Turner 1999

Hairpin Loops

Folding Free Energy Change

Hairpin loops of 4 or more unpaired 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 (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), 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.      

Frequently Occuring Tetraloops

Tetraloop sequences, i.e. hairpin loops with four nucleotides, that occur frequently in the database of known secondary structures receive an enhanced stability in the form of a free energy bonus. These bonuses are sequence-dependent and appear in a lookup table. 

Short hairpin loops

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

Parameter Tables

Length dependent initiation parameters are available in plain text or 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. The plain text file already extrapolates out to lengths of 30 nucleotides.

          The terminal mismatch tables are available in plain text.  These parameters are also available in html.

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

          The lookup table of for tertraloops with enhanced stability is available as plain text or html.


A set of references is available here.