or over a decade, the laboratory of Professor D.H. Turner at the
University of Rochester has been estimating nearest neighbor
parameters for RNA based on melting studies of synthetically
constructed oligoribonucleotides.
Stacking Energies
Energy rules were first derived for stems containing canonical
base pairs: WatsonCrick (WC) base pairs and GU wobble pairs. In the
sample helix at the left, the total free energy is given by the
addition of 7 free energy terms, 1 for each pair of adjacent base
pairs. This includes energy contributions for both base pair stacking
and hydrogen bonding. Such nearest neighbor rules work very
well for WC base pairs, and satisfactorily for single GU pairs
surrounded by WC pairs. They break down for 2 or more consecutive GU
pairs and for noncanonical pairs. These stacking energies are given
in 16 (4 by 4) tables of 16 (4 by 4) numbers. We adopt the convention
that A, C, G, U/T correspond to 1, 2, 3, and 4, respectively. For a
stack:
5'WX3'
3'ZY5'
the corresponding energy would appear in the
W^{th} row and Z^{th} column of 4 by 4 tables, and in
the X^{th} row and Y^{th} column of that table. For a
more explicit explanation, look here.
Stacking energies at 37° may be viewed directly here. Alternatively,
one may generate energy parameters for folding at arbitrary temperatures.
Hairpin Loop Energies
Hairpin loop free energies are the sum of up to 3 terms.
 A purely entropic term that depends on the loop size (the number of
single stranded bases in the loop), is given in the hairpin
column of the LOOP energy table. Loop energies at 37° may be
found here. For
loops larger than 30, an extra term, 1.75RTln(size/30), is added,
where R is the universal gas constant and T is absolute temperature.
 There is a favorable stacking interaction between the closing
base pair of the hairpin loop and the adjacent mismatched pair. These
energies are given in special hairpin loop terminal stacking
energy tables. At 37°, these free energies may be found here. Terminal
stacking energies are not added in triloops (hairpin loops of size 3).
 Certain tetraloops (and, coming soon, triloops) have special
bonus energies attached to them. This list of tetraloops, and their
bonus energies at 37°, is given here.
Interior and Bulge Loop Energies
Interior and bulge loops are closed by 2 base pairs.
Interior loop energies are the sum of up to 3 terms.
 As with hairpin loops, there is a purely entropic term for
interior loop energies that depends on the loop size. This may be
found in the interior
column of the LOOP energy table. Loop energies at 37° may be
found here. For
loops larger than 30, an extra term, 1.75RTln(size/30), is added.
 As with hairpin loops, there are special terminal stacking
energies for the mismatched base pairs adjacent to both closing
base pairs. Each of these energies are taken from special interior
loop terminal stacking energy tables.
At 37°, these free energies may be found
here.
 For nonsymmetric interior loops, there is an asymmetric loop
penalty. At 37°, these free energies may be found
here. (This
section is slightly incomplete.)
 New rules for small symmetric and nearly symmetric interior loops
have been derived by the Turner group and will be used at this site.
 The bulge loop destabilizing energies are stored in the
bulge
column of the LOOP energy table. Loop energies at 37° may be
found here.
This energy is purely entropic, and the usual logarithmic extension
applies. For bulge loops of size 1 only, that stacking contribution
of the closing base pairs is added.
Multibranched Loop and Free Base Energies
Free bases are single stranded nucleotides that are not in any loop. As a
mathematical formality, we say that free bases are in the exterior
loop. There is not much experimental information available for multibranched
loops or exterior loops. For multibranch loops, a free energy function of
the form:
E = a + n_{1} × b + n_{2} ×
c,
is used, where a, b and c are constants,
n_{1} is the number of singlestranded bases in the
multibranched loop and n_{2} is the number of stems that form the
loop. The parameters a, b and c are called the offset, free base penalty and
helix penalty, respectively. Their current values, for folding at 37°,
are given here. They have
been determined empirically. The reason for this affine energy function is
mathematical expediency. That is, this allows the folding algorithm to execute
in a reasonable time. Energy reevaluation of structures uses
JacobsonStockmeyer theory to assign multibranch loop energies. The
corresponding free energy function for exterior loops is 0.
The affine energy function that is used in multibranched loops is a purely
entropic free energy term. This term is absent from exterior loops. In
addition, we use single base stacking rules for both multibranch and
exterior loops. These contain both enthalpic and entropic components.
Single base stacking refers to a stacking interaction between an unpaired
base at the end of a helix and the adjacent terminal base pair of the helix.
Any single stranded base adjacent to the closing base pair of a stem in a
multibranch loop or in the exterior loop is given a single strand stacking
energy. These dangling base energies at 37° may be found here. When a
singlestranded base is adjacent to 2 stems, only 1 singlebase stacking
term, the most favorable one, is used.
At this time, we do not consider coaxial stacking of adjacent helices in the
folding algorithm. Nevertheless, data
for coaxial stacking have been included in an energy
calculation function that reevaluates the energies of predicted
structures. This energy reevaluation is not employed on the mfold web
servers.
The references below contain the published record of the development
of the Turner energy rules for RNA folding. The articles highlighted
by red outlined stars are the most significant. They summarize the state of
the energy rules when they were published and sometimes contain new
results as well.

Freier et al., 1985

Freier, S.M., Alkema, D., Sinclair, A., Neilson, T., & Turner, D.H. 1985.
Contributions of dangling end stacking and terminal basepair
formation to the stabilities of XGGCCp, XCCGGp, XGGCCYp, and XCCGGYp helixes.
Biochemistry, 24, 45334539.

Freier et al., 1986

Freier, S.M., Kierzek, R., Jaeger, J.A., Sugimoto, N., Caruthers, M.H.,
Neilson, T., & Turner, D.H. 1986.
Improved freeenergy parameters for predictions of RNA duplex
stability.
Proc. Natl. Acad. Sci. USA, 83, 93739377.

Sugimoto et al., 1987a

Sugimoto, N., Kierzek, R., & Turner, D.H. 1987a.
Sequence dependence for the energetics of dangling ends and terminal
mismatches in ribonucleic acid.
Biochemistry, 26, 45544558.

Sugimoto et al., 1987b

Sugimoto, N., Kierzek, R., & Turner, D.H. 1987b.
Sequence dependence for the energetics of terminal mismatches in
ribooligonucleotides.
Biochemistry, 26, 45594562.

Turner et al., 1987

Turner, D.H., Sugimoto, N., Jaeger, J.A., Longfellow, C.E., Freier, S.M., &
Kierzek, R. 1987.
Improved parameters for prediction of RNA structure.
Cold Spring Harb. Symp. Quant. Biol., 52, 123133.

Turner et al., 1988

Turner, D.H., Sugimoto, N., & Freier, S.M. 1988.
RNA structure prediction.
Annu. Rev. Biophys. Biophys. Chem., 17, 167192.

Jaeger et al., 1989

Jaeger, J.A., Turner, D.H., & Zuker, M. 1989.
Improved predictions of secondary structures for RNA.
Proc. Natl. Acad. Sci. USA., 86, 77067710.

Jaeger et al., 1990

Jaeger, J.A., Turner, D.H., & Zuker, M. 1990.
Predicting optimal and suboptimal secondary structure for RNA.
Meth. Enzymol., 183, 281306.

Longfellow et al., 1990

Longfellow, C.E., Kierzek, R., & Turner, D.H. 1990.
Thermodynamic and spectroscopic study of bulge loops in
oligoribonucleotides.
Biochemistry, 29, 278285.

SantaLucia et al., 1990

SantaLucia, J.Jr., Kierzek, R., & Turner, D.H. 1990.
Effects of GA mismatches on the structure and thermodynamics of RNA
internal loops.
Biochemistry, 29, 88138819.

Peritz et al., 1991

Peritz, A.E., Kierzek, R., Sugimoto, N., & Turner, D.H. 1991.
Thermodynamic study of internal loops in oligoribonucleotides:
symmetric loops are more stable than asymmetric loops.
Biochemistry, 30, 64286436.

SantaLucia et al., 1991

SantaLucia, J.Jr., Kierzek, R., & Turner, D.H. 1991.
Stabilities of consecutive A.C, C.C, G.G, U.C, and U.U mismatches in
RNA internal loops: Evidence for stable hydrogenbonded U.U and C.C.+ pairs.
Biochemistry, 30, 82428251.

Zuker et al., 1991

Zuker, M., Jaeger, J.A., & Turner, D.H. 1991.
A comparison of optimal and suboptimal RNA secondary structures
predicted by free energy minimization with structures determined by
phylogenetic comparison.
Nucleic Acids Res., 19, 27072714.

SantaLucia et al., 1992

SantaLucia, J.Jr., Kierzek, R., & Turner, D.H. 1992.
Context dependence of hydrogen bond free energy revealed by
substitutions in an RNA hairpin.
Science, 256, 217219.

Serra et al., 1993

Serra, M.J., Lyttle, M.H., Axenson, T.J., Schadt, C.A., &
Turner, D.H. 1993.
RNA hairpin loop stability depends on closing base pair.
Nucleic Acids Res., 21, 38453849.

Serra et al., 1994

Serra, M.J., Axenson, T.J., & Turner, D.H. 1994.
A model for the stabilities of RNA hairpins based on a study of the
sequence dependence of stability for hairpins of six nucleotides.
Biochemistry, 33, 1428914296.

Walter et al., 1994

Walter, A.E., Turner, D.H., Kim, J., Lyttle, M.H., Muller, P., Mathews, D.H.,
& Zuker, M. 1994.
Coaxial stacking of helixes enhances binding of oligoribonucleotides
and improves predictions of RNA folding.
Proc Natl Acad Sci USA, 91, 92189222.

Walter & Turner, 1994

Walter, A.E., & Turner, D.H. 1994.
Sequence dependence of stability for coaxial stacking of RNA helixes
with WatsonCrick base paired interfaces.
Biochemistry, 33, 1271512719.

Wu et al., 1995

Wu, M., McDowell, J.A., & Turner, D.H. 1995.
A periodic table of symmetric tandem mismatches in RNA.
Biochemistry, 34, 32043211.

Serra et al., 1995

Serra, M.J., Turner, D.H., & Freier, S.M. 1995.
Predicting thermodynamic properties of RNA.
Meth. Enzymol., 259, 243261.
Michael Zuker
11/18/96