Development and References

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: Watson-Crick (WC) base pairs and G-U 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 G-U pairs surrounded by WC pairs. They break down for 2 or more consecutive G-U pairs and for non-canonical 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:

the corresponding energy would appear in the Wth row and Zth column of 4 by 4 tables, and in the Xth row and Yth 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.

  1. 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.

  2. 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).

  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. Multi-branched 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 multi-branched loops or exterior loops. For multi-branch loops, a free energy function of the form:
E = a + n1 × b + n2 × c,
is used, where a, b and c are constants, n1 is the number of single-stranded bases in the multi-branched loop and n2 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 re-evaluation of structures uses Jacobson-Stockmeyer theory to assign multi-branch loop energies. The corresponding free energy function for exterior loops is 0.

The affine energy function that is used in multi-branched 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 multi-branch 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 multi-branch 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 single-stranded base is adjacent to 2 stems, only 1 single-base 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 re-evaluates the energies of predicted structures. This energy re-evaluation 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 base-pair formation to the stabilities of XGGCCp, XCCGGp, XGGCCYp, and XCCGGYp helixes. Biochemistry, 24, 4533-4539.

Freier et al., 1986
Freier, S.M., Kierzek, R., Jaeger, J.A., Sugimoto, N., Caruthers, M.H., Neilson, T., & Turner, D.H. 1986. Improved free-energy parameters for predictions of RNA duplex stability. Proc. Natl. Acad. Sci. USA, 83, 9373-9377.

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, 4554-4558.

Sugimoto et al., 1987b
Sugimoto, N., Kierzek, R., & Turner, D.H. 1987b. Sequence dependence for the energetics of terminal mismatches in ribooligonucleotides. Biochemistry, 26, 4559-4562.

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, 123-133.

Turner et al., 1988
Turner, D.H., Sugimoto, N., & Freier, S.M. 1988. RNA structure prediction. Annu. Rev. Biophys. Biophys. Chem., 17, 167-192.

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, 7706-7710.

Jaeger et al., 1990
Jaeger, J.A., Turner, D.H., & Zuker, M. 1990. Predicting optimal and suboptimal secondary structure for RNA. Meth. Enzymol., 183, 281-306.

Longfellow et al., 1990
Longfellow, C.E., Kierzek, R., & Turner, D.H. 1990. Thermodynamic and spectroscopic study of bulge loops in oligoribonucleotides. Biochemistry, 29, 278-285.

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, 8813-8819.

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, 6428-6436.

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 hydrogen-bonded U.U and C.C.+ pairs. Biochemistry, 30, 8242-8251.

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, 2707-2714.

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, 217-219.

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, 3845-3849.

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, 14289-14296.

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, 9218-9222.

Walter & Turner, 1994
Walter, A.E., & Turner, D.H. 1994. Sequence dependence of stability for coaxial stacking of RNA helixes with Watson-Crick base paired interfaces. Biochemistry, 33, 12715-12719.

Wu et al., 1995
Wu, M., McDowell, J.A., & Turner, D.H. 1995. A periodic table of symmetric tandem mismatches in RNA. Biochemistry, 34, 3204-3211.

Serra et al., 1995
Serra, M.J., Turner, D.H., & Freier, S.M. 1995. Predicting thermodynamic properties of RNA. Meth. Enzymol., 259, 243-261.

Michael Zuker