues across a single nucleotide bulge, the terminal AU 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.

## 37.1 Examples

### Single C bulge with multiple states

ΔG°37 = ΔG°37(Watson-Crick-Franklin Helix) + 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(special C bulge) + ΔG°37(CG followed by GC) – RT ln(3)

ΔG°37 = -3.4 kcal/mol -3.3 kcal/mol + 4.1 kcal/mol + 3.8 kcal/mol -0.9 kcal/mol -2.4 kcal/mol - 0.616 × 1.099 kcal/mol

ΔG°37 = -2.76 kcal/mol

Note that this loop has three available states because any of the three Cs in the top strand can be the bulge.

### 3 nucleotide bulge

ΔG°37 = ΔG°37(Watson-Crick-Franklin Helix) + 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 = –2.4 kcal/mol + 4.1 kcal/mol + 0.5 kcal/mol + 3.2 kcal/mol

ΔG°37 = 5.4 kcal/mol

## 37.2 Parameter Tables

Bulge loop parameters are available as plain text for initiation free energy parameters.