Turner 2004

Hairpin Loops

Folding Free Energy Change

Hairpin loops of 4 or more 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 (GG 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), GG first mismatches receive a bonus, 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

Hairpin loops of 3 unpaired nucleotides

For hairpin loops of 3 nucleotides, the folding free energy change is estimated using:

ΔG°37 hairpin (3 unpaired nucleotides) = ΔG°37 initiation (3) + ΔG°37 penalty (all C loops)

As opposed to longer hairpin loops, hairpin loops of three nucleotides do not receive a sequence-dependent first mismatch term.  All C hairpin loops of three nucleotides receive a stability penalty.

Special hairpin loops

There are hairpin loop sequences of 3, 4, and 6 nucleotides that have stabilities poorly fit by the model.  These hairpins are assigned stabilities based on experimental data.

Short hairpin loops

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

Folding Enthalpy Change

Hairpin loops of 4 or more nucleotides

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

ΔH°hairpin (>3 unpaired nucleotides) = ΔH°initiation (n) + ΔH° (terminal mismatch) + ΔH° (UU or GA first mismatch) + ΔH° (special GU closure) + ΔH° (all C loops)

As with the free energy change equation above, n is the number of nucleotides in the loop, the terminal mismatch parameter is the sequence-dependent term for the first mismatch stacking on the terminal 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 the all C loops receive a penalty.

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

ΔH°penalty (all C loops; > 3 unpaired nucleotides) = A'n + B'

Hairpin loops of 3 nucleotides

For hairpin loops of 3 unpaired nucleotides, the enthalpy change is estimated using:

ΔH°hairpin (3 unpaired nucleotides) = ΔH°initiation (3) + ΔH°penalty (all C loops)

Hairpin loops of three nucleotides do not receive a sequence-dependent first mismatch term.  All C hairpin loops of three nucleotides receive a stability penalty.

Special hairpin loops

Hairpin loops of 3, 4, and 6 nucleotides that have stabilities poorly fit by the free energy model are assigned enthalpy changes based on experimental data.

Parameter Tables

Length dependent initiation parameters are available in plain text for free energy changes and plain text for enthalpy changes.  The plain text initiation tables include an extrapolation out to lengths of 30 nucleotides. These initiation parameters are also available in 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. For enthalpy changes, ΔH°initiation (n>9) = ΔH°initiation (9).

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

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

The table of special hairpin loops is available in plain text for free energy change for 3, 4, or 6 nucleotides; plain text for enthalpy change for 3, 4, or 6 nucleotides; and in html. The special hairpin loop sequences include the identity of the closing basepair.

References

A set of references is available here.