# 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}(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 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/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.

# Folding Enthalpy Change

## Singe Nucleotide Bulge Loops

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

ΔH°_{bulge} (n=1) = ΔH°_{bulge initiation}(n) + ΔH°(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 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:

ΔH°_{bulge} (n>1) = ΔH°_{bulge initiation}(n)

Experimentally-derived parameters are available for bulge loop initiations up to n=3. For n>3, the initiation is approximated as that for n=3.

# Parameter Tables

Bulge loop parameters are available in html or as plain text for initiation free energy parameters or initiation enthalpy parameters. The plain text initiation parameters include an extrapolation out to lengths of 30 unpaired nucleotides.

# References

A set of references is available here.

# Examples